Commonwealth Bureau of Census and Statistics, MELBOURNE. OFFICIAL. STATISTICS, COMMONWEALTH OF AUSTRALIA. The Private Wealth of Australia and Its Growth AS ASCERTAINED BY VARIOUS METHODS. TOGETHER WITH A Report of the War Census of 1915. PREPARED UNDER INSTRUCTIONS FROM THE MINISTER OF STATE FOR HOME AND TERRITORIES. BY G. H. KNIBBS. CM.a. Fellow of the Royal Statistical Society, Membre de I'lnBtitnt International de Statistiqiie, Honorary Member American Statis- tical Association, and of the Soci^tede Statistiquede Paris, &c.,<£c. COMMONWEALTH STATISTICIAN. By authority: McCARRON, BIRD & CO., Printert. 479 Collini Street. Melbourne. 0.8. , No. 332], /^(jsi-r*! , \ fa Commonwealth Bureau of Census and Statistics, MELBOURNE. OFFICIAL. STATISTICS. COMMONWEALTH OF AUSTRALIA. The Private Wealth of Australia and Its Growth AS ASCERTAINED BY VARIOUS METHODS, TOGETHER WITH A Report of the War Census of 1915. PREPARED UNDER INSTRUCTIONS FROM THE MINISTER OF STATE FOR HOME AND TERRITORIES. BY G. H. KNIBBS. C.M.G.. Fellow of the Royal Statistical Society, Merubre de I'lnstitut International de Statistique. Honorary Member American Statis- tical Aesociation.andof the Sociitede Statistique de Paris, <&c..&c. COMMONWEALTH STATISTICIAN. By autKority : McCARRON. BIRD & CO.. Printers. 479 Collin* Street, Melbourne. C.S., No. 332], 4 EXCHANGE PREFACE. As indicated by the title, the matter contained herein relates mainly to the private wealth of Australia, and an examination of the various methods adopted here and elsewhere for the purpose of estimating the wealth of a community. It includes also a brief report of the results of the War Census in respect of {a) males of military age, (6) net private income of the people, (c) net private assets of the people. Many of these latter have already appeared from time to time in the publications of the Bureau. The three principal methods of estimating the wealth of a community, viz., (i.) by means of a wealth-census, (ii.) by the use of probate-returns, (iii.) by the inventory-method based on mis- cellaneous statistical and other records, are considered in some detail, and the advantages and disadvantages of each are discussed. An estimate of the private wealth of Australia based on pro- bate returns was made in 1911 by Mr. A. M. Laughton, F.I. A., F.F.A., the Government Statist of Victoria, who obtained a total of £990,000,000, which he subsequently increased to £1,031,000,000. Reasons are given herein for the opinion that owing to defects inherent in the probate-return methods, this estimate is below the truth, and this opinion is supported by the War Census recoixls, which, although clearly incomplete, gave for the private wealth of Australia in 1915 a total of £1,643,000,000. A further evidence of the defect in the method based upon probate-returns is an estimate for 1915 contained herein based upon the inventory-method. This estimate gave a total for Australia of £1,620,000,000. For the sake of comparison an allowance should be made for items which are excluded from private wealth in the inventory-method, but are included therein at a wealth-census and in probate-returns. These are such assets as the locally held securities in respect of public and municipal debt. With this allowance the comparable inventory total becomes about £1,760,000,000 as at the 30th June, 1915, or Preface. say £355 per head of population. This total is an estimate of all the private material wealth existing in Australia at 30th June, 1915, whether owned by Australian residents or not, with the addition of a sum of £140,000,000 estimated as the value of locall}' held securities m respect of loans to Australian Governments and local governing bodies. The portion of the Australian total be- longing to persons not resident in Australia is difficult to estimate but is probably in the neighbourhood of £175,000,000. As a result of the careful review of the several estimates, the conclusion arrived at is that the most satisfactory wealth estimates will be obtained by means of a combination of the wealth census and inventory inethods. G. H. KNIBBS, Commonwealth Statistician. Commonwealth Bureau of Census and Statistics, Melbourne, 25th February, 1918. SYNOPSIS. PART I.— THE NATURE OF NATIONAL WEALTH. Chapter I. — Introduction. 1. General 2. Value, how estimated : its uncer- tainty . . 3. Importance of clear statements as to methods of estimation 4. Sense in which wealth is at- tributable to individuals 5. Wealth under private ownership 6. Wealth under commiuial owner- ship Page 1 Page 7. Wealth under national ownership 4 8. Variation in valuation cases . . 4 9. The fluctuation of wealth . . 5 Chapter 11. — Various Modes of Estimating Wealth. 1. A census of wealth 2. Probate returns . . 3. The devolution interval 4. The devolution rate 5. Comparison of methods PART II.— WAR CENSUS OF 1915. GENERAL. Chapter I. -Legislation isation. and Organ - 1. Legislation 2. Forms of inquiry War Census (1st Schedule) War Census (2nd Schedule) 3. Issue of forms 4. Staff 5. Accommodation . . Chapter U. 1. General -Recruiting and War Appeals. 8 8 8 9 . 10 11 . 11 Loan . 11 !. Recruiting appeal 5. War loan appeal. . Chapter III. — Males of Military Age. 12 13 General Enemy origin Health Age Conjugal condition dants Occupation Records and index and depen- 13 13 14 15 16 16 19 PART ra.— WAR CENSUS OF 1915. WEALTH AND INCOME. Chapter I. — Grades of Ownership. 1. General 2. Groups adopted . . 3. Individuals 4. Partnerships 5. Trusts 6. Companies 7. Institutions Chapter U. — Net Income. 1. According to States — (i.) Total net income (ii.) Net income of individuals 2. According to size of net income — (i.) Grouping. . (ii.) Income of persons resi- dent in Australia (iii.) Australian income of non- residents (iv.) Average net income in each group Chapter HI. — Net Assets. 20 20 20 20 20 21 21 22 22 24 24 25 27 (i.) Aggregate net assets 28 (ii.) Net assets of individuals 29 2. According to size of net assets — (i.) Crrouping 30 (ii.) Net assets of persons resident u\ Australia . . 30 (iii.) Australian net assets of non-residents 31 (iv. ) Average net assets in each group 33 3. Debt , or negat ive wealth 33 4. Wealth unrepresented by mater- ial value 35 5. Possible incompleteness of the War Census 36 Synopsis. Page Chapter IV.— Special Classes of Assets. 1. General 37 2. Cash in hand . . . . . . 37 3. Shares and debentures in com- panies . . . . . . 39 4. Land values . . . . . . 39 5. Relation between improved and unimproved values . . . . 42 Page 6. The distribution of freehold estate 44 7. Live stock — (i.) General . . . . . . 44 (ii.) Horses . . . . . . 45 (i'i.) Cattle 45 (iv.) Sheep . . . . . . 46 8. Vehicles 46 PART IV.— THE RELATIONS BETWEEN WEALTH AND INCOME. Chapter I. — The Correlation of Wealth and Income. 1 . Numbers whose wealth and income are between given limits, Commonwealth 2. Aggregates of assets between given limits arranged accord- ing to given limits of income. Commonwealth 3. Numbers in each State and Ter- ritory arranged according to given limits of income 4. Aggregates of income in each State according to given limits of income 5. Aggregates of wealth in each State, according to given limits of income 6. Numbers in each State arranged according to given limits of 48 50 52 53 54 7. Aggregate assets arranged accord- ing to given limits of assets . . 8. The average incomes, assets and ratios of incomes to assets. States and Commonwealth . . 9. The significance of income as related to assets 10. Comparison with other countries 11. Income — assets, relation of part- nerships and companies 55 56 60 61 63 Chapter II. -The Wealth and Income Surface. Correlation of income and assets 64 Frequency, multiplied by 1000, and per unit of range (Poiuid ster- ling) of wealth and income, etc., Australia, 30th June, 1915 . . 65 The graphs of the plutoprosodic (or wealth and income) surface 65 Frequency according to income and wealth . . . . . . 66 PART v.— THE ESTIMATION OF WEALTH FROM PROBATE RETURNS. Chapter I. — The Interval of Devolution. 1. The interval of devolution method 68 2. Determination of the interval of devolution . . . . . . 69 3. The defect of the devolution- interval method . . . . 80 Chapter II. — The Rate of Devolution. 1. The devolution -rate method . . 81 2. Discussion and technique of the devolution-rate method . . 82 3. The error of treating the entire population as a single age-gro\ip 83 4. The error of estimations of wealth by attributing it to a single age-group of 21 years and upwards . . . . . . 84 5. Determination of factors for correcting large group-results 85 6. Determination of the multipliers, independent of, and dependent upon, the death-rate, for deduc- ing the total wealth from the wealth disclosed in probate . . 86 7. Should the general death-rate be used 8. Estimation of the uncertainty in the values of the correction- factors . . 9. Cause of uncertainty in results .. 10. Effect of change in the rate of mortality upon the ctmiputa- tion of private wealth 11. Arithmetical example of effect of progressive change in death- rates 1 2. Correction to reduce group-resvilts to results given by a continuous curve 13. Correction in any age-group for variation of wealth with death- rate in the group 14. Difference of death-rate not de- terminable from relative num- ber of deaths in probate and non-probate classes. 15. Variation of mortality in age- groups according to occupation 89 90 92 94 95 96 97 98 Synopsis. Page 16. Life Assurance Society's experi- ence of variations in death- rates, according to size of policy, etc. . . . . . . 99 17. Estimate of possible correction based vipon supposititious dis- tributions of wealth and mor- tality 100 ! 18. Consequence of assuming that life assurance rates should be adopted 101 19. Consequence of death-rate being less aniong the wealthy . . 103 20. Existing statistical data point to the conclusion that the devolu- tion-rate method naust be applied to each sex separately 105 21. Variation in the relative amounts contributed in each age-group and its consequence . . . . 107 22. Necessity for a correction for in- frequent appearance of large estates . . . . . . Ill 23. Examjjle of variations in thefactor k and their consequences .. 112 24. Variation of the factor k with variation of the death-rate . . 113 Page 25. Estimate of secular variat ion of k for Australia .. .. ..114 26. Correction for wealth of absentees 115 27. Effect of insurance jiolicies in probate returns .. ..116 28. Ratio of net to gross values of estates in probate returns . . 117 29. Effect of re-grants and re-seals 119 30. Corrections for wealth passing by settlements .. .. ..119 31. The distribution of wealth among the dying, Victoria .. ..121 32. Distribution according to age probably not constant . . 126 33. Correction for variations in the age-distribution . . . . 126 34. Combined corrections . . . . 128 35. Empirical correction of probate results 128 36. The growth of Australian wealth 128 37. Comparison with other estimates of private wealth . . . . 130 38. Probate and general distribution of wealth according to size of estate 130 39. Conchisions regarding the pro- bate method . . . . . . 131 40. Graphical representation . . 132 PART VI.— THE INVENTORY METHOD OF ESTIMATING WEALTH. Chapter I, — Estimate of Australian Private Wealth for 1915. 1. General 136 2. Basis of estimate 136 3. Details of estimation — (i.) Land and improvements 137 (a) New So tit h Wales . . 137 (6) Victoria 139 (c) Queensland . . 139 (d) South Australia 139 (e) Western Australia . . 140 (/) Tasmania 141 (g) Territories . . 141 (h) Commonwealth 142 (ii.) Live stock 142 (iii.) Agricultural, dairying and pastoral implements and machinery 144 (iv.) Manufacturing plant and machinery 145 (v.) Mining properties 145 (vi.) Coin and bullion 146 (vii.) Private railways and tramways 148 (viii.) Shipping . . 148 (ix.) Agricultural and pastoral products 149 (x.) Locally manufactured products . . . . 150 (xi.) Mining products (other than gold) . . . . 150 (xii.) Imported merchandise . . 151 (xiii.) Clothing and personal adornment . . . . 151 (xiv.) Furnituie and fittings, books, pleasure vehicles, etc 152 4. Aggregate of detailed estimates 153 Chapter II.— Earlier Australian Inventory Estimates. 1. Estimate for 1890 and earlier years . . . . . . . . 154 2. Estimates for 1903 and earlier years . . . . . . . . 155 Chapter HI.— ^Comparison of Earlier Estimates with those for 1915. 1. Aggregate amounts . . . . 156 2. Relative distribution of private wealth according to class . . 157 3. Private wealth per head in each class . . . . . . . . 158 Synopsis. Page Chapter IV.— Estimates of the National Wealth of the United States of America. General Census of Census of Census of Census of Census of Census of 159 159 159 160 160 161 1850 1860 1870 1880 1890 1900— (i.) General . . . . . . 161 (ii.) Farm and factory property 161 (iii.) Taxable real property . . 161 (iv.) Exempt real property . . 162 (v.) Live stock .. .. 162 (vi.) Farm implements and machinery (vii.) Manufacturing machinery, tools and implements (viii.) Gold and silver coin and bullion . . (ix.) Railroads and their equip- ment (x.) Street railways, etc. (xi.) Products of agrictdture, manvifactures, and mining . . (xii.) Clothing, furnitiu-e and kindred personal pro- perty (xiii.) Aggregate for 1900 Estimate for 1904 Estimate for 1912— (i.) General . . (ii.) Taxable real property and improvements 162 162 162 162 163 163 163 164 164 164 165 Page (iii.) Exempt real property and improvements . . 165 (iv.) Live stock . . . . 165 (v.) Farm implements and machinery . . . . 165 ( vi. ) Manufacturing machinery, tools and implements 165 (vii.) Gold and silver coin and btilUon . . (viii.) Railroads and their equipments (ix.) Street railways (x.) Telegraph systems (xi.) Telephone systems (xii.) Pulhnan and other cars not owned by railroads (xiii.) Shipping and canals (xiv.) Irrigation enterprises . . (xv.) Privately-owned water- works . . (xvi.) Privately owned central electric light and power systems (xvii.) Privately - owned gas systems (xviii.) Agricult\u"al products . . (xix.) Manufactured products 166 (xx.) Imported merchandise 166 (xxi.) Mining products (xxii.) Clothing and articles of personal adornment . . (xxiii.) Furniture, carriages and kindred property . . 167 (xxiv.) Aggregate for 1912 . . 167 10. Details for 1900, 1904 and 1912 167 165 165 165 165 165 165 166 166 166 166 166 166 166 166 PART Vn.— MISCELLANEOUS ESTIMATES OF WEALTH. Chapter I. — Estimates of the National Wealth of the United Kingdom. 1. General . . . . . . 168 2. Sir William Potty's estimate (about 1679) 168 3. Gregory King's estimate (1688) 168 4. Estimates based on Decker's figures (1740) 169 5. Beeke's estimate of wealth of Great Britain (1800) . . . . 169 6. Colquhoun's estimate (1812), and others based thereon . . 170 7. Giffen's estimates for 1865 and 1875 171 8. Giffen's estimate for 1885 ; . 172 9. Giffen's estimate for 1903 . . 172 10. Harris and Lake's estimate, 1903- 1906 .. 173 11. Mallet's estimate, 1905 and 1906 12. Chiozza Money's estimate, 1908 173 173 Chapter H. -Estimates of Wealth in France. 1. Various early estimates.. .. 173 2. M. de Foville's estimate, 1886 . . 174 3. Edmond Thery's estimate, 1908 174 Chapter HI. — Estimates of Wealth in Germany. 1. Bucher's estimate, 1908 .. 174 2. Helfferich's estimate, 1910-11 174 3. Estimate of wealth in Prussia, 1911 174 Synopsis. PART Vra— CONCLUSIONS. iX Page Chapter I. — Limitations and Uses o£ Wealth Estimates. 1. Limitations 2. Uses 176 177 Chapter II. — Census of Wealth and Income. 1. General 177 2. War Census of 1915 . . . . 178 3. Advantages and disadvantages of census method . . . . 178 4. Suggestions for future action . . 178 Chapter HI. — Succession Method of Estimating Private Wealth. 1. Succession methods . . . . 179 2. Statistical requirements for an accurate succession method 179 Chapter IV. — The Inventory Method of Estimation. 1. General . . . . . • • • 180 2. Advantages and disadvantages of the inventory method . . 180 3. Suggestions for future action .. 180 APPENDIX. Bibliography . . . . • . ..181 THE PRIVATE WEALTH OF AUSTRALIA AND ITS GROWTH AS ASCERTAINED FROM THE WAR CENSUS OF 1915 AND FROM PROBATE RETURNS. Together with A REPORT ON THE WAR CENSUS OF 1915. PART I —THE NATURE OF NATIONAL WEALTH. CHAPTER I.— INTRODUCTION. !■ General. — The aggregate Private Wealth of any homogeneous community constituting a nation, together with its corporate possessions, may be called its National Wealth. A clear vmderstanding of the essential character of such wealth is important, since confusion of thought is common in regard thereto. For this reason it is necessary to pay attention both to the nature of its component elements and the means of estimating their value, as well as to the uncertainties and limitations of such estimates. In regard to ownership, the wealth of any country may mean several things, viz., either (i.) the wealth owned by the people domiciled therein (a) the corpus itself being within the country, or (6) without that restriction ; or (ii.) the wealth within the country irrespective of the domicile of the owner. Owing to what has been called the " anonymity" of capital, wealth may — to a considerable extent — be owned by persons not only not domiciled in a country, but even by those who owe it no allegiance. In respect of value an estimate of national wealth may be founded upon more or less shrewd guesses at the average wealth per unit of population ; upon rough com- putations based \ipon statistics of bankmg deposits, together with houses and land occupied ; and similar data. Such guesses, however, have no authority, since their degree of accurracy cannot be ascertained. A census of the wealth of a group in any community, either taken at random, or better, properly selected, gives a result of greater we'ght. Estimates may also be founded upon returns of income — a method which, however, is very precarious ; upon the value of estates of deceased persons, considered as representative of the rest of the community. This latter method would appear to have claim to considerable confidence. With proper precautions, doubtless any or all of these methods may well be employed. Estimations based on the values of the estates of persons dying have been sup- posed by many to be of peculiar value, iiiasinuch as the responsible evaluation of estates for the purposes of probate presumably furnishes results of more than ordin- ary accuracy. In fact, the estates of deceased persons are assumed to be, as it were, a most appropriate parcel, viz., one taken quite at random, and sufficiently large to be representative. The method of estimating the total wealth from probate retiu-na will consequently be exhaustively considered. The best result is, of coiu'se, fur- nished by a complete census of wealth, provided that the valuations are carefully made upon a common basis. 2 Thw Nature of National Wealth. 2. Value, how estimated : its uncertainty. — The term " Wealth" has, of covirae, no vinique meaning, nor is the value of anything which may be classed as wealth always susceptible of exact expression in terms of money. This applies more particularly to the corporate possessions of a people. Though the values in which estimates of wealth are expressed must necessarily be exchange-values, these are by no means fixed and unalterable, nor are they, though necessarily the common basis of all comparisons, readily ascertained with a high degree of accuracy. Wealth — in the sense which we are considering — is ordinarily represented by tangible securities, e.g., currency, consols, inscribed stocks, bonds, shares, real- estate, etc. The values of these, however, often rapidly fluctuate with public credit or popular appreciation. For this reason estimates of value need to be made- — as far as possible — in normal times, and changes of value do not necessarily represent actual changes in the physical element constituting the wealth. When the piu-pose is to ascertain the material basis of wealth the method will of course differ {e.g., the numbers, rather than the values of flocks and herds would then be important). 3. Importance of clear statements as to methods of estimation. — It has already been said that mere guesses are without real value, at least for comparative piu:- poses, and it is evident from what has preceded, that the proper estimation of the total wealth of any commimity is not a simple matter. Some so-called estimates are little better than examples of " statistical charlatanism." Statistical estimates, in order to possess authority, must be well founded, and consequently the basis upon which they rest must be declared. When they are given on personal authority only, their value cannot be ascertained. For this reason statisticians and other publicists recognise that mere personal opinion, or a mere statistical ipse dixit, must not be allowed weight, not only because it lends itself to statistical imposition, but also because the reliableness of the results put forward cannot be indicated. In his" Sozialstatistik" (Leipzig, 1908), G. Sclinapper-Arndt sajs : — concerning certain tables purporting to give the national wealth of a number of civilised countries — that the greater part of the particulars have been merely fabricated.^ Very little consideration will shew the force of this remark. For, qviite apart from the basic difficulty of accui'ately estimating in terms of money vario\.ia forms of wealth, very few 2oeople can say off-hand, with any exactitude, the value of what they possess. Moreover, values themselves have a wide range, viz., from those disclosed under conditions of " forced sale" to those when sales are under the most favourable conditions for the seller. Hence even when a comprehensive census of wealth is under- taken, and all persons are required to furnish, under appropriate categories, the value of all material wealth possessed by them, with every safeguard to avoid repeated inclvision of the same items (as when encumbrances exist) the result is subject to a larger miargin of micertainty than is commonly appreciated. A comparison of estimates of value made at " boom" times with those ntiade at ordiiiary times is but an extreme case of this uncertaiiity. It is evident, from these and similar considerations, that comparisons of wealth estimated as existing at different dates are subject to a large measuie ot uncertainty, quite apart from that arising from the varying significance of the money standard, and deductions based on such estimates, expressed in terms of poiuids sterling, have to be used with corresponding caution. * His exact statement is : — " dergrosste TeildieserDaten ist nun giinzlich aiis der Luft gegriffen" ; vide op. cit., p. 2.59. Introduction. 3 A careful consideration of the whole matter will disclose that among estimates of wealth with any pretensions to accuracy there are two, at least, which take a high place, viz. : — (1) Estimates furnished in a Census of Wealth (usually made by its possessors); (2) Estimates of wealth disclosed through death (probate returns). The first is usually fairly complete, and is of a precision governed by the integrity of the returns themselves. \^Tiere the returns do not systematically either understate or overstate, the final result may be regarded as of high precision. Although, as above stated, the second method is obviously of the nature of a representative parcel, it is only a partial return, since probate returns are not required for estates of small value, and therefore the total wealth will be vmderstated if no allowance be made for this fact. Moreover, for short periods the retiu'ns themselves are subject to a considerable measure of uncertainty as " representative parcels," inasmuch as large estates come luider review only with great irregularity. It will be necessarv to consider these limitations. 4. Sense in which wealth is attributable to individuals. — A person living in any community may possess wealth consisting of lands, goods, or instruments of credit, (a) within the territoiy occ\jpied by that commv.m.ity, or (6) without it. In the former case there can be no doubt that such wealth is part of the communal or national wealth : in the latter case, the purpose of the estimate would determine whether the inclusion or exclusion of particular items was necessary. For ordmary purposes (6) would be included in estimates of national wealth, inasmuch as such wealth has exchange-value, notwithstanding that the corpus itself is not in the territory occupied by the community. There may, however, in some cases be a measure of tuacertainty as to the total wealth to be accredited to a country, owing to uncertainties of nation- ality and domicile. For example : — Let us suppose that A, an individual living in the commimity considered, has property therein of value IF, subject to an encum- brance of w, held over it by F, the latter being abroad. The value to be recorded is W^w ; and, if questions of domicile were always definite, and a census of wealth was complete, there could be no luicertainty in respect of the estimation of the communal wealth. If, however, F were only temporarily abroad, and his real domicile were in the commiuiity, the total wealth ought to be W, the part W—w belongmg to A, and the part «> belong to F. ^ 5. Wealth under private ownership. — The term private wealth is used in contra- distinction to public or semi-public wealth. In Australia the term would cover all that wealth, the proprietorship of which resides in indi\'iduals in their private ' The importance of questions of nationality and domicile have come into prominence thrcmgh recent events. Dual nationality, and the system by means of which all the res])nnsitiiliti('s of nation- ality can be avoided, and all its benefits secured, are reflected in (|ucstions of ownership. The estab- lishment also of local comi)anies almost wliolly with foreiRii capital, the propdrtion of local capital being merely nominal, may reduce the m-t value of large properties to a negligible hical location of wealth and the domicile of its ownership is of the first degree of importance, but also that the wealth of a territory may be advantage- ous or disadvantageous, according as its usufruct and potentialities are nationally enjoyed by the country in question, or by a foreign i)eople. See " Gli insegnamenti della guerra circa il trattaiiiento degli stranieri, " by Prof. P. Fedozzi, " Scientia, 1., xii., 1915, pp. 402-418," and '• Nationality and Naturalisation," by Dr. E. J. Schuster, Contemporary Keview, Jan. 1917. pp. 93-99. 4 The Nature of National Wealth. capacity, and is not vested either in the Federal Government, a State Government, or any form of Local Government. It thus comprises all wealth (i. ) which is under the dii'ect control of the individual proprietors thereof. (ii.) which is administered in trust or by delegation in the interest of individual proprietors. (iii.) which by the intermediary of shares, debentui-es, stock, mortgages, or other means is allocated directly or indirectly, wholly or m j^art to individual proprietors. (iv.) which is collectively owned by groups of private persons without any specific allocation to individual proprietors. Section (iv.) comprises such forms of wealth as the property of Clubs, Chm-ches, Schools of Art, Mechanics Institutes, etc. These may for certain jDurposes be con- veniently classed as social private weallh. 6. Wealth under communal ownership. — ^In all well-developed modern com- mvuiities a considerable quantity of wealth is vested in local governmg bodies of various types, whose scope and functions are tisually prescribed by legislation or by regulations of the central government. These bodies include city, municipal, borough, shire and similar councils ; irrigation-trusts ; tramway -trusts ; school- boards ; hospital-boards ; fire-brigades ; watex'works -boards ; harbomr-trusts ; etc., etc. The property held by them covers a wide field, and includes such items as roads, railways, tramways, jDublic buildiiigs, plant, machinery, reservoirs, water channels, etc., etc. The several bodies controlling these forms of wealth are required to administer them in a public capacity for the benefit of the commvmity resident within the ambit of the jm'isdiction of the body in question. The property is in a sense owned by the persons who make up that community, but it is owned by them collectively not individually, and the constitution of the corporate controlling body is usually not amenable to direct alteration by the members of the community in question. 7. Wealth under national ownership. — All those forms of wealth the proprietor- ship of which vests in the central governmg body may be conveniently classed as bemg vmder national oumership. In the case of AustraUa and other federations, this is somewhat complicated by the fact that there is usually not one but two such bodies (which divide the central control between them), viz., the Federal Government, and, in respect of any given part, a State Government. It will be convenient, however, to class the property of Federal and State Governments under the one general heading of iiational ownership. In Australia the principal items of property which are the subject of national ownership are Crown Lands, Government Rail- ways and Tramways ; Government Buildings ; Naval and Merchant Fleets ; Waterworks ; Harbour Works ; Telegrai^hs and Telephones ; Defence Works ; and Naval and Military equipment and material. 8. Variation in valuation cases. — From the foregoing classification of ownership under the three heads of private, conmmnal, and national, it will read'ly be vmderstood that it is quite impossil)le to obtain any estimate of the value of all property on the basis of exchange value, suice many properties, while rendering great services to the community, would possess little value in exchange, owing to the absence of any market for the property m question. This is especially the case with many of the Introduction. 5 items of commuyial and national ownership. For example, a building erected and eqmpped as a Parliament House or as a Public Library would be of little value, in proportion to its cost, for any other purpose, and thus being practically unsaleable, cannot be properly said to have any value in exchange. In other cases, as for example Government Railways, there is no doubt that if offered for sale they would realise high prices, but in tlie absence of any sales of this nature it is impossible for any one to say what their exchange value might be, and how it would compare with their cost of construction. Another class of property under national ownership, viz. Crown Lands, occupies a somewhat different position from either of the foregoing. In closely settled districts there is practically always a market for real estate, and within reasonable limits a fair exchange value could always be ascertained in respect of the Cro\\-n Lands in such districts. In sparsely settled pastoral districts on the other hand, where the land is usually occupied mider some form of lease from the Crown, this does not apply, and it is even less applicable in the case of the huge tracts of unoccupied lands which make up so large a proportion of the Crown Lands of Australia. Much of both of these latter classes will probably have considerable exchange-value in the future, and possibly in the near future, but at present there is no basis on which anything deservmg the name of an estimate of their value could be made. In the case of private wealth on the other hand there is not the same difficulty, and in most cases reasonably accurate estimates of the exchange value can readily be made. Thus we see that although both private and national wealth may be productive in varying degrees, or may even involve varying degrees of loss, and that these facts may materially affect the exchange value of the wealth, they are in themselves irrelevant. The exchange- value is the only relevant matter in estima- tions of jDrivate wealth, other questions may therefore be dismissed from con- sideration, notwithstanding that for particular purposes other bases of estimation may be necessary, for example the value of railway and other public services aa already indicated. 9. The fluctuation of wealth. — ^It is important, however, to bear in mind that wealth is not a fixed, it is always a fluctuating, quantitj*. In a country' like Australia — a large and compact island continent — in which a considerable portion of the wealth consists of flocks and herds, the fluctuations are quite considerable, not merely because the physical elements of the wealth vary considerably with abund- ance or dearth of rainfall, but also because their exchange -values are materially affected by the same causes. Drought conditions, for example, may not only cause substantial losses in actual numbers, but also, because of the long distances to markets, may prejudice their exchange-values. It Is obvious, from considerations analogous to the above, that estimates of wealth to be of the highest value and to serve for comparative purposes, must be based upon average conditions. It follows, therefore, that a census of wealth which merely gives values at a particular moment will, ordinarily, but imperfectly repre- sent such average conditions. On the other hand, however, it rarely happens in extensive territories, that physical conditions are specially adverse or specially favourable throughout the entire area at any given time : consequently, as the territory embraced in any estimate is increased in size, the result of any estimate tends more and more to express average conditions. The range of fluctuation for different classes of wealth is by no means identical. In the case of sheep and cattle in Australia, for example, the variations of exchange- value are very large, while those for houses and buildings, plant and machinery, etc., 6 The Nature of National Wealth. are, relatively thereto, only small. In so-called " boom times," values ascribed to land are vuiusually high ; at the collapse of a " boom" they are very low : national secm-ities fluctuate greatly with national credit, with the probability of war, or of the fortunes of war, etc. ; estimates for probate or other duties are usually too low, while estimates, made without regard to the liabiUty to duty, are likely to be too high. In order that a Census of Wealth should funiish a normal result, therefore, it is requisite that the period covered should be sufficient to fiirnish average values. The period over which the values are taken should conseqxiently be commensurate with the fluctuation periods, which, aa said, are diverse for different classes of wealth. A census of wealth representing values at a particular moment may be consequently very unsatisfactory if the selected moment should happen to be one at which other than average conditions obtain ; and this fact has to be kept in view. CHAPTER n.— VARIOUS MODES OF ESTIMATING WEALTH. 1. A census of wealth. — A comiDrehensive census of wealth fimiishes a direct estimate of such part of the possessions of a community as can be expressed in terms of money values. Such a census indicates the wealth as referred to a particular moment of time, and its worth depends upon the care with which the estimates of exchange value are made. The nature of the War Census, and of its merits and limitations are dealt with in Parts II., III., and IV. 2. Probate returns. — In practically all civilised coimtries there are what are generally known as " succession" duties, based upon the value of the estates which pass to successors in title. Owing to this a valuation has perforce to be made on the death of possessors. Such valuations are available in Australia in the " probate returns," and afford a means of gauging the wealth of the entire commmiity, foras- much as the returns shew the wealth possessed by a part of the community which can be regarded — as pointed out — as a " fair sample." The methods which have been adopted for ascertaining the ratio between what passes to successors in a luiit of time (one year) and the total wealth of the commiuaitj% are two, viz., (i.) the determination of the avei'age interval of time between the passing of estates to the successors in title, and (ii.) the ascertainment of the average rate of the passing of estates during any period under review. The first may appropriately be called the devolution-interval method, and the second the devolution-rate method. Obviously the two methods are — in the last analysis — essentially the same, the number of years in the devolution interval being the reciprocal of the annual rate of devolu- tion. At first sight it might therefore appear that it is a matter of little moment which method we follow. This surmise is, however, not correct, for reasons which are given hereinafter, and which, briefly expressed, are that the devolution-interval method is the more complicated and \mcertain, and that the corrections — which must be applied to any crude estimate of its value — are not readily computed or easily ascertained. 3. The devolution interval.— Since the average length of life differs in the case of males and females, the devolution interval varies accoi'ding to sex : moreover, aa the rate of mortality is diminishing for both sexes the interval is lengthening for both. For this reason, if it be treated as a constant quantity, deduced estimations of the Various Modes of Estimating Wealth. 7 aggregate of wealth, based upon any value founded on past experience, are con- sequently luisatisfactory unless they are corrected for the increased " expectation of life." The interval is, of course, the weighted average period between the sue cession to wealth in one generation and its passing on to the next. The determina- tion of the " weights" to be used in ascertaining the weighted average introduces complexity into the method. There is a fundamental defect in the devolution-interval method, which it is important to consider. It is this : — All wealth created durmg the life-time of any individual obviously operates virtually as a reduction of the period intervening between " successions." Thus this period, when exactly ascertained, should be altered by way of correction. The data, however, furnish no information by means of which the necessary correction can be evaluated. Wealth that is conveyed during the lifetime of possessors causes estimates of the total deduced from a correct estimate of the devolution-interval to be under- stated. The matter is later considered in detail. 4. The devolution-rate. — The fmidanaental conception of the devolution-rate method of estimating the aggregate wealth is that the persons dymg during any period constitute a " fair sample" of the living, as regards the possession of wealth. If the wealth of those dying be known, that of those living could be deduced by multiplying by the ratio of the living to the dymg. That proportion of the dying, whose estates are suflficiently large to come under review in probate returns, give aa aggregate of wealth which is too small, and consequently the wealth of the remainder must be estimated in order to furnish the total wealth of the dying. This then is the prhiciple of the method. In applying it, however, it is necessary to bear in mind that the distribution of wealth varies according to both age and sex, and therefore the death of those dying should be dealt with according to age-groups and for the sexes separately. If the period of review be short, one year for example, the infrequency of the appearance of large estates in probate returns is such that it will occasion large discrepancies in the result deduced for successive j^ears, according as a large estate appears, or does not appear, in the returns. Consequently accui'ate results can be expected onlj' if the estimate is extended over a sufficient number of years. We shall see later that this should be at least 10 years in Australia. But since in 10 years values may change considerably, the result applies, not to any moment of time, but represents rather — in any community in which wealth is increasing — a decennial average referable to a moment somewhat later than the mean of the period. We may call this the weighted mean, the weighting factor bemg the wealth. This m brief is the principle. But in detail, the matter is not quite so simple. Accoimt must be taken of the passing on of wealth before death, for this, by reducing the wealth appearmg in the probate-returns impairs their value as a " fair sample." Moreover, it assvunes that the death-rate depends solely upon age. If, however, the condition of life — as regards wealth — is affected, those represented in probate- returns are again not a " fair sample" of aU persons of the same sex and age. It is then evident that before the method can be regarded as quite satisfactory these featiu-es must be examuied and corrections applied if necessary. 5. Comparison of Methods. — It will be necessary, later, to compare the estimate of wealth obtained by means of the War Census, with that obtained from probate returns. After a full exposition of the two, a part will be devoted to the discussion of any discrepancy between the results. This is the more necessary- as the present uistance is believed to be uiiique in respect of making such a comparison. PART n.— WAR CENSUS OF 1915— GENERAL. CHAPTER I.— LEGISLATION AND ORGANISATION. 1. Legislation. — ^The War Census was authorised by the Commonwealth War Census Act 1915, assented to on the 23rd July, 1915. This Act provided that it " shall continue in operation duriiig the continuance of the present war and no longer, and that a census or censiises shall be taken in such States, Territories or parts of the Commonwealth, and on such day or days, or within such period or periods as the Governor-General appomts by proclamation." In accordance with this provision a proclamation, issued on the 25th August, 1915 (see Commonwealth Gazette, 25. 8. '15, p. 1633), fixed the period for the Census of 1915 as from 6th to 15th September. A fiu'ther Act, the War Census Act (No. 2) 1915, assented to on 6th September, 1915, required the transmission by post, free of charge, of all papers provided for in the principal Act. Two schedules to the principal Act furnished tentative forms of inquiry, pro- vision being made in Section 8, of that Act, that modifications and additions might be prescribed. A regulation setting forth these forms of inquiry as amended in accord- ance with the Act was issued oia 10th August, 1915. 2. Forms of Inquiry. — As already indicated, the forms of inquiry provided for were two. That contained in the amended First Schedule to the Act, and known as the ''^Personal Card,^' was as follows : — Commonwealth of Australia. WAR CENSUS (1ST Schedule). Write Clearly. Personal Card. To be filled in by all Males aged 18 and under 60. 1. Name in Full (Underline Surname.) 2. Full usual Postal Address (including State) — (If away from usual residence when filling in card, the postal address to be given here is that of your usual residence.) 3. Date of Birth :— Day Month Year State Age last Birthday years. 4. State whether Married (M), Widower (W). or Single (S) 5. State Number and Relation of Dependent Relatives (it any) 6. State whether your tJeneral Health is Good, Bad, or Indifferent 7. If suffering from Blindness, Deafness, or Loss of a Limb, give particulars 8. What is your present Occupation ? 8a. State Grade of Occupation (If employing labour other than domestic, insert E ; if working on own account but not employing labour, insert O ; if assisting but not receiving salary or wages, insert A : if in receipt of salary or wages, insert W : if out of work for more than tlie week prior to 30th June, 1915, insert N.) 8b. If you are an Employee, what is the Occupation of your Employer ? 9. What other Occupation (if any) could you undertake ? 10. What Military Training (if any) have you had ? 11. State number and (li's 458; 763,892 9,625,174 71,833 565,337,460 163,803,435 154,623,129 67,869,080i44,945,491 842,734 F. Ter. C'wealth. £ 271,047 71,513 419 342,979 921,985,433 302,240,561 1,283,004 248,137,367 144,635,865 25,181,146 1,643,463,376 The net assets shewn in the preceding table are exclusive of the property of Federal, State or Local Governments, and may consequently be considered as repre- senting the total private wealth of Australia as at 30th June, 1915. This total of £1,643,463,376 includes the Australian j^roperty of non-resident individuals, partner- shijDS and companies. The amount, however, so held by non-residents, cannot be determined with any degree of accuracy, but on the basis of the War Census returns it is roughly estimated that it lies between £150,000,000 and £200,000,000. It would thus appear that the aggregate private wealth of AustraUan residents as at 30th Jime, 1915, was approximately £1,470,000,000, or nearly £300 per head of population. As in the case of incomes in Chapter II., the assets of Australian partnerships are included in the returns of the individual partners. The partnership figures shewn in the above table relate to non-resident partnershijis only. The item " Trust Funds," is made up of several categories of whicli the most important are the total values of trust-estates, and the Australian funds of Life Assurance Companies, Frieixdly Societies, and Trade Unions. As these funds were in every case excluded from the returns of individuals either by instruction as in the case of Life Assurance policies, etc., or by special adjustment prior to tabulation as in the case of beneficiaries in trust estates, the possibility of duplication of such returns has been eUminated. Net Assets. 29 In the case of " Companiea," the net assets of the Australian companies were taken from special returns obtained from, these companies, such net assets being computed without deducting the Uabihties to share and debenture holders. From the total net assets so computed, the aggregate amoimt of " Shares and debentures in companies" sheNvai on the various individual and other cards was deducted, the balance represeiitiiig approximately the interest iii Australian companies held by- persons not resident in the Commonwealth, together with the margin, if any, be- tween the share valuations of the several shareholders, and the valuation of net assets made by the company officials. With absentee companies, that is, comiDanies registered outside Australia, but trading in the Commonwealth, the procedure followed was that of includmg the net assets of the company held in Australia. (ii.) Net assets of individuals. — The aggregate net assets of individuals shewn m the preceding table amounts to £1,224.225,994, of which £921.985,433 was recorded in respect of males, and £302,240,561 in respect of females. Particulars concemmg the number of retxirns of residents and of non-residents of each sex allocated to each State or Territory are shewn in Chapter II., p. 23, the figures hi this case being, of course, the same for incomes as for assets. The aggregate net assets represented bj' such reti.u*iis are shewn in the followmg table : — Aggregate* Net Assets of Individuals as at 30th June, 1915, recorded in respect of each State and Territory of Australia. state or Territory. N. S. Wales Victoria Queensland S. Australia W. Australia Tasmania Nor. Territory Fed.Territory Total, C'wlth Aggregate Net Assets recorded in respect of Residents of Australia. Males. Females. £ £ 362,193,858106,750,464 289,313.023 112,166,443 103,382,820 30,139,736 93,677,702 29,018,284 £ £ 468,944,322 12,252,941 2. 401,479,466 1 805,873 1 133,522,556 42,132,404 26,355,451 763,892 271,047 918,090,197 10,464,596 9,458,596 71,833 71,513 Persons. Aggregate Net Australian Assets recorded in Respect of Non-Residents. Total Net Assets Recorded. Males. Females. 122,695,986 52,597,000 35,814,047 835,725 342,560 298,141,465 1216231662 100,925 314,578 276,912 144,007 £ 180,745 358,687 60,487 166,904 165,695 166,578 Persons. 3Iales. Females. 3,895,236 4,099,096 £ 4,433,686 2,164,560 161,412 481,482 442,6071 310,585| £ 364,446. 290,118; 103,483. 93,992; 42,409, 26,499, 763, 271, 799il08,931,209 "113,525,130 30,200,223 29,185,188 10,630,291 9,625,174 71,833 71,513 Persons. 7,994,332 '921,985,433 473,378,008 403,644,026 133,683,968 123,177,468 53,039,607 36,124,632 835,725 342,560 302,240,561 1224,225,994 The total of £1,216,231,662 for residents of Australia represents average net assets of £246 per head of pojiulation. The correspondmg averages per head of population for the several States and Territories are as follows : — New South Wales, £251; Victoria, £282 ; Queensland, £193 ; South Australia, £279 ; Western Aus- tralia, £163; Tasmania, £181 ; Northern Territory, £176; and Federal Territory, £136. It should be noted that owing to the exclusion from the individual retiu-ns of interests in trust fvuids the figures here given somewhat miderestimate the net assets per head of population. The inclusion of such fimds with an allowance for those, the title to which is held outside the Commonwealth, would have the effect of increasing the average per head by from 15 to 20 per cent., and for the Commonwealth as a whole would probably give a result in the neighbourhood of £293. The average net assets per individual return recorded in respect of each State and Territory is shewn in the following table : — 30 War Census of 1915. — Wealth and Income. Average Net Assets per Individual Return as at 30th June, 1915, recorded in respect of each State and Territory of AustraUa. Average Net Assets per Return Average Net Australian Average Net Assets per Return for all Returns. state or recorded in respect of Residents of Australia. Assets per Return recorded in respect of Non-Residents. Territory. Males. Females. Persons. Males. Females. Persons Males. Females. Persons. N.S.W. . . 691 398 592 4,096 3,350 3,692 695 405 596 Vic. 729 370 574 2,309 1,841 1,991 730 374 576 Q'land 524 295 446 1,383 657 978 525 295 446 S.A. 745 360 594 4,085 1,056 2,049 746 361 595 W.A. 498 342 457 2,408 1,841 2,159 501 346 460 Tas. 531 358 471 889 2,563 1,368 532 363 473 N.T. 592 835 607 592 835 607 F.T. 403 369 396 403 369 396 Aver. C'wlth 665 367 555 2,938 2,285 2,562 667 372 558 2. According to size of net assets. — (i.) Grouping. For the purpose of tabulating the results accordmg to size of net assets, the particulars relative thereto were classi- fied imder 16 net assets groups, of which one comprised those cases in which the return shewed that the net assets were nil, or that there was an excess of liabilities over assets. (ii.) Net assets of persons resident in Australia. — ^The succeeding table fvu-nishes for each sex and for the sexes combined the number of cases recorded in respect of persons actually or usually resident in the Commonwealth in each of the groups mentioned in sub -section (i.) above. It also gives the proportion per cent, of total represented by each such group. Assets* of Persons Resident in Australia — Number of Returns classified according to Net Assets. Number of Returns. Proportion per cent. Net Assets at 30th June, 1915. Males. Females. Total. Males. Females Total. Debt and nil 249,693 110,036 359,729 18.0910 % 13.5556 % 16.4114 Under £100 . . 533,315 392,146 925,461 38.6402 48.3095 42.2210 £100 and under £250 198,668 115,846 314,514 14.3941 14.2714 14.3486 £250 £500 135,689 76,772 212,461 9.8311 9.4577 9.6928 £500 £750 66,101 35,895 101,996 4.7892 4.4220 4.6532 £750 £1,000 39,746 19,905 59,651 2.8797 2.4522 2.7214 £1,000 £2,500 88,779 40,336 129,115 6.4323 4.9691 5.8904 £2,500 £5,000 37,593 12,885 50,478 2.7237 1.5873 2.3029 £5,000 £10,000 18,176 5,183 23,359 1.3169 .6385 1.0657 £10,000 £15,000 5,313 1.362 6,675 .3849 .1678 .3045 £15,000 £20,000 2,366 530 2,896 .1714 .0653 .1321 £20,000 £25,000 1,283 279 1,562 .0930 .0344 .0713 £25,000 £50,000 2,179 406 2,585 .1579 .0500 .1179 £50,000 £75,000 641 81 722 .0464 .0100 .0329 £75,000 £100,000 249 26 275 .0180 .0032 .0126 £100,000 and ipwards md upwards 417 49 466 .0302 .0060 .0213 Total 1,380,208 811,737 2,191,945 100.0000 100.0000 100.0000 Total £500 i 262,843 116,937 379,780 19.0436 14.4058 17.3262 "Exclusive of the value of (i.) interests in trust estates, (ii.) assurance and annuity policies, (iii.) prospective beneiits from Friendly Societies and Trade Unions. These three items are included In- bulk under " trust funds." Net Assets, 31 Of the returns received from resident males, 19 per cent, related to net assets of £500 and vipwards, while about 14i per cent, of those relative to resident females were in respect of net assets of £500 and upwards. For the sexes combined net assets of £500 and upwards were represented by somewhat less than 17^ per cent, of the returns. The aggregate net assets represented by the returns shewn in the preceding table amounted to £1,216,231,662, of which £918,090,197 was recorded in respect of males, and £298,141,465 in respect of females. The average net assets per rettirn for resident males was thus £665, as compared with an average of £367 per return for resident females, and an average for returns of residents of both sexes of £555. The aggregate net assets for each group and the proportion per cent, in each case is given in the following table in respect of persons actually or usually resident in Aus- tralia : — • Assets* of Persons Resident in Australia — Aggregate Net Assets disclosed by Returns. Aggregate Amount. Proportion per cent. Net Assets at 30th June, 1915. 1 "■ 1 Males. Females. Total. Males. Females Total. Under £100 . . £ 17,119,415 £ 10,975,234 £ 28,094,649 ; 1.8647 o/ 3.6812 % 2.3100 £100 and under £250 31,914,274 18,394,332 50,308,606 1 3.4761 6.1697 4.1364 £250 £500 48,160,783 27,018,916 75,179,699 5.2458 9.0625 6.1814 £500 £750 40,282,127 21,696,178 61,978,305 4.3876 7.2771 5.0959 £750 £1,000 34,331,262 17,164,250 51,495,512 i 3.7394 5.7571 4.2340 £1,000 £2,500 139,001,263 61,609,345 200,610,608 15.1403 20.6645 16.4944 £2,500 £5,000 130,573,375 44,097,969 174,671,344 14.2223 14.7910 14.3617 £5,000 £10,000 125,229,936 35,341,151 160,571,087 13.6403 11.8538 13.2023 £10,000 £15,000 64,180,648 16,431,170 80,611,818 6.9907 5.5112 6.6280 £15,000 £20,000 40,752,518 9,191,428 49,943,946 4.4388 3.0829 4.1065 £20,000 £25,000 28,770,393 6,226,123 34,996,516 3.1337 2.0883 2.8775 £25,000 £50,000 74,371,012 13,771,239 88,142,251 8.1006 4.6190 7.2472 £50,000 £75,000 38,955,747 4,926,254 43,882,001 4.2431 1.6523 3.6080 £75,000 £100,000 21,379,702 2,240,902 23,620,604 2.3287 .7516 1.9421 £100,000 and up^ ;vards upwards 83,067,742 9,056,974 92,124,716 9.0479 3.0378 7.5746 Total 918,090,197 298,141,465 1,216,231,662 100.0000 100.0000 100.0000 Total £500 and 820,895,725 241,752,983 1,062,648.708 j 89.4134 1 81.0866 87.3722 • Exclusive of the value of (i.) interests in trust estates, (ii.) assurance and annuity policies, (iii.) prospective benefits from Friendly Societies and Trade Unions. These tluee items are included in bulk under " trust funds." It will be seen that net assets of £500 and upwards aggregated nearly 89^ per cent, in the case of male residents, about 81 per cent, in the case of female residents, and somewhat less than 87^ per cent, in the case of residents of both sexes. From these figures taken in conjunction with those relating to the number of returns, it appears that in the case of male residents 19 per cent, of the retun^a accovmted for nearly 89J per cent, of the net assets, that in the case of female residents 14^ per cent. of the retvims accounted for 81 per cent, of the net assets, and that for tlie sexes com- bined somewhat less than 17i per cent, of the returns accounted for somewhat less than 87^ per cent, of the net assets. (iii.) Australian net assets of non-residents. — The next table furnishes in respect •of non-residents the number and proportion of returns under each of the net asset groups : — 32 War Census of 1915. — Wealth and Income. Assets of Persons non-resident in Australia — Number of Returns classified according to Net Assets. Number of E«turns. Proportion per cent. Net Assets at 30th June, 1915 Males. Females. Total. Males. Females Total. Debt and nil 437 1,110 1,547 32.9563 % 61.8729 49.5833 Under £100 185 65 250 13.9517 3.6232 8.0128. £100 and under £250 121 63 184 9.1252 3.5117 5.8974 £250 £500 133 62 195 10.0302 3.4560 6.2500 £500 £750 89 45 134 6.7119 2.5084 4.2949 £750 £1,000 68 27 95 5.1282 1.5050 3.0449 £1,000 £2,500 92 121 213 6.9382 6.7447 6.8269 £2,500 £5,000 66 108 174 4.9774 6.0200 5.5769 £5,000 £10,000 54 106 160 4.0724 5.9086 5.1282 £10,000 £15,000 24 33 57 1.8100 1.8395 1.8269 £15,000 £20,000 13 16 29 .9804 .8919 .92951 £20,000 £25,000 9 12 21 .6787 .6689 .6731 £25,000 £50,000 17 16 33 1.2820 .8919 1.0577 £50,000 £75,000 / 6 13 .5279 .3344 .4167 £75,000 £100,000 3 1 4 .2262 .0557 .1282 £100,000 and upwards 8 3 11 .6033 .1672 .3526 Total 1,326 1,794 3,120 100.0000 100.0000 100.0000 Total £500 a md upwards 450 494 944 33.9366 27.5362 30.2565 Of the returns received relative to non-resident males about 34 per cent, related to net assets of £500 and upwards. The corresponding proportion in the case of females was about 27 1 per cent., and for the sexes combined 30 J per cent. The aggregate net assets represented by the returns specified in the preceding table were £7,994,332, of which £3,895,236 was accounted for on returns relating to males, and £4,099,096 on those relating to females. The average amount of net assets per return for non-resident males was thus £2938, as compared with £2285 per return in the case of females, and £2562 per return for the sexes combmed. The aggregate net assets in each group for each sex and the proportionate distribution over the several groups are shewn in the following table : — Persons Non-resident in Australia — Aggregate Net Assets disclosed by Returns. Aggregate Amount. Proportion per cent. Net Assets at 3 0th June, 1915 Males. Females. Total. Males. Females Total. £ £ £ % % % Under £100 . . 5,761 2,901 8,662 .1479 .0708 .1084 £100 and juder £250 19,752 10,390 30,142 .5071 .2.535 .3770 £250 £500 47,436 22,745 70,181 1.2178 .5549 .8779 £500 £750 54,661 28,043 82,704 1.4033 .6841 1.0345 £750 £1,000 58,068 22,865 80,933 1.4907 .5578 1.0124 £1,000 £2,500 148,771 188,949 337,720 3.8193 4.6095 4.2245 £2,500 £5,000 232,935 376.151 609,086 5.9800 9.1764 7.6190 £5,000 £10,000 376,033 752,509 1,128,542 9.6537 18.3579 14.1168 £10,000 £15,000 300,429 387,114 687,543 7.7127 9.4439 8.6004 £15,000 £20,000 226,704 273,422 500,126 5.8200 6.6703 6.2560 £20,000 £25,000 192,566 268,248 460,814 4.9436 6.5441 5.7642 £25,000 £50,000 591,900 557,215 1,149,115 15.1955 13.5936 14.3741 £50,000 £75,000 398,930 373,828 772,758 10.2415 9.1198 9.6663 £75,000 £100,000 252,648 75,221 327,869 6.4861 1.8351 4.1013 £100,000 and upwards md upwards 988,642 759,495 1,748,137 25.3808 18.5283 21.8072 Total 3,895,236 4,099,096 7,994,332 100.0000 100.0000 100.0000 Total £500 { 3,822,287 4,063,060 7,885.347 98.1272 99.1208 98.6367 Net Assets. 33 (iv.) Average net assets in each group. — In the succeeding table the average net assets m each group are given, these averages having been obtained, as in the case of incomes, by totalling the net amounts on the several returns and dividing by the number of returns. Average Net Assets per Return ; Australia, 30th June, 1915. Net Assets at 30th June, 1915 Average per Return for Australian Residents. Average Australian Net Assets per Return for Non-residents. Males. Females. Total. Males. Females Total. £ £ £ £ £ £ Under £100 32 28 " 30 31 45 35 £100 and under £250 161 159 160 163 165 164 £250 ,, £500 355 352 354 357 367 360 £500 „ £750 609 604 608 614 623 617 £750 ,, £1.000 864 862 863 1 854 847 852 £1,000 „ £2,500 1.566 1,527 1,554 1,617 1,562 1,586 £2,500 „ £5.(100 3,473 3,422 3,460 3,529 3,483 3,500 £5,000 ,, £10,000 6,890 6,819 6,874 6,964 7,099 7,053 £10,000 ,, £15,000 12,080 12,064 12,077 12,518 11.731 12,062 £15,000 ., £20,000 17.224 17,342 17,246 17,439 17,089 17,246 £20,000 .. £25,000 22,424 22,316 22,405 1 21,396 22,354 21,944 £25,000 ., £50.000 34,131 33,919 34,098 ' 34,818 34,826 34,822 £50,000 ,, £75,000 60,773 60,818 60,778 56,990 62,305 59,443 £75.000 ,, £100,000 85,862 86.189 85,893 84,216 75,221 81.967 £100,000 and upwards 199,203 184,836 197,693 123,580 253,165 158,922 Average Assets — All Returns 665 367 555 2,938 2,285 2,562 £500 and upwards 3,123 2,067 2,798 8,494 8,225 8,353 3. Debt, or negative wealth. — A complete census of wealth includes " net assets," not only when they are positive, but also when they are negative, that is when the "net return" shews the individual to be "in debt." Suppose, for example, A owes B £3000, and is possessed of wealth to the value of £2000. If B regarded the debt a perfectly good one, he would shew himself as possessed, in addition to his other items of wealth, of £3000. But A would shew that he is "in debt", on the whole, £1000. Restricted to these facts the proper return of aggregate wealth would obviously be £3000 — £1000 = £2000, that is, the value of the negative wealth should be suljtracted from the value of positive wealth. Thus any mortgagee credits himself only with the money lent on the mortgage, while the mortgagor virtually credits himself only with the value of the equity of redemption. It is clear from this that where the net results of the assets of any group or groups of persons are negative, they should strictly be deducted from the net results of the group or groups of persons whose assets are positive. Since the returns do not permit the analysis of indivitlual cases, this may occasionally lead to some uncertainty as to the grouping according to the amount of wealth possessed. ' In general, however, such grouping will be substantially correct. With a view to ascertaining the extent and the nature of the error involved in the omission of the debts shewn on the returns relating to negative wealth, a special tabulation of 5703 cards, shewing debt, was made from a parcel of 51,514 which hatl been classed as " Nil and debt." The returns in question related to several counties of the State of Victoria, and were taken from a total of 244,772 returns (in- cluding the 51,514 mentioned above), which gave a total net assets of 1 122,489,039 when no allowance was made for the " debt" items contained in the "nil and debt " groups. The aggregate amount of debt so tabulated was £289.785, or say 2^ per thousand of the total covered by the class of cards from which the sample was drawn. In view of the relative smallness of the amount and of the evidence deduced in the succeeding section relative to the possible incompleteness of the War Census, it was 34 War Census of 1915, — ^\Vealth and Income. not deemed advisable to carry the investigation further, or to make any specific allowance in the aggregate for such results, more particularly as the evidence fur- nished by a close scrutiny of many of the so recorded " nil " cards indicated that further inquiry would probably disclose small net assets. For the purpose of analysing the progression in the returns of debts, and also of small net assets, and for the further pvirpose of furnishing a suitable basis for the estimation and analysis of material lying below the range of probate data, the follow- ing tables have been compiled from the returns for one of the Victorian districts : — Frequency of the Possession of small amounts of Wealth, based upon 25,932 Cases in Victoria, Australia (Total Population embraced about 77,350).* Debts. Assets. Range of Debts or Assets. Observed Numbers. Average Value per Person, f Average Value per Person, t Observed Numbers. Males. Females Persons. Males. Females. Persons. £ £ £ 267 123 390 3.74 0-10 3.74 3,635 3,658 7,293 109 16 125 14.10 10-20 14.10 908 1,120 2,028 57 10 67 24.85 20-30 24.85 782 790 1,572 28 3 31 34.86 30-40 34.86 549 481 1,030 20 5 25 44.89 40-50 44.89 448 407 855 15 2 17 54.89 50-60 54.89 467 385 852 13 1 14 64.89 60-70 64.89 297 241 538 7 1 8 74.89 70-80 74.89 295 214 509 4 1 5 84.89 80-90 84.89 237 200 437 5 5 94.90 90-100 94.90 197 155 352 525 162 687 23.25 Totals 23.25 7,815 7,651 15,466 40 4 44 V 100-250 156.38 2,012 1,669 3,681 10 2 12 ? 250-500 353.50 1,292 1,016 2,308 6 1 7 ? Over- 500 2217.8 2,269 1,458 3,727 581 169 750 ? AllAssets 405.77 13,388 11,794 25,182 • Viz., males, 37,420 ; Females, 39,930. t Calculated from frequency ciurve. Average Value in Range Ratio of Observed Numbers. Range of Assets. PER Individual. of Males to Males. Females Persons Persons. Males. Females Persons. £ £ £ £ 0- 100 . 24.17 21.78 23.25 0.5053 7,815 7,651 15,466 100- 250 . 157.07 155.55 156.38 0.5466 2,012 1,669 3,681 250- 500 . 356.. 56 349.60 353.50 0.5598 1,292 1,016 2,308 500- 750 . 607.99 595.82 602.34 0.5356 586 508 1,094 750- 1000 . 864.24 862.18 863.. 39 0.5895 372 259 631 1000- 2500 . 1568.4 1507.7 1543.6 0.5910 734 508 1,242 2500- 5000 . 3536.8 3349.9 3482.5 0.7095 320 131 451 5000-10000 . 7149.9 6707.1 7059.4 0.7955 175 45 220 Over 10000 . 25744.3 15910.9 24970.9 0.9123 82 7 89 Totals 544.57 248.21 405.77 0.5316 13,388 11,794 25,182 Net Assets. 35 Aggregate Assets o! Persons Possessing Wealth, between various ranges thereof. Debts. Range Assets. Pro- por- of Pro- tion of Debts portion Males. Fe- Per- Total or of Total Males. Females. Persons. males. sons. for Males. Assets. held by Males. £ £ £ £ £ £ £ £ 999 460 1,459 .685 0- 10 0.4984 13,595 13,681 27,276 1,537 226 1,763 .872 10- 20 0.4477 12,803 15,792 28,595 1,416 249 1,665 .851 20- 30 0.4974 19,433 19,632 39,065 976 105 1,081 .903 30- 40 0.5330 19,138 16,768 35,906 898 224 1,122 .800 40- 50 0.5240 20,111 18,270 38,381 823 110 933 .882 50- 60 0.5481 25,634 21,133 46,767 843 65 908 .928 60- 70 0.5520 19,272 15,638 34,910 524 75 599 .875 70- 80 0.5796 22,093 16,026 38,119 340 85 425 .800 80- 90 0.5423 20,119 16,978 37,097 474 474 1.000 90-100 0.5.596 18,695 14,710 .33,405 8,830 1,599 10,429 .847 Totals 0.5310 190,893 168,628 359,521 ? ? ? 100-250 0.5490 316,029 259,618 575,647 ? 9 ? 250-500 0,5646 460,676 355,192 815,868 ? ? ? Over 500 0.7468 6,323,056 2,143,927 8,466,983 581* 169* 750* 0.775t All Assets 0.7135 7,290,654 2,927,365 10,218,019 £ £ £ £ • £ 0- 100 0.5310 190,893 168,628 359,521 100- 250 0.5490 316.029 259,618 575.647 250- 500 0.5646 460,676 355,192 815.868 500- 750 0.5407 356.280 302,677 658,957 750- 1000 0.5901 321,497 223,305 544,802 1000- 2500 0.6005 1,151,223 765,907 1.917,130 2500- 5000 0.7206 1,131,781 438,844 1,570,625 5000-10000 0.8057 1,251,240 301,818 1,553,058 Overl0,000 0.9499 2,111,035 111,376 2,222,411 All Assets 0.7135 7,290,654 2,927,365 10,218,019 * Numbers only. t Ratio of numbers only ; amounts not known. 4. Wealth unrepresented by material values. — Returns of wealth are subject to certain limitations which it is important to notice. Book debts, for example, may be under or over estimated. Consols, inscribed stock, debenture, and bank-notes intrinsically are not wealth, but depend upon the aggregate wealth — and its security — of the community issuing them. Suppose, for example, that a national loan of £500,000,000 were liold wholly by the citizens of any nation, the private wealth would include this amount — or its market equivalent — while a statement of the national wealth, that is, of the people in their corporate as well as in their individual capacity — the two being combino-';_^'-'5_«o rH » I^ -«■ CI N r^ r- tH sflifli— esoOTfcosocOTHto 00 r* r-t .»t t^ u': c: t^ o cc ^"^^ CO -* Noo'TfcnrH'— ' c-i «D(MM'-IC!«O5COt2a0C5'*'^ oicot^eO'^MOooccotO'-io 00 O 05 05 t^ O ?D tH^O^GO '"l^t^..'^^ coc^r»?or^?D(Mr-c-]oiirtcco c^J-^OeOGsCiinooinoiccooo ci lyi Ci f^x tyi a ^^^ cc os o oo o irfo'crto'-^cfNTHi-r CO* tOO-^t^i-0^t~t-lMOt^3c^ T-t'MOOCOr-r-^l'-ClCOCCQO'^vC OS— It^OOSCI^'MNO-tCOOO-* r-ltOCCOrHCCOOrCiOOO'^'-lO cc o CO ©SCO 00 in 51 o 00 ci'-i.cs^ T-Tt-Tpj'c^orco io ^wTcf '-' '^ ■* Ci -^ Cl rH C-1 oocoooooo°o o o c o o o o c o O o • N « "l" i.O «C t~ OO Cj o o o ■ '-d «*< -jl VI trt =41 --rf --rt ^Tco lO mc*Jc*l S3 - T3 1=5 Sooooccoocooo OOCCCCOOOOOO io'-*c-]w^>Acot^aoosOoO w c»l irt W-rt '-rt V) C4l « «) ^- -„,- e»lt <3iOcD05(Moor^TH-»i<^eo^H'^ OWOCOCOOOOSi-HOOOSeOMCO cowrHi*io«»nr^05ir5c050'30 'oOTj'coosorHO'-Hint^tCmoo C i>- in oj N ■* « o_oo^>o_ CO OT o 00 « o^oo ci^'* o; ci ' fff-* TO Cf M'cf-^"cf Cf 00 ca o c t^ i.'r cc CI I- --1 00 N -J CO CO -t o ci ^. t - 1^ ^-t 00 in -^ in ci in o o> T c; ci r-<_^c-^c^a_^c;_ci^o '•'r-Tcccc'ci co'cc Gc'-t-'cc '^ in'o'i^ — — -^ — ^Oinooccoci -.* CO Cl lO -^ Cl MinxT-iciint^vnoocTiccoJo O'Hooot-i^inm'jicooscoc] t> in X CO in in t^ i^ 05 CO CO C5 00 oscocoin-^.-^coocococoo 00 i-i o t^ -* in o ci ci in i- co o\ ^ -^^rH cTcf '+"' "^^-^ ^ r-rr-Tin'T-ri-rr-rr-r cfco''** OOCOOi-IOSdClrHt^COin'^QO ■^coaicot^ccoiOoo^ocdin ooot^coc^rHocoinoi C5_^in CO ^ co'ci'cfin oo"'**t~ Qo'in co""-" co'--^" i000>COi-coincoNcor-co .-I in Tj<_^t~-_co_t> o oo_^^__co_^'-i_^co__t^_ •* cj't-' oo''T-roo' i^-'t-h i-TiCrH oft'ci'oo" O5cooot^-*t~-*c0'-ieooci-* ococioooinincJrHci -*__co o cfcfcicfT-Ti-HrHi-Ti-r cTco'cf eocDoooinin-*-^c?ci o^o^o ^ r.r-*'"oo"t-'''*'oo'^'"co''in r-^'oo oTco CO CI c ci CO --H CO ci CI O". m CO ci cocoincoocoin^^occ co^in co^ ■^t'co'in ■^'"■*''co'co''co'co'cf CO m sa co—t t^ • cj CO ■* in CO I- a; en — ^ c • C*< C«l Crt C*< C4l -^ VI C^ _• „' ^,- . c*^■v^v^ r-occoooocoooo ooooococoooo wj^cjco-^incoi^oooiooo J CrtC*) C*< VlC« C^ '^ VI C^ r-Tco'o h) crtcitv) Special Classes of Assets. 41 The succeeding table gives, for the Commonwealth aa a whole, a distribution of the number and unimproved values of freehold estates according to grade of owner- ship : — ca cS en Xi B a S W ^ ^ fl 3 o ^ a H a o E u tf » a •a p a eS a ifttOOOOMOJOO-^ceOlOC^lM rHini.ir3c~O)r- to ic ■* N "-^00 00 oo" rHtDrHMC-lTH-^OO-^OJCOtOO >-<'CNt~Oi^'*rt00t>'-IC<3N 5Dvn^mfMC<5I5!MiHrHOO«0 00 to t~ to" § o M OS^10iinOinOTl5Mt^I^vO'^ rao^os^co^in ir:_^c-i^o^in oo «o ^_^o O o''M'M''oo''o''nrcO *f r-To'rH'r-r C^ lO ^ r-H ,-1 iS I - -c rr •?] -c » — 1 CC L^ OT-* to p.j;.-:-ii-3:^Ococcc:;?ioo to »lGC •i-'i-x'-r'^'x'i-'in'ino'o'' t- 00 -* H r-. r-( r-i ,J. to Less than £100 £100 and under £200 £300 „ £400 £400 „ £500 £500 „ £600 £600 „ £700 £700 „ £800 £800 „ £900 £900 „ £1,000 £1,000 „ £3,000 £3,000 „ £5,000 £5,000 and over 3 o ■*oooor^o-«tvnoot-<-'r-itoeo N-*cocoTiiTjiNaOt~i-l'!l<->*COi-lO OSCOOCOCOOOOSr-fOOOStOCOCO to_t-- rH^-* o^co^in_i> OS lo M to_oo * oo"'*"oo'o>"os'-H'o'r-r»n"r-"to"m"oo •»i*iotOr-tOoooinr-t--#oocito to_oo Oi— tio^Ht^coosoto ^„to ci 00 to -^ f^i r-rcroro(rocr»n"i> oT eoosto-^oiOt-i-HcorfiO'^eo OSrHC-l^CCJinrHr-dOOI^OOlO oo^-'i^^o^t^ o o i> CO 00 o t^ '^^^ ' lo'tsT-.^* f-TcTto'orco'u^racr^-'irt"'-^" t^f-HC-lr-tOSOSt^t-OOtOOr^-^ tOOOt-r-t-^C^COiHCOOSOScO ■^o^tooocoooaoior-iooosoo-* 'Ji'ointototot^coc^c^oowco ^ M"-<"oo"'"in"a5*to"in"-* r-Tco oo"oo '-leocscO'fl'irj'^'^oiO'nirjrH iM O IM tc O to -^ ■^^N (N OS CJ 0^ to o to o to (M ?i ■■* — (.-lrHr-lr-l^rHCT^t-r-l-^OCOOtD-^OS meo-^cocotoooinoocscoN oo_i> oo_^rt__co o_oq_co oo__os_^oo_^c_o^ '** 1.-5 o"r^"cs"OT "m" ■*"to"r-"e'f T-f o co" '^rHto^Ht^inoDC^o-^'-'iooo '^tO'O'^tOOStOC^lr-'t^OST^CS Ooooicooot^coeotocscoto '-iC-OCOCOt^O'tl-lOO-ftD.-l '*-■*_'* ■* ^J^ >0 to 00 t^ O 00_(M '"** '-t"Ti>'co"t— "os'co'os'os'cooo'co'r-i 1>" tOrit^OSCOI^tSCSOOOCOOOto csE^coos^-<*'?acoc;tooo os^rH t> rH"o'ocroo"t^t^to"to"o'»^ M rf rH rH t^ CO 00 •OOOOOCOCOoO •oocooccccco M CO -* >.0 to 1^ 00 OS o c o t+) ■-,) t soococcoo 3C;CC;_ ^_ OOOOOOCCOOoO Or-MCO'^intOt-OOOSOoO ' t<< c Debt and Nil. UndGr £100 £250 £500 £750 £1000 £2500 £100. and under and under and under and under and under and under £250. £500. £750. £1000. £2500. £5000. Deficit ami Nil— MALES. 5,351 28,254 7,254 5,762 3,456 2,382 7,285 3,713 Under £50 32,676 56,984 19,097 14,740 7,516 4,428 7,511 1,884 £50 and under £100 82,684 151,113 37,583 23,368 10,745 6,109 12,569 2,833 £100 „ £150 91,378 205,757 70,047 38,319 14,843 7,761 14,454 4,512 £150 „ £200 .. 26,893 69,435 41,001 28,308 12,868 6,984 12,643 4,434 £200 „ £300 .. 7,948 18,086 18,372 17,540 10,751 7,057 16,479 6,792 £300 „ £500 2.043 3,170 4,448 6,166 4,538 3,775 12,156 7,382 £500 ,, £750 443 391 623 1,050 940 869 3.681 3,408 c £7.50 „ £1,000 .. 126 76 126 265 256 231 1,074 1,372 O £1,000 „ £1.500 .. 89 32 80 104 124 98 638 869 „ £1,500 „ £2,000 33 13 22 43 29 31 180 234 § £2,000 „ £3,000 17 3 11 19 21 14 72 110 o o £3,000 „ £4,000 6 2 3 10 3 20 22 ^ £4,000 „ £5,000 1 1 1 1 2 14 16 " £5,000 and upwards Totals 5 1 1 4 3 12 249,693 533,315 198,668 135,689 66,101 39,746 88,779 37,593 £150 and under £156 . . 7,686 18,987 8,977 5,310 2,173 981 1,748 587 £156 „ £200 . . 19,207 50,448 32,024 22,998 10,695 6,003 10,895 3,847 Deficit and Nil— FEMALES. 8,356 178,979 39,124 14,305 3,900 1,567 2.319 609 Under £50 56.217 110,456 50,379 42,926 20,464 9,974 10,235 762 £50 and under £100 . . 37,581 78,533 15,068 10,489 6,112 4,577 13,888 1,637 £100 „ £150 5,974 19,669 7,242 5,258 2,790 1.858 6.659 3,175 £150 „ £200 1,004 3,083 2,331 1,902 1,193 829 2,963 2,544 £200 „ £300 479 986 1,115 1,126 846 560 2.231 2,243 0. £300 „ £500 229 323 410 523 368 335 1,284 1,155 P £500 „ £750 102 72 124 154 132 117 443 411 o £7.50 „ £1,000 .. 32 25 34 52 41 40 155 163 o £1,000 „ £1,500 28 13 13 21 29 30 101 108 E £1,500 „ £2,000 13 1 2 9 10 12 31 33 £2,000 „ £3,000 11 6 4 4 4 3 20 32 o £3,000 „ £4,000 7 1 4 2 5 ^ £4.000 „ £5,000 .. 3 2 2 4 £5,000 and upwards Totals 1 2 2 110,036 392,146 115,846 76,772 35,895 19,905 40,336 12,885 £150 and under £156 . . 317 908 597 419 232 147 541 425 £156 „ £200 .. 687 2,175 1,734 1,483 961 682 2,422 2,119 Deficit and Nil— PERSONS 13,707 207,233 46,378 20,067 7,356 3,949 9,604 4,322 Under £50 88,893 16^.440 69,476 57,666 27,980 14,402 17,746 2.646 £50 and under £100 120,265 229,646 52,651 33,857 16.857 10,686 26,457 4,470 £100 „ £1,'>0 97,352 225.426 77.289 43,577 17,633 9,619 21,113 7,687 £150 „ £200 27,897 72,518 43,332 30,210 14,061 7,813 15,606 6,978 £200 „ £300 8,427 19,072 19,487 18,(i6(i 11.597 7,617 18,710 9,035 «3 £300 ,, £500 2.272 3,493 4,858 6.689 4,906 4.110 13,440 8,537 u £500 „ £750 545 463 747 1,204 1,072 986 4,124 3,819 § £750 „ £1,000 158 101 160 317 297 271 1,229 1,535 O £1,00(1 ,, £1,500 117 45 93 125 153 128 739 977 (A £l..'>(i(i ., £2.000 46 14 24 52 39 43 211 267 S £2,0(11) ,, £3.000 28 9 15 23 25 17 92 142 o £3.00(( ., £4,000 13 2 4 14 5 25 29 S', tl.noo „ £5,000 4 1 1 3 2 2 14 20 £5,000 and upwards Totals 5 1 1 4 3 5 14 359,729 925,461 314,514 212,461 101,996 59,651 129,115 50,478 £150 and under £156 . . 8.003 10.895 9.574 5,729 2,405 1.128 2,289 1,012 £156 „ £200 . . 19,894 52,623 33,758 24,481 11,656 6,685 13,317 5,966 The Correlation of Wealth and Income. 49 the distribution of these is given according to ranges of income and ranges of assets, the aggregates for each range of income, and for each range of assets being also shewn. If these distributions conformed perfectly to curves of a known type it would be possible to compute the mutual relations of wealth and income. Owing to limita- tions of numbers, however, and to the incompleteness of the returns, the progressions of the numbers only approximate to well-defined (and smooth) curves. The figures given in this part relative to income and assets relate in each case to " net income" and " net assets." furnished by Individuals as at 30th June, 1915. (Exclusive of Absentees.) Numbers of Persons in each Assets Group. , , Aggregate £5000 £10,000 £15,000 £20,000 £25,000 ! £50,000 1 £75,000 £100,000 Total for of and under and inider and under and under and under and under and under and All Values Incomes. £10,000. £15,000. £20,000. £25,000. £50,000. £75,000. £100,000. upwards. of Assets. 1,869 1 519 200 95 189 60 30 41 66,460 548 82 20 13 13 1 145,513 4,163,492 647 118 38 12 13 3 327,835 24,308,245 905 1 141 40 14 19 3 2 448,195 55,089,955 1,156 1 168 46 18 20 5 1 203,980 34,312,169 2,745 375 97 41 32 6 1 1 2 106,324 25,190,643 4,069 915 258 89 76 19 3 1 49.108 18.388,257 2,819 1,030 387 126 137 16 5 3 15,928 9,603,396 1,448 650 325 180 164 11 6 3 6,313 5,392,909 1,178 : 648 404 261 348 47 6 7 4,933 5,993,503 449 324 232 147 315 57 16 7 2,132 3,676,422 258 : 256 208 140 402 125 25 26 1,707 4,149,389 52 53 58 66 211 104 28 21 659 2,248,692 24 ■^2 30 41 104 50 32 36 375 1,685,277 9 1 12 23 40 136 134 ! 94 270 746 7,300,348 18,176 5,313 2,366 1,283 2,179 641 249 417 1,380,208 201,502,697 154 1 18 5 2 1 1 46,630 7,092,731 1,002 1 150 41 16 19 '\ 1 157.350 27,219,438 214 50 15 10 15 ~ 2 4 249,476 143 24 7 2 2 1 301 592 6,716,909 193 13 8 3 3 1 168;i06 11,416.318 269 25 7 3 52,929 6,2.50.478 461 25 7 5 1 16,348 2,769,270 1,292 86 19 8 7 2 1 11,001 2.641.110 1,584 329 38 17 19 2 1 6,617 2.498,288 519 407 134 47 23 5 1 2,691 1,632.945 204 179 127 62 30 1 1,145 969,926 162 122 102 67 102 4 2 1 905 1,089,209 63 48 32 28 73 8 1 364 629,439 50 39 17 17 77 24 5 4 317 771,511 14 8 8 3 26 7 4 6 102 360.818 6 4 3 5 11 10 6 2 58 258.390 9 3 6 5 14 9 6 29 86 655,896 5.183 1.362 530 279 406 81 26 49 811,737 38,660,507 57 5 2 1 3.651 557,963 404 20 7 3 12.697 2,211,307 2,083 569 215 105 204 67 32 45 315.936 691 106 27 15 15 2 447,105 10,880,401 840 131 46 15 16 4 495,941 35,724,563 1,174 166 47 14 22 3 2 501.124 61,340,433 1.617 193 53 23 21 5 1 220,328 37.081,439 4,037 461 116 49 39 8 2 2 117,325 27,831,753 5,653 1,244 296 106 95 21 3 2 55,725 20,886.545 3.338 1.437 521 173 160 21 5 4 18.619 11,236,341 1,652 829 452 242 194 12 6 3 7.458 6,362,835 1,340 770 506 328 450 51 8 8 5.838 7,082,712 512 372 264 175 388 65 16 8 2.496 4,305.861 308 295 225 157 479 149 30 30 2,024 4,920,900 66 61 66 69 237 111 32 27 761 2.609,510 30 26 33 46 115 60 38 38 433 1,943,667 18 15 29 45 150 143 100 299 832 7.9.56.244 23,359 6.675 2,896 1.562 2,585 722 275 466 2,191,945 240.103.204 211 23 5 4 2 I 1 50.281 7,650,694 1,406 170 48 19 19 4 1 170,047 29,430.745 50 The Relation between Wealth and Income. 2. Aggregates of assets between given limits arranged according to given limits of income, Commonwealth. — In tlie following table are shewn the aggregates of wealth of the males, females, and persons, the nvxmbers of which were given in the preceding table, the aggregates of the incomes being repeated in the final columns. Distribution in Respect of Individuals of Australian Debt Aggregates of Assets. and Assets Groups. i^ — :» Nil. £100 £250 £500 £750 £i000 ' £25cl No. of Under and under and under and under and under and under and un Persons. £100. £250. £500. £750. £1000. £2500. £5001 £ £ £ £ £ £ 1 £ 1 Deficit and Nil- -MALES 5,351 694,636 1,177,570 2,052,253 2,118,199 2,059,145 11,656,698 13,095. Under £50 32,676 1,584,976 3,104,982 5,240,035 4,572,289 3,818,478 11,304,420 6,366 £50 and under £100 82,684 4,228,634 5,988,097 8,255,118 6,529,629 5,279,649 19,276,323 9,350 £100 £150 91,378 6,905,518 11,067,901 13,428,330 8,968,096 6,672,895 22,166,436 15,052 £150 £200 26,893 2,753,747 6,595,873 10,058,936 7,847,938 6,037,111 19,374,692 15,155 £200 £300 7,948 781,694 3,062,239 6,317,693 6,566.353 6,096,203 25,771968 23,674 CQ £300 £500 2,043 144,243 768,286 2,255,186 2,808,435 3,273,772 19,837,140 26,009 1= £500 £750 443 19,433 107,637 390,299 592,783 760,654 6,163,252 12,237 Bh £750 £1,000 126 3,704 21,086 99,532 161,072 202,041 1,834,990 4.899 o £1,000 £1,500 89 1,885 13,770 38,967 77,707 85,989 1,105,560 3,235 ^ £1,500 £2,000 33 747 4,163 15,944 18,384 26,933 325,032 .S95 1^ £2,000 £3,000 17 138 2,002 6,547 12,967 12,085 120,767 415. o £3,000 £4,000 6 321 1,087 6,038 2,817 38,025 86 K £4,000 £5,000 1 10 200 367 1,729 19,831 57 £5,000 and upwards Totals 5 147 489 2,237 1,761 6,129 43 249,693 17,119,415 31,914,274 48,160,783 40,282,127 34,331,262 139,001,263 130,573 £150 and under £156 7,686 720,041 1,424,556 1,861,283 1,311,201 845,500 2,652,126 1.991 £156 £200 19,207 2,033,706 5,171,317 8,197,653 6,536,737 5,191,611j 16,722,566 13,163 Deficit & Nil— FEMALES 8,356 5,072,207 5,899,669 4,859,714 2,321,280 1,337,485 3,423,330 2,064 Under £50 56,217 3,132,666 8,269,102 15,167,734 12,290,021 8,579,531 13,901,712 2,476 £50 and under £100 37,581 1,921,916 2,396,753 3,734,515 3,752,857 3,962,940 21,132,151 5,151 £100 „ £150 5,974 659,580 1,152,046 1,875,713 1,709,469 1,597,608 11,134,215 10,283 £150 „ £200 1,004 123,072 387,260 691,855 737,443 730,842 4,928,803 8.871 £200 „ £300 479 45,465 187,913 406,554 520,591 486,140 3,678,251 8.277 m £300 „ £500 229 14,741 70,908 192,852 227,193 290,238 2,130,582 4.1(14 O £500 „ £750 102 3,193 21,385 58,483 81,338 102,640 753,000 1,526 ;^ £750 „ £1,000 32 1,397 5,874 18,282 25,656 35,007 266.065 595 o £1,000 „ £1,500 28 647 2,341 7,713 18,029 26,347 166,965 :i03' m £1,500 „ £2,000 13 80 340 3,298 6,325 10,546 49,108 123, s £2,000 „ £3,000 11 270 741 1,350 2,363 2,525 33,274 121 £3,000 „ £4,000 7 253 2,475 1,630 8,167 24; ^ £4,000 „ £5,000 3 600 1,138 If £5,000 and upwards Totals 771 3,722 i 110,036 10,975,234 18,394,332 27,018,916 21,696,178 17,164,250 61.609,345 44.09; £150 and under £156 317 34,017 96,527 . 149,864 143,713 128,865 901,048 1,42C £156 „ £200 687 89,055 290,733 541,991 593,730 601,977 4,027,755 7,45] Deficit & Nil- -PERSONS 13,707 5,766,893 7,077,239 6,911,967 4,439,479 3,396,630 15,080,028 1,5,15{ Under £50 88,893 4,717,642 11,374,084 20,407,769 16,862,310 12,398,009; 25,206,132 8,84J £50 and under £100 120,265 6,150,550 8,384,850 11,989,633 10,282,486 9,242,589! 40,408,474 14,50i £100 £1.50 97,352 7,565,098 12,219,947 15,304,043 10,677,565 8,270,5031 33,300,651 25,335 £150 £200 27,897 2,876,819 6,983,133 10,750,791 8,585,381 6,767,953 24,303,495 24,02f £200 £300 8,427 827,159 3,250,152 6,724,247 7,086,944 6,582,343 29,450,219 31,951 Bi £300 £500 2,272 158,984 839,194 2,448,038 3,035,628 3,564,010 21 967,722 30,17£ o £500 £750 545 22,626 129,022 448,782 674,121 863,294 6,916,252 13,76f ^ £750 £1,000 158 5,101 26,960 117,814 186,728 237,048 2,101,055 5,49f o £1,000 £1,500 117 2,532 16,111 46,680 95,736 112,336 1,272,525 3,62f H £1,500 £2,000 46 827 4,503 19,242 24,709 37,479 374,140 l,01f a £2,000 £3,000 28 408 2,743 7,897 15,330 14,610 154,041 53( o £3,000 £4,000 13 321 1,340 8,513 4,447 46,192 IK >5 £4,000 £5,000 4 10 200 967 1,138 1,729 19,831 i: £5,000 and upwards Totals 5 147 489 2,237 2,532 9,851 5]( 359,729 28,094,649 50,308,606 75,179,699 61,978,305 51,495,512 200,610,608 174,67 £150 and under £156 8,003 754,058 1,521,083 2,011,147 1,454,914 974,365 3,553,174 3,41ji £156 £200 19,894 2,122,761 5,462,050 8,739,644 7,130,467 5,793,588 20,750,321 2U,61{): The Correlation of Wealth and Income. 51 immediately following the aggregates of the wealth. Thus the two last columns for males, females, and persons, shew, according to given ranges of income, what may be regarded as the income associated with the possession of a given amount of wealth. In a later table the ratios of income to wealth are shewn in the form of percentages. Assets as at 30th June, 1915, in each Income Group. AOGREGAXES OF ASSETS. £10,000 aiul uiuler £15.000. £15.000 ! £20,000 aiul uiirter \ and under £20,000. i £25,000. £25,000 and under £50,000. £50,000 ! £75,000 and under and under £75,000. 1 £100,000. £100,000 and upwards. All Values. Aggregate of Incomes. £ £ £ £ £ £ £ £ £ £ 2,988.941 6,231,582 3,460,818 2,110,039 6,498,655 3,772,417 2,590,121 7,333,864 77,790,445 ;,618.281 957,455 340,458 283,690 412,219 61,866 41,665,576 4,163,492 1,361,630 1,399,757 630,721 272,604 439,793 182,305 66,195,228 24,308,245 i,996.601 1.691,313 667,605 319,840 625,604 178,813 162,482 93,903,549 55,089,955 ",536.156 1,992,539 810,111 398,593 642,620 285,128 76.022 79,564,947 34,312,169 J,l-19,027 4,445,835 1,650,122 904,978 1,050.806 358,459 82.689 207,379 99,119,831 25,190,643 ",925,010 10,860,543 4,384.461 2,005,526 2,488,597 1,117,485 245,955 143,493 104,267,330 18,388,257 J,893,872 12,414,585 6,631,287 2,784,613 4,446,574 974,337 419,939 327,960 68,164,568 9,603,396 J,339,311 7.980,033 5,636,786 4,012,285 5,200,828 670.139 489,014 406,972 41,957,129 5,392,909 3,550,560 7,931,189 6,938,130 5,833,517 11,297.904 2,838,592 487,776 874.131 49,311,214 5,993,503 1.265.293 3,996,725 4,021,276 3,289,574 10,771,318 3,442,878 1,377,628 878.551 32,329,755 3,676,422 ,954.375 3.193,713 3,629,202 3,167.780 14.014,312 7,336,296 2,135,056 3,688,558 39,688,842 4,149,389 399,487 655,508 1,016,196 1,465.065 7,514,373 6,358.597 2,400,273 2,841,435 22,785,309 2,248,692 177.745 282,280 532,161 999,003 3,736.449 3,071,700 ' 2,774,654 5,936.983 17,590,373 1.685,277 73:647 147,591 403,184 923,286 5,230,960 8,356,736 8,138,093 60,428,416 83,756,101 7,300,348 5,229,936 64,180,648 40,752,518 28,770,393 74,371,012 38,955.747 21,379,702 83,067,742 918,090,197 201,502,697 992.739 220,041 85,997 42,201 36,262 50.538 12.233,981 7,092,731 5,543.417 1.772,498 724,114 356,392 606,358 234,590 76,022 67,330,966 27,219,438 611,523 275,084 157,720 294,934 285,758 983,578 3.816,663 4.982,105 2.215,599 1,521,500 591,11 501,472 102,696 52,393 39,028 263,090 113,929 134,903 121.520 118;096 313.224 652.020 2,280,103 2,223,374 1,809,303 576.700 303,095 132,213 49,380 100,478 218,502| 42,250 68,439 109,931 172,400 388,255 1,041,425 1,378,049 1,511,189 640,021 368,280 67,416 107,141 112,825 512,314 73,363 88,502 95,047 28,033 247,046 650,937 705,413 919.146 3.312,945 2.465,472 2,833,674 948,590 391,170 499,587 426,255 71,363 54,485 112,8; 121.8 287,933 68,258 243.174 452,174 ,44(1,271 473,773 593,236 580,573 171,098 1 460,750 82,153 158,194 436 330, 534: 527, 147,95 116,982 186.225 148^295 637,146 700,142 280,265 6,379,212 29,068,881 65,341,283 43,806,391 30,635,630 19,924,462 23.803.723 24,067,057 15.850,588 9,238,268 10,527,877 5,535,667 7.054,829 2,892,704 2,066,774 8,327.331 6,716,909 11,416,318 6,250,478 2,769,270 2,641,110 2,498,288 1,632,945 969„926 1,089,209 629,439 771,511 360,818 258,390 655,896 ■),341.151 16,431,170 9,191,428 6,226,123 13,771,239: 4,926,254 2,240,902 9,056,974 298,141,465 38,660,507 60,867 224,891 118,096 40,139 69,792 28,033 3,396.551 16,527,911 557,963 2,211.907 6.843,105 i;232,539 1,557.477 1.VI.SC..247 2.27cS,297 5,42(1,413 14,677,206 17,396,690 10,195,632 9,452,689 4,.587,842| 3,695.185 758,204 334,6731 186,619: 3,723,908 454,387 765,624 789,125 928.207: 1,963,346 5,036,481 8,911,390 7,860,160 8,747,433, 4.597,976 3.932,297| 1,148.409' .'.81.. 541 503,662 2,328,541 325,940 341,043 319,840l 508,524( 1,077,378, 2,393, 78l| 3,826,038 5,390,334 7,344,706 3,929,595 3,536,060 1,532,481 1,106,144 1,036,111 7,010,969 485,.582 528,295 720,651 670,65:3 1,297,852 3,139,534 5,151,987 6,119,974 14,610,849 13,236,790 16.847,986 8,462,963 4,127,619 5,730,547 ■,571,0871 80,611,818 49,943,946 34,996,516 88,142,251 43,882,001 23,620,604; 92,124,716 1,216,231,662 4,148,671 133.229 236,790 178,813 285,128 471,341 1.239,362 1,262,270 738,397: 3.081,766 3.895,0521 8.776,567 6,832.370 3,664,936, 8,937,309 2,761,219 7,794,614 162,482 76,022 164,8421 245.9.55 419.939 489,014 645,970 1,377,628 2.571,917 2,730,549 3,309.5651 207,379 291,450 444.942 406.972 1,060,356 1,026,846 4,325,704 3,541,577 6.217,248 8,665,502! 66,807,628 106,859,326 107,006,859 110,001,619 124,539,179 99,489,409 122,923,554 128.334,387 84.(115,156 51,195,397 59,839,091 37.865.422 46.743,671 25,678,013 19,657.147 92,083,432 280,908 1,997,389, 85,997 842,210 82,340 426,184 64,295 606,358 50,.538 234,590 "6,022 15,630,532 83,8.58,877 10,880,401 35,724,563 61,340,433 37,081,439 27,831,753 20,886,545 11,236,341 6,362.835 7,082,712 4,305,861 4,920,900 2,609,510 1,943,667 7,956,244 240,163,204 7,650,694 29,430,745 52 The Relation between Wealth and Income. 3. Numbers in each State and Territory arranged according to given limits of income. — In the following table are given the miniljers of males, females and persons whose incomes lie Ijetween the limits indicated m the first column. The general si'miZani?/ of the distributions for each State is obvious, although by no means iden- tical ; the measure of their agreement or difference can only be fully appreciated by expressing each as a ratio to the totals in the last lines. The calculation of these ratios has not, however, been undertaken. Commonwealth, States and Territories. — Number of Returns in Respect of Individuals in each Income Group for year ended 30th June, 1915. (Exclusive of Absentees.) Income Group. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wealth. Deficit and Nil— MALES 17,940 24,182 7,044 9,213 6,000 1,936 141 * 4 66,460 Under £50 46,239 47,965 19,360 18,053 6,915 6,798 114 69 145,513 £50 and under £100 121,505 94.175 48,969 31,301 14,272 17,206 254 153 327,835 £100 „ £150 179,483 124,590 67,184 38.633 23,631 1 14,162 277 235 448,195 £150 „ £156 19,377 11,700 6,982 3.604 3,788 1,113 47 19 46,630 £156 „ £200 63,797 41,651 21,314 11.970 14,610 3,772 147 89 157,350 £200 „ £300 42,337 27,899 15,166 7.789 10,317 2.568 195 53 106,324 £300 „ £500 20.005 14,420 1 6,786 3,293 3,215 1,280 71 38 49,108 £500 ,, £T50 6,576 4,849 2,080 993 953 440 28 9 15 928 £750 „ £1,000 .. 2,541 2,018' 833 418 336 161 5 1 6,313 £1,000 „ £1,500 .. 1,989 1,613 664 292 249 119 5 2 4.933 £1,500 „ £2,000 . . £2,000 „ £3,000 . . 846 694 278 165 97 50 2 2,132 683 534 232 134 80 40 4 1,707 £3,000 „ £4,000 . . 262 212 102 41 26 16 659 £4,000 „ £5.000 . . 153 132 42 29 16 3 375 £5,000 and upwards 314 266 80 50 27 9 746 Totals 524,047 396,900 197,116 125,978 84,532 49,673 1,290 672 1,380,208 Deficit & Nil— FEMALES 78,038 91,464 37,683 24,971 9,383 7,822 34 81 249,476 Under £50 97,215 112,760 35,440 34,993 10,281 10,810 22 71 301,592 £50 and under £100 57,738 65,849 19,318 13,800 6,120 5,250 9 22 168,106 £100 „ £150 20,016 18,745 5,887 3,972 2,883 1,406 10 10 52,929 £150 £156 . . 1,506 1,238 347 261 224 75 3,651 £150 £200 . . 4,868 4,403 1,292 960 794 373 4 3 12,697 £200 £300 . . 4,347 3,899 1,081 818 516 338 1 1 11,001 £300 £500 2,531 2,487 649 507 244 196 3 6,617 £500 , £750 1,033 1,018 256 210 102 72 2,691 £750 £1,000 .. 487 420 93 80 33 29 1 2 1.145 £1.000 £1,500 . . 380 321 87 59 22 33 2 1 905 £1,500 £2,000 .. 153 117 48 31 6 9 364 £2,000 , £3,000 .. 96 127 39 29 12 11 3 317 £3,000 £4,000 .. 43 42 8 7 2 102 £4,000 £5.000 .. 18 27 5 6 1 1 58 £5,000 and upwards 40 29 9 5 2 1 86 Totals 268,509 302,946 102,242 80,709 30,623 26,428 86 194 811,737 Deficit & Nil— PERSONS 95,978 115,646, 44,727 34,184 15.383 9,758 175 85 315,936 Under £50 143,454 160,725 54,800 53,046 17,196 17,608 136 140 447,105 £50 and under £100 179,243 160;024i 68,287 45,101 20.392 22,456 263 175 495,941 £100 „ £150 199,499 143,335 73.071 42,605 26,514 1 15,568 287 245 501,124 £1.50 „ £156 .. 20,883 12,938; 7,329 3,865 4,012 1,188 47 19 50,281 £156 „ £200 .. 68,665 46,054 22,606 12,930 15,404 4,145 151 92 170,047 £200 „ £300 46,684 31,798' 16,247 8,607 10,833 2,906 196 54 117,325 £300 „ £500 22,536 16,907 7,435 3,800 3,459 1,476 71 41 55,725 £500 „ £750 7,609 5,867 2,336 1,203 1,055 512 28 9 18,619 £750 „ £1,000 . . 3,028 2,438 926 498 369 190 6 3 7,458 £1,000 „ £1,500 .. 2,369 1,934 751 351 271 152 7 3 5,838 £1,500 „ £2,000 .. 999 811 326 196 103 59 2 2,496 £2,000 „ £3,000 .. 779 661 271 163 92 51 7 2,024 £3,000 „ £4.000 . . 305 254 110 48 26 18 761 £4,000 „ £5,000 . . 171 159 i 47 35 17 4 433 £5,000 and upwards 354 295 89 55 29 10 832 Tote lis 792,556 699,846 299,358 206,687 115,155 76,101 1,376 866 2,191,945 4. Aggregates of income in each State according to given limits of income. — In the following table are shewn for each State and the Commonwealth the aggregates of the" net incomes" for males, females and persons arranged according to limits of income, which correspond to the numVjers given in the precedmg table. The totals The Correlation of Wealih and Income. 53 for the Commonwealth agree, of course, with the final column m the tables of sections 1 and 2 of this chapter. The identity or difference of the distributions (of Liicomes) is revealed by dividing by the totals in the final lines. The ratios so found shew how the aggregates of incomes in the various groups are distributed according to the magnitude of the income. This relative distribvition has been given for the Common- wealth as a whole on p. 25 for each sex and for persons. Commonwealth, States and Territories. — Aggregate Net Income in Respect of Individuals in each Income Group for year ended 30th June, 1915. (Exclusive of Absentees). Income Group. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wealth. £ 1 £ £ £ £ £ £ £ £ Deficit and Xil— ]VL\LES Under £50 1.346,629 1,344,100 577,961 496,697 189,478 203,409 3',226 1,992 4,163.492 £50 and under £100 9,056.099 6,942.318 3,640,033 2,309,471 1,062,040 1,268,883 18,477 10,924 24.308,245 £100 „ £150 22,138,778 15,342,756 8,195,896 4,700,410 2,940,994 1,709.780 33,259 28,082 55,089.955 £150 „ £156 2,952,944, 1,771,307 1,059,049 556,5721 572,648 170.227 7,094 2,890 7,092.731 £156 „ £200 11,033,838^ 7,195,857 3,686,565 2,057.652' 2.556.557 647,398 25,894 15.677 27,219.438 £200 „ £300 10,033,534: 6,621.978 3,596,728 1.851.5041 2,409.338 619,549 45,904 12,108 25.190,643 £300 „ £500 7,499,992 5,424,691 2,523,270 i;224,142, 1,192,731: 483,357 26,068 14,006 18,388.257 £500 „ £750 3,982,406 2,909,034 1.251,685 603,058! 571,7731 264,067 16,024 5,349 9,603,396 £750 „ £1,000 2,133,023, 1,756,787 719,252 357.102' 286.297 134,882 4,589 977 5.392.909 £1,000 „ £1,500 2,405,4471 1,970,412 806,417 355,325! 300.9141 147,027 5,450 2,511 5.993.503 £1,500 „ £2.000 1,463.144' 1,198.171 475,794 285.670 165,372 85.244 3,027 3.676.422 £2,000 „ £3,000 1,660,607; 1,292,882 561,502 330,752 194,5601 100,808 8,278 4.149.389 £3,000 „ £4,00 885,838' 727,467 352,259 142.312 89,4001 51.416 2.248.692 £4,000 „ £5.000 688,736: 590,296 188,724 133,077, 71.088; 13.356 1.685.277 £5,000 and upwards 3,127, 681j 2,468,791 764,902 567,619 304,888 66,467 7.300.348 Totals . . 80,408,696 57,556,847 28,400,037 15,971,363'l2,908,078 5,965,870 197,290 94,5161201,502,697 Deficit & Xil-FEJIALES .. Under £50 2,172,002 2,580,592 787,523 728,971 211,538 234,429 '490 1,364 6,716.909 £50 and under £100 3,944,533 4,431,332 1.322.016 937,136 425,362 353,788 689 1,462 11,416,318 £100 „ £150 2,357,247 2.218,041 695.171 464,959 346,461 166.241 1,214 1,144 6,250,478 £150 „ £156 230,374 j 189,906 52.886 39,383 33,970; 11,444 557,963 £156 „ £200 847,711 767,043 225,648 167,939 135,743 66,024 '681 '5I8 2,211,307 £200 „ £300 1,050,496 933.813 257.698 196.1381 121.4491 81.118 203 205 2.641,110 £300 „ £500 952,342 938,986 246,747 193,0751 91,013 75,068 1,057 2.498.288 £500 „ £750 621,395; 621.493 156,008 125.988! 64,395 43,666 1.632,945 £750 „ £1,000 414,814; 354.785 78,305 67,958 26,493 24,727 960 1,884 969,926 £1.000 „ £1,500 458.656 383.522 105,187 70,867 26,073 41,430 2,443 1,031 1,089,209 £1,.500 „ £2,000 262,037 202.603 84,178 53,371 11,427 15,823 629,439 £2,000 „ £3,000 236,288 312.160 90.201 69,805| 28,537 28,322 6'i98 771.511 £3,000 „ £4,000 154,461 146.699 27,875 24,7221 7,061 360,818 £4.000 ., £5.000 79,995 121,381 21.819 26.9701 4,162 4,063 258,390 £5,000 and upwards 347,090 204,348 56.947 31,511 10,226 5,774 655,896 Totals . . 14,129,441 14,406,704 4,208,209 3,198,793 1,536,849 1,158,968 12,878 8,665 38,660,507 Deficit & Nil-PERSONS Under £50 3,518,631' 3,924,692 1,365.484 1,225,668 40V,016 437,838 3',716 3,356 10,880,401 £50 and under £100 13,000,632111,373,650 4,962.049 3,246,607 1,487,4021.622,671 19,166 12,386 35,724,563 £100 „ £150 24,496,02517,560,797 8,891,067 5,165,369 3,287,455:1,876,021 34,473 29,226 61,340,433 £150 „ £156 3,183,3181 1,961,213 1,111,935 595,955 606,618: 181,671 7,094 2,890 7,650,694 £156 „ £200 11,881,549' 7,962,900 3,912,213 2,225,591 2,692,300! 713,422 26,575 16,195 29,430.745 £200 „ £300 11,084,030! 7,555,791 3,854,426 2,047,642 2,530,787 700,657 46,107 12,313 27.831.753 £300 „ £500 8,452,334! 6,363,077 2,770,017 1,417,217; 1,283,7441 558,425 26,068 15,063 20,886.545 £500 „ £750 4,603,801 3,530,527 1,407,693 729,046' 636,1681 307,733 16,024 5,349 11,236,341 £750 „ £1,000 2,547,837 2,111,572 797,5,57 425,060 312,790! 159,609 5,549 2,861 6,362,835 £1,000 „ £1,500 2,864,103' 2,353,934 911,604 426,192 326,987! 188,457 7,893 3,542 7,082,712 £1,500 „ £2,000 1,725,181 1,400,774 559,972 339,041 176,799 101,067 3,027 4,30.5.861 £2,000 „ £3,000 1,896,895 1,605,042 651,703 400;557 223,097 129,130 14,476 4,920,900 £3,000 „ £4,000 l,040,299i 874,166 380,134 167,034; 89,400 58,477 2.609,510 £4,000 „ £5,000 768,7311 711,677 210,543 160,047 75,250 17,419 1.943.667 £5,000 and upwards 3,474,771| 2,673,139 821,849 599,130 315,114 72,241 7,956.244 Totals . . 94,538,137 71,963,551 32,608,246 19,170,156 14,444,927 7,124.838 210,168 103,181 240,163,204 5. Aggregates of wealth in each State, according to given Umits of income. — In the following tal.)le the aggregate amoiuits of wealth are sliewn for CiU-h State within given limits of income ; correspondmg to the aggregates of income shewn ui the table of section 4, and the numbers of males, females, and persons shewn in section 3. 54 The Relation between Wealth and Income. This table, together with the preceding, brings the States into comparison in respect of the wealth and income in each income group. The ratios of the assets in each column to the total thereof shew the relative distribution according to ranges of income, and are by no means identical for the various States. These ratios, however, have not been regarded as of sufficient importance to tabulate. Commonwealth, States and Territories. — Aggregate in Respect of Individuals oJ the Net Assets as at 30th June, 1915, in each Income Group. (Exclusive of Absentees.) Income Group. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C wealth. Deficit and Nil— MALES Under £50 £50 and under £100 £150 £156 £200 £300 £500 £750 £1,000 £1,500 £2,000 £3,000 £4,000 £100 £150 £156 £200 £300 £500 £750 £1,000 £1,500 £2,000 £3,000 £4,000 £5,000 £5,000 and upwards Totals Deficit & Nil-FEMALES Under £50 £50 and under £100 27,891,182 11,965,531 21,961,578 33,957,551 4,640,397 25,543,127 40,475,776 43,709,944 30,202,069 17,822,806 21,671,017 13,881,423 16,748,141 9,462,531 7,400,660: 34,860,125] 26,469,298: 14,151,514' 20,379,996 28,145,762 3,504,545 20,320,552: 29,447,810i 32,101,623| 20,418,9101 13,172,4851 15,153,704 10,281,281 12,064,066 6,995,9311 6,608,941 30,096,605! £ 5,607,439 4,753,499 8,825,562 13,471,383 1,765,464 8,562,997 11,946,523 11,886.716 6,876,826 5,027,319 5,820,768 3,510,759 4,567,880 3,120,023 1,657,037 5,982,625 362,193,8581289,313,023 103,382,820 £100 £150 £156 £200 £300 £500 £750 £1,000 £1,500 £2,000 £3,000 £4,000 £150 £156 £200 £300 £500 £750 £1,000 £1,500 £2,000 £3,000 £4,000 £5,000 £5,000 and upwards Totals 8,120,07i 20,573,042 14,325,510 10,755,940 1,359,069 6,109,491 9,328,730 9,477,989 6,671,184 4,139,314 4,392,238 2,286,765 2,133,487 1,362,073 636,566 5,078,994 106,750,464 Deficit & Nil-1'ERSONS Under £50 £50 and under £100 £150 £156 £200 £300 £500 £750 £1,000 £1,500 £2,000 £3,000 £4,000 £100 £150 £156 £200 £300 £500 £750 £1.000 £1.500 £2,000 £3,000 £4,000 £5.000 £5,000 and upwards Totals 36,011,254 32,538,573 36,287,088 44,713,491 5,999,466 31,652,618 49,804,506 53,187,933 36,873,253 21,962,120 26,063,255 16,168,188 18,881,628 10,824,604 8,037.226 39,939,119 11,637,978 24,512,827 17,184,369 11,731,886 1,239,277 6,187,227 8,636,444 8,820,930i 5,456,2771 3,325,919 3,969,264 1,857,129 3,012,994 1,138,171 1,056,128 2,399,623 112,166,443 38,107,276 38,664,341 37,564,365 39,877,648 4,743,822 26,507,779 38,084,254 40,922,553 25,875,187 16,498,404 19,122,968 12,138,410 15,077,060 8,134,102 7,665,069 32,496,228 4,464,858 7,556,352 4,326,398 3,052,142 354,934 1,498,789 2,132,703 2,068,078 1,478,068 622,005 703,284 473,537 688,080 248,267 200,430 271,811 30,139,736 10,072. 12,309, 13,151, 16,523, 2,120, 10,061, 14,079, 13,954, 8,354, 5,649, 6,524, 3,984, 5,255, 3,368, 1,857, 6,254, 297 14 851 14 960.13 11.607,025 7,071,842 8,824,327 10,518,821 1,256,443 7,007,301 9,101,505 8,636,591 5,198,949 2,969,285 3,145,168 2,546,982 3,460,691 1,780,980 1,182,217 9,369,575 4,811,400 2,238,977 2,927,271i 4,267,544! 635,35ll 3,515,959' 5,130.707: 4,564,828! 3,096,07l| 1,746,673, 2,042,430 1,246,199 1,695,290 935,0041 645,151| 2,633,549 £ 1,051,1851 1,454,2151 3,203,534 3,473, 198| 420,2451 2,333,089' 2,933,833: 3,234,544' 2,282,958, 1,181,162' 1,422.4201 857.943 1,106,296' 490,840, 96,367 813,622 £ I 352,027, 14,161i 25,633 31873, 8,460 25,131 56,092 60,159 82.477 28,549 27,684 5,168' 46,478 15,837 47,327 37,417 3,076 22,810 27.585 72,925 6,308 8,850 28,023 93,677, 702|42,132,404 26,355,45l[ 763,892 271,04 £ 77,790,445 41,665,576 66 195,228 93.903,549 12,233,981 67,330,966 99,119,831 104.267,330 68.164,.)68 41,957,129 49,311,214 32,329,755 39,688.84a 22,785,309 17,590,373 83,756,101 918,090,197 2,539,993 7,900,093 4,817,110 2,919,757 287,521 1,570,029 2,067,841 2,034,519 1,359,605 644,076 803,403 604,076 691,101 136,857 150,448 491,855 29,018,284 ,147,018 ,971,935 641,437 438,578 543,964 577,330 169,346 671,110 558,554 613,361 948,571 151, (I5S 151,792 917,837 332,665 861,430 1,633,876 2,686,596 1,506,778 1,095,699 69,107, 541,491! 742,389 842,4181 492,846! 298,4301 197,729 76,585 263,248 "570 16,834 656,609 2,087,869 1,641,098 1,076,338 86,643! 614,96l| 891,436' 812,069' 392,608 192,205, 434, .5351 237,575| 236,468 7,336 22,632 68,214 11,549 3,946 9,924| 14,580 3, 0171 2,111 1,561 2,307 3",77o| 2",i53 193 3,987 11,054 10,464,596 9,458,596 6,445,276 4,925,573 4,434,049| 5,363,243! 704,458! 4,057,4.501 5,873,096 5,407,2461 3,588,917 2.045,103! 2,240,159 1,322,784 1,958,538, 935,004 645,721 2,650,383 1,707,794 3.542,084 4,844,632 4,549,536, 506,888! 2,948,0501 3,825,269! 4,046,613 2,675,566' 1,373,367 1,856,955 1,095,518' 1.342,764 498,176 118,999 881,8361 160 12,208| 29,451 16,159 15,216 29,068.881 65,341.283 43,806.391 30.635.630 3.396,551 16,527,911 23.803,723 24,067,057 15,850,588 9.238.268 ■, 10,527,877 5,535,667 7,054.829 2,892;704 2,066,774 8,327,331 71,833 71,513 363,576 24,085! 28,650! 33,434| 8.460' 28,901 56,285' 60,159! 82,477 28.7091 39,892; 5,1681 75,929 4,835 30,41 49,438 39,724 3,076 24.963 31,572 83,979 6,308 25,009 43,239 468,944.322 401,479.4661133.522.556 12269.5986 52,597,000 35,814.047! 835,725' 342,560 1,216.231.662 298,141,465 106,859,326 107,006,859 110,001,619 124,539,179 15,630,532 83,858,877 122,923,554 128,334,387 84.015,156 51.195,397 59,839,091 37,865,422 46,743,671 25,678,013 19,657,147 92,083,432 6. Numbers in each State arranged according to given Umits of assets. — In the following tal)io are slicwn the nuiiihers of males, females and persons whose " net assets" lie Ijetween the limits shewn in the first column. These numbers have therefore no immediate relation with the arrangements according to " net incomes." The Correlation of Wealth and Income. The ratio of each to the total at the bottom of the column in which it is found shews the relative distribution of persons according to ranges of assets, and, if tabulated, would reveal the degree of identity or difference between the several States and Territories of the Commonwealth. They have not been regarded as of sufficient importance to tabulate. This tabulation has been already given for the Common- wealth as a whole, however, see p. 30. Commonwealth, States and Territories.— Number of Returns in Respect of Individuals in each Assets Group as at 30th June, 1915. (Exclusive of Absentees.) Assets Group. Nil and Debt— MALES. Under £100 £100 and under £250 £250 £500 £750 £1,000 £2,500 £5,000 £10,000 £15,000 £20,000 £25,000 £50,000 £75,000 £500 . . £750 . . £1,000 £2,500 £5,000 £10,000 £15,000 £20,000 £25,000 £50,000 £75,000 £100,000 N.S.W. Vic £100,000 and upwards . 97,731 209,892 73.986 48,03 22,860 13,595 31,148 14,1 7,233 2,248 1,008 572 989 295 108 173 Q'land. S.A. W.A. Tas. 72.5561 150,233 55,100, 38,065| 19,116 11,877 27,654 12,492 5,998 1,620 731 393 650 186 80 149 33,056 76,177: 29,912 21,589 10,566: 6,298! 12,5671 3,967 1 1,758 530 231 125i 220 63! 26 1 31 17,429; 48,1221 18,984 13,906 6,712 3,968 9,487 4,187 2,035 525 226 108 176 55 19 39 Totals Nil andDebt-FEMALES. Under £100 £100 and under £250 . . £250 £500 £760 £1,000 £2,500 £5,000 £10,000 £15,000 £20,000 £25,000 £50,000 £75,000 £500 £750 . . £1,000 £2,500 £5,000 £10,000 £15,000 £20,000 £25.000 £50,000 £75,000 £100,000 524,0471 396,900 197,1161 125,978 £100,000 and upwards Totals 38,0781 129,766 37,494 24,260 11,629 6,317 13,369 4,569 1,892 559 230 115 16 34 5 25 Niland Debt— PERSONS. Under £100 £100 and under £250 . . £250 £500 £750 £1,000 £2,500 £5,000 £10.000 £15,000 £20.000 £25.000 £50.000 £75,000 £500 . . £750 . . £1,000 £2,500 £5,000 £10,000 £15,000 £20.000 £25.000 £50,000 £75.000 £100,000 43,122! 145,179' 42,242: 27,951 13,162 7,610 15,699; 5,056 1,937 493! 179 100, 148 31 16l 21! 12,607 51,190 15,445 10,119 4,485: 2,318! 4,181 1,159 517 121 38 21 34 4 3 19,444: 29,035; 13,0431 8,872' 4,173i 2,457 4,715 l,617l 6601 230 97 45 89 24 15 16 N.T. F.T. G'wealth. 84,532 9,069 19,029 7.336 5,064 2,609 1,505 3,120 1,124 471 158 70 39 53 18 1 49,673 8,221 40,883 11,159 8,172 3,854 2,155 4,296 1,258 481 107 49 27 33 9 2 3 268,509' 302,946: 102,242 80,709 £100,000 and upwards Totals . . 135,809 339,658 111,480 72,297 34,489 19,912 44,517' 18,741| 9,125 2,807 1,238 1 6871 1,156 329 113 198| 115,678 295,412 97,342 66,016 32,278 19,487 43,353 17,548, 7,9351 2,113 910 493 798 217, 96 170! 45,663 127,367 45,357; 31,708: 15,051 8,616^ 16,748 5,1261 2,275 651 269, 146' 254 67 29 31 4,6821 11,942 5,498: 3,873 1,680 869 1,438 401 164 42 18 4 10 2 3321 491! 196; 111 38 34 46 19 15 1,290 30,623 25,650 89,0051 30,143 22,0781 10,566 6,123 13,783 5,445 2,516 632 275 135 209 64 21 42 3,291 13.043 3,9711 2,370! 1,0781 628 1,342 439 186 39 14 12 14 1 336 111 45 27 12 42 15 249,693 533,315 198,668 135,689 66,101 39,746 88,779 37,593 18,176 5,313 2,366 1,283 2,179 641 249 417 672 1,380,208 26,428 24,126 40,977 18,54ll 12,745| 5,853 1 3,326 6,153 2,018 824 272 115 49 99 26 15 16 12,360 32,072 11,307 7,434 3,68 2,133 4,462 1,563 657 197 84 51 67 19 86 31 111 20 18 2 2 4 3 1 110,036 392,146 115,846 76,772 35,895 19,905 40,336 12,885 5,183 1,362 530 279 406 81 26 49 194 811,737 336 523 213 120 43 40 53 19 20 3 2 1 1 792,556 699,846 299,3581 206,687 115,1551 76,101 1,376 107 447 131 63 29 14 46 18 7 ■3 i 359,729 925,461 314,514 212,461 101,996 59,651 129,115 50,478 23,359 6,675 2,896 1,562 2,585 722 275 466 866 2,191,945 7. Aggregate assets arranged according to given limits of assets.— The numbers in the following table are the aggregates of the wealth possessed by the males, females and persons respectively shewn in the table of section 6. Like them they have no direct relation with the numbers arranged according to the magnitude of income. The ratio of each aggregate of assets for each asset-group to the total of these aggregates (at the foot of the columns) is by no means identical for each State. The ratios would shew the relative distributions according to the magnitude of the assets ; they have already been given for the Commonwealth as a whole, viz., on p. 31. 56 The RELATIO^ BETWEEN Wealth and Income. \ Commonwealth, States and Territories. — Ag gtejate in Respect of Individuals of the Net Assets 1 in each Asset- Group as at 30th June, 1915. (Exclusive of Absentees.) Assets Group. N,S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wealth. | £ £ £ c £ £ £ £ £ Nil & Debt— MALES Under £100 6,778,032 4,657,078 2,444,176 1,596,151 995,831 618,468 18,329 11.350 17,119,415 £100 and under £250 11,847,614 8,830,654 4,839,271 3,079,976 2,093,879 1,174,189 30,433 18,258 31,914,274 £250 „ £500 17,013,903 13,530.492 7,700,957 4,926,509 3,138,668 1,796,270 38,530 15,454 48,160,783 £500 „ £750 13,960,232 ll,667,803i 6,417,081 4,060,031 2,546,251 1,590,375 23,307 17,047 40,282,127 £750 „ £1,000 11,763,474 10,278,545 5.412,309 3,434,956 2,119,560 1,282,093 29,718 10,607 34,331,262 £1,000 „ £2,500 49,016,305 43.615.567 19,261,233 14,806,314 7,313,256 4.856,058 67,853 64,677 139,001,263 £2,500 ,, £5,000: 49.304,480 43. .539. 160 13,613,885 14,532,191 5,582,786 3,885,555 68,479 46,839 130,573.375 £5,000 ,, £10,000i 50.189,620 41,011,274' 12.033,262 14,049,889 4,545,168 3,249,174 109,218 42,331 125,229,936 £10,000 „ £15,000i 27.111,542 19.617,337: 6,419,640 6,349.439 2,758,151 1.899,180 25,359 64,180,648 > £15,000 „ £20,000 17.-323,116 12.663,937; 3,956,277 3,891,761 1,647,795 1,211,844 38,578 19,210 40.752,518 £20,000 „ £25,000 12.900,114 8,770,6511 2.784,046 2,431,905 1,009,019 851,269 23,389 28.770.393 £25,000 „ £50,000 33,767,772 22,207,915 7,503.094 5,937,082 3,070,483 1,830,952 28,440 2'5',274 74,371,012 £50.000 ., £75.000: 18.034.840 11,282,205 3,814,601 3,298,269 1,440,069 1,085,763 38.955,747 • £75,000 „ £100.000, 9,312.967 6,869.864 2.250,402 1,600, 566' 1,267,354 78,549 21,379,702 J £100,000 & upwards Totals . . 33,869,847 30,770,541 4,932,586 9,682,663 2,604,134 945,712 262,259 83,067,742; 362,193,858 289,313,023 103,382,820 93,677,702 42,132,404 26,355,451 763,892 271,047 918,090,197 j Nil&Debt-FEM.iLES Under £100 . . 3,634,119 4,033,069 1,411,486 1,114,394 4i'l,747 365,771 1,126 ■3'522 10.975.234 ; £100 and under £250 5.967,286 6,657,064 2,455,001 1,799,626 880.499 628,814 2,812 3,230 18.394.332 ' £250 „ £500 8,532,338 9.885,815 3,535,422 2,869,678 1,359,823 8:^6,065 3,210 6,565 27.018.916 £500 „ £750 7,022,666 7,983,301 2,671,500 2,348,016 1,013.122 653,317 3,083 1,173 21,696,178 £750 „ £l,000i 5,456,148 6,562,229 :i,000,760 1,845,022 746,817 546,345 5,167 1,762 17,164,250 £1,000 ., £2..500| 20,595,997 23.923,308 6.328,154 6,505,780 2,167.529 2,072,527 9,654 6,396 61,609,345 £2,.500 „ £5.00o! 15.692,222 17:242,730 3,970,978 4,325,683 1.363,714 1,493,082 9,560 44,097,969 £5.000 „ £10.0001 12,885.951 13,260.626 3,477,867 3,282,241 1,119.086! 1.271,201 36,164 8,015 35,341,151 £10.000 „ £15.000 6,784,656 5.905,520 1,469,552 1,277,986 512,026 470,813 10,617 16,431,170 £15.(100 „ £20.000 4,017.648 3,073,930 661,157 842,346 314,778 250,279 31,290 9,191.428, £20.000 ,, £25,000l 2,527,778 2,262,196 459,687 597,318 88.194 290,950 6,226.123 £25.000 ., £50,000 5.655,295 4,904,460 1,159,987 1,167,036 363,243 521,218 13.771,2:',;) £50,000 ,, £75,000 2,079,558 1,903,507 253,449 497,508 124,018 68,214 4,'.»2 ^ ^1 << Cl o c ^5 << (iJ o 3 New South Wales. Victoria Queensland. £ £ £ £ O' £ £ O'. Deficit and Nil •? 1,555 9 ? 1.095 9 b ? 796 9 Under £50 29 259 11.20 28 295 9.49 30 246 12.20 £50 and under £100 75 181 41.44 74 216 34.26 74 180 41.11 £100 £150 123 189 65.08 123 226 54.42 122 201 60.70 £150 £156 152 239 63.60 151 300 50.33 152 2.53 60.08 £156 £200 173 400 43.25 173 488 35.45 173 402 43.03 £200 £300 237 956 24.79 237 1,056 22.44 237 788 30.08 £300 £500 375 2.185 17.16 376 2,226 16.89 372 1,752 21.23 £500 £750 606 4.593 13.19 600 4,211 14.25 602 3,306 18.21 £750 £1,000 839 7,014 11.96 871 6,527 13.34 863 6.035 14.30 £1,000 £l,50r 1,209 10,895 11.10 1.222 9,395 13.01 1,214 8.766 13.85 £1,500 £2,000 1,729 16,408 10.54 1,726 14,815 11.65 1,711 12,629 13.55 £2.000 £3,000 2,431 24.521 9.91 2,421 22.592 10.72 2.420 19,689 12.29 £3,000 £4.00C 3,381 36,117 9.36 3,431 33.000 10.40 3,454 30,588 11.29 £4.000 £5.00C 4,502 48.370 9.31 4,472 50,068 8.93 4,493 39,453 11.39 £5,000 and upwards . . Groups . . 9,961 111.020 8.97 9,281 113,145 8.20 9,561 74,783 12.78 AliL 153 691 22.14 145 729 19.89 144 524 27.48 Income Group. South Australia. Western Australia. Tasmania £ £ 0' £ £ o- £ £ 0/ Deficit and Nil 9 1,260 ?° ? 802 9 9 543 9° Under £50 '28 392 7.14 27 324 8.33 30 214 14.02 £50 and under £100 74 282 26.24 74 205 36.10 74 186 39.78 £100 „ £150 122 272 44.85 124 181 68.51 121 245 49.39 £150 „ £156 154 349 44.13 151 168 89.88 153 378 40.48 £156 „ £200 172 585 29.40 175 241 72.61 172 619 27.79 £200 „ £300 238 1,169 20.36 234 497 47.08 241 1,142 21.10 £300 „ £500 372 2,623 14.18 371 1,420 26.13 378 2,527 14.96 £500 „ £750 607 5,236 11.59 600 3,249 18.47 600 5,189 11.56 £750 „ £1,000 854 7,104 12.02 852 5,198 16.39 838 7,336 11.42 £1,000 „ £1,500 1,217 10,771 11.30 1.208 8,203 14.73 1,236 11,953 10.34 £1,500 „ £2,000 1,731 15 436 11.21 1,705 12,847 13.27 1,705 17,159 9.94 £2,000 „ £3,000 2,468 25,826 9.56 2,432 21,191 11.48 2,520 27,657 9.11 £3,000 „ £4,000 3,471 43,439 7.99 3.438 35,962 9.56 3,214 30,678 10.48 £4,000 „ £5,000 4,589 40,766 11.26 4,443 40,322 11.02 4,452 32,122 13.86 £5,000 and upwards . . 11,352 187,392 6.06 11,292 97,539 11.58 7,385 90,402 8.17 All Groups . . 127 744 17.07 153 498 30.72 120 531 22.60 Income Group. NORTH] :rn Ter ritory Federj LL Terr ITORY. Commonwealth. £ £ % £ £ .0 £ £ 0- Deficit and Nil 9 2,497 '•> 9 222 9 , 9 1,170.5 9 Under £50 '28 124 22.58 '29 230 12.61 28.6 286.3 9.99 £50 and under £100 73 101 72.28 71 309 22.98 74.1 201.9 36.72 £100 „ £150 120 115 104.35 119 159 74.84 122.9 209.5 58.67 £150 „ £156 151 180 83.89 152 162 93.83 152.1 262.4 57.98 £156 „ £200 176 171 102.92 176 256 68.75 173.0 427.9 40.43 £200 „ £300 235 288 81.60 228 520 43.85 236.9 932.2 25.41 £300 „ £500 367 847 43.33 369 1,919 19.23 374.4 2,123 17.64 £500 „ £750 572 2,946 19.42 594 701 84.74 602.9 4,280 14.09 £750 „ £1,000 918 5,710 16.08 977 8,850 11.04 854.3 6,646 12.85 £1,000 „ £1,500 1,090 5,537 19.69 1,256 14,012 8.96 1,215 9,996 12.15 £1,500 „ £2,000 1,514 2,584 58.59 1,724 15,164 11.37 £2,000 „ £3,000 2,070 11,620 17.81 2,431 23,251 10.45 £3,000 „ £4,000 3,412 34,576 9.87 £4,000 „ £5,000 4,494 46,908 9.58 £5,000 and upwards . . 9,786 112,274 8.72 All Groups . . 153 592 25.84 141 403 34.99 146 665 21.95 58 The Relation between We.^lth and Income. Commonwealth, States and Territories. — Average Net Income and Average Net Assets as at 30th June, 1915, in each Income Group, and Percentage of Income on Assets in Respect of Individuals. (Exclusive of Absentees). FEMALES. Income Grovp. 43 . a«i a^- §t £ c8-»^ II 1^ << ^1 .^-< i =<; New South Wales. Victoria. QUEENSL.\ND. Deficit Under £50 £100 £150 £156 £200 £300 £500 £7.50 £1,000 £1,500 £2,000 £3,000 £4,000 £5,000 and Nil £50 and under £100 £150 £156 £200 £300 £500 £750 £1,000 £1,500 £2,000 £3,000 £4,000 £5,000 and upwards . . All Groups . . 22 68 118 153 174 242 376 602 852 1.207 1,713 2,461 3,592 4,444 £ 104 212 248 537 902 1.255 2,146 3,745 6,458 8,500 11,559 ' 14,946 22 224 3l'676 35,365 126975 398 /o 10.38 27.42 21.97 16.96 13.86 11.28 10.04 9.32 10.02 10.44 11.46 11.07 11.34 12.57 6.83 13.32 23 67 118 153 174 240 378 611 845 1.195 1,732 2,458 3,493 4,496 7,046 £ 127 217 261 626 1.001 1,405 2,215 3,547 5,360 7,919 12,365 15,873 23,724 27,099 39,116 82.746 48 370 10.60 25.67 18.84 15.28 12.38 10.84 10.66 11.40 10.67 9.66 10.91 10.36 12.89 11.49 8.52 £ £ 9 118 22 213 68 224 118 518 152 1,023 175 1,160 238 1.973 380 3,187 609 5.774 842 6,688 1,209 8.084 1,754 9.865 2,313 17,643 3,484 31,033 4,364 40,086 6,327 30.201 12.97 41 10.33 30.36 22.78 14.86 15.09 12.06 11.92 10.55 12.59 14.96 17.78 13.11 11.23 10.89 20.95 295 13.90 Income Group. South Australia. Western Australia. Tasmania £ £ % £ £ o/ £ £ 0- Deficit and Nil ? 102 ? ? 174 9 9 84 9 Under £50 21 226 9.29 21 261 8.05 22 193 11.40 £50 and under £100 68 349 19.48 70 246 28.46 67 313 21.41 £100 „ £150 117 735 15.92 120 380 31.58 118 766 15.40 £150 £156 151 1,102 13.70 152 309 49.19 153 1,155 13.25 £156 £200 175 1,635 10.70 171 682 25.07 177 1,649 10.73 £200 £30€ 240 2,528 9.49 235 1,439 16.33 240 2,637 9.10 £300 £500 381 4,013 9.49 373 3,453 10.80 383 4.143 9.24 £500 £750 600 6,474 9.27 631 4,832 13.06 606 5,453 11.11 £750 £1,000 849 8,051 10.55 803 9,043 8.88 853 6,628 12.87 £1,000 £1,500 1,201 13,617 8.82 1,185 8,988 13.18 1,255 13,168 9.53 £1,500 £2,000 1,722 19,486 8.84 1,905 12,764 14.92 1,758 26.397 6.66 £2,000 £3,000 2,407 23,831 10.10 2,378 21,937 10.84 2,575 21,497 11.98 £3,000 £4,000 3,532 19,551 18.01 3,531 3.668 9.63 £4.000 £5,000 4,495 25,075 17.93 4,162 570 730.18 4,063 22,632 17.95 £5.000 and upwards . . 6,302 98,371 6.41 5,113 8,417 60.75 5,774 68,214 8.46 All Groups . . 40 360 11.11 50 342 14.62 44 358 12.29 Income Group. Northern Territory. Federal Territory. Commonwealth. £ £ o/ £ £ % £ £ 0/ Deficit and Nil ? 340 9 9 49 9 ? 116.5 9 Under £.")0 22 451 4.88 19 205 9.27 22.3 216.6 10.28 £50 and under £100 77 335 22.99 66 96 68.75 67.9 260.6 26.06 £100 „ £150 121 156 77.56 114 231 49.35 118.1 578.8 20.40 £1.50 „ £156 152.8 930.3 16.43 £1.% „ £200 i70 943 18.03 i73 718 24.09 174.2; 1.301.7 13..38 £200 „ £300 203 193 105.18 205 3,987 5.14 240.1' 2,164 11.10 £300 „ £500 352 3,685 9.55 377.6 3,637 10.38 £500 „ £750 606.8 5,890 10.30 £750 „ £1,000 960 160 600.00 942 8,080 11.66 847.1 8,068 10.50 £1,000 „ £1,500 1,222 6,104 20.02 1,031 15,216 6.78 1,204 11,633 10.35 £1,500 „ £2,000 1,729 15,208 11.37 £2,000 „ £3,000 2,066 9,8i7 21.05 2,434 22,255 10.94 £3,000 „ £4,000 3,537 28,360 12.47 £4,000 „ £5,000 4,455 35,634 12.50 £5,000 and upwards . . 7,627 96,829 7.88 All Groups . . 150 835 17.96 45 369 12.20 48 367 12.97 The Correlation of Whalth and Income. 59 Commonwealth, States and Territories.^ — Average Net Income and Average Net Assets as at 30tb June, 1915, in each Income Group, and Percentage of Income on Assets in Respect of Individuals. (Exclusive of Absentees). PERSONS. §1 X itage onie sets. =s S li Income Group. ^2 |£^ 5;a C t; X II g5^ <;>H •<< ■ a -< > ^ < > ^ > S . and 3, page 66, shewing the surface. If the quantities in the table are divided by 1,000, they give tl\e numbers of males and fe- males who .are included on the average in a range of xto x+\ pounds sterling income, and ;/ to ;/ + 1 pounds sterling wealth ; the average extending all over the double-range A'l to A'a and Ti to \\. 2. From ttXoOtos, wealth, and 7r/)o(To5os, income as opposed to principal, or tt/joctoSu-oj, apper- taining to income. The Wealth and Income Surface. 65 Frequency, multiplied by 1000, per unit of Range (Pound Sterling) of Wealth and Income, i.e., 1000 times the Number of Persons of a given Range of Wealth and a given Range of Income divided by the Product of the Range of Wealth into the corresponding Range of Income. Australia, 30th June, 1916. Aver. Value Under 100- 250- 500- 750- 1,000- 2,500- 5,000- 10,000- 15,000- 20,000- 25,000- 50,000 75,000- Range. of In come. 100. 250. 500. 750. 1,000 2,500 5,000 10,000 15,000. 20,000. 25,000. 50,000. 75,000. 100,000 Males— Under 50 28.6 11396 2546 1179 601 352 100 15 2.19 .328 .080 .052 .0100 .0008 50-100 74.1 30222 5011 1869 860 488 167 23 2.59 .472 .150 .048 .0100 .0024 100-150 122.9 41151 9339 3022 1187 621 193 36 3.62 .564 .160 .056 .0150 .0024 .ooieo 150-200 168.2 13887 5466 2265 1030 559 169 35 4.62 .670 .180 .073 .0160 .0040 .00080 200-300 236.9 1809 1225 702 430 282 110 27 5.49 .750 .192 .080 0130 0024 .00040 300-500 374.4 1.58.5 148 123 91 75 40 15 4.07 .915 .258 .089 .0150 .0038 .00060 500-750 602.9 15.64 16.61 16.7 15 14 9.81 5.45 2.26 .824 .309 .106 .0203 .0023 .00080 750-1000 854.3 3.04 3.360 4.24 4.09 3.70 2.87 2.03 1.16 .520 .252 .144 .0243 .0018 .00120 1000-1500 1215 .640 1.066 .832 .990 .780 .850 .695 .471 .259 .161 .104 .0278 .0037 .00050 1500-2000 1724 .260 .293 .344 .230 .250 .240 .187 .179 .129 .093 .058 .0252 .0046 .00130 2000-3000 2431 .030 .073 .076 .084 .056 .0480 .0440 .0516 .0512 .042 .028 .0161 .0050 .00100 3000-4(100 3412 .013 .012 .040 .012 .0130 .00880 .0104 .0106 .016 .013 .0084 .0042 .00110 4000-5000 4494 '.010 .007 .004 .008 .0080 .00640 .0048 .0044 .006 .008 .0042 .0020 .00130 Owr 5000 9786 •• .\verage asset Males .. 32.10 160.6 354.9 609.4 863.7 1565.7 3473.3 6889.8 12079.9 17224.2^22424.3 34130.8 60773.3 85862.2 Females — Under 50 22.3 2091 6717 3434 1636 798 136 6.09 .57 .096 .028 .008 .0020 .00400 50-100 67.9 15707 2009 839 489 366 185 13.09 .77 .052 .032 .012 .0030 .00400 100-150 118.1 3934 966 426 223 149 89 25.40 1.07 .100 .028 .0020 150-200 169.4 617 311 152 96 66 39 20.35 1.84 .100 .028 '.020 .0080 200-300 240.1 99 74 45 34 22 49 8.97 2.58 .172 .038 .016 .0028 .00080 .00040 300-500 377.6 16 14 10 7.36 6.70 4.28 2.31 1.58 .329 .038 .017 .0038 .00040 500-750 606.8 2.9 3.04 2.27 2.11 .187 1.18 .657 .415 .317 .107 .038 .0034 .00080 750-1000 847.1 1.0 .90 .416 .65 .640 .442 .244 .155 .143 .101 .049 .0044 .00010 1000-1500 1204 .26 .17 .017 .23 .24 .134 .086 .065 .048 .041 .027 .0082 .00030 .00010 1500-2000 1729 .02 .026 .036 .040 .096 .041 .026 .025 .017 .0128 .011 .0056 .00060 2000-3000 2434 .06 .028 .016 .016 .012 .013 .013 .010 .0078 .0034 .0034 .00308 .00104 .00020 3000-4000 3537 004 .016 .008 .003 .003 .003 .0016 .0016 .0001 .00104 .00028 .00016 4000-5000 4455 .002 .012 .0008 .0001 .0001 .00044 .00040 .00024 Over 5000 .-Vverage asset Females . . 27.98 158.7 351.9 604.4 682.3 1527.4 3422.0 6818.6 12064.0 17342.0 22316.0 33919.3 60817.9 86188.4 Persons 30.35 159.9 353.8 607.6 863.2 1553.7 3460.3 6874.0 12077 17246 22405 34098 60778 85893 Note. — The frequency for persons is the sum of the two values above. 3. The graphs of the plutoprosodic (or wealth -and-income) surfaces. — The upper graph represents the plutoprosodic surface for males, and the lower graph the pluto- prosodic siu-fa^e for females, by means of contours shewing the number per square unit (multiplied by 1000), possessed of any given income and any given wealth. Thus, if any contour be followed, say 10, on the graph for males, a succession of points taken thereon shews the wealth and incomes associated with that degree of frequency, while if a succession of points taken on contoiu- 20 be followed, the fre- quency will be double. Thus wealth £3000 associated with incomes of £495 occur as frequently in Australia as wealth £5000 associated with incomes of £2(5G, and bothoccur with half the frequency with which wealth amounting to £2500 is associ- ated with incomes of £412. The numbers for the curves marked a i are as follows : — Letter Male Female 35,000 20,000 b 20,000 15,000 c 15,000 10,000 d e / 9 h 10,000 5,000 4,000 3,000 2,000 5,000 4,000 3,000 2,000 1,500 1,000 The immense advantage which the graph possesses as com]iared with tabidar results is obvious from the above illustration of its interpretation : it is only by means of the contoxirs of the plutoprosodic surface that the way in which wealth and income are associated in any commvuiity can be completely defined. 66 The Relation between Wealth and Income. 4 Freciuency according to income and wealth.— In order to observe the change of frequency for any given income, the co-ordinate value is taken on the left hand vertical line, and the intersection with the contours of the horizontal line with this value gives the relative frequency according to the wealth corresponding. Similarly, for any given amount of wealth the co-ordinate value is taken on the top horizontal line, and the intersection with the contours of the vertical line with this value gives the relative frequeuf y according to the income corresponding. Fig. 2. Plutoprosodic Surface (Males). i 12000 £iaoo Fig. 3. Plutoprosodic Surface (Females). The Wealth A^•D Income Surface. 67 Tiie upp.^r flaure (1) shews the contours of tha phitoijroso.lic surface for lual.s, liasi-d upon 1,380,208 War Census returns for males, and the lower figure (2) the piutoprosoilii- surface for females, based upon 811,737 War Census returns for females. The frequencies imlicatiui.' verti<-al lici-iiits are as shewn by figures written on the contour lines. These denote the numlier of persons in the tot;il< con- sidered, nuiltiplied by 1000, for a range of £1 of wealth and £1 of income. The intersection of the vertical lines witli the contoiu-s shews the freciuency with variations of income for given values of wealth. Similarly, the intersections of the horizontal lines with the contours shew the frequency for given incomes with variations of the amount of wealth. Where the ranges of wealth or income, or both, are more extended than one pound sterling, the frequencv numbers should be multiplied by the product of the two ranges and divided by 1000. Thus, if the range of wealth be from £7000 to £7500. and that of income from £500 to £510, the nnUtiplier will be 500 x 10 = 5000. This divided by 1000 gives 5, the factor to be multiplied into the frequency value as shewn. It will be sufficiently accurate to adopt the value of the contour pass- ing through the centre of the range-area in question. For males this is approximately 2.45 : the required frequency is therefore 12.25 : similarly for females, and with the same double range, the required frequency will be 0.864 x 5 = 4.32. It will be observed that the surface for males is fairly regular, but that for females is very irregular. The irregularities are probably accidental, and with larger numbers would most likely disappear. The values of curves a i have been referred to in the preceding paragraph. The plutoprosoiic surface, it will be seen, represents the whole system of relations that e.xist between wealth and income, by means of a three dimensional figure on which the contours are the intsrsections of planes parallel to th3 bas3 at the successive heights indicated by the figures. PART V. THE ESTIMATION OF WEALTH FROM PROBATE RETURNS. CHAPTER I.— THE INTERVAL OF DEVOLUTION. 1. The interval of devolution method. — The method of determining the aggre- gate of private wealth from the aggregate amount appearing as inheritance, by taking accoLint of the average interval between the inheritance and the passing on of an estate, lt the average interval between " successions to title," is known as the " interval of devolution'" method. It is a metliod that has been used more frequently than any other. We shall consequently refer to it at some length, and may point out that it has recently been discussed by Mallet, ^ and very fully and more recently by Corrado Gini. ^ In this method, as employed l)y Mony, 1877, and by Bailleux de Marisy, 1878, it was assumed that the mean dviration of life could be regarded as the devolution interval. Ten years later Verrijn Stuart, viz., in 1888, made the same assumption, as also did F .S. Nitti quite recently,' viz., in 1904. In December, 1878, L. Vacher pointed out that the devolution-interval should be the arithmetic mean between the times when persons receive, and when they transmit to their heirs, their inheritances. This suggested the idea that a fundamental period to be ascertained was the "duration of a generation" determined as the interval between the births of parents and children, but it was demonstrated by Coletti that increase in the duration of life could sensibly distm-b the coincidence of the interval between the births and that between the deaths. It was simultaneously pointed out by Gini, and by Lavergne and Henry, 1908, that there is a sensible difference between the interval from the deaths of parents to the deaths of children, and the interval between the deaths of testators and the deaths of their heirs ; in fact, that the latter interval is apjjreci- ably shorter owing to the influence of " successions" by collateral relatives, the widowed, and 'strangers in blood.' Mallet, in 1908, ascertained the devolution- interval by computing the mean duration of the life of heirs by means of life-tables. In 1909, March indicated another method based upon the difference in the mean age of testators and the mean age of their heirs (intervalle moyen des vmtations sticcessives). It was not long before it wtis perceived that the amount of the " succession" was of importance in forming the " average interval." Mony, Bailleux de Marisy and Vacher took cognisance of this, and de Foville shewed that it is also necessary to add the amount of settlements (donazioni), which are, of course, virtually anticipa- tions of inheritance. 1. Journal Eoy. Stat. Soc, Ixxi., pp. 65-84, 1908. 2. L'Ammontare e la Composizione della Ricchezza delle Nazioni), 1914, Torino, pp. 712, vide pp. 50-132. 3. See bibliography appended hereto. The Interval of Devolution. 69 Gini shewed that the interval between two settlements was sensibly equal to the interval between two successions. Attempts to evade the pajTnent of duty reduce the amount coming into evidence, and Vacher endeavoured accordingly to ascertain the magnitude of the evasions, with the result that he — and others also — found that the ascertained amounts did not agree with the estimations made by officials of various departments of Finance. In the attempt to obtain a multiplier from the average devolution-interval for individual estates, Gini pointed out that the arith- metic mean is unsatisfactory, and that the harmonic mean should be used ; and further, that many estates are ceded by persons of advanced age against service to be rendered to them or their descendants ; and yet again, that it is very important that account should be taken of the influence on the annual amount of devolution of variations in the wealth of a country. No method is quite free from this difficulty. 2. Determination of the interval of devolution. — The duration of a generation, regarded as the interval between two successive generations, was determined directly by Turquan. Using 4^ million schedules, he computed that from years 1892 to 1896 the average age of fathers of " legitimates" (so-called) in France, was 33 years 7 months, and that of mothers of " legitimates" 29 years 10 months 13 days. In -the following table the results are given for a number of countries, as well as the period to which these dates apply : — Average Duration of a Generation. Average. Fathers of Mothers of Country. Period. (so-called) " Legiti- (so-called) " Legiti- Authority. mates." mates." \ France 1892-96 33.6 29.9 Tiu-quan " 1892-1900 29.33 International Statistics* Paris 1903-05 32.4 28.1 Gini Rome 1894-96 36.5 29.6 Raseri Udine 1872-82 34.0 30.5 Raseri Tasmania . . 1904 33.68 29.05 Gini New South Wales 1904 34.1 29.7 Gini 1893-1900 29.55 International Statistics* Finland 1881-85 1886-90 1891-1900 31.53 31.63 31.14 do. do. do. Sweden 1871-80 1881-90 1891-1900 32.63 32.27 32.22 do. do. do. Denmark . >> 1880-84 1885-89 1890-94 1895-1900 31.37 31.33 31.37 30.40 do. do. do. do. Published in the Statistique g^n^rale de la France. The preceding examples may bo called instances of determination by the direct method. Riimelin ajipears to have been the first to adopt an indirect method. In this the mean ages of the persons marrying are ascertained, and the interval between marriage and the birth of the first cliild, and half the mean interval between the birth of the first and last child. In tliis way the interval between the births of the parents 70 The Estimation of "Wealth from Probate Returns. and that of the middle child is presvimed to be sufficiently well ascertained. Riimelin found the interval between marriage and the birth of the first child to be one year ; between the births of first and last child 12.2 to 12.5 years ; and thus the interval between marriage and the birth of the middle child to be slightly over 7 years. By this method he calculated the average interval between the births of parents and of children to be as follows : — Germany, 36.5 ; England, 35.5 ; France, 34.5 years. This method is, of coiu'se, not accurate, because the interval between marriage and the birth of the fii'St child cannot be regarded as exactly one year. Four years' experience in Australia, for example, gives the result 1.19 years, and shews that the interval varies with the age of the parent (in this case the mother), the result being as follows : — Interval between Marriage and Birth o! First Child, Australia, 1908-1911. Ages of Mother Under 20 20-24 25-29 30-34 35-39 40-44 45 & over All Mothers Interval from Marriage to Birth of First Child 0.63 0.97 1.44 2.02 2.70 3.36 2.97 1.19 Again the children do not follow at equal intervals, and there is little doubt that the interval differs somewhat in different countries. Vacher adopted an indirect method, which may be described as follows : — Let n equal the number of births occurring in the ith year after marriage. Then the sum of the products m divided by the total births gives the average interval between marriage and the birth of all children, i.e. : — (1) io = 2(m)/ Sn This average interval i^ added to the average age of persons marrying gives the interval between the birth of parents and births of all children. In this way Vacher found 33.06 for France in 1880. It has been wrongly assumed that the methods are equivalent ;. they give, however, sensibly different results. The character of these methods was discussed by Gini, who makes the following observations : — " With Vacher's and Riimelin's methods the interval between births of parents and children is not accurately ascertained, but the method gives the interval between the births of all persons marrying, whether prolific or not, and the births of the children. Since the non-prolific marrying are as a rule older than the prolific, the interval between the births of parents and children computed by this method is too large. Moreover, even prolific parents enter into the results in a different way by the various methods. In the method of Turquan, a parent is taken account of in the computa- tion each time he has a child, whereas in Rvimelin's method the parent enters once only. Moreover, as more prolific parents are ordinarily younger, Riimelin's method will give a higher interval than Turquan's. Vacher's method gives a still higher figure than Riimelin's, since each parent, tho^lgh he appears but once in the cal- culation of the age of persons marrying, nevertheless appears as many times in the calculation of the interval between marriage and birth as he has children ; and further, the parents who have more children shew a larger interval between the birth of the parent and the birth of the middle child. Gini gives an instructive example, which may be here reproduced as illustrative of the significance of the difference of the methods. The Interval of Devolution. 71 Example. — Let there be 3 families, in which, in the period 1890-1900, 7 children were born, \iz., 5 as issue of a fatlier born in 1870 and mai-ried in 1889, born in the years 1890, 1891, 1893, 1897, 1900 ; 2, aa issue of a father bom in 1861 and married in 1890, born in the years 1893 and 1895. The third husband, bom in 1850 and married in 1889, let it be supposed has no issue. (a) Method of Turquan. — Average age of fathers at the birth of children: — = 4 (20 + 21 + 23 + 27 + 30 + 32 + 34)= 26.7 {h) Method of Rumelin. — Interval between birth of father and birth of middle child : — = i (19 + 29 + 39) + 11 i (1 + 2 + 4 + 8 + 11)+ \ (3 + 5)[ = 33.6 (c) Method of Vacher — Interval between birth of fathers and births of children : — = J (19 + 29 + 39) + i (1 + 2 + 4 + 8 + 11 + 3 + 5) = 33.9. Thus Vacher gives a larger number than Rumelin, and Rumelin a larger number than Turquan. The data for Paris and also for New South Wales shew that the results obtained according to Tiu-quan'a and Vacher's methods are not the same, the difference for Paris araomiting to 2.6 years for males, and 3.5 years for females ; and in New South Wales to 2.7 years for males, and 2.9 for females. In this instance Gini states that Riimelin's method cannot be employed. Li discussing which of the three methods is jDreferable, Gini makes observations that may be summarised as follows : — From the demographic point of view the difference between ages of parents and children is of importance, as this is the interval between two generations ; and the schematic example given indicates that it might be obtained as follows : — I (1890 + 1891 + 1893+1897 + 1900+1893 + 1895) — 1 (1870+ 1861) = 28.6 ; the first part denoting the years of birth of sons (7) and the latter of the fathers (2). From the economic point of view, i.e., in the case of the valuation of the private wealth of a country, Gini affirms that it is important to recognise that : — • If the property left by a jDerson is derived entirely from his own thrift, then the amount of the properties left at their deaths by the children of two generations will be in proportion to their numbers. In that case the method of Turquan should be used, as it takes the age of parents into account every time they have children. But of properties left to successors it not infrequently happens (in Europe at least) that only a relatively small portion is due to thrift, the greater portion having been inherited. The amount of property left by the children at their deaths will therefore be less than proportionate to their number. Turquan'a method would, therefore, by taking the interval between the births of parents and children, furnish too small a result for the calculation of the private wealtli. It ought also to be observed that in order, at any given moment, to obtain the average devolution-interval (denoted by Gini by i^i) we must determine the mean interval between the births of parents and children, not merely for those persona who actually register children, but for thoae persons who actually die. in the meantime the average age of persona marrying, the interval between marriage and tiist birth and the interval between first and last births, may have altered. 72 The Estimation of Wealth from Probate Returns. The whole position maj-, therefore, be summed up as follows : — The various methods (Vacher, Riimelin, Turquan) adopted in the determination of the duration of generations are not at all equivalent, and lead to sensibly different results. For the pvu-pose of the calculation of private wealth none of them is exact, as the resialt according to Turquan is too small, and according to Vacher and Riimelin too large. It is, therefore, necessary to be satisfied with I'ough approximations. In another direction, a source of error lies in the fact that in the case of persons dj- ing the interval between births of parents and births of children is taken as equal to that found for persons who at that time register the birth of children. Those who deduce the interval of devolution from the interval between the birth of parents and the birth of children, regard this latter as coinciding with the interval between the death of parents who have survived grand-parents and the deaths of children who siu-vive parents. Setting the data out in the form of inequalities, Gini has shewn that : (a) If it be assmned that the interval between the death of parents and the death of surviving children corresponds to the interval between the birth of parents and the birth of their children, an error is made which, according to the nature of the cases, may lie in either direction, but the amount of which is generally not very serious. (6) If the mean dviration of life remain constant, the interval between the birth of parents and the birth of their children is greater than the inter- val between the death of parents and the death of surviving children. (c) If the mean duration of life increase, there may be a difference in the opposite direction. It will certainly be an advantage if the increase in the duration of life can be taken into account. But we have to con- sider that the influence of that increase is more complex than has hitherto been believed, and that the increase in the mean diu-ation of life is different, and probably very different (?) in the case of heirs from that of the total population {op. cit, pp. 60, 61). This deduction is of doubtful application in Australia. He adds further that those avithors who have calculated private wealth by the method of the interval of devolution have assumed that this interval corresponds to the mean interval between the death of parents leaving property and the death of children inheriting property, an hypothesis, however, which he points out is not in accordance with reality {tale ipotesi non corrisponde a realfd). He has shewn by an example which, though only schematic, leads to substantially correct conclusions, that the interval of devolution is notably smaller than the interval between the death of parents leaving property and the death of children inheriting {ibid., pp. 61-63). Dividing testators into three classes, viz. (i.) married or widowed persons with issue ; (ii.) married or widowed persons without issue ; and (iii.) unmarried persons ; and making certain suppositions which, even when they are not strictly true, do not sensibly prejudice the result, he establishes mathematically that the intei'val of devolution is appreciably smaller than the mean interval between the deaths of parents and the deaths of their children. These suppositions are : — (a) That the possessors of property of one generation die before those of the following generation ; he discusses also the limitations to this supposi- tion. The Interval of Devolution. 73 (b) That the heirs of a married person 'with pre-deceased issue' are the widow, widower, or the (siirviving) children ; and that the heirs of a widower or widow are the children ; that the heirs of an unmarried person are brothers, cousins, nephews, or 'strangers in blood' ; that the heir of a husband or wife, pre-deceased without issue, is always the surviving wife or husband ; and that the heirs of the latter are brothers, cousins, nephews, or 'strangers in blood'. Then, taking into account the experience in Italy from 1872 to 1905, as to the frequency among deaths of unmarried as compared with married, and the experience of Budapest and France as to the proportion of marriages dissolved without issue, and assuming also the relation which the value of property left by the predeceased husband or wife to the surviving partner bears to the value of the property that the latter leaves to the children, assumed as 1 to 10, he deduces for the mean interval between deaths of parents and the deaths of their children, i,^, and the proper devolu- tion interval, id, a difference of 8 years, the latter being the smaller, i.e. : — ^yf^ = 34 years ; but id = 26 years only. This does not piirport to be an exact or definite relationship between the two methods of estimating the devolution-interval, but is taken merely as shewing unquestionably that " the devolution-interval is appreciably smaller than the mean interval between the deaths of parents and the deaths of their children. Celibacy, the failure of issue in many marriages, and inheritance between husbands and wives, which result in the succession of persons of a more advanced age, explain the difference between these two intervals." Gini points out that historical data afford evidence of the trvith of this conclu- sion, and that in every dynasty of sufficient duration it is found that the average length of a reign is less than the average interval between the death of a king and the death of an ascendant who preceded him. He gives four examples, to which we here add two others, viz., the experience in the Houses of Hapsburg and Hohen- zoUern. It may be remarked that, since among monarchs bachelordom is quite exceptional, the difference is due exclusively to the absence or predecease of sons. In the table below the four first results are those given by Gini : — Mean Duration of Survival of a King Number of to his Predecessor in Years. Period When the Predecessor was Dynasty. Considered. Reigns. All Reigns. An Ascendant. A Collateral. England 1035-1901 34 25.5 30.4 19.2 France . . 996-1850 36 23.7 26.6 17.1 Savoy . . 1060-1900 38 22.1 24.6 16.8 OldenViurg 1481-1906 16 26.6 27.9 20.7 Hapsburg 1273-1848 26 22.1 23.8 18.2 HohenzoUern . . 1415-1888 19 24.9 5.9 21.5 The differences between the figures in the 5th and 6th cokunns vary from 4.4 to 11.2 years. 74 The Estimation of Wealth from Probate Returns. Gini argues that a better approximation of the values of i^ and id can be ob- tained whenever figures are available shewing the degree of relationship of heirs to whom portions of the properties are left, and he gives instances from Italian and French statistics. In Italy a distinction is made between 8 categories, viz. : — OroupA. (a) Ascendants and descendants (exclusive of adopted children;; (6) uncles and nephews ; (c) great uncles and great nephews. Group B. [d) Husbands and wives ; (e) brothers and sisters ; (/) other relatives up to the sixth degree ; (gr) relatives beyond the sixth degree, " strangers in blood," and institutions other than benevolent or mutual aid. There is another category, viz., {h) benevolent and mutual aid institutions. On distributing successions of very small amounts (less than 100 francs) between the two groups, Gini obtained for the five financial years 1903-4 to 1907-8, for property left less succession duties, the following result, expressed in francs : — Group A, 3,434,301,000 = 78.1% ; Group B, 961,855,000 = 21.9%. For group A, the interval of devolution corresponds to the interval ^,„ between the death of parents and the death of surviving children, there being compensating features ; and the interval of devolution for group B, denoted by k, by Gini, is much shorter. He found the value for the former to be 34 years, and for the latter 17. Hence the weighted mean is 30.28 years, i.e., 34 is multiplied by 0.781 plus 17 by 0.219. Gini classified " donations," which here would be known presumably as "settle- ments," and for the combined figures in francs for the six financial years 1900-1 to 1905-6 he obtained : — Group A, 4,675,910,000 = 80.4% ; Group B, 1,139,099,000 = 19.6%. With the values 34 and 17 aa in the preceding case, these weights give 30.67 years. Gini concluded that these two values, viz., 30.28 and 30.67, are probably somewhat iinder the mark, and he supposed therefore that the true devolution interval is about 31 years, betraying incidentally the imprecision of the result. In France there are no less than 14 categories, which can be grouped in a similar manner, with the result that in groups A and B, the values in francs of the net pro- perty, viz., property left, less succession duties, are as follow : — Grovip A, 3,526,179,000 = 77.5% ; Group B, 1,024,059,000 = 22.5%. Weighting the values 34 and 17 accordingly, he obtained 30.17 years as the true devolution interval, which does not differ very greatly from the preceding result. His conclusion was that the hypothesis that the interval of devolution corresponds to the interval between the death of parents and the death of children sm-viving them, does not hold good in reality; in fa«t, that the interval of devolution is shorter by about three or four years [op. cit., p. 67). Gini recognises that for males and females, the interval of devolution is con- spicuously different, the former generally leaving much larger properties than the latter, while the mean duration of life of females is greater than that of males. He then shews algebraically that, if the mean interval between the deaths of parents and children is calculated without taking these facts into account, the figiu-e is too low for computing private wealth ; vide his work, pp. 67-68. He remarks that in Italy the proportion of properties left by males compared with that left by females is about 2 to 1, but in German and Anglo-Saxon countries is much higher, being in Victoria (1908) about 5 to 1 ; in Massachusetts (1898-91) about 3 to 1, and even aa high as 14 to 1 in 1829-31. The Interval of Devolution. 75 It has also been recognised by him that it is necessary to take account of the conaequencp of the age of marriage in persons of various social classes ; richer males, for example, marrying later than poor males ; and for this figures are given for Den- mark by Rubin and Westergaard, for England by the Registrar-General (49th Report), for the nobility of Sweden and Finland by Fahlbeck,for Italy in the Movi- mento della popolazione secondo gli atti dello stalo civile, 1896 and later, for Austria in the population returns of 1895, and the following years. In regard to brides, there appears to be no regularity, the age being almost the same for all social classes in Denmark ; in England brides of the better classes are older ; while in Sweden and Finland brides of the nobility are younger than those of the population as a whole. The general conclusion may be drawn, however, that the moan age of persons of both sexes marrying is generally higher for the richer section of the population in the countries referred to. Consequently, if each case be weighted proportionately to the value of the property, a higher figure would be obtained than that arrived at by a simple arithmetic mean. In pointing this out Gini adds that, though the circum- stances indicated have the effect of thus making the exact figiire for the interval of devolution greater, other circumstances have a contrary effect. He remarks that rich persons have less children, and ordinarily these follow one another at longer intervals. He infers that oia the whole it is probable that the interval between marriage and the birth of the middle child is greater for the poor than for the rich; vide p. 70. The influence of fecundity on the interval he points out can be concluded from available data ; thus, in Paris, where the fecundity is low, it is 5 years ; in New South Wales, Australia, 7.6 years. Further, celibacy is more frequent among the rich than anaong the poor, as also is childlessness of parents ; hence collateral successions are more frequent, the effect being, as he has shewn, that the interval of devolution is sensibly shorter than for direct successions. Henry and Lavergne(seebibliographj') point out another circumstance which has the effect of making the weighted mean of the intervals of devolution smaller than the simple mean. They observe that it may be admitted that, in the average number of cases {i.e., in Continental Europe), the property of the married person dying first is equal to the property of the svirviving partner. But a portion of the property of the partner dying first goes to the surviving partner. On that accoimt the second inheritance which the children make from their parents, and which they will enjoy for a shorter time, will be greater than the fii'st inheritance. Using B to denote the proportion of the property left by the partner first dying to the sm-viving partner, Gini derives the first of the two formulae shewn below as a fii'st approximation. But since in Italy in recent years the proportion of married males to married females dying waa found to be as 4 to 3, owing to the fact that husbands predecease their wives more frequently than survive them, it waa necessary to take this into account, and also the fact that (at least in Italy) the property of the husband in relation to that of the wife is about 2 to 1. Having regard to these circumstances Gini deduced the second formula ; and taking the values for i,„ = 34, k = 17, and ^ = ^j^ ^^' tained from the first formula 32.52, and fi-om the second 32.84; vide op. cit., p. 71. The formulae referred to are : — {2).. id .corrected, = 2 i,„/ (2-f g), to a 1st, and = ( - ^■»(+'^ ) /(— + ^ to a 2nd approximation. This is of course valitl 0!ily for Italy and countries aimilarly circumstanced. 76 The Estimation of Wealth from Probate Returns. Other circiunstances which exercise a different influence in different nations are (a) the average age of persons marrying ; (b) fecundity ; (c) prevalence of cehbacy ; (d) the infertihty of marriages ; (e) the relative frequency of succession by husbands and wives, and by collateral relations. Gini remarks that in Italy these circiunstances caused variations even from province to province. He adds that "on the other hand no influence is exercised on the calculation of the interval of devolution by the fact that the testators leave larger amounts of property when they are more advanced in age," and he mentions that Mallet and Beneduce regard this fact as important. It may be remarked, e?i passant, that this can hardly be correct, and will be referred to later. According to Gini it is not a question of the mean age of testators, but only of the interval between their death and that of their heirs. These are reasons for the statement that the interval between the death of a testator and that cf his heir is different when the testator is older and therefore, on the average, richer, than when he is younger, and consequently on the average poorer. But the interval is greater in the second case and not in the first. If a testator has more than average time to augment his hereditary property, this augmentation may be due to two causes, either (a) because he dies at a greater age than the average, and then it has to be assumed that his heir will have less than the average time to augment the inheritance left to him ; or (6) because the person from whom the testator himseK inherited died younger than at the average age, in which case the capital he inherited mvist have been less than the average. It there- fore seems clear, he adds, that — if the interval of devolution be not on the average different for categories of the population more or less rich — the fact that testators dying at an advanced age leave more property in individvial cases can have no influence. As previously indicated, the validity of this view is questionable, and to this point we shall retui'n. Gini's svrmming up in regard to methods of evaluating the devolution-interval is as follows : — (i.) The various methods used for calculating the interval between the birth of parents and the births of children give different results, which are al- ways approximate, but may be either in excess or in defect. (ii.) The taking of the mean interval between the birth of parents and the births of children as equivalent to the interval of devolution is based on sup- positions which are not supported by facts. (iii.) It is necessary, first of all, to make use, not of a simple arithmetic mean, but of a weighted arithmetic mean, which takes cognisance of the fact that the interval of devolution is different for categories of persons with more or with less property. (iv.) Regard must be had to the fact that the interval between the birth of parents and the births of children does not, on account of many cir- cumstances, correspond to the interval between the death of parents and the death of their surviving children. (v.) It would certainly be desirable, but is not generally possible, to take all these circimnstances into account. But it is possible and necessary to have regard to one most important circvmistance, viz., that the interval between the death of parents and thedeath of their children is apj^reciably longer than the interval between the death of testators and the death of their heirs. This circumstance is due to the fact that the interval in the case of successions by strangera in blood, by collateral relatives, and by husbands or wives, is shorter than in the case of direct succession. The Interval of Devolution. 77 (vi.) It should therefore be remembered that if this circumstance is not taken into account, the calculated interval of devolution is about 3 or 4 years too high. The figures for the interval of devolution, now put at about 33 to 34 years, should, therefore, be lowered to, say, 29 to 31 years {op. cit., pp. 72-73). Illustrating by a detailed example for Italy in 1905, Gini calc\ilatea the mean age of bridegrooms at 29.10, and of brides at 25.13 years, and gives the following results for the years 1902-1906, which shew a small but definite change : — — 1902. 1903. 1904. 1905. 1906. Bridegrooms . . Brides Differeiices 29.29 25.22 4.07 29.27 25.21 4.06 29.25 25.18 4.07 29.10 25.13 3.97 29.07 years 25.07 4.00 By weighting the corresponding figures for Italian provinces (1905) by the ratio of the inheritances in every province to the inheritances in the whole kingdom, he obtains the result for bridegrooms =29.07, and for brides =24.91 years. All these figures are approximately 29 and 25 years. In Italy the mean interval between the date of marriage and the mean date of birth of all children can be taken as aboixt 8 years. The mean age of fathers at the mean date of the births of their children in Italy is probably not far from 34 years, and of mothers from 30 years. These fig\ires agree fairly with those found by Raseri for Udine, viz., fathers = 34, and mothers = 30.5, and for Rome, viz., fathers = 36.5, and mothers = 29.6. Basing his conclusion on these various sets of figures, Gini takes the mean interval between the birth of fathers and children as 35 years, and between the birth of mothers and children as 31 years. Owing to the increase in the duration of adult life, however (presumably for 1882 to 1901 ; vide op. cit., p. 76) he cal- culates from this the interval between the death of parents and children for fathers = 36.17 years, and for mothers =32.17 years. These intervals, bethinks, correspond to the devolution-interval in 78-80% of all cases of inheritance, while in the balance of cases it is not more than 17 years. Taking 80%, this gives the devolution-interval from fathers to sons =32.34 years, and from mothers to daughters = 29.14 years. For adult ages, the difference in the dvrration of life for males and females is about 6 months. Assuming, it would seem somewhat at hazard, that propertj- inherited by males is to pi-operty inherited by females as 3 to 2, and that property left by males is to property left by females as 2 to l,he deduces the devolution -interval id for Italy as 31.8 years ; and by a similar calculation, that for France as 29.4 years. Mallet, he points out, and as mentioned before herein, end eavoiu-ed to determine the devolution- interval by means of the figures shewing the expectation of life of heirs from 272 cases in which all particulars were known ; and used the English Life Tables, 1891- 1900 ^. He fovind the simple means (that is, weighted merely according to niunbers) of the expectation of life i\n = 24, and the weighted mean (that is, weighted by the aggregate amoiuit or product of the numbers and amount per individual) i „, =r 26.9 years. Arguing from the pecvdiaritios in English inheritances (more frequent trans- mission of real than of personal property to lineal descendants, no transmissions of real property to widows, etc.), Mallet thought the devolution-interval sho\ild be taken as about 24 years {loc. cit.), but Gini justly points out, and it is recognised by Mallet, 1. See JoTir. Boy. Stat. Soc, Ixxi., pp. 80-83, 1908. 78 The Estimation of Wealth from Probate Returns. that 272 cases are too limited a basis ; further, that the mean expectation of life may possibly be greater for those possessing property than for others ; and again, that amongst those possessing property it possibly increases with the amount of property. If this were so. Life Tables would be required giving the expectation of life at single ages for possessors of property only, and the figures would have to be weighted according to the amount of property : this cannot at present be done. Harper proposed to use the British Insurance Offices' Life Table O'^^, and by that means found i"^ — 27.4 years. This appears to Gini to be too low, partly because the greater expectation of life of females is disregarded, and partly because the mean expectation of life of heirs was not weighted in proportion to the projDerty inherited. Gini himaelf proposes the use of the difference between the mean age of testators and the mean age of heirs, and to weight the ages proportionately to the property involved, and he arrives at the following conclusions : — " The devolution-interval is given by the difference between the weighted mean age at which persons inherit, and the weighted mean age at which they transmit the inherited property ; where the ages of the various persons are weighted proportion- ately to the amount of the inheritance." Aa, however, it is not possible to follow up individual persona from the moment when they inherit to the moment when they, in their turn, transmit their inheritance, this has to be modified as follows : — " The devolution-interval can be determined, as a first approximation, by meana of the difference between the weighted average age of heirs and the weighted average age of testatoi-3 of the same year." This, denoted by i'd, will be the exact devolution-interval only if the mean duration of life of proprietors remain constant. Since, however, this continues to increase, a second approximation should be made, when the weighted ages of both testators and heirs have been determined for a long series of years, together with the respective values of i'd- Then we are able to state that " the devolution-interval can be determined from the difference between the weighted average age of the testators of a given year and the weighted average age of heirs at id j^ears before." Mallet's calculations, he asserts, fm-nish the data for this. They give the simple and weighted averages of ages of heirs = 45.2 and 41.0 years respectively. From the same figures Gini computes the ages of testators for the two years 1905 and 1906, and found the simple and weighted averages of ages of testators = 64.4 and 69.7 years respectively. This gives the mean devolution-interval = 69.7 — 41 = 28.7 years. Gini maintains, however, that this is too small, because the mean dui-ation of life of proprietors increases with the time. On the other hand it must not be for- gotten tliat the average age of heirs was calculated on a very small number, and that the average age of testators refers to possessors of at least £100. For Victoria, Australia, in 1908, the simple and weighted averages of the ages of testators was found by Gini to bo respectively : — Males. Females. Persons. 64 1 and 72.2 years. 64.1 and 68.2 years. 64.1 and 71.5 years. The Interval of Devolution. 79 For France, in 1900, the simple average age of testators was 61 years 7 months. The use made of this figure in subsequent calculations (by which March found the devolution-interval = 29 years 5 months^ is pointed out by Gini to have been liased upon several erroneous assumptions, viz., that the heirs were supposed to be dis- tributed in ages as the people living, and that the simple mean was satisfactory. March, having found the mean age of the living at the 1901 Census to bo 31 years 2 months, deducted it from the simple mean of the ages of the testators 61 years 7 months, the difference 29 years 5 months being assumed to represent the mean devolution-interval. The computation Gini points out is, however, unsatisfactory, because on the one hand the heirs are distributed in respect of age quite differently to the living, and on the other hand because the calculation of the average age from the simple instead of the weighted mean leads to sensible error. It is, however, to March that credit is due for having first thought of derivins: the devolution-interval from the difference between the mean age of testators and the mean age of heirs. In closing this apercu of Professor Gini's criticism of the devolution -interval method, it may be remarked that he recognises the grave limitations to which it is subject, and on this matter we shall offer later some further observations. It is quite clear that the devolution-interval is dift'erent as between country and country, and the data necessary for its proper computation are at least as elaborate as the data necessary for computing by another and more direct method. Before proceeding with a discussion of tliis, it will not be inappropriate to give Gini's general con- clusions in respect of variotis methods of computing private wealth. These are as follow : — (a) All methods have both advantages and disadvantages. (6) It is impossible to assert that one is theoretically superior to another ; but it must, on the contrary, be held that according to the statistical data available for a covmtry, so is one or the other method the better. (c) Though the method of the devolution-interval seemed, for a long time, to be the safest, new elements of uncertainty are continually being discovered in it ; its application in Italy was, however, justified in the past, inasmuch as the necessary data for the other methods were lacking. (d) The method of the capitalisation of incomes may perhaps give fair results for the United Kingdom, but cannot be based on any secure foundation in other countries. (e) In Sweden, Himgarj- and France the Inventory-method may perhaps lead to the best results. {J) A plausible application of any other method to all forms of wealth can hardly be conceived. But that does not imply that in the valuation of the different categories of wealth it is necessaiy always to use the same method. [The author appears to ignore the essential conceptual difference between the rate-of-devolution method and the interval-of- devolution method.] {g) Further, if in the case of any countrj-, one method appears preferable to the others, the latter may still offer useful elements for the purposes of independent estimate or checking. (h) There are methods, such as that of the proportion between existing and hereditary property, which, although they may not lead to a satisfactory evaluation of the wealth of any given country, may serve in a comparison of the wealth of dift'erent countries, so far as the uncertainty and tlie inexactitude of the evaluations in various countries depend upon imiform circumstances. 80 The Estimation of Wealth from Probate Returns. (i.) Finally, it appears that hitherto the statisticians have been often too exclusive in the choice of their methods, and consequently the maxim to be observed by anyone who undertakes the calculation of wealth is : — " The best method consists in taking advantage of all methods" {op. ciL, pp. 140-141). .3. The defect of the devolution-interval method. — The preceding discussion by Gini of the devolution-interval method exposes the complexity of its assumptions, and reveals something of its inherent uncertainty. The fact that it depends upon so many changing factors, the precise estimation of which is not unattended with difficulty, and the appropriate corrections for which moreover are uncertain, and the further fact that its pitfalls are not obvious, indicate that it should be abandoned if any method, the intrinsic character of which is more obvious, can be employed. It will be seen later that there are elements also which it does not embrace. Professor Gini's very able discussion of the proper computation of the devolu- tion-interval shews conclusively that factors must be apj^hed which take account, not only of the magnitude of successions and of settlements, but also of sex differ- ences in regard thereto, and of the variation of these with time. Let us fix our attention upon the question of the devolution-interval in regard to the persons (with the requisite wealth) living at say the present moment. An infinitesimal group at age x will live on the average say e^. years, e^. being the expecta- tion of life for the age x ; in other words, this period will be the crude devolution- interval for all persons of age x. We will, however, be in error if we assvime that the (I/e3.)th part will pass in one year. In order to find the true amount it will be necessary to take into account the manner in which e^ is ascertained, because the number of persons of any age x does not decrease with the lapse of time in a linear manner. When account is taken of the non-linear character of the decrease it is immediately evident that ive are concerned, not unth the expectation of life or devobition- interval, but with the devolution -rate or instantaneous rate of mortality ; and the average of this taken over one year will be the rate of mortality for the middle of the year. It is, of course, true that there are analytical relations between the " expectation of life" at various ages and the rate of mortality at various ages, l)ut if we posses the latter we need not concern ourselves in regard to the former in order to ascertain with what rapidity the wealth of the community will pass to successors. In fact, the necessity of ascertaining the devolution-interval was for no other purpose than this. From this point of view it is at once seen that the attempt to introduce the general devolution-interval iyito the question is a useless complication, not merely because it needs so many correcting modifications, but also because the fundamental idea that this interval is required, or is the appropriate quantily to use, is really invalid. In short, the crude basis of the idea, viz., that if the existing wealth in anj' generation passes in the interval i to another generation, the ith part passes in one year is not correct. The rapidity of passing is measured by the deatli-rato itself, and in order to measure the rate of devolution of estates it merely requires that the frequency of deaths in various age-groups — and, since the amount per individual passing at death varies with age, the relative importance of each age-group in respect of wealth — should be known. Thus the idea of the " devolution-interval" should be abandoned and in its place the idea of the " rate of devolution," should be adopted, computing this latter by means of the death-rates at different ages, weighted according to the average amount of wealth possessed at these ages. For this purpose only statistics of the rate of mortality for different ages and of the ages of persona dying and of the size of The Rate of Devolution. 81 their estates is needed. It will be seen that the mere statement cf this method indicates at once its superiority over the method of ascertaining the devolution- interval. In principle it is direct and, so far aa it goes, exact. Unfortunately, however, the conception put forward, though lacking nothing in accuracy as regards principle, is inadequate in regard to the proper definition of aU the relevant circumstances. This will appear as we proceed, and we shall endeavour to exhibit its limitations as well as tc illustrate its technique. We shall call the method which we now proceed to examine the " Devolution-Rate Method" in contra-distincticn to the " Devolution -Interval Method." To what has been said, it may be added that the rate-of -devolution method might quite appropriately Ije called the rigorous "parcel method," because the fundamental conception is that the incidence of death is indiscriminate, and therefore those dying in each age-group are, with some limitations, a representative sample of the entire group. CHAPTER n.— THE RATE OF DEVOLUTION. 1. The devolution-rate method. — In his contribution to the discussion of Messrs, Harris and Lake's paper on "' Estimates of the Realisable Wealth of the United Kingdom based mostly on the Estate Duty Returns," ^ Sir T. A. (then Mr.) Coghlan made an important suggestion that the " only true way of ascertaining the wealth of those alive from the an:iovmt of those who had died during a given period, was to take into consideration the ages of persons both living and dying" (p. 736). He advised the formation of age-groups, the finding of " the average wealth possessed by the persons in each category" (i.e., age-group), and then by " multiplying the amount so ascertained by the numbers then living belonging to each category" (group), " they would arrive at the total wealth of the community" (ibid). This suggestion was applied by Mr. Bernard Mallet in his paper of 18th February, 1908 (Jom-n. Roy. Stat. Soc, Ixxi., pp. (55-84, 1908), and he deduced values for England for 1905 and 1906 by this method (loc. cit., p. 74). The statement of the method aa it appears above needs some qualification, which will be discussed in due course. The principle of the devolution-rate method more rigorously stated is as follows : (i.) Assimiing that at each age those dj-ing fairly represent, in respect of wealth possessed, the living at the same age, the ratio at that age of the living to the dying is the factor to be multiplied into the aggregate, wealth possessed by the dying in order to express the wealth of the living. (ii.) Since experience has shewn that the mortality-rate at any age differs as between males and females, and that the average wealth possessed also differs, the wealth possessed by the sexes should be estimated separately in order to secure precision in the results. 1. .Idiirii. Hoy. Stat. Soc. Ixix., pp. 709-732. 82 The Estimation of Wealth from Probate Returns. (iii.) If the incidence of death varies as between different classes of either sex at any age, a like observation to (ii.) applies, mutatis mutandis. (iv.) The effect of all circumstances tending to produce a systematic difference in the average wealth possessed at any age as between the living and dying at that age must be evalued and allowed for, in order to secure correct results. In regard to the last, it will be seen hereinafter that there are such diiferences,. and therefore Coghlan's principle and Mallet's application of it need some amend- ment. The devolution-rate method has virtually been used by Laughton * and by Gini in the work previously mentioned. 2. Discussion and technique of the devolution-rate method.^ — Sufficient has already been said to indicate clearly in what sense the method can be conceived as being founded upon the devolution-rate. In formulating the statement of its technique the notion of the method as a " parcel-method" will be kept mainly in view, though wc shall use either conception indifferently, since they both are appro- priate, and both points of view have value. In some cases it may be easier to grasp the significance of the facts from the one or from the other point of view. The whole matter, however, will appear more definite if it be borne in mind that, subject to certain limitations, the dying are to be taken as a sample of the living in regard to the wealth coming into evidence in the " successions." The limitations referred to, however, are important, for it will be found that there are reasons for believing that the living must be regarded as in some respects differently characterised in regard to wealth from the dying ; and it is also to be borne in mind that the rigoiu- of the " pai'cel" assumption increases as the age-group diminishes, since the death-rate varies conspicuovisly from age to age. We proceed to consider the teclmique of the method. Probate returns reveal the fact that D persons dying in any age-group were, in the aggregate, possessed of the amount of M'ealth xv, say. If they be regarded as a fair sample of the group, then the aggregate of wealth, W, in the same age-group, will be the ratio of the living to the dying {L/D = R say) multiplied into the wealth possessed by the D persons, i.e. : — (3) W= ivL/D = wR = iv/r. in which r, the reciprocal of R, is the death-rate. It has been suggested, however, that the general rate of mortality of the age- group does not accurately represent the class whose wealth comes under review in probate returns, forasmuch as it has been supposed that the death-rate for that class will be less, for example, than that for all classes combined. Thus Mr. A. M. Laughton, the Government Statist of the State of Victoria, expresses the opinion that " it is probable that the rate of mortality among persons having property is below that prevailing in the general community ; and that it will approximate to the rate among assured lives." ^ It may be added that probably each country has its special characteristics as regards this. If the view expressed be just, then the multiplier R will not be strictly correct. This is a point which must hereinafter necessarily be fully considered. 1. Vic. Year Book, 1911-12 pp. 215-217. 2. Victorian Year Book, 1911-12, p. 216. The Rate of Devolution. 83 3. The error of treating the entire population as a single age-group. — The most elementarj- application of the preceding formula would be to treat the entire popula- tion as forming a single age-group, that is, to assume that the living and dying are similarly constituted as regards wealth. In this case the aggregate of wealth, \V, of the community, or at least that part of it which ivoiild pay probate, is : — (4). W Pw/D = W/T Rw; the heavy letters having the same meaning as indicated above, viz., in § 2, but applying to the entire probate-paying group. We shall see later that this assumption leads to a result very much in excess of the truth, if applied to the entire population. For in the State of \'ictoria for the years 1908 to 1912 inclusive, we obtain the following results, I. to IV., according as they are calculated for males and females together or separately. In the Table hereunder (I.) shews the result obtained by computing with the total population as a single age-group ; (II.) shews that obtained by computing with all males as a single age-group ; (III.) is based on a computation with all females as a single age-group ; and (IV.) giv^es the result obtained by combining com- putations (II.) and (III.). Table shewing Corrections required for various methods of Estimating Wealth from Probates, Victoria, 1908-1912. Item. Year 1908. 1909. 1910. 1911. 1912. (I.) Net Value Estates, "Persons" (Unit £1000) Reciprocal of Death-rate . . Product (Unit £1,000,000) (1) .. 6,717 78.68 528.5 6,178 87.36 539.8 7,031 87.05 612.0 7,976 7,776 86.78 81.77 692.2 635.8 Factor to correct t Error of Method (reciprocal of factor) Correctly deduced amount (Unit £1,000,000) .3275 3.053 173.1 .4138 2.411 223.3 .3.542 2.823 216.8 .42161 .3954 2.372 2.529 291.8: 251.4 (II.) Net Value Estates, ''Males" (Unit £1000) Reciprocal of Death-rate Product (Unit £1,000,000) (2) .5,580 69.04 385.2 4,883 76.92 375.6 5,481 78.08 428.0 6,382 78.75 502.6 5,962 74.65 445.1 Factor to correct t Error of Method (reciprocal of factor) . . Correctly deduced amoimt (Unit £1.000,000) .3341 2.993 128.7 .4219 2.370 158.5 .3580 2.793 153.2 .4343 2.303 218.3 .4099 2.440 182.4 (III.) NetValue Estates, "Females" (Unit £1000) Reciprocal of Death-rate Product (Unit £1,000,000) (3) . . 1,137 90.92 103.4 1,295 100.6 130.3 1,.550 98.12 152.1 1,594 96.55 153.9 1,814 90.36 163.9 Factor to correctf Error of Method (reciprocal of factor) . . Correctly deduced amount(Unit £ 1 ,000.000) .4292 2.330 44.4 .4969 2.012 64.7 .4174 2.396 63.5 .4775 2.094 73.5 .4204 2.379 68.9 (IV.) Sum of (2) and (3) (Unit £1,000,000) Factor to correct *f Error of Method (reciprocal of factor) . . Correctly deduced amount(Unit£ 1,000,000) 488.6 505.9 580. 1 656.5 .3543 .4414 .3737 .4445 2.822 2.266 2.676 2.250 173.1 223.3 216.8 291.8 609.0 .4126 2.424 251.4 • Is not required practically. t To give the results of infinitesimal grouping. 84 The Estimation of Wealth from Probate Returns. It will be seen from these results that, when males and females are treated separately, the sum of the two is uniformly less (on the average about 5h per cent.) than when the population is treated without distinction of sex. This is due to the great disparity between the amounts contributed by females and males. From what is shewn later it will be seen further that correction factors are necessary ; these are shewn in the table and indicate the magnitude of the error in the assumption that the results for all ages can be treated as a single group as has often been done ; it will also be observed that these correcting factors are different from j^ear to year. The correction-factor for "persons," for the average of the 1908-1912 results, is 0.3822. Here it may be observed that any popvilation consists roughlj- of equal nvunbers of the sexes, but the data shew that not only have females on the average much less wealth than males, but also there are fewer possessing wealth ; hence result (1), see table, based on the number of persons, will in general be of less accuracy than that based upon a consideration of the data for the sexes treated separatelJ^ An analogous observation applies to the age-groups among either sex. It is due to this latter that the large correction factor is required, and to this we shall now refer. The correction-factor for the average of the 1908-1912 results for " males " is no less than 0.3908 ; and the correction-factor for " females," on the same basis, no less than 0.4471. (The way in which these correction-factors are deduced is explained hereinafter.) It is fairly evident from these examples that the method, even with the use of the deduced correction -factors, cannot be expected to yield results of high acciuracy, since the correction-factors vary greatly from year to year. Assuming that the persons of each age dying are characterised, in respect of wealth possessed, similarly to those living of the same age, then it follows that for the dying to correctly represent the living, it is essential either that the numbers dying in each age-group must be proportional to the numbers living in the same groups ; that is to say, the death-rate must be the same for all ages, or that by some complex relation the wealth-ratio will be fortuitously identical. The latter supposition is obviously excluded as a general possibility ; and above .5 years of age the death-rate is small where the numbers of the popiilation are relatively large, and large (for the older ages) where the numbers of the population are relatively small. Hence, a priori, it is obvious that the whole range of life cannot be treated as a single age- group. To do so cannot yield an accurate result, or one even approximately correct. We have already seen that it does not do so, for the correcting factor, instead of being nearly unity, was only about 0.4. 4. The error of estimations of wealth by attributing it to a single age-group of 21 years and upward.^ — The characteristic defect in the assumption that the popula- tion may be treated as a single age-group will apply to any large age-group, but will be less seriovis if we exclude the ages, viz., the earlier ages of life, which, while they contribute little or nothing to the probate-returns, exhibit considerable fluctuations in their death-rates. It has sometimes been assumed, in estimating wealth from probate-returns, that it would be sufficiently accurate to regard adult lives as constituting a homo- geneous group, and consequently that it would be satisfactory to suppose that the whole of the wealth disclosed in such retiuTis coiild be divided by the total number of adults dying in order to obtain the average per individual. This, it was thovight, could be regarded aa the average wealth per head of all adults ; hence, by multiply- The Rate of Devolution. 85 ing this average by the total number of adults living, the aggregate private wealth would be ascertained, subject of course to some correction for tlie fact that there is no necessity to make probate returns for less than a certain amount. This very erroneous method has even been usetl in official statistics. The method approximates, however, somewhat more closely to the truth than the previous assumption imder which the entire population was treated as a single age-group, and was used in Victoria for estimating tlie average net value of estates for 1898-1902. The amount per head of deceased adults was computed, and this amount, multiplied by the nmnber of adults at the middle of the period (or rather those disclosed at the Census of 1901) was regarded as indicating the total private wealth. It will be seen later that the error of this assvunption is considerable, and that the method should not be followed. As already indicated, it virtually treats the entire population (of both sexes) of 21 years of age and upward as a homogeneous age-group, and attributes the net wealth disclosed in the probate returns to the adults dying. It therefore supposes that they may be taken to fairly represent the adults living, and that no serious error will be made in supjaosing that the whole wealth of the commiuiity belongs to the adults. In this method the value of R in formula (4) will be the reciprocal of the death- rate for all ages from the beginning of 21 iipwards, and the magnitude of its errors is fvilly illustrated in the tables hereunder, that is to say, the result so deduced must be multiplied by the correcting factor indicated in the table to give the proper result. This factor would be, of coiuse, unity if the method were correct, consequently its reciprocal shews the magnitude of the error arising from neglecting it. Table of Corrections for Results (wrongly) based upon assumption that Wealth disclosed belongs wholly to those of 21 Years of Age and upwards. Year. 1908. 1909. 1910. 1911. 1912. i 1908-1912 Reciprocal of Death- Males rate 21 to end of life Correcting factor to be applied to result . . 53.43 0.4317 58.76 0.5524 60.20 0.4643 59.86 0.5714 58.74 0.5209 58.156 0.5066 Reciprocal of Death- ' Females i rate 21 to end of life 72.30 Correcting factor to be applied to result . . 0.5398 78.19 0.6393 77.24 0.5303 74.33 0.6202 72.82 0.5216 74.884 0.5678 Reciprocal of Death- Persons rate 21 to end of life 61.68 Correcting factor to be j applied to result . . i 0.4551 67.32 0.5753 67.82 0.4821 66.41 0.5831 65.11 0.5212 65.619 0.5221 It is seen from this that the factor of correction has increased, but it is still only about 0.5 ; that is to say, this method gives results uhich are about double their true value. 5. Determination of factors for correcting large group-results. — It has already been indicated that if the population be taken either as a whole, or as adults of 21 years of age and upwards, we obtain, aa the average result of Victorian probate returns for 1908-1912, an indication that the following corrections are required : — S6 The Estimation of Wealth from Probate Returns. Factors of Correction, based on Victorian Probate Returns, 1908-1912. Group considered. Correcting Factor when Computation embraces : Error of Neglect of Correction Factor. "Per- sons." Males. Females "Per- sons." Males. Females All ages Adults (21 and over) . . 10-year groups 1-year groups . . 0.3822 0.5221 0.9855 0.9997 0.3908 0.5066 0.9873 0.9997 0.4471 0.5678 0.9817 0.9997 2.616 1.915 1.0147 1.0003 2.559 1.974 1.0129 1.0003 2.237 1.761 1.0186 1.0003 As the method followed increases in precision, the correction-factor approaches unity, hence it is evident that there is no material advantage in considering "adults" as a homogeneous age-group, as compared with the assumption that the entire population can be so regarded ; and this is so even if the sexes be separately con- sidered. It has not yet been indicated in what way the corrections have been deduced. It will suffice, however, to note that the validity of the assumption of homogeneity increases as the age-group taken diminishes (supposing, of course, the numbers to be sufficiently great) ; and since the sexes are very differently characterised as regards wealth, it is necessary to treat them separately. Hence formula (3), viz., W — Rw, flhould be applied to small age-groups only, and their sums taken. (The sexes should also, of course, be treated separately). It is established later that 10-year groups require a correction factor of sensibly unity (0.98 to 0.99), and single year groups practically no correction at all (0.9997). The details will appear later. It will suffice here to observe that a theoretically ideal method supposes that the continuous variation of both R and tv is determined according to age, and that the methods of the infinitesimal calculus are employed, see formula (21) hereinafter. 6. Determination of the multipliers, independent of, and dependent upon the death-rate, for deducing the total wealth from the wealth disclosed in probate. — For rough computations, and on the assumption that the relative amount of wealth according to age and the death-rate according to age remain constant, a factor may be readily determined which, multiplied into the total wealth disclosed, will give the aggregate for the same class in the population (living) of the same age. Further, if it be supposed that any increase or diminution of death-rate affects the death-rate at all ages similarly, a factor may be computed which will take account of the changing death-rate and permit of the introduction in the formula of the reciprocals of the death-rate for any particular j^ear. These factors are denoted respectively by the letters h and a, the approximate values being accented, and the exact values, computed on infinitesimal methods, being unaccented. We proceed to the detailed consideration of the matter. The fundamental assumption is that, in each age- group, the ratio of those persons dying whose estates come under review for probate, to the total number in the group actually dying, is the ratio d/D (or deceased persons possessing estates to total dying), and that this holds for the living. It must also be assumed that the average value of the estates for such age-group is the same for the living as for the dying. On these assimiptions we may deduce the required factors, viz., those which, multiplied into the total wealth disclosed by probate, will give the aggregate of estates similarly liable to come under review for probate. The Rate of Devolution. 87 Let this factor be denoted by k' ; then obviously, by mere definition : — (5) k' {w^ + 10,^ + etc.) = W^ + Wg + etc, = W, say, the total wealth, the suffixes denoting here the successive age-groups. But since it is assumed that the distribution of wealth among the living is the same as among the dying, it follows that, for each age-group, W = Pw/D = Rw ; that is, the recipro- cal of the death-rate for the age-group multiplied by the wealth revealed in the probates for the group. Hence, substituting this for W, and dividing both sides of the equation by if , + ^w., + ^tc. = Hw, we obtain (6) it' = 'E,{R . w/Sw); each suffix for R being the same as that for the corresponding w throughovit. That is to say k' is the weighted value of the R's, the weights being the relative dis- tribution according to age of the wealth disclosed by probate. From the last formula it is at once evident that the factor k' depends merely upon the product of the relative distribution of wealth according to age into the reciprocal of the death-rate according to age ; that is, it is affected by changes both in the distribiition of wealth according to age, and in the mortality according to age. The result is important, for it exposes definitely the invalidity of the attempts to deduce this factor merely from the duration of a generation, from the general death- rate, or the expectation of life at age 0, or by any similar process ; in short, it shews that what is known as the devolution-interval method, which we have already con- sidered at length, is an invaUd method, There is, of com'se, as already implied, no necessary relation between the factor k' and the general death-rate for either sex (or for " persons") of the ages diu'ing which it is found through probate that wealth appears in evidence (or if we please, the death-rate for all ages), a point to which reference will be made later. Let, however, a' be a factor which, multiplied into Rq, the reciprocal of this death-rate,* will give k' ; that is : let — (7) a'Ro = k' ; so that a'i?o ('<^i + Wg "^ ®**'") ~ ^ then of course — (8) a' = k'/Ro = lliRto) / {Ro .'^w) By applying this formula it can be discovered whether a ' is fairly constant. More accurate results will, of course, be obtained if the factor be deduced for the sexes separately, the method becoming quite rigoroiis when the age-groups are infinitesimal. From what has preceded it is clear that it is impossible to deduce the factor which must be multiplied into the wealth appearing in probate retm-ns, unless at least two things are known, viz., (a) the relative amount of wealth contributed by people in the different age -groups ; and (b) the death-rates for the ditl'erent age-groups, or, as will be shewn, their relative ^■alue. * That is, for all ages or for the range of ages appearing to be of conseaiience in probate matters. ss The Estimation of Wealth from Probate Returns. In all probability the second of these (b) dc es not in general change very rapidly with lapse of time ; the former (a) changes somewhat irregularly because of the irregular way in which large estates come under review. To find the values of Rw/Hw it is, of course, necessary to have the absolute death-rates ; but if we assume that the death-rates in each age-group vary as the . general death-rate, then their mutual relation is sufficient, taken in conjunction with that general death-rate. It will be most convenient to work with reciprocals 1/r^ etc., of the death-rates, say R , R , etc., or to find the relation of these to the reciprocal of the death-rate for the aggregate of all groups concerned, R^ , say. That is, if the values oi p = R / R^ , p ^z= R / R^, etc., be found, it might be expected that they probably will not •change greatly tor moderate intervals of time, and, given these for any epoch, the group-rates can be approximately determined therefrom by multiplying by the general death-rate or death-rate of the aggregate. Hence from (6), (7) and (8) we have : — (9) k' = R,)^ ipu') / Hw, and (10) a' = ^ipio) /2w; or, if u be written for w/llw, then this last expression takas the form (11) a' = p,u, + pjj,^ -f etc = 21 {pu) which is independent of the absolute values both of the death-rate and the wealth at each age. Then it would follow that (12) W = a'i?o2w = k'I,w that is to say, the aggregate wealth of the living (whose estates would be subject to probate) is the product of the wealth actually appearing in probate returns, multi- plied by the product of the factor a' into the reciprocal of the general death-rate ' (or the death-rate of a large group of ages, e.g. 15 to 85). 7. Should the general death-rate be used ? — Before furnishing numerical results for comparisons, the questions may be considered whether Rg may be taken as the general death-rate, or whether it should be the death-rate for the ages within the limits for which probate returns appear. These may be taken as from say 10 or 15 years of age upwards. The death-rate for the ages to 9 and that for the wliole ■of life in the State of V^ictoria are respectively : — Death-rates, Victoria, 1908-1912. Years. 1908. 1909. 1910. 1911. 1912. 1908-12. Age-group, 0-9 Males '"emales Whole of life Males Females .0157 .0125 .0144 .0110 .0135 .0105 .0130 .0099 .0139 .0112 .0128 .0102 .0131 .0105 .0127 .0104 .0154 .0127 .0134 .0111 .0143 .0115 .0133 0105 Being thus approximately identical throughout, there would apparently be no striking advantage in taking /?„ as the recijjrocal of the death-rate for all ages from 10 years of age to the end of life ; it will probably be always siifficient to take it as the reciprocal of the general death-rate. Later this point will be further discussed. The factor a ' may be regarded as a correcting factor to a crude result obtained by multiplying the total wealth by the reciprocal of the general death-rate. The Rate of Devolution. 89 To compute a value of the factor a' or of the factor k' , to be applied to " per- sons," it is obvious that in the former case we must take account of differences in the wealth contributed, and in the latter the differences both in weaUli and death-rates. To compute this for persons, let a '„j denote the factor for males, a '/ for females, and a\ for persons ; 'Lio^, Hw/, and Su-^ the aggregate wealth, subject to probate, for males, females, and persons respectively ; and Rm, Rf, and Rp the reciprocals of the death-rates for males, females, and persons respectively : then obviously the weighted result is : — (13) a' = {a\nRm^' a'jRf^uy)/Rj, ^iVp and these formulae will, of course, though only approximate, probably be sufficiently accurate for practical pmposes. For strictly accurate results the values of a' and k' for " persons" should be determined directly, in the same manner as for males or for females. 8. Estimation of the uncertainty in the values of the correction-factors.— It is obvious from what has preceded that the results deduced from single years must be sxibject to a considerable margin of uncertainty. The irregularity of the appearance of large estates in the returns necessarily involves this, and the fact is perhaps more strikingly seen in the values deduced for the coefficients a' and k' which, it will later be shewn, are sufficiently accurate for the purpose in question : — Victoria, 1908-1912. Values of a' Values of k' Year. Males. Fe- males. "Per- sons." Males. Fe- males. " Per- sons." 1908 1909 1910 1911 1912 .338 .427 .363 .440 .415 .438 .506 .425 .487 .444 .332 .420 .359 .427 .405 23.3 32.9 28.3 34.6 31.0 .39.8 50.9 41.7 47.0 40.1 26.1 36.7 31.3 37.1 33.1 Group Value, 1908-12 Average Value .3961 .397 .4556 .3878 .460 1 .389 1 29.86 30.0 43.33 43.9 32.65 32.9 Since both these coefficients are independent of the absolute amount of the wealth revealed in probate returns, and a' is also independent of the absolute death-rate, it is clear that for any one year these returns can afford only a very rough indication of the wealth possessed by the liviin/. FiVen quinquennial rt^sults are inadequate to furnish anything like a very exact estimate of the margui of uncertainty. In the absence of anything better, however, a deduction may be drawn by applying the theory of errors. If then the averages be taken (shewn in table) and the probable error of a single value and of the average is deduced by applying the usual formulae, viz. : — /j Iw1 ] (15) p = i)robable error of single year =0.674 "y , _ i i' • /j [^] 1 (16) po = probable error of » years = 0.674 \ („(,, _i) | • then the results are as follow, viz. : — 90 The Estimation of Wealth from Probate Returns. a' ± 1 k'± Range of Probable Error. Males. Females. Persons. Males. Females. Persons. For the probable error of a single year Tor the probable error of a mean of 5 years .030=7^5 .013=3.3 % .023 = 5.1 .010 = 2.3 % .028=7.2 .012=3.2 % 3.0 = 10.0 1.3=4.5 o/ 3.3 = 7!5 1.5 = 3.3 3.0 = 912 1.4=4.1 There are, no doubt, much larger " systematic " errors than these, viz., errors due to the tendency to make the element of estimate of value a " conservative one," but such errors cannot be readily determined, and their estimation is not a question of mathematical technique. Quite apart from this the ivealth deduced from the aggregate coming under review in probate in any one year is probably in error not les.i than 7%, even if the death-rate be taken into account, and not lesfi than 9% if %t be neglected ; and further, the mean of five years' results reduces these amounts respectively only to about 3% and 4%. Group-values for 10 years would pro- bably be only 2% in error in either case, and the deduced result could be regarded as applying to the middle of the period. 9. Cause of uncertainty in results. — In order to see whether deductions of wealth from probate returns are entitled to much confidence, the effect both of the absolute amounts of the wealth in the returns, and the absolute values of the death-rates should be eliminated. To do this it will suffice to compute a table of values of u, viz., of the ratios of the wealth passing at any age to the total w^ealth passing, and also one of values of pu, for a series of years, for which pvirpose the Victorian data for the years 1908-1912 are taken (see tables hereunder). Variation in the values of u is, of course, caused by the irregular appearance of large estates among probate- returns. Even for a considerable population, the frequency with which very large estates appear in such returns will be irregular compared with that with which smaller estates appear. This is conspicuously shewn in any returns of the number of estates of different magnitude. We take an illustration from Prussian retvmis, the reason for obtaining which has now become manifest : — Prussian Estates of Various Sizes, 1911. Size of Estates Number of Estates Relative Frequency Size of Estate in Millions Sterling. Over 5 1 Over 1-5 to 5 30 Over- 769 to 1-5 88 22 Over- 371 to -769 329 82 Over- 175 to -371 1,003 251 Over084 to - 1 75 3,003 751 It is at once obvious froni this table that the falling in of very large estates through death will be rare ; nevertheless, when it does occur, it will greatly prejudice the evaluation of the factors a and k for the year in question, since the ratio of ii = w/llw for some particular age-group will be greatly altered. Obviously we are not con- cerned with changes in the abfiolute amounts, but only in their ratio to the total, azid this is what is shewn in the tables hereinafter. Similar remarks apply to variations of death-rate, but there is no reason to lielieve that these fluctuate greatly. In the following table any effect due merely to variations in the absolute amount of wealth is eliminated as explained. The ratio of the wealth of each group to the total is expressed from year to year in the upper part of the table. In the lower part of the table is given the product of this ratio, into the ratio which the reciprocal of the death-rate of this group bears to the reciprocal of the general death-rate : — The Rate of Devolution. 91 Values o£ u and of pu, Victoria, 1908-1912. Males. Females. Age- Group. 1908. 1909. 1910. 1911. 1912. 1908- 1912. 1908. 1909. 1910. 1911. 1912. 1908- 1912. * Values of u. (Total net value of probates for all ages =1^ 10-U .. 000 000 000 000 000 0001 000 000 001 001 000 0004 15-20 .. 001 000 000 001 001 0006 002 001 001 001 001 0010 21-29 .. 006 015 005 006 006 0075 007 012 005 010 013 0093 30-39 . . 017 018 021 021 019 0191 031 042 052 030 027 0360 40-49 . . 053 081 064 093 069 0723 099 077 060 078 066 0746 50-59 . . 105 117 090 147 181 1298 101 182 095 199 123 1406 60-69 . . 170 241 223 212 186 2051 249 244 189 189 174 2041 70-79 . . 310 342 400 295 298 3269 282 255 435 319 409 3484 80-89 .. 315 176 188 215 222 2244 214 178 138 134 135 1553 90 & over 023 010 009 010 018 0142 015 009 024 039 052 0303 ♦Values of pu. (Total net valvie of probates for all ages = 1). 10-14 .. 001 000 000 001 001 0005 000 002 005 005 000 0025 15-20 .. 003 001 002 003 005 0028 007 003 002 007 002 0041 21-29 .. 021 056 017 021 021 0258 018 030 012 025 034 0243 30-39 . . 039 044 049 049 044 0449 060 077 096 055 057 0691 40-49 . . 065 103 082 140 092 0952 121 094 089 108 101 1014 50-59 . . 087 087 070 107 131 0981 088 171 079 163 099 1204 60-69 . . 059 080 075 064 061 0677 088 083 072 073 064 0745 70-79 . . 043 045 054 041 044 0454 039 034 061 042 062 0484 80-89 . . 020 012 013 013 016 0150 014 012 009 008 024 0099 90 & over 001 000 000 000 001 0006 001 000 001 001 002 0009 * A decimal point is to be understood as preceding each of the values. It will at once be seen how greatly the values for any age-group differ from year to year. Moreover, they differ considerably as between localities. The State of- New South Wales is in most respects comparable to that of Victoria. Its population, social and economic progress, and racial characteristics are sensibly identical, and it might reasonably be expected that the values of u or of pii would be identical for the two. But that the fact is far otherwise appears from the values given in the following table : — Age-groups 10- 15- 21- 30- 40- SO- 60- 70- 80- 90 & 14 20 29 39 49 SO 69 79 89 over N.S.W. 1911 u (males) 000 001 007 027 077 175 243 343 119 009 Vict. 1911 000 001 006 021 093 147 211 295 215 010 Vict. 1908-12 000 001 007 019 072 130 205 327 224 014 N.S.W. 1911 (ii) females 002 001 032 038 039 061 137 191 501 028 Vict. 1911 001 003 021 049 140 107 064 041 013 000 Vict. 1908-12 001 003 026 045 095 098 068 045 015 001 N.S.W. 1911 (pu) males 003 002 021 059 094 114 076 043 007 000 Vict. 1911 000 003 021 049 140 107 064 041 013 001 Vict. 1908-12 001 003 026 045 095 098 068 045 015 001 N.S.W. 1911 ipn) females 000 002 008 069 050 043 040 024 027 001 Vict. 1911 005 007 025 055 108 163 073 042 008 001 Vict. 1908-12 002 004 024 069 101 120 074 048 010 001 Note. — A decimal point is to be understood as preceding each of the above values. 92 The Estimation of Wealth from Probate Returns. The results shew that even for a community which may be supposed to be similarly circumstanced economically, an identical factor should not be assumed ; for u, though independent of the absolute amount of wealth, and pu both of the absolute death-rate and the amount of absolute wealth, vary considerably. The fact i=. that the proportion of persons dying who contribute to the probate returns to the general population of the same age-group is very variable, viz., for the reasons above indicated. These last tables reveal the fact that results from year to year materially differ and, since it is evident that the aggregate of wealth itself of the whole community does not fluctuate in this erratic way, the inference to be drawn is that, to secure anything like a reliable estimate, the average for a number of years should he taken, preferably, it is thought, ten, since that is long enougli to include the ordinary periods of financial vicissitudes. ^ It has already been mentioned that Gini had noticed the effect of change in the mean duration of life upon the devolution- interval. A like remark applies also to the factor R, which is to be multiplied into the wealth contributed by each age-group of deceased persons. A careful examina- tion of the evidence in the last three tables will shew an indication of progressive change with time. If the death-rate diminish, the factor R will increase. And here it may be stated that Australian mortality experience (1881-1890 and 1901-1910) shews the necessity of recognising that no factor can be regarded as of constant value. We now pass to the consideration of this point. 10. Effect of change in the rate of mortality^ upon the computation of private wealth. — The change of the death-rate for almost every age-group in Australia is remarkable. This is seen 'n\ the followmg table : — Values of R., viz., Numbers Living to 1 Dying.* Per- Exact Males- —Australia. Males — Q'land. Females — Australia. Females — Q'land. sons Age. Eng. 1886. 1896. 1906. 1886. 1896. 1906. 1886. 1896. 1906. 1886. 1896. 1906. 1911t. 0-5 23.9 28.5 37.4 21.6 29.8 39.3 26.8 32.5 43.8 24.2 34.3 45.6 24.4 5-10 254.5 329.6 452.1 249.0 294.1 451.7 284.9 344.8 499.0 302.7 323.2 495.0 312.7 10-15 394.3 439.8 517.6 352.4 444.0 495.5 419.8 517.6 566.9 452.5 565.0 625'8 522.0 15-20 188.0 271.0 328.3 t63.1 162.0 270.6 253.2 315.1 375.1 202.1 409.8 434.4 549.9 20-25 126.7 187.1 247.3 t48.8 116.9 191.8 168.2 224.6 270.4 123.5 256.8 285.9 313.3 25-30 115.0 152.5 208.9 t65.5 107.2 167.2 129.0 170.7 213.4 105.1 173.0 222.2 [241.2 30-35 112.2 134.4 178.3 t72.9 104.2 144.2 118.5 139.8 178.4 108.1 145.2 179!3 35-40 98.1 113.1 142.0 81.4 91.5 117.6 102.9 119.8 151.4 100.6 122.8 151.1 [ 148.1 40-45 80.4 95.5 108.8 67.8 84.7 94.4 91.8 118.7 132.1 87.4 121.1 127.2 45-50 62.5 76.0 82.6 54.5 70.0 72.4 79.4 99.6 116.4 81.7 102.4 112.7 [ 78.4 50-55 47.4 57.3 64.2 44.4 51.5 55.4 64.1 77.7 93.5 71.5 76.9 91.0 55-60 35.6 40.3 47.3 35.2 38.8 43.2 48.5 55.3 66.3 54.2 56.2 64.4 \ 36.8 60-65 27.0 27.6 32.4 26.4 29.8 30.5 36.5 37.6 42.7 39.2 39.1 40.4 65-70 17.8 18.9 20.8 19.2 20.2 20.0 22.3 26.2 27.2 26.7 26.9 26.1 } 17.2 70-75 13.2 13.8 12.9 14.1 14.3 13.9 16^5 17.1 16.4 18.8 18.4 18.3 75-80 8.58 8.70 8.42 9.79 9.43 9.21 10.1 10.1 10.4 11.6 11.0 11.5 1 80-85 5.89 5.70 5.74 6.70 6.54 6.26 6.19 6.51 7.07 7.28 6.99 7.31 85-90 4.13 4.01 3.89 4.60 4.77 4.26 4.53 4.49 4.63 4.92 4.96 4.75 \ 7.5 90-95 2.95 2.96 2.62 3.29 3.61 2.85 3.03 3.16 3.04 3.45 3.69 3.08 95-100 2.11 2.10 1.79 2.21 2.81 1.91 2.23 2.08 2.01 2.28 2.25 2.03 1 100-105 0.73 0.63 0.71 0.72 0.89 0.71 0.75 0.71 0.72 0.78 0.71 0.72 1 * These are the nuiiiluTs that must be multiplied into the wealth appearing in the net values in the probate returns fur tlif a^^■-^'n>u1^s in iiuesticjn. Thev depend upon 10-years' results, viz., 1881 to 1890, 1891 to 1901), and 1901 to 1910 inclusive. t These depend upon 3-years' residts, viz., 1910, 1911, 1912, and the population of 1911 only. t The smalhiess of these numbers is due to the heavy death-rate for the ases in question. The Queensland climate was apparently inimical under the conditions of early settlement, but is now very satisfactory. 1. In a conmiunication made by the writer to the IMinister of Home Affairs of Australia, in February 1910, it was stated that ten years' experience would be necessary for a reliable basis for an estimate of tills character. It will be seen that these results confirm that opinion. 2. This has been considered in the -Appendix A to Vol. I. of the Report on the Census of the Com- monwealth of Au.stralia ; see pp. 378-389. The Rate of Devolution. 93 The values of R are based upon tlie Life Tablea prepared in connection with the 1911 Australian Census, and shew how very different these values may be for different States, those for Queensland being given Ijy way of com- parison with the values for the Commonwealth. They also show that the factors by which the amovmts revealed in probate must be multiplied vary very markedly with time. The results for the past 30 years may be very fairly represented by an ■equation of the form — • (17). Rt = Ro + at In the following tables the reciprocals of the death-rates are given bj'^ formulae of the above type : — Secular Changes in the Reciprocals o! the Rates of Mortality, Commonwealth of Australia, 1881-1912. Males. Values of R* Relative Weight for Probate. Females. Values of R. Relative Weight for ProVjate. Age. Vict. Experi- N.S.W. Experi- Vict. Experi- N.S.W. Experi- ence, ence, ence, ence, 1908-12. 1911. 1908-12. 1911. 0-9 30.6+1.37 t .0000 .0000 33.1 + 1.77 t .0000 .0000 10-14 . . 339.7 + 1.45 t .0001 .0004 384.2^8.09 t .0004 .0015 15-20 . . 144.2 + 7.08 t .0006 .0005 205.7 + 6.30 t .0010 .0005 21-29 . . 83.7 + 5.52 t .0075 .0066 120.0 + 4.37 t .0093 .0032 30-39 . . 81.7 + 3.08 t .0192 .0271 85.9^3.23 t .0360 .0383 40-49 . . 66.2 + 1.11 t .0723 .0771 76.9 + 1.91 t .0746 .0386 50-59 . . 37.4 + 0.68 t .1297 .1750 48.2+1.16 t .1406 .0613 60-69 . . 20.3 + 0.22 t .2051 .24.25 27.1 + 0.27 t .2041 .1366 70-79 . . 11.4—0.01 t .3269 .3428 13.2^0.02 t .3484 .1912 80-89 . . 5.5-0.01 t .2244 .1191 5.4 + 0.03 t .1553 .5012 90 & over 3.0-0.01 t .0142 .0089 3.0-0.00 t .0303 .0276 1.0000 1.0000 1.0000 1.0000 * Note. — t = r— 1880, where T is the year for which the value is to be found. If these are weighted according to the average wealth contributed in five yeara* experience (1908-1912) in Victoria, and one year's experience (1911) in New South Wales, the following resxilts will be obtained, viz. : — Change of i?o with Time. State of— Males. * Females.* Persons, t Victoria, 1881-1912 Ro = NewSouth Wales, 1911 T?, = 21.12 + 0.3242« 24.13^0.3867 < 28.14 + 0.5388 < 19.29^0.3536/ 22. 6 J- 0. 368 « 22.7 + 0.376 < * Exact. t Approximate results only. The result for persons has been deduced merely from the result for males and females by weighting according to the total wealth, or, what is the same thing, by the population and wealth contributed per individual; that is, it has been computed by the formula : — (Ao) Kp = — , approximately only. 94 The Estimation of Wealth from Probate Returns. These resvilts, dedviced from the death-rates for the Commonwealth, are applic- able to the Commonwealth only on the supposition that the mean Victorian dis- tribution of wealth apcording to age for the period 1908-1912 apjolies, or that New South Wales distribution in 1911 applies, as the case may be. The close agreement for "persons" is merely fortuitous, and the results differ sensibly for both males and females owing to the very different distribution of wealth according to age. At the present time the necessary information does not exist for a rigorously accui'ate computation applicable to the whole of Australia. 11. Arithmetical example of effect of progressive change in death-rates. — The effect of the variation in the death-rate can be made arithnietically apparent by adopting a known distribution and applying it to the reciprocals of these rates. For five-year age groups from 15-20, 20-25, etc., to 100-105, one smoothing of the resxiltg. for males and females gave the following proportions in ten thousands, viz. : — Males 6 27 53 83 130 279 463 616 744 890 1,124 1,462 2,086 1,392 495 123 26 1 Females 8 27 72 143 230 350 492 621 774 1,008 1,361 1,701 1,532 967 466 188 57 3 These, multiplied by the reciprocals of the group death-rates, gave the following results, viz., those in the left-hand side of the table : — Variations in the Values of k ' and a ', through Changes in the Death-rates, Australia. Values of V Values of a' Year. Commonwealth. Males. Females. Queensland. Males. Females. Commonwealth. Males. Females. Queensland. Males. Females. 1886.0 1896.0 1906.0 24.29 26.20 29.52 32.45 37.73 43.25 21.77 24.88 26.94 37.96 39.01 42.79 .4024 .3749 .3666 .4438 .4358 .4288 .4213 .3539 .3265 .5574 .4112 .3769 These quantities (on the left-hand side, h' , see formula 9) are the factors — if the distribution of the total wealth in each age -group be as supposed, which, multiplied into the aggregate wealth appearing in any probate return, give the aggregate of the wealth of the living of all ages taken together. The quantities on the right-hand side are also factors, but must be multiplied by the reciprocal of the general death- rate. The quantities on the right-hand side are the values a', which, when mxilti- plied by the reciprocals of the death-rates (of males, females, or persons as the case may be). The quantities k' and a' can be used with death-rates for ages 15 to 85, the important period of life as far as probates are concerned, or ages 15 to 105, or yet again, to 105, that is to say, the ordinary crude death-rates. Inasmuch as these last are always the most readily available, it is preferable to adopt them.^ The values of bbth k ' and a ' are given in the table above for the Commonwealth and for Queensland, because the progression of the death-rates was so entii'ely different in the two cases, and this is reflected in the results, although the distribution of wealth is assvumed to be identical. 1. The average over a quinquennium or a decennium will always be sufficiently accurate, as is abundantly manifest from the following results for the Commonwealth : — Males 1886.0 1896.0 1906.0 Females . . 1886.0 1896.0 1906.0 Average of rates Decennial rate . . Census rates 0-105 15-105 15-85 16..597 16.565 16..")64 15.213 14.894 14.318 14.298 14.299 13.844 13.436 12.453 12.426 12.416 12.997 12.478 13.703 13.677 13.678 11.467 11.186 11.578 11.553 11.550 10.521 10.149 9.945 9.920 9.915 10.136 9.625 These death-rates are expressed per 1,000 of the same se.x. The Rate of Devolution. 95 12. Correction to reduce group-results to results given by a continuous curve. — We have seen that if the whole laojjulation be treated as a single age-group, the error is 80 great that we get the correct result only after miiltiplying by about 0'4. If we treat the whole of the wealth as belonging to persona of 21 years of age and upwards, which is substantially true, the factor of correction becomes about 0'5, that is, it is slightly nearer unity. It is, of course, also true that even a ten-year group will not give a theoreticallj' faviltless result, since the smaller the group the more accurately will the facts be represented, inasmuch as, in their ideal form, the curves of variation of wealth with age, and of deatli with age, must be regarded as continuo\.;s. In tlie nature of the case, group-methods are, of coiu'se, only approximate, and before adopting them it is necessary to inquire whether the eri'or, consequent upon the adoption of a group of any particular size, is negligible or not. It has already been shewn that the error of ten-year groupings is very small in comparison with the uncertainty of the data, and it may be added that five-year age-groupings might well be regarded as rigorously exact. We shall consider first the question of the error of ten-year age-groupings, and shall deduce a factor of correction whicli will probably be sufftciently exact for ten-year groupings in other countries. The rigorous solution can be developed in the following form. Put (19) p = i2/i?o = A {x) • ''Sa; = hW/W = /, {x) hx yf:.{x) dx tlius being unity between the limits of age comprised, say, 10 to 105, or if we prefer it from age to the end of life. Then (20) SW = RhW = RWf, (x) 8x = /?o Wf, (x) f, [x) hx ; consequently (21) W = RoW / pudx the limits being the extreme ages in question. By graduation of the curves p and i« for yearly values it was found that for " males," " females," and " peraons" this last expression gave correcting factors of about 0.9873, 0.9817, and 0.9858 respectively, instead of vmity, to be applied to the group-results adopted (viz., about 10 years) to reduce them to what would be given by 1-year groups, and further, a factor of about 0.9997 to reduce them to what wovdd be given by infinitesimal groups, i.e., by 0.9870, 0.9814, and 0.9855 respectively. That is, the group-results forepersons" should be multiplied by 0.9858 x 0.9997 = 0.9855, and similarly for males and females. That is, the group-results for " persons" require to be multiplied by say 0.986. If, however, only 1.4°o be allowed to partially (or wholly ?) compensate for a defect due to the wealthier classes possiblj' living — as has been supposed — somewhat longer than the average, then no correction need be applied, and the group-result may be regarded as correct. It will, however, be decidedly preferable to retain the reduction and consider tho other question inde- pendently. Five-year groupings would require reduction by factors 0.9967, 0.9954 and 0.996."5 for" males," " females," and" persons" respectively to reduce to infinitesimal groupings. We now consider the question of the possible magnitude of a correction for variations in the death-rate with wealth. 96 The Estimation of Wealth from Probate Retttrns. 13. Correction in any age-group for variation of wealth with death-rate in the group. — If in any age-group it should hapjjen that the death-rates have any aj'ste- matic relationship to the wealth of the classes within the group, then the assumption that the dying represent the living is not quite correct. This question may be presented in several ways. First, let us suppose that the people of any limited age- group, divided into claases according to wealth possessed, have characteristic death- rates according to class. Then the aggregate of wealth W of the entire group would be made up of the wealth W, W", etc., of the classes. And, similarly, the aggregate of the wealth (tv) of the dying would be made up of w', w" , %o" ' , etc., the amounts accruing by the deaths in the several classes. Then obviously we have : — (22) TF = Tl" + W" + etc. = R 'lu' + R"w" + etc. = XRw where R is the recipi'ocal of the death-rate for the whole, and R', R", etc., are the reciprocals of the death-rates of the several classes. Thus it is alao immediately evident, on dividing both aides of the preceding equation by Rw, that . R' w' R' w (23) A= • \ • h etc. R w R 10 that is, A is the sum of the 'products of the relative death-rate of the class (aa compared with that of the age-group as a whole) into the relative wealth of the class, that is its ratio to the wealth of the whole group. Or again, writing i?o for XR, we have for Rq, the proper reciprocal to vise as multiplier, the weighted mean of the reciprocals of the death-rates, viz. : — . w' „ w" (24) Ro = XR = R' . [- R . h etc, w w This formula indicates that the process is exactly analogous to that of forming groups according to age, and it may be also observed that the remarks regarding the adoption of a continuous method also apply in their due measure. There would, however, not be the same necessity to form small groups, since the distribution of death-rate according to wealth will not, at the outside, have wider limits than from 1 to 2, and, furthermore, is itself very questionable. We may state the whole matter in other terms, as follows : — The assimaption that the persons dying in any age-group represent the living may possibly be defective in two particulars, to which reference may now appro- priately be made. First, the frequency of death among the section of the community with estates sufficiently large to conie under review for probate may perhaps be less than the average on account of their better financial ability to secure themselves against adverse influence. In some countries this is unquestionably the case, but in Australia the favourable climatic conditions would probably minimise such a consequence. Unquestionably, no assumption one way or the other can be made with safety. Of course, if death is less frequent among the rich, there will be larger numbers of rich persons living than is implied by dividing by the average death-rate (or multiplying by its reciprocal), and the result foiind without regard thereto, viz., {Rw/Hw) will be too small ; i.e., R must be multiplied by a factor somewliat greater than unity, 1 + ^> say. tliat is A — 1 = !^, if this were the only thing to be taken into account : see formula (23). On the other hand, those whom death eliminates at any age are evidently differentiated vitally from those who remain, and the question arises whether this greater vital endowment is characterised on the average by greater endowment of The Kate of Devolution. 97 wealth. If it be go, then it follows that the wealth factor {u — w/'Ew) ^shovi\d be increased, i.e., it should be multiplied by a quantity somewhat greater than unity, 1 4-71, say, or if this were the only matter to be taken into account, A — 1 = T^. Hence the total result must be multiplied by the product of tlieso factors, viz., by (1 + i^) (l+7j). In other words, tlie result is perhaps more properly indicated by the expression w (I + 71) ^ w (25) W = R{\ + g -^- '- = (I + I) it" — - ,say. These two correction-factors are similar in kind, and in fact can hardly be re- garded as distinct, forasmuch as the supposition that the living in any age-group may be differentiated from the dying in respect of wealth may be regarded as including also the differentiation in mortality due to wealth. Both may, therefore, be em- braced under one factor, say (1 + ^), where ^ is sensibly equal to ^+ tj (forasmuch as ^71 may be considered negligible) ; thus we may assume that A — 1 = t,+ y] = ^- Unforttuiately no satisfactory data for the determination of these factors exist, and at present we can safelj' infer nothing in regard to them, nor even obtain a rough idea of the magnitude of their joint effect. If we suppose that each age-group is divided into classes corresponding to in- dividual wealth, and that the death-rate has been ascertained for each, and suppose also that the range of wealth in each class is not very large, any correction of the tj'pe of 7) for any class in question will necessarily be negligible, and the correction may then be regarded as of the type of t,. Remembering that the s\im of the factors w' /w, w" /w, etc., is unity, we may put formula (23) in the following form, viz.: — w' R' - R u/' R" — R (26) ^= . + . ~ + etc. w R w R which shews that the correction depends on the proportion of the wealth contributed by each class to the total, and the relative difference of the mortality rates. Since R necessarily lies between the least and greatest values of R' R^, some of the quantities will be negative and some positive. 14. Difference of death-rate not determinable from relative number of deaths in probate and non-probate classes. — We may note lirst of all that tho existing returns do not afford the means of deducing the death-rate even of two such (crucial divisions as the non-probate and probate classes of the population. For the data are : — p ; r ; d = d' -\- d" ; these symbols denoting respectively the total population of an ago-group, the death-rate, the total death?., those of the non-probate class, and of the probate class respectively, the total deaths being equal to those in the two classes. Suffixes may be added to denote the successive age-groups. If we assume a rate r' corresponding to d', the corresponding population P' is determined ; and P" ( ^- P — P') gives with d" the death-rate r", while r is obviously in no way affected. Or if we assume relations such as r' = ^r, then we have P' = d' /^r. Or again, if wo make r" = y*". that is, equal to yrf' / P' = d!' / P" we have at orxCe '{d' / d" = P' /P", and we can divide P in this ratio. The same can be done, of course, for each age-group. As there is no valid reason, however, for assuming the values of ^ or y, we can infer nothing in regard to the ili vision of the population into non-]>robato and probate classes. 98 The Estimation of Wealth from Probate Returns. 15. Variation of mortality in age-groups according to occupation. — ^The attempt was made to ascertain whether " occupation," as determined at a Census, would throw any light upon the uncertainty arising through possible differences in the rate of mortality according to wealth -classes. The resiilt of the analysis is as follows : — For the Commonwealth of Australia and for the years 1908-1912 the relation of death-rate to class of occupation of males, according to age-groups, was found to be as indicated in the following table : — Ratio of Rate of Mortality in each Class of Occupation to the Rate for the Total Male Population in the same Age-group, AustraUa, 1908-1912. Ratio to Death-rate of Males in same Age-group for each Class of Occupation . Age Primary Pro- fessional. Com- mercial. Transport (5roup. Pro- ducers. and Com- munication Industrial. Domestic. Death Rate. VI. I. III. IV. V. II. 1;V 19 .. .40 .74 .65 .92 1.19 .70 .0027 20-29 . . .65"] .80^ .92"! 1.10^ 1.33^ i.on .0039 30 39 . . .69 Av .88 Av .97 Av 1.03 Av. 1.35 Av. 1.38 Av. .0057 40-49 . . .69 y .83 > .90 y .95 l- 1.39 Y 1.61 \ .0099 .50-59 . . .65 .(SI .84 .84 .93 .91 .94 1.01 1.44 1.40 1.33 1.28 .0178 60-64 . . .69 .85 .84 1.01 1.50 1.09 .0306 65 & over .88 .96 .56 1.20 1.57 .81 .0928 All ages .83 .91 .76 .83 1.38 1.26 .0119 The "primary producers" {VI. ), with the lowest death-rate, include persons engaged in agriculture, dairying, ijastoral pm-suits, forestrjr, fisheries, water con- servation and mining. The "professional" class (I.), also with a relatively low death- rate, includes all persons engaged in government, law and its administration, health, religion, charity, education, science, and amusement. The " commercial" class (III.), also with a death-rate under the average, includes all persons engaged in banking, finance, and in the sale and storage of commodities. The class "transport and communication" (IV.), which has a death-rate about the average, consists maiiily of employees of the railway and postal departments, and all persons engaged in the carrying trade, whether by land or water. The "industrial" class (V.), with a death-rate distinctly above the average, comprises jjersons engaged in manufacturing industries, in the building trade, and in the construction of rail and road ways, bridges, and similar things. The "domestic" class (II.), with the highest death-rate of all, includes all engaged in the svipply of board and lodging, as well as all engaged in other domestic occupations. It is evident on consideration that the correlation of wealth and death-rate is not on all fours with that of occupational class and death-rate, and, moreover, it is also evident, from the arithmetical nature of the case, that the moi'e frequently instances of wealth appear among the different occupational classes the mere will the relation between wealth and rate of mortality tend to equalise. Thus, for group-results of sufficient magnitude, we may sujapose that the marked differences of death-rate shewn in the table are, in the correlation of wealth and mortality, considerably reduced, and, as a not wholly improbable assumption, may accept for a supposititious computation the correlation shewn in the table hereinafter between wealth and death-rate. Thk Rate of Devolution. 99 16. Life Assurance Society's experience of variations in death-rates, according to size of policy, etc. — The experience of the Au.straliaii Mutual Provident Society and of the Scottish Widows' Fund throws some light on the question of the relation of wealth and mortality, and has consequently been considered. We remark first that the possible variation to be expected in death-rates for any age-group may also be roughly gauged by referring to the A.M.P. experience for the period 1849-1903. Instead of considering a number of age-groups we may consider the large group for the ages 20 to 59 only, and the same age-group for the Commonwealth for males for 1891-1900. The results are as follow : — Whole Life Assurances .. Healthy .00723 Loaded .01053 Factor 1.46 Endowment „ .. „ .00468 „ .00652 „ 1.40 Commonwealth Male Death Rate .. .01095 This gives us some idea of the range in the rates of mortality. It is not, however, in the range in an age-group that we find what is essential. It is the average variation with wealth ; some slight indication as to this is to hand in the report on the Mortality Experience of the Australian Mutual Provident Society for the 40 years 1849-1888, by Mr. Richard Teece (see pp. 42-43). Rate of Mortality per 10,000. Assurance. A.M.P. Society. Scottish Widows' Fund. Age Group. Under £500to Under Over £500 and Over £500 £1000 £1000 £1000 under. £500 25-29 . . 40 43 41 30 51 36 30-34 . . 49 47 48 49 59 42 35-39 . . 60 67 62 60 76 60 40-44 . . 76 93 82 68 98 76 45-49 . . 94 104 98 109 110 90 50-54 . . 117 1.39 1 25 127 145 136 55-59 . . 148 165 154 181 239 202 60-64 . . 221 245 229 231 323 314 65-69 . . 379 447 405 438 440 435 70-74 . . 530 427 486 577 697 675 75-79 . . 7.34 881 813 10,27 965 971 It will be seen that these results are by no means unequivocally in favour of the assumption that (at least as far as the class insuring is concerned, probably the thriftier class) mortality-rates are in favour of the wealthier section. On page 41 of the same report it is stated that in America "the heavier rate of mortality prevails among lives assured for larye sums," though in (ireat Britain and Europe the contrarj' is the ca?e. On the experience of the Scottish Widows" Fund, 1835-1884, G. C. Stenhouse says, that in general " the mortality decreases as the sum assured increases.'" In Part II. of the same report, pp. 13-14, Mr. Teece suggests "that in the United States and these Colonies" (the Australian States) " men with sufTicient means to assure for large sums are those who are actively engaged in business, and who are annoyed, harassed, and impaired in health by the vicissitudes attendant on business pursuits in young covmtries, while the corresponding class in Great Britain is composed chiefly of men of leisure .... enabled to lead comparatively tranquil lives .... which tends so greatly to prolong life." 100 The Estimation of Wealth from Probate Returns, In the face of the preceding evidence, a priori judgments as to the correlation between wealth and mortality must be regarded as of little value, and in any cage it is quite certain that the occupational class "primary producers," with the lowest rate of luortality, contains an immense majority who are certainly by no means wealthy. We have thus shewn not only that we are not entitled to regard the whole occupational variation of death-rate as applying to the wealth -variation (since occupations characterised by a high rate of mortality are among those which are also characterised by considerable wealth), but also that the experience of life insurance in Australia lends no real support to the view. 17. Estimate of possible correction based upon supposititious distributions of wealth and mortality. — The probate-returns shew that for Victoria in the years 1908- 1912 the distribution of wealth averaged as follows : — Average Distribution of Estates According to Net Value, Males, Victoria, 1908-1913. Net Average Relative Relative Relative Range of No. Value. Value. No. No. Value Value. £ £ (Unit 2814) (Unit 8488.2). (Unit £6,020,147) Excluded 5674.2 Unknown Excluded .668 .00000 Under £100. . 438.8 19,079 43.5 (A) .155 (B) .052 .00317 £100-£.300 .. 626.2 117,260 187.3 .223 .074 .01948 £300-£500 .. 384.6 151.743 394.5 .137 .045 .02521 £500-£1000 . . 424.6 308.429 726.4 .151 .050 .05123 £1000-£3000 533.8 936,719 1754.8 .190 .063 .15560 Over £3000 . . 406.0 4,486,917 11051.5 .144 .048 .74531 Total 2814.0 6,020.147 1.000 1.000 1.00000 8488.2 The proportions of the number of estates of various magnitudes to the total number coming under review for probate are shewn in column (A) in the table for males only. Many estates do not come vmder review at all, on the average about 5700, if everyone dying is regarded as possessed of some wealth. Hence, since ordinary statistics yield the death-rate for the entire age-groujD only, it is necessary that these should be entered as persons the wealth of wliose estates, so far as the present element of the inquiry goes, is zero. In this way the proportions shewn in column marked (B) are obtained. We see from this table that the distribution of size of estate follows a curve of the hyperbolic type, and from the table of mortality according to occupation that, for practically any age-group which seriously affects the result, the relative mortality of the different occupations ranges between about 0.6 or 0.7 to about 1.5. Un- fortunately, however, there are no available data for correlating the two results, and consequently ^ (or A) cannot really be ascertained. It remains, therefore, to formulate some plausible supposition, and to ascertain what the value of this cor- recting factor would be if such supposition were really applicable. This will give at least a very rough indication of the extent of the nncertainty in any deduced result which neglects' the correction. Although, as pointed out, no definite correlation between occvipation and wealth has been ascertained, we shall nevertheless assume for our purpose that a somewhat analogous range of variation of death-rate applies to differences of wealth possessed ; the assum])tion being arbitrarily based on the general but very uncertain ground The Rate of Devolution. lOl that financial resources can command a degree of comfort and attention that conduce to longevity. The difference between moderate and considerable wealth, if it really be in favoiir of the latter, can however be only very slight. Thus, with gome ex- ceedingly slight degree of plausibility, it may be supposed that the persons of zero wealth have the highest mortality -rate (or lowest factor R), and those of the greatest wealth the lowest mortality-rate (or highest factor R). It should be noted that the ratio {R' — R)/R is independent of the absolute value of the death-rate, and the ratio w' /w is similarly independent of the absolute amount of the wealth of each class within a group ; further, the relative numbers in each class are necessary only to ensure that the weighted mean of the death-rate gives the general death-rate. Hence, we may regard the above table as a possible representation of the existing facts, even if not a probable one. Having regard to every aspect of the matter, it is likely that the variation of death-rate with wealth, if it exist at all, does not pass through a wider range than say 1 to 1 J or 1.064 to 0.798. Thus, taking into account the relative numbers in each class, the relative reciprocals of the death-rates may be (arbitrarily) assumed to be those shewn in the following table, line i. being taken from the preceding table : — Total Relative Numbers only. or Mean. Value of EstateSjTotal i. .000 .003 .020 .025 .051 .156 .745 1.000 Numl)er oF Estates ii. .67 .05 .07 .05 .05 .06 .05 1.00 Values of reciprocals of death-rates, relative iii. .94 .99 1.04 1.10 1. 15 1.20 1.25 1.00 Products of i. and iii.* .0000 .0000 .0009 .0024 .0076 .0314 .1885 .2308 * The difference of iii. from unity only has been used. The values in to]) line may thus be taken as those of tv'/w, and the difference between the values in lino iii. and unity as the values of (R'—R)/R, etc. Thus the value of this factor, viz.. A — 1 or ^, is the algebraic sum of the products of Ime i., tlio top line, by these differences. This gives the result ^ = + 0.2308, a pro- portion which, of course, is serious. It is evident from the table that the result depends almost wholly on the difference from the mean of the death-rate of persons |)03Sossing the large estates ; since neglecting all whose estates are imder €3000 the result would have been ^ = + 0.1885. It is thus quite clear that the doath-rate of tliose who are the main contributors to the probate wealth -returns profoimdly influence the results, and here it may be observed that the death-rate of so restricted a class must vary greatly from year to year; indeed, a determination for a period of anything less than 10 years is probably of small value. In any case it is to be observed that it is unsafe in the light of the available evidence to assume the death-rate of the wealthy in any age-group differs systematically from the death- rate of the entire group. It must be based upon statistical evidence before it can be admitted. 18. Consequence of assuming that life assurance rates should be adopted. — It has been suggested by Mr. A. M. Laughton, Government Statistician of Victoria. " that the mortality-rates amongst property owners will correspond with the rates relating to assured lives as given in the published experience of the Australian 102 Tdtj ESMJjiATION OF WEALTH FROM PrOBATE RETURNS. Mutual Provident Society" (Victorian Year Book, 1912-13, pp. 270-271). Regarding this it may be said that the experience of a large assurance company necessarily includes a very large body of recently selected lives, and although the A.M.P. experience, which haa been used, dates back to 1849, tlie number of policies issued in the earlier years of the Companj'^'a history was go small, compared with the number issued in more recent years, that the experience may properly be regarded as one in which medical selection had plaj^ed a very prominent part. The effect produced by thia cause is that a rate of mortality shewn is much lighter than that experienced by a similar body of lives not subject to medical selection, and consequently for the purpose in view the A.M.P. rate must be considered as being probablj' unduly favour- able, and as giving too high a inviltiplier. It is, moreover, for reasons already pointed out, by no means certain or even probable that the possession of wealth and acceptance as a satisfactory life by an insurance office are coincident facts, or that the " healthy-life" experience of an insurance office is to be considei'ed as applicable only to the wealthy. The signifi- cance of the A.M.P. mortality rates for healthy and loaded lives appears in the follow- ing table of the reciprocals of those rates (or rather the vahies of q^) which will be sufficiently near for the purpose. These are, of covirse (approximately) the factors to be employed. They are given for the ages 25, 35 ... . 95, viz., the central ages of the more important groups (see A.M.P. Report on Mortality Ex]3erience, 1849-1903). Reciprocals of Qx (Males) A.M.P. Society, 1849-1903, and Australia, 1881-1890, 1901-1910. Relative Weight. Whole Life. Endowment. Ausi 'RALIA. Age. Healthy Healthy Healthv. and Healtliy. and 1881-1890 1901-1910 Loaded. Loaded. 25 .008 278 270 272 258 ; 116 223 35 .019 193 176 224 213 105 158 45 .072 124 113 140 131 1 70.2 92.3 55 .130 69.4 64.4 77.5 78.7 40.4 .5.5.1 65 .205 29.0 27.2 21.8 25.9 75 .327 14.0 12.7 10.8 10.4 85 .225 5.2 5.4 5.3 5.1 95 .014 1.7 1.7 ■ . 1 1 3.0 2.1 The column, " relative weight," shews the inean for the years 1908-1912 of the net wealth contributed by the successive probate groups, and is probably sufficiently accurate for the period 1901-10. We indicate the difference according to the general values in the two last columns. These results are as hereunder : — Taking the reciprocals of the average death-rates for the period 1901-1910 as a basis, the results would be : — A.M.P. Mortality of healthy males (1849-1903) would give the 1901-1910 result multiplied by 1.2481 A.M.P. Mortality of healthy and loaded malea (1849-1903) would give the 1901-1910 result multiphed by 1.1576 Actual Mortality AustraUa, 1881-1890, would give the 1901-1910 result multiplied by . . . . . . . . . . . . 0.7885 The Rate of Devolution. 103 Taking the reciprocals of the average death-rates for 1881-1890, the reaulta would be : — A.M.P. Mortality of healthy males (1849-1903) would give the 1881-1890 result multiplied by 1.5828 A.M.P. Mortality of healthy and loaded males (1849-1903) would give the 1881-1890 result multiplied by . . . . . . . . 1.4681 Actual Mortality Australia, 1901-1910 1.2682 In view of the fact that the value of 1 + ^ was found to be about 1.1490, on the suppositions made, and that the resrdt based on the 1901-1910 mortality, compared with the A.M.P. experience of (1849-1903) for " healthy and loaded male lives," gives 1.1576, it might perhaps be assumed that a correction-factor of 1.15 is probably justifiable. This, however,. I do not believe to be the case. It would be so only if the assumption referred to had any validity. After a wide review of the question, and in the light of all the available evidence, it seems that in Australia at any rate, there is grave reason to doubt the existence of a definite correlation of wealth and longevity, and, if so, the supposition by means of which ^ was estimated above has no validity. It is certainly not based upon evidence, and rests merely ujaon a more or less plausible assumption, against which, as has been shewn, there is at least some evidence. We now indicate the numerical consequences of a difference in the mortality rates of classifications according to wealth within the same age-group 1 9. Consequence of death-rate being less among the wealthy. — Suppose that the population at any age is divided into two classes differing in wealth, and that the wealthy experience a lower rate of mortality than the less wealthy. This will have the effect of altering the distribution with the lapse of time (when the transfer of the survivore of any age-group to a group of greater age is considered). It will follow as a consequence that the aggregate of the wealthier classes will tend to relatively increase with age as compared with the aggregate of the less wealthy class, other things being equal. Other consequences will also follow, which we shall now proceed to consider. We shall assume that : — (i.) The average unit of wealth is w' for the poorer sub-group ; and "•' (1 -| «') for the richer sub-group ; (ii.) That this imit does not increase with time, or if it does increase, that it increases with time alwaj'S by the same ratio whether the amount be large or small ; (iii.) That the death-rate for the poorer sub-group is r, and for the richer [r — h), where h is a positive quantity. The following propositions follow as a necessary consequence of these three assump- tions : — (n) Since by hypothesis the numbers of the poorer sub-group are decreasing more rapidly than those of the richer sub-gi'oup, the ratio of the numbers dying with large estates (or paying probate) to the number dying with sniall oatatos (or who do not jjay probate) should tend to be an increasing ratio. (/>) Since by liypothesis the individual wealth of the persons remaining alive is unaltered, and, owing to the greater death-rate of the poorer sub- group there are relatively fewer in that group, the average for the combined sub-groups must tend to increase with age. 104 The Estimation of Wealth from Probate Returns. (c) Since by hjiDothesis the individual wealth is the same, and death has more rapidly decreased the poorer sub-group than it has the richer sub-group, the ratio of the aggregate possession of the latter to the former will be an increasing ratio. These results are perhaps seen more clearly when set out formally (algebraically). In the table herevinder m denotes the numbers in tho poorer sub-group, and n those in the richer, the death-rates being respectively r and {r—h). After a \init of time the groups are reduced by death to m (1 — r) and n [1 — (r -h)] respectively, and the aggregate of wealth will be as shewn in the table hereunder, provided we suppose that the tvealth does not pass by death to persojis in the same age-rjroaps. The i^rocesses by means of which the various quantities are obtained are obvious. Epoch. Numbers. I. II. Living Initially m + n Li^^ng after ^m(\-r) + n{\-r+h) unit time Wealth. I. II. mw' -f nw' (1 + m') m (1-r) w'-f n{\-r + K)iv' (l + tt') Ratio of Wealth. II. to I. n(l+M') Average. "V + mT^) \n(l + u') h \ where V=h/a+r-h) .) The above, however, represents only the effect on the living. We can establish the caae for the dying in a similar way. Let the persons in the two classes, each individual possessing respectively iv' and w' (1 + u'), be again to and n ; and the respective death-rates initially r^ and r^. Then the average wealth, when a unit of time has elapsed, will be : — (27). Total wealth of dying mr w' -\-nr^tv Number dying mr^ + nr 1 '^w'[\ + ~ r \ mr +7ir,J If, then, we suppose that r, and r^ change with time in the same ratio, say become ur^ and ur^ (therefore that they preserve the samo ratio to each other) then we have : (28). Total wealth of dying Number dying i( 1 — r, )fjbr^w' + n{\ — r„)}xr.-:w '{\-\-ii) TO (1 — r^) ^ir^+n (1 — r^) jxr^ \ 71) 1 -'•, and if, as we previously supposed, r^ be less than r,, tho fraction (1 — '•,) / (1 — r.) will be less than unity, thus the ivealth-average will become greater. It is important to observe that the expressions (27) and (28) cannot be used with any great assurance to deduce values of r, and r^, because they represent, after all, very small changes. We shall illustrate this point by considering a numerical instance. The Rate of Devolution. 105 The death-rate for the age-group 60 to 70 for "persons" is abovit 0.034. Suppose then that we aasvune r^ is about .04, and /•, about .02, and that the ratio of w to n ia as 3 to 2 (whicii is about the proportion of the non-probate class to the probate class). Then in tliese two last expressions we should have : — / 2 X 0.02 u \ w' 1 + = w' (1 + 0.25 u') V 3 X 0.04 -f 2 X 0.02/ 2 X .02 u \ 1+ -— = ?^•' (I + 0.253886 m'). S.^t:!!' 0.04 + 2x .02 / O.ftS It will be seen that the influence is extremely small ^ for even so great a difference of t\ and i\ as is iinplied in the ratio 2 to 1. It is moreover evident that so small a quantity could be easily' mt'sUod by other elements affecting the results, viz., changes in the rate of acciunulation of wealth, irregularities in the deaths, in the sizes of estates coming under review, and so on; in fact, it goes far to shew that no analysis of the respective nximbers or of the respective amounts appearing in age-groups is likely to lead to anything definite, either as to relative mortality among the non- probate and probate classes, or as to the possible rate at which the wealth of either actually grows. In the jareceding table shewing symbolically the averages for the living at the commencement and end of a period, the results, on the basis supposed, would be respectively (1-f 0.40 «') and (1 + 0.041517 u'), so that the difference between the beginning and end of a period will be relatively very small, and the conclusion drawn equally applies, for although u' may be large the relative changes therein will be small. 20. Existing statistical data point to the conclusion that the devolution-rate method must be applied to each sex separately. — The retmns of Victoria for 1908-1912, given in tho table hereunder, shew that there is a remarkable constancy in the ratio of the number of the non-probate to tho probate class, from 40 to 90 years of age for both males and females, and certainly to somewhat regular changes in the average wealth in each age-group, but, as already pointed out, nothing can be deduced from this table in regard to the relative death-rates of the probate and non-probate classes. Column (7), shewing the wealth per head of the dying, reveals a marked increase with age, the maximum being, for males, inthe group 80-89, nnd the niaxiimun for females in the group 70-79. This difforence shews, of course, tliat the factors a and A-will differ for the sexes. Other striking features of difference are that the wealth per head ia roughly between three and four times as great for the males as for the females, and that the ratio of the non-probate to the probate class differs materially. The con- clusion is that separate returns should be made out for males and females, and, in com- putations of total wealth, that formulae (3) to (12), and (19) to (28) cannot be applied to the sexes taken together on the assumption that they may be considered as forming a homogenef>us population. The same observation is accentuated by the character- 1. If W = 0, the ratio of the lower <|iiaiitity to the upikt is I.O; if it' ^ 1.00, tlie ratio beconies 1.0031 ; if ititlnity, it becomes l.Olfjj. 106 The Estimation of Wealth from Probate Returns. iatic difference in the death-rates. From this it follows that, in order to deduce accurate results, we must, in the application of the devolution-rate method, treat the sexes separately, and not attempt to combine them so as to calculate results for "persons" merely. This dictum will be confirmed by a study of the table herevmder : — Aggregates from Probate Returns, Victoria, 1908-1912, and also for 1913-1915. Deaths. Ratio of No. of No. of Persons Non- Wealth Average Dying No. of Probate Total Dying. Aggregate per Net Value Age- Group. Less No. of Estates in to No. of Net Wealth. Head of Dying. per Estate. Estates in Probate Probate. Probate Retiu-ns. Returns. (2)-^(3) (fi)^(r)) (1) (2) (3) (4) (5) (6) {"') Males £ £ £ Under 10,323* 9 1147.0 10,332 1,978 0.191 220 15 6,622* 3 2207.3 6,625 1,662 0.251 554 15 to 20 996 62 16.06 1,058 16,066 15.19 259 589 45 13.09 634 9,922 15.65 220 21 „ 29 1,475 424 3.48 1,899 212,565 112 501 969 351 2.76 1,320 175.5()2 133 500 30 „ 39 1,629 790 2.06 2,419 541,445 224 685 1,040 545 1.91 1,585 481,916 304 884 40 „ 49 2,395 1,680 1.43 4,075 2,045,368 502 1,217 1.336 1,034 1.29 2.370 1, 044.699 441 1,010 50 „ 59 2,489 1,850 1.35 4,339 3,669,819 846 1,984 1,8.11 1,420 1.30 3.271 2,758.309 844 1.942 60 „ 69 2,835 2,266 1.25 5,101 5,801,455 1,137 2,560 1,639 1,454 1.13 3,093 3,676,352 1,188 2,528 70 „ 79 4,308 3,586 1.20 7,894 9,247,324 1,171 2,579 2.117 1,837 1.15 3,954 5,805.820 1,469 3.180 80 „ 89 2,669 2,149 1.24 4,818 6,348,237 1,318 2,954 1,822 1,365 1.33 3,187 5,045,662 1 ,583 3.696 90 and 337 169 1.99 508 402,654 796 2,383 over 206 127 1.62 333 474,384 1,425 3,735 Females Under 8,191 7 11.70 8,198 2,838 0.350 405 15 5,188 6 864.6 5,194 2.718 (».523 453 15 to 20 1,025 18 56.94 1,043 7,745 7.43 430 545 15 36.33 560 4.4o 8,193 9,478 2,326 6,184 2,492 2,548 1,071 70-79 5,423 11,848 15,053 3,421 9,974 4.216 2,776 1,2.32 80-89 3,514 8,005 11,394 1,772 6,187 2,115 3,242 1,193 90 & over r96 839 877 205 890 313 2,963 1,529 Total All Ages 21,166 68,813 47,761 11,763 55,726 12,335 Average per Deat Weahh Absent's 1,624 3,655 i 720 909 h occur- 1 1 ring, V ictoria. Ratio Va LUES OF T HE AbOVI :. Males. Females Under 15 .0006 .2464 II .0001 .0011 .2403 .0004 £ 0.21 £ 0.41 15-20 .0050 .0246 .0005 .0028 .0293 .0010 1.5.4 7.47 21-29 .0366 .0468 .0081 : .0205 .0622 .0087 , 120.5 30.92 30-39 .0631 .0.582 .0214 .0643 .0729 .0347 255.5 105.3 40-49 .1282 .09.36 .0647 .1118 .0866 .0735 ! 479.5 187.9 50-59 .1545 .1106 .1346 .1429 .0916 .1411 844.7 340.8 60-69 .1758 .1191 .1984 i .1977 .1110 .2020 1156.8 402.9 70-79 .2562 .1722 .3152 i .2908 .1790 .3418 1270.6 422.7 80-89 .1660 .1163 .2386 .1507 .1110 .1714 1423.3 341.8 90 & over .0140 .0122 .0184 1 .0174 .0161 .0254 1045.3 349.8 Totals 1.0000 1.0000 1.0000 I 1.0000 1.0000 1.0000 i 1 no The Estimation of Wealth from Probate Returns. Distribution oi Wealth, according to Age and Sex, as revealei in Probate Returns Victoria, 1908-1915, and New South Wales, 1911-13 and 1911-15.— con«. New South Wales. Average Males. Females. Wealth Age Last per E state. Birth- N. S. Wales. day. No. of Number Aggre- gate Net No. of Number Aggre- gate Net Probate Dying. Wealth, Probate Dying. Wealth, Returns. £1000. Returns. £1000. Males. Females Under 15 21 9,208 5.94 13 7,553 6.27 £ .283 £ 482 28* 15,487 6.73* 15 12,644 t *6.11 240* 407* 15-20 59 780 13.56 13 625 4.60 229 1 352 89 1,323 25.0 24 1,017 10.3 281 , 428 21-29 489 1.830 144 ' 119 1.660 23.0 295 i 194 775 3,090 285 197 2,795 78.2 368 ! 397 30-39 748 2.155 456 296 1,802 185 610 i 6;: 5 1,203 3,707 984 478 3,046 348 818 728 40-49 1,301 2,969 1,565 388 1,798 329 1,203 847 2,014 4,913 2,695 702 3,038 579 1,338 825 50-59 1,691 3.933 .'^,782 586 2,030 495 1,645 844 2,815 6,702 5,224 1,024 3,452 902 ; 1,856 881 60-69 1,900 4,313 4,581 773 2,609 987 2.411 1,277 3,141 7,376 7,813 1,292 4,321 1,539 2,487 1,192 70-79 2,033 4.916 6,884 836 3,083 1,246 3,386 1.490 3,291 10,546 11,927 1,413 5,276 1,999 3,624 1,415 80-89 835 2,201 5,333 409 1,676 1,693 6,387 4,138 1,447 3,863 6,906 678 2,929 2,192 4,773 3,234 90 & over 88 270 194 46 296 117 2,207 2.535 143 451 290 94 495 244 2,025 2,596 Total All 9,165 32,575 21,9.59 3,479 23,132 5,085 Ages Ab- 14,946 528 57,458 36,155 3,203 5,917 165 39,613 7,898 724 Average per Wealth Death sentees 940t 5,298t 269 1,054 occiu-rin 5, N.S.W. I Iatio Va LUES OF ■] DHE AbOV E. Males. Females Under 15 .0023 .2827 .0003 .0037 .3265 .0012 £ 0.65 £ 0.83 .0019* .2695 .0002* .0025* .3192 .0008* 0.43 0.48 15-20 .0064 .0239 .0006 .0037 .0270 .0009 17.36 7.32 .0060 .0230 .0007 .0041 .0257 .0013 18.93 10.11 21-29 .0534 .0562 .0066 .0342 .0718 .0045 78.85 13.90 .0518 .0538 .0079 .0333 .0706 .0099 92.26 27.99 30-39 .0816 .0662 .0208 .0851 .0779 .0364 i 211.7 102.6 .0805 .0645 .0272 .0808 j .0769 .0440 265.6 114.2 40-49 .1420 .0911 .0713 .1115 .0777 .0647 527.1 182.8 .1347 .0855 .0745 .1186 .0767 .0733 548.6 190.6 50-59 .1845 .1207 .1267 .1684 .0878 .0973 707.3 243.7 .1883 .1166 .1445 .1731 .0871 .1142 779.4 261.2 60-69 .2073 .1324 .2085 .2222 .1128 .1942 1062.1 378.4 .2102 .1284 .2161 .2183 .1091 .1949 1059.2 356.3 70-79 .2218 .1.509 .3135 .2404 .1333 .2450 1400.3 404. 1 .2202 .1835 .3279 .2388 .1332 .2531 1130.9 378.9 80-89 .0911 .0676 .2429 .1176 .0724 .3329 2423.0 1009.9 .0968 .0672 .1910 .1146 .0739 .2776 1787.7 • 748.5 90 & over .0096 .0083 ! .0088 .0132 .0128 .0229 719.5 393.2 .0096 .0078 .0080 .0159 .0125 .0309 642.1 493.0 Total 1.0000 1.0000 1.0000 1 1.0000 1.0000 1.0000 * The results i^hcwii in lieavy lype are for New South Wales for the years 1911 to 1915; the results in the lighter type being for 1911 to 1913. t This discrepancy is tlie effect of proportional distribution of the " not stated" as regards age. t Including nayal and military forces. The Ratk of Devolution. Ill We shall now consider the causes of the irregularities referred to and the mode of eliminating their prejudicial effect. 22. Necessity for a correction for infrequent appearance of large estates. — Very large estates appear but infrequently in probate returns, the infrequency increaeing with the size of the estate and diminishing with the size of the population. Let ua consider any table shewing the number of estates of different magnitvide in any territory {e.g., the table from the Prussian Returns). It is manifest that if we take the devolution-period to be 22.2 years (which perhaps, however, is somewhat below the correct amount), the average frequency in Prussia of the appearance of estates of these sizes, in a probate aggregate for all age-groups, will be the number existing divided into the devolution-period. Thus, if we call this period K, and the niunber N, the frequency, F, is N/K, or the average interval of appearance K/ N. It is obvious from this that the average frequency of appearance in a particular age-group will be considerably less. If we assume that it is equally likely to appear in the probate-class in any age-group, then the relative freqviency in that age-group to the frequency of apjjearing in the aggregate of the age-groups is measured by the number of probates in the former to the number for the latter (the aggregate number). Let the nimiber of probate estates in any age-group be denoted by J5',with a suffix to define the particular group, and the number for all groups by E = S-B' : then this relative frequency is only the ( E' / E)th part of what we found before, since the average frequency for the age-group is : — (29). F' = F . E'/E. Thus, if we take the nmnber k, the multiplying factor deduced for Victoria for the period 1908-1912, multiplied by the ratio of the Prussian death-rate to the Vic- torian death-rate, we obtain 22.2, which may be regarded as holding approximately for Prussia. Accepting this, we should get the following results : — Prussian Population as at 1911. Size of Estate in millions, sterling No. of Estates Years Estates per 10 years Over 5 4 5.5 1.8 1.5 to 30 .74 13.5 .75 to 1. 94 .24 42.3 50to .75 127 .17 57.2 0.25to.50 574 .04 259 Owing to the large rate of infantile mortality for Prussia, this figure 22.2 is perhaps rather too small ; but even so, it will not touch the argument, and the frequency shewn will be affected only by the ratio of 22.2 to the true value. Detailed probate statistics for as long a period as five years are at present avail- able in Australia for two States only, viz., Victoria and New South Wales. In the Victorian retiu-ns for 1908-12, for estates of males of over £50,000 thei'e is only an average of 11.8 jaer axmum, and over £100,000 only 3.2 per annum, corresponding to an aggregate nvmibor of 8488 deaths. It is evident from this that tlie appearance of the larger estates will be relatively rare, and since tliej' may occur at any age, tho values of pu — see formula (11) — are subject to large variations, and con- sequently the values of a and of k. It is only by studying the experience of each age-group and the fluctuation in the values oi pu that we can hope to ascertain what the general trend with time is, and whether tho results of a particular year for each age-group differ from the average. Wheii for a sufficient number of years such details are to hand, the average trend can be ascertained, and appropriate cor- rections can be made. 112 The Estimation of Wealth from Probate Returns. Suppose, for example, a very large estate comes under review in probate returns, say once in 7 years (on the average). Then for the (average) six years in which such an estate has not appeared the computed results will be in defect, because the estate is in existence, though the evidence of that existence and the measure of its magnitude are not to hand. On the other hand, suppose it is included in an annual, or even in a quinquennial mean. The result will be greatly in excess of the true annual result, and sensibly in excess of the true quinquennial result. A more or leas definite appreciation of this consideration has, without doubt, led statisticians to regard with favour a multiplier which does not oscillate rapidly like that derived from the results of a single year. Bvit it has ordinarily been for- gotten that even when such a multiplier is used, a single year's results are of very limited value. The conclusion is that in order to improve the technique a study must be made when sufficient returns are to hand of the frequency of estates of different sizes. For this reason it is important that tabulations should be made of sizes of estates in different age-groups. From the table of values of pu — see formula (11) — the important groups are : — less than 30 ; 30 to 49 ; 50 to 69 ; 70 and over; the extra work, however, involved in tabulating in smaller groups would not be con- siderable, and it would be a great advantage in studying the characteristic of wealth frequency and its variation with age. As already pointed out, there is an average annual progression in the value of p of a sensible amoimt. In the following tables the frequency for estates of various magnitudes are given, but not the distribvition of this frequency according to age. In general, however, not only are the data insufficiently comjolete, but also it is impracticable to apjDly corrections for the appearance or non-appearance of large estates ; it is preferable, therefore, to take the mean of a sufficient range of years to be able to accept the result as substantially accurate. 23. Example o£ variations in the factor k and their consequences. — The impossibility of regardmg the results deduced from any one year as at all satisfactory owing to the infrequent appearance of large estates and other irregularities in the data, is well illustrated by taking the Victorian yearly data for the years 1908 to 1915. Table shewing the Variations in the Factor I; Computed from Victorian Probate Returns, 1908-1915,? and New South Wales Probate Returns, 1911-1915. Total Total Total Wealth Total Wealth Total Wealth Males Year. Factor k Amount Males Factor k Amount Females and Males. Probates (Probates) Females Probates (Probates) Females £1000. £1,000. £1000. £1000. (Probates) £1000. 1908 .. 23.06 5862.7 135193.9 39.02 1265.4 49375.9 184,569 1909 . . 32.46 5115.8 166058.9 49.99 1364.6 68216.4 234,275 1910 .. 27.95 5785.0 161690.8 40.90 1646.0 67379.2 229.070 1911 . . 34.20 6776.6 231759.7 46.10 1692.5 78024.3 309,784 1912 .. 30.60 6560.7 201413.5 37.98 1972.8 74926.9 276,340 1913 . . 25.04 6730.2 168524.2 42.13 1637.7 68996.3 237.521 1914 .. 31.89 6618.0 211048.0 38.66 1863.8 72054.5 283,102 1915 .. 30.50 6959.4 212261.7 40.24 1800.3 72444.1 284,706 Total 29.517* 50408.4 1487950.7 41.638* 13243.1 551417.6 2,039,368 Average 29.463t 185994.0 41.885t 68,927 254,921 1911-15 32.26§ 41453.8 1337300 -^5 = 267460 44.30§ 8952.1 396578 -^-5 = 79315 346,775 * Computed from totals. Similarly the totals give 32.040 for " persons." f Average of the factors for individ\ial years. } The factors are smaller than those in § 8, as they have been reduced in order to obtain more exact results. § The totals give 34.40 for " persons." The Rate of Devolution. 113 It may be noted also that these averages would correspond to the date 1912.0, and indicate that the uncorrected estimate for the wealth of Victoria (including the absentees) was then £254,021,000, of which 72.9613 per cent, belonged to males, and 27.0387 per cent, belonged to females. These results for Victoria may be compared with those of New South Wales in section 21 herein. The mean of the tliree results are k = 27.75 and 39.37 for males and females respectively; but the three years 1911-13 taken together give 29.95 and 37.81 for the factors k, corrected for a continuous wealth cm-ve. We thus have the following results, viz. : — Victoria. 1908-191.5 k = for males 29.52; for females, 41.64 X.S.W., 1911-1913 „ „ 29.95 „ „ 37.81 X.S.W., 1911-1915 „ „ 32.26* „ „ 44.30* * Deduced frcnu later flgiires for Xew South Wales for 1911 to 1915 inclusive. the result being thus in very close agreement for males, and in fair agreement for females. If one constant is to be used for males and females combined, these must be weighted according to the aggregates of wealth. This gives (for the same periods): Victoria (loersons), k = 32.01; X.S.W. (persons), k = 31.43; or N.S.W. frojpa 1911 to 1915 (persons), k = 34.42 ; or if we combine the results for Victoria 1908-15 with those of N.S.W. 1911-1915, weighted according to the totals of the probates (inckiding absentees), viz., for the former 64.66 millions sterling, for the latter 50.41 millions, we get for " persons" 33.07 for the two States combined, which would correspond with the epoch year 1912.7 about, and might be accepted as a value for the Commonwealth. 24. Variation of the factor k with variation of the death-rate. — ^^> have seen that the factor k varies witli changes in the distribution of wealth according to age, and also with relative variations of mortality according to age (i< and d). The latter must, of course, be (imperfectly) reflected in the general death-rates. This will now be considered. For the Commonwealth and Queensland with a distribvition of wealth according to age at least approximately correct, we found values, see § 11, which gave the following values for k, when corrected from 5-year groups so as to give a continuous distribution instead of grotips. viz., the numbeis in the first two lines below ; these take tlie place of those on p 94. 1886.0(1881-1890) 1896.0(1891-1900). 1906.0(1901-1910). Commonwealth k^^^'Sl 24.21 ; F 32.30 ; M 26.14 ; F 37.56 ; M 29.43 ; F 43.05 Queensland k^^= 21.70; 37.79; 24.80; 38.83; 26.85; 42.60 Decennial death- rate* C" wealth .016597 Do. do. Q'land .019551 Commonwealth ttj,^ = .4019 Queensland ctio ~ .4243 * Expressed at per 1000 of the mean population of the year. The suffl.xes 10 denote that the value is a mean for a period of 10 years ; and M and F denote males and females respectively. If those values of k are multiplied by the corresponduig dcciMinial death-rates given on tlie third and fourth lines, the values of a shewn in the two last lines above are obtained, and these, divided by the death-rates of any year, will furnish aj^proxi- mately the corresponding value of the factor k, i.e, the factor for the year in question. These are as follow : — 013703; .014318; .011578; .012453; .009945 ,014691 ; .014249 : .010562 ; .012124; .008829 .4426 ; .3742; .4348 ; .3665 ; .4281 .5551 ; .3533; .4101 ; .3255 : .3761 114 The Estimation of Wealth from Probate Returns. 1886. 1896. 1906. Commonwealth k^ =M 24.26; F .31.80; M 26.46; F 38.31 Ratios . . 1.000 ; 1.000 ; 1.091 ; 1.205 Queensland k^ = 22.76 ; 36.76 ; 24.81 ; 38.98 Ratios .. 1.000; 1.000; 1.090; 1.060 M 30.52 ; F 44.00 1.258; 1.384 29.75 ; 48.47 1.307; 1.319 The results, which, as stated, apply to the years in question only (not to the decennium as a whole), shew that while the range of uncertainty due to variation of death-rates is probablj' not very great, it is not negligibly small. In order to deal with the probate results as a totality (i.e., for persons), we may suppose that the ratio of wealth appearing through deaths of females bears a constant ratio to that appearing through the deaths of males. This, for the years 1908-1915 m Victoria, and 1911-1913 for New South Wales combined, gives the ratio 0.24880 to 1,* the totals being for males £76,578,929, and females £19,053,467. These ratios applied as weights to the factors k for males and females, give the following Com- monwealth results for persons, viz. : — 1886, k = 25.76 ; 1896, k = 28.82 ; 1906, k = 33.21 Ratios 1.000 1.119 1.289 It would seem also that we might weight the death-rates of males and females pro- portionally to the total wealth, to ascertain the change of the factor k. Using the mean of the rates of the group of years in the successive decennia, we obtain the following weighted death-rates, viz. :— Instant .. .. 1886,0 1896.0 1906.0 Weighted, combined death-rate irreciprocal .016035 =1/61.162 :013786 =1/73.527 :011966= 1/83.570 The ratio of the first reciprocal 0.061162 to the others is 1.2022 and 1.3664. If the vakies of k for " persons" be computed from those given for males and females in the table in § 11, we get, for the same years, viz., 1886.0, 1896.0 and 1906.0, the values 25.99, 28.60, 32.38 respectively, the ratios of the second and third to the first being 1.1000 and 1.2459. The two are only in fair agreement. The weightmg of the death-rates is probably not the best course to follow. 25. Estimate of secular variation of k for Australia. — The reduction of the death-rate tends — other things being equal — to ensure an increase m the factor k, and as that reduction has been fairly regular, it is possible to adopt a regvilarly pro- gressive value of this factor without material error. Of course, the general death- rate is largely affected by the infantile and early death-rates, which have no effect on the probates, and is therefore not quite satisfactory. Bvit if we take the re- ciprocals of the death-rates from the age 20 to the end of life, and deduce the weighted results for " persons," the ratios of the second and third to the earliest result are 1.0909 and 1.1493. The growth for 10 and 20 years of the coefficient k might be regarded, therefore, as very approximately given by the following ratios, viz. : — * When later the 1911-15 results for New Soutli Wales wvre substituted for those of 1911-13, thia ratio became 0.24111 to 1. The Rate of Devolution. 116 According to Life Tables and estimated distribution Deduced values for years 1886, 1896 and 1906 Weighted reciprocals of crude death-rates Weighted reciprocals of death-rates, 20 to 10.5^ From formuhi (30) hereiuider . . 1.100 ; 1.246 1.119 ; 1.289 1.202 ; 1.366 1.091 ; 1.149 1.1046; 1.2219 If we suppose the factor to change uniformly, that is, if we adopt the formula (30) kt = kge^^ = kom^ = kg (1.01)* as expressing it, and make >n = 1.01, we get the results shewn in the hist hne aljove. From what has preceded we may assume that the value 33.40 for persons may be adopted for the year 1913 (average for the entire year) for Austraha treated as a whole. * The following values are thus indicated for the Commonwealth for the successive years in the table : — Values of k for " Persons," Australia, viz., the Multipliers for the Crude Estimation of the Indication of Wealth as given by the Probate Returns. Year ^ Year k Year k Year k Year k Year k 1878 23.34 188o 25.03 1892 26.83 1899 28.77 1906 30.84 1913 33.40 1879 23..58 1886 25.28 1893 27.10 1900 29.06 1907 31.15 1914 33.73 1880 23.81 1887 25.53 1894 27.37 1901 29.35 1908 31.46 1915 34.07 1881 24.05 1888 25.79 1895 27.65 1902 29.64 1909 31.78 1916 34.41 1882 24.29 1889 26.04 1896 27.92 1903 29.94 1910 3.2.42 ' 1917 V 1883 24..54 1890 26.31 1897 28.20 1904 30.24 1911 32.74 1918 ') 1884 24.78 1891 26.57 1898 28.48 1905 30.54 1912 33.07 1919 ? It is not to be understood that the precision is certainly as indicated by the figures as given ; these factors may possibly be in error even in the units place ; they are found by making m = 1.01, and k for 1913, 33.403. 26. Correction for wealth of absentees. — The New Soutli Wales and also the Victorian retiu-ns shew that an appreciable amount of wealth belongs to " absentees," viz., to persons whose estates, and generally whose domicile, are in New South Wales or Victoria, but who die outside the State. The State records do not furnish their age at death, consequently all that is known is their numbers and the \-alues of their estates. The following table shews the results for the years 1908-15 inclusive, and are divided according to sex and into two four -year groups. A small niunber of " unsjiecified" cases are also included, i.e., cases for which the ages are not given : — 1. The actual results were :— Males. 0.01693. 0.01.'').')3: 0.01-J68 : Females, 0.01316. 0.01202, 0.011.'>4. The weights applied were : Males 1, females 0.2627. piviup for the weighted rates 0.01614, 0.01480, and 0.014IK! : the reciprocals are 61.96, 67.57, and 71.28. the ratios of the second and third to the lirst heing l.dlHIJand 1.1504. 2. This would give 33.734 as the average for the year 1914. 15y taking the aggregate of all tlie probates of Victoria for 1908-191.'>, of New South Wales for 1911-1915. of Queensland for 1916, we obtain the following distribution for the several age-groups as liefore : — Males .00012 .00059 .00804 .02429 .06950 .13863 .20752 .32274 .21420 .01431 Total 1.00000. Females .00057 .00110 .00916 .03847 .07438 .13292 .19632 .30745 .21198 .02765 Total l.ooooo. This gives with the mean of the ratios of the living to the dying for Victoria an == 33.416, which would coincide with the epoch 1914.0 for 1914.5, this is ab(mt 33.583, whidi may '« compared with 33.734 above. Having regard to all the facts the latter is believed to be the more accurate value. 116 The Estimation of Wealth from Probate Returns. Ratio of Absentees to Probate Totals , excluding Absentees.* Victoi'ia. N. S. Wales. Q'land. Period. 1908-11. 1912-15. 1908-15. 1911-13. 1911-15. 1916. Ratio of Numbers. Males Females Persons .0832 .0630 .0760 .0709 .0591 .0666 .0769 .0610 .071;^ .0598 .0474 .0563 .0629 .0455 .0579 .0969 .1027 .0982 Ratio of Amounts (Net Values). Males .0544 .0563 .0554 .14.58 .1465 .24::7 Females . . .0704 .0764 .0735 .1423 .1334 .6767 Persons .0576 .0605 .0592 .1452 .1442 .3075 * In these results the inispecifled cases as to age are not included : they have been distributed (proportionally) among the age-groups. The results for New South Wales differ sensibly from those of Victoria as regards " amounts," though not as regards " numbers " ; while those of Queensland differ in both respects. The latter, however, cannot be regarded as normal in view of the probable influence of the war on the results, and consequently no appreciable error will probably arise if they are simply proportionally distributed among the age- groups. Having regard to the inherent limitations of ascertaining the rate of devolution, the imprecision of the distribution suggested will be relatively negligible. If a ^ factor be used, the simplest method will be to merely add the absentee cases to the aggregate of the fully specified and vxnspecified cases before multiplying by the factor. If, however, the aggregate of wealth is deduced from the fully specified cases only, the total of which is B, and the totals for the absentees and unspecified be A and U respectively, then the correction factor c, to be multiplied into the result, will be : — (31) c = (-B -f U + A) / B or, if the unspecified cases have been distributed, and i?' = S + C/, we have (31a) c = {B' + A) / B' as the correcting factor. This is probably of the order of 1.07 or 1.08 for the entire Commonwealth. 27. Effect of insurance policies in probate returns. — In a country like Australia, where life assurance is relatively widespread, the inclusion of the amounts of insur- ance paid in probate returns has the effect of making them appear too favourable in respect of accurately representing the wealth of the balance of the population, inas- much as the executors of deceased persons have received the full value of the policies with all bonuses, etc., while the value which can be regarded as (potentially) possessed by the balance of the population is, of course, only the fvill " surrender -value. "^ 1. This has been pointed out by Mr. A. M. Laughton, F.I.A., F.r.A., etc., and see Victorian Year Boolv, 1913-14, pp. 589-592. The Rate of Devolution. 117 The opposite is the case with regard to annuities, pensions, superannuation allow- ances, etc., which tend in the direction of causing an under-estimate of the amount of wealth possessed by the living. We proceed to form a quantitative estimate of these influences on the results. From recent returns it appears that of the total claims under assurance policies paid by life assurance companies in Australia, about four -sevenths of the total is payable in respect of the death of the policyholder, and about three -sevenths in respect of the maturity of policies. For the five years 1908 to 1912, the total amount of the claims made in Australia \inder life assiu-ance policies was £11,884,748, which, on the basis quoted above, would represent a payment of abovit £6,790,000 in respect of death benefits. For the five years under consideration, the amount of the assurance policies in force in Victoria represented about 32 per cent, of the total for Australia, and consequently the paj-ment for death benefits in Victoria in respect of life assurance policies was approximately 0.32 X £6,790,000, or about £2,170,000 in the aggregate for the five years 1908 to 1912, or say, on the average £434,000, in a year. Similarly, for the same period, the amount paid as annuities by life assurance companies in Victoria was approximately £25,000 per anninn. From the returns of one of the largest of the Australian companies, it appears that, as at 31st December, 1913, the appropriate reserve value of svmis assured and bonuses aggregating to £96,750,000 was £29,300,000, or about 30% of the face value of the policies, while, in the case of life annuities of £79,000 per annum, the capitalised value was £665,000, or on the average about 8.4 years' pvu-chase. It would thus appear that for the 5 years 1908 to 1912, the exclusion in the case of Victoria of con- sideration of the special features of life assurance and annuity policies w'ould have the effect of overstating the wealth of that State by k times 70 per cent. - of £434.000, or about £300,000 X h, in respect of assiu-ance, and of imderstating it by the absolute amount of £25,000 multiplied by 8.4, viz., £210,000 in respect of amiuities. The quantity k denotes the appropriate multiplier iised for converting amount subject to probate into total wealth. \^'ith a multiplier of say 32,^ the net result would be an overstatement of about £9,400,000 in the estimate of the total wealth of Victoria. A correction for this would reduce the estimate to about 96 per cent, of the imcor- rected total wealth.* Consequently, in order to allow for the overestimate due to the falling-in of life policies at death, the results for the Australian States should be multiplied by about 0.96. 28. Ratio of net to gross values of estates in probate returns. — In certain cases the only available data are the gross values of the estates appearing in probate returns. Where this is the case, it is clearly necessary to deduce the latter from the former in order to ascertain the total private wealth. Unfortimately, however, complete information does not exist as to the relation between the two values, inasmuch as available information connecting these extends back only a few years. The circumstances are different in each State : each will therefore be referred to in turn. Victoria. — The retiuris for 1908-15 give the ratios in tlie table hereinider, in which the available results for New South Wales, South and ^\'estern Australia, and Qiieensland are also given for comparison. 2. That is 100% — 30°o, vide supra. 3. The result for 190S-12 for Victoria is about 32.64. 4. If we take £233,000,000 as the average tot-al wealth for the period considered, the result is 0.9596. 90 Ab- and sent- over ees. ,9158 .9382 ,9229 .9624 .9183 .9438 J 13 The Estimation of Wealth from Probate Returns. Ratio of Net to Gross Values of Estates. State. Victoria. S.A. W.A. N.S.W Q'ld. Year . . 1908. 1909. 1910. 1911. 1912. 1913. 1914. 1915. 1912. 1912. 1902-11. 1916. Males .. .8425.8194.8626.8624.8663.8669.8771.8645 ? ? ? .6754 Females .8878.8734.9200.8988.9175.8900.9085.9191 ? ? V .8504 Persons .8502.8302.8747.8694.8776.8713.8838.8751 .8353 .7258 .8907 .7031 This ratio or factor of reduction is, however, not uniformly distributed in regard to age, as one might naturally expect, and differs for males and females. It has consequently been taken out in sex and age-groups, the results being as follows : — Ratio of Net to Gross Value of Estates according to Age-groups, Males and Females, Victoria, 1908-12. Years. Ages. 1908-12. 10-14. 15-20 21-29 30-39 40-49 50-.59 60-69 70-79 80-89 Males 1.0000 .8840 .7877 .6858 .7505 .8079 .8171 .8687 .9236 Feniales .970,'. .8712 .8730 .8276 .8521 .8888 .8784 .9132 .9326 Persons .9823 .8802 .8071 .7268 .7700 .8245 .8290 .8781 .9249 The ratio of the net to gross values appears for every age to be characteristically different for males and females. A curve drawn through the group-values for each sex indicates that the encumbrance on estates increases in each to the age of about 35 or 36, and then diminishes, the ratio of net to gross values being about 0.67 in the case of males, and about 0.815 in the case of females. This dissimilarity is confirmed when the results are taken out for all ages in one group, the result for Victoria for the period 1908-1912 being as follows : — Including absentees Males .85176 Females .90139 Persons .86167 Excluding „ „ .84658 „ .89715 „ .85673 Except that there is less encmnbrance on the estates of females, the two con- tinuous curves, which are indicated by the group-values in the preceding table, are very similar. (See Fig. 7, page 133.) The facts shew that males and females cannot be regarded as a homogeneous oTOup, and consequently probate results should not be grouped together for " per- sons," but kept separately for males and females ; the grouping of them together tends to increase the measure of uncertainty when deductions are made of the total private wealth either from net or from gross value. Neiv South Wales. — ^The relation of gross and net values for New South Wales depends upon retiu-ns for the decade 1902-1911. Mr. J. B. Trivett, Statistician of that State, gives the results, shewn later, from Probate Court and Stamp Duty returns ; see Official Year Book, New South Wales, 1912, p. 257. The gross value irrespective of encumbrances, was shewn in his report, also the net value of the estates, since it is upon these that the duty is paid. The two retiu-ns liave not been co-ordinated year by year, however, and the nmnbers are not in exact agreement, inasmuch as Probate Coiu-t returns refer to the year ending 31st December, and the Stamp Duty returns to the year ending 30th June. This involves some difficulty in ensuring a satisfactory determination of the ratio in question. However, the average ratios for the periods 1902-5, 1906-8, 1909-11^, are 0.8322,0.8669, and 0.9526 respectively, while the ratio for the whole period 1902-11 is 0.8907, though the mean of the tliree ratios is only 0.8839. The results indicate that for New South Wales there is probabi}^ an iixcrease of about 0.018 per annum on a mean of about 0.884, and for Victoria about 0.017 on about 1. Obtained by dividing tlie total values, gross or net, by the number of estates, and ascertaining the ratio of the quotients. The Rate of Devolution, 119^ 0.840 ; in other words, the rate of the improvement for Victoria is about 60% of that of New South Wales. Such results cannot, of course, be extrapolated in order to discover the relationship between net and gross values for earlier jDeriods. South AiiMralia and Western Australia. — The only resiilts available for the States of South and Western Australia are those for 1912, the results bemg : — for the former, 1391 estates, the gross and net values of which were respectively £2,408,732 and £2,011,589 ; for the latter, 864 estates, the gross and net values being £841,800 and £605,622. These give the ratios 0.83528 and 0.72575. For the State of Queensland there are no available data shewing the relationship of gross and net values before 1916. For that year the data give the result shewn in the preceding table (earlier part of this section). For the State of Tasmania there are no available data. The Commonwealth.- — By weighting the preceduig results we obtain a factor for the Commonwealth, viz., 0.8620, which may be applied throughout if we assume that this relation is constant. Such assumiDtion is, of course, a precarious one, for it is quite possible that the indication of the results for New South Wales for the past ten years and those for Victoria applj' generally. 29. Effect of re-grants and re-seals. — In estimating wealth from probates, it is necessary to take account — inter alia — of the amounts appearing in what are known as re-grants and re-seals. The former denote second probates granted, for example, where the values of the estate are found to be quite different from what initially appeared to be the case : the latter denote actions taken by the probate authorities of a State (other than that in which the possessor of the wealth was domiciled) for the portion of the estate within the territory over which they have jurisdiction. The aggregates of the numbers for a combination of States are obviously in excess of the number dying; the aggregates of the wealth, however, contain no such duplica- tion, but the k factor to be applied would probably be that of the State in which they initially arise, not the State to which they are referred. In view of the great measure of vmcertainty in the " multiplier," however, it will suffice to add their values to the probate-totals. 30. Corrections for wealth passing by settlements. — In Chap. I., § 1, of this part, p. 68, it is mentioned that de Foville has shewn that accoimt must be taken of settlements, which are virtually anticipations of inheritance, and also that Gini has established that, in Italy, the interval between successive settlements was sensibly equal to the interval between successions. It is obvious that when wealth is conveyed by gift diu'ing a lifetime, the a»(. Males. Males. Net Values Age Crude Data. Smoothed Results. per Probate. Ratio Probates last From to Deaths Birth- No. of No. of Net No. of No. of Net Sm'th- Again from day. Deaths Pro- Values. Deaths Pro- 1 a lues ed Sm'th- Smooth' d E«sults. US' bates. bates. Results ed. £1,000 i 1 £1,000 ^ £ 55 718 313 i 652.3 783 324 649.8 2,006 2,006 .414 56 753 316 412.7 769 318 671.8 2,113 2,113 .414 57 738 314 999.9 753 313 691.1 2,208 2,208 .415 58 757 365 860.8 734 311 709.4 2,281 2,283 .424 59 678 299 652.0 710 311 727.7 2,340 2,340 .438 60 859 315 553.5 694 314 748.0 2,382 2,389 .452 61 556 227 604.1 697 318 772.3 2,429 2,438 .456 62 698 305 1070.4 715 3.25 805.8 2,479 2,487 .455 63 764 335 738.5 740 333 847.3 2,544 2,538 .450 64 758 350 984.0 780 346 895.0 2,587 2,590 .444 65 1,013 424 979.4 827 359 952.8 2,654 2,654 .434 66 803 353 955.5 866 373 1022.9 2,742 2,742 .431 67 839 387 800.0 903 388 1106.1 .2,851 2,851 .429 68 1,006 431 1072.3 943 405 1217.9 3,007 3,007 .429 69 895 452 1717.8 982 426 1313.1 3,082 3,082 .434 70 1,214 511 1679.2 1,019 446 1390.3 3,117 3,117 .438 71 910 439 1331.3 1,056 468 j 1451.2 3,101 3,101 .443 72 1,073 497 1326.4 1,093 493 1 1501.9 3,046 3,046 .451 73 1,115 509 1378.2 1,131 521 1546.6 2,969 2,969 .461 74 1,150 514 1548.1 1,167 551 1581.1 2,870 2,870 .472 75 1,349 607 1612.2 1,204 580 1609.0 2,775 2,775 .482 76 1,226 557 1590. .2 1,241 599 1633.9 2,728 2,728 .483 77 1,151 573 1643.7 1,277 612 1654.1 2,702 2,702 .479 78 1,443 654 1485.6 1,297 616 1668.3 2,708 2,708 .475 79 1,214 560 1456.0 1,291 604 1672.4 2,769 2,769 .468 80 1,393 643 .2644.9 1,.'^44 577 1655.1 2,869 2,850 .464 81 1,000 466 1150.5 1,177 532 1572.9 2,957 2,930 .452 82 1,084 485 1515.4 1,097 483 1451.2 3,005 3,020 .440 83 971 427 1004.2 1,000 424 1329.4 3,136 3,120 .424 84 968 424 1437.2 898 367 1197.4 3,262 3,220 .409 85 734 294 779.6 775 315 1055.4 3,350 3,320 .407 86 647 292 1012.0 626 264 903.1 3,420 3,410 422 87 484 209 902.5 504 £09 740.8 3,545 3.490 .415 88 400 154 512.5 404 159 578.5 3,638 i 3,540 .394 89 322 119 433.8 315 125 426.2 3,410 3,580 .397 90 244 83 211.4 243 95 284.2 2,992 3,620 .391 91 148 58 143.8 183 69 203.0 2,942 3,650 .377 92 124 47 104.7 136 48.0 152.2 3,171 3,670 .353 93 96 32 706.8 98 32.0 114.7 3,584 3,670 .327 94 64 24 240.9 69 21.3 89.3 4,192 3,660 .309 95 47 16 45.8 40.3 14.2 68.0 4,789 ! 3,650 .352 96 41 10 21.4 27.3 9.5 50.7 5,337 3,640 .348 97 22 7 4.6 18.2 6.3 36.5 5,793 3,620 .346 98 19 12 2.6 11.7 4.2 24.4 5,809 ' 3,580 .358 99 10 2 0.8 7.0 2.8 14.2 5,070 1 3,530 .400 100 9 2 5.4 4.3 1.9 6.1 3,211 ! 3,470 .442 101 7 1 0.1 2.9 1.3 4.0 3,420 102 2 1.8 0.9 2.4 3,350 103 1.1 0.6 1.0 3,250 104 1 0.7 0.4 0.4 105 0.3 0.3 0.3 106 0.2 0.2 0.2 . . 107 3 2 V.O 0.1 0.1 0.2 108 1 0.1 0.1 109 0.1 110 & 1 1 over 1 0.1 Unspec. 16 7 8.1 Totals 68,813 21,017 A t8363.3 68,813 21,017 ^ 18363.3 1 j 1 124 The Estimation of Wealth from Probate Returns. Distribution of Wealth among the Dying, according to Probate-Returns, Victoria, 1908-1915. 55,726 Deaths o£ Females.— con*. Females 1 Females. Net Values 1 !Et,atio Crude Data. I Smoothed Results. | pei Probate. Probates Age to last From 1 Deaths Birth- Xo. of No. of Net No. of No. of Net smoc )th- Again from day. Deaths. Pro- bates. Values. Deaths. Pro- bates. Values. ed Results. smooth- ed. Smooth' d Results. £1,000 £1,000 £ £ 8,612 1 2 8,612 0.1 0.1 400 000 1 1,539 o!o 1,539 0.1 0.1 401 .000 2 553 0.0 553 0.2 0.1 402 .000 3 417 0.0 417 0.3 0.2 403 .001 4 322 0.0 333 0.4 0.2 404 .001 5 288 0.0 286 0.5 0.2 405 .002 6 250 1 0.2 249 0.6 0.3 406 .002 7 226 1 0.1 220 0.7 0.3 407 .003 8 199 1 2.1 198 0.8 0.4 408 .004 9 167 0.0 180 0.9 0.5 409 .005 10 159 3 1.0 163 1.0 0.0 410 .006 11 150 0.0 153 1.1 0.7 412 .007 12 154 0.0 155 1.3 0.8 414 .008 13 167 2 1.2 169 1.7 0.9 416 .010 14 188 4 0.8 187 2.3 1.0 418 .012 15 211 3 0.6 208 3.2 1.1 3 44 420 •015 16 240 3 0.7 233 4.0 1.2 3 00 423 .017 17 262 6 3.0 262 5.2 1.5 2 88 426 .020 18 296 5 1.4 292 6.6 2.1 3 18 429 .023 19 320 6 1.7 317 8.1 2.7 3 33 433 .026 20 318 10 4.8 337 10.0 3.7 3 70 437 .030 21 335 12 2.3 354 12.2 5.0 4 10 442 .035 22 399 21 8.7 370 1.48 6.4 4 33 447 .040 23 411 15 7.4 382 18.0 8.0 4 44 453 .047 24 363 20 11.6 388 21.5 9.8 4 56 462 .055 25 353 19 4.2 392 25.1 11.7 4 66 471 .064 26 390 33 19.7 393 29.5 13.8 4 68 480 .075 27 387 40 16.2 392 34.0 16.0 A [1\ 489 .087 28 442 39 20.8 .389 38.5 18.3 4 75 497 .099 29 370 42 16.2 386 43.1 22.7 £ 27 504 .112 30 404 51 16.3 382 48.2 25.5 S 29 510 .126 31 357 49 11.2 375 54 28.4 S 26 515 .144 32 .390 52 41.3 373 59 31.4 L ►32 520 .158 33 345 55 14.1 378 64 34.5 39 525 .169 34 399 79 67.2 384 69 37.8 I .48 531 .180 35 413 81 51.7 394 75 41.4 £ ►52 538 .190 36 458 85 53.4 407 81 45.4 t ►60 548 .199 37 372 79 38.5 416 87 49.9 I ►74 561 .209 38 489 116 82.5 422 94 55.0 f >85 577 .223 39 437 109 48.8 426 101 60.8 ( )02 597 .237 40 479 116 66.9 430 108 67.4 { )24 625 .251 41 338 79 50.8 436 115 75.9 ( ►60 655 .264 42 521 136 97.2 445 121 82.9 ( ►85 675 .272 43 420 118 60.4 458 127 89.6 '06 700 .277 44 458 132 92.1 478 133 96.0 r2l 720 .278 45 555 145 110.4 507 137 102.4 ^47 740 .270 46 468 117 147.0 530 141 108.8 ^72 762 .266 47 503 162 89.0 543 145 115.2 r95 786 .267 48 528 145 79.2 548 149 121.6 i 516 812 .272 49 556 165 113.7 547 153 128.0 i 537 838 .280 50 573 162 159.1 541 157 134.4 J 556 862 .290 51 439 125 111.5 534 160 140.8 J 580 885 .300 52 557 190 171.9 523 163 147.2 ( )03 908 .312 53 504 162 174.0 511 165 153.6 i )31 930 .323 54 535 172 134.0 503 167 160.0 i )58 951 .332 55 470 145 140.8 496 109 166.4 ; )85 970 .341 The Rate of Devolution. 125 Distribution of Wealth among the Dying, according to Probate-Returns, Victoria, 1908-1915. 55.726 Deaths o? Females. — COIit. Females Females Net Values Ratio Probates to Deaths Age Crude Da ba. Smoothed Results. per Probate. last From Birth- No. of No. of Net No. of No. of Net smooth- Again from day. Deaths. Pro- bates. Values. Deaths. Pro- bates. Values. ed Results. smooth- ed. Smooth'd Results. £1,000 £1,000 £ £ 55 470 145 140.8 496 169 166.4 985 970 .341 56 522 191 252.3 491 171 172.8 1,010 990 .348 57 503 178 274.8 489 174 179.2 1,030 1,010 .356 58 496 176 150.4 486 177 185.6 1,048 1,028 ..364 59 507 180 171.3 486 181 192.0 1,061 1,044 .372 60 543 191 175.2 492 185 199.5 1,078 1,058 .376 61 390 168 176.2 505 190 208.1 1,095 1,073 .376 62 557 210 258.7 525 196 217.3 1,109 1,089 .373 63 583 207 200.7 552 204 227.6 1,116 1,105 .370 64 552 214 171.3 587 214 239.0 1,117 1,121 .365 65 710 255 355.6 633 226 253.0 1,120 1,137 .357 66 593 220 247.6 676 241 272.0 1,129 1,153 .357 67 708 275 309.9 717 258 292.0 1,132 1,168 .360 68 810 301 270.2 746 277 316.0 1,141 1,182 .371 69 738 284 326.4 787 297 324.0 1,091 1,195 .377 70 984 355 355.3 818 317 370.0 1,167 1,207 .387 71 720 272 539.4 858 336 400.0 1,191 1,218 .392 72 912 327 297.1 945 351 428.1 1,220 1,228 .371 73 969 355 394.1 1,034 364 446.1 1,226 1,244 .352 74 1,078 351 541.3 1,090 369 452.1 1,225 1,244 .339 75 1,149 426 467.0 1,113 370 450: 1 1,217 1,252 .332 76 1,143 360 360.5 1. 101 365 440.1 1,206 1,259 .331 77 993 3.'^7 467..'^ 1,070 351 428.1 1,220 1,221 .328 78 1,101 349 39.5.7 1.031 332 406.1 1.223 1,217 .322 79 924 297 397.2 980 311 380.0 1,222 1,215 .317 80 1,034 312 349.8 924 289 347.0 1,201 1,180 .312 81 705 218 267.7 859 .'^65 315.0 1,189 1,170 .308 82 834 247 279.9 790 2.38 284.0 1,193 1,170 .301 83 735 216 239.0 726 211 254.0 1,204 1,180 .291 84 750 213 262.1 662 185 224.0 1,211 1,200 .280 85 573 166 235.4 591 160 196.0 1.225 1,220 .271 86 527 135 162.4 513 136 169.0 1,243 1,240 .265 87 404 100 115.7 428 112 143.0 1,277 1,270 .262 88 371 100 115.2 355 91 119.0 1,308 1,300 .256 89 254 65 87.4 287 73 97.0 1,329 1,330 .254 90 251 66 101.7 225 57 77.0 1,351 1,350 .253 91 152 36 44.8 175 44 59.0 1,341 1,330 .251 92 119 35 72.2 127 34 45.0 1,324 1,300 .268 93 103 15 20.9 97 25 33.0 1,320 1,260 .258 94 76 15 9.4 74 17 23.0 1,353 1,230 .230 95 52 16 23.5 56 13.5 15.0 1,111 1,140 .241 96 46 10 19.4 41 9.5 8.0 842 1,030 .232 97 27 3 18.3 30 6.3 5.0 793 910 .210 98 27 4 6 21 4.2 3.0 714 780 .200 99 16 1 0.2 14 2.8 2.0 714 640 .200 . 100 13 2 2.3 8.5 1.9 1.2 632 490 .223 101 3 0.0 5.5 1.3 0.7 320 102 4 2 0.6 3.3 0.9 0.4 103 2 0.0 2.0 0.6 0.3 104 0.0 1.2 0.4 0.2 105 2 1 0.4 .9 0.3 0.1 106 1 0.0 .6 0.2 0.1 107 1 0.0 .4 O.l 0.1 108 0.0 .3 0.1 109 0.0 .2 0.1 110 & over 1 0.0 .1 0.1 Unspec. 2 3 1.0 1 Totals 55,726 11,764 12330.9 55,726 11764.0 12330.9 126 The Estimation of Wealth from Probate Returns. 32. Distribution according to age probably not constant. — In order to obtain the values in the table of § 25, a constant relative distribution of aggregate wealth according to age-groups was assumed. Such constancy is, however, improbable. We may now consider the question further. If the ratio of the number of probates to the total number of persons dying in a given age-group be constant from year to year, and the death-rate in that age-group be also constant, it will follow as a consequence that the numbers of probates will vary from year to year as the numbers living in the given age-group of the jjopulation, and if at every date the average wealth for that group be relatively the same (i.e., similarly related but not necessarily identical in amovuit) the aggregate amounts of the probates in that age-group will vary as the numbers ; in short, the wealth in any age-group will vary with the population in that group. Thus, if we have the absolute or relative con- stitution according to age of the population at two dates, i.e., if we have for each date, either (.32) P = Pj -f P,^ + etc., ov \ -= p^ + p^ + etc., we can deduce for one date the probate distribution of the relative amovmt of the probates from the given distribution at the other date. As in Chapter II. of this part, let Ux, denote Wx/Sw, and in (32) above let accented quantities denote values at any jDarticular date, which are to be referred to a date for which the distribution is known, then, subject to the assumption referred to holding good, we have : — (33). .u'n = frUnPn/ Pn = h^hi P'n / Pr the constants g and h being so taken that Eu' =1.' Thus a probable distribution scl:ieme (series of values of %i') can be deduced, based upon known age -distributions of the 23opulation. Similarly, it could be based upon the ratio of the number of deaths occurring in the various age-groups. 33. Correction for variations in the age-distribution. — From the several censuses the ratios of the relative distributions of population according to age ^ are as shewn in the following table. It will be noticed that the variations are very irregular. Ratios of Relative Populati< 3ns. Males. Females. Age- group 1881. 1891. 1901. 1911. 1881. 1891. 1901. 1911. 0-9 1.173 1.154 1.060 1. 1.284 1.243 1.085 1. 10-14 1.193 1.068 1.188 1. 1.295 1.139 1.210 1. 15-20 1.02.5 .921 .963 1. 1.115 1.006 1.010 1. 21-29 .920 1.110 .905 1. .901 1.064 .975 1. 30-39 .893 1.032 1.106 1. .795 .880 1.009 1. 40-49 .926 .740 .909 1. .809 .689 .832 1. 5(>-.59 .946 .844 .773 1. .782 .835 .780 1. 60-69 .868 .996 1.089 1. .668 .825 1.022 1. 70-79 .585 .652 .922 1. .462 .542 .773 1. 80-89 .500 .579 .768 1. .345 .493 .744 1. 90 & over .455 .818 .757 1. .425 .450 .600 1. All Ages 1. 1. 1. 1. 1. 1. 1. 1. 1. AlthouRh P'/P is not the same quantity as p'/p {e.g., one may be greater while the other is less than unity), it is easily shewn that when the factors o and h are applied to their respective cases, so as to make the sum unity, the resultant values of u',^ are identical. 2. See (lensus o Ithe ("omnionwealth of Australia, 1911, Vol. II., p. 37, Table 22. The Rate of Devolution. 127 Computed Relative Distribution of Probate Aggregates. M. VLES. Females. Age- group 1881. 1891. 1901. 1911.* 1881. 1891. 1901. 1911.* 9 .0000 .0000 .0000 .00000 .0000 .0000 .0000 .00000 10-14 .0002 .0002 .0002 .00012 .0013 .0010 .0008 .00057 15-20 .0008 .0007 .0006 .00059 .0022 .0017 .0013 .00110 21-29 .0105 .0118 .0081 .00804 .0147 .0149 .0108 .00916 30-39 .0306 .0332 .0297 .02429 .0543 .0518 .0469 .03847 40-49 .0910 .0681 .0699 .06956 .1069 .0785 .0748 .07438 50-59 .1852 .1548 .1185 .13863 .1846 .1699 .1253 .13292 60-69 .2545 .2734 .2500 .20752 .2329 .2480 .2424 .19632 70-79 .2667 .2783 .3291 .32274 .2523 .2551 .2871 .30745 80-89 .1513 .1640 .1819 .21420 .1299 .1600 .1905 .21198 90 & over .0092 .0155 .0120 .01431 .0209 .0191 .0201 .02765 All Ages 1.000 1.000 1.000 1.0000 1.000 1.000 1.000 1.0000 * This distribution is for tlie agfjregate of Victoria. 1908-15 ; New South Wales, 1911-15 ; and Queensland, 1916 ; these being the whole of the available material. The relative weights are : Males, 1.0 ; females, 0.2368. The epoch to which the results apply is about the beginning of 1914. The numbers living to 1 dying have been ascertained from the 1911 Census Life Tables, Part XI. of the Report, vide pp. 1209-1218, and are shewn for the epochs 1886.0, 1896.0, and 1906.0.^ By interpolation and extrapolation we obtam values corresponding to the middle of the census years ; and these, multiplied by the ratios above given, furnish the variations in the values of k for males and females. In order to combine these, the weights 1 and 0.2368 are used respectively for males and females, and in this way k is found for " persons." The R factors used were as follow : — Ratios of Living to Dying, Australia.* Males. Females. Age- group 1881. 1891. 1901. 1911. 1881. 1891. 1901. 1911. 10-14 371.9 417.1 450.9 473.3 371.7 468.7 542.4 610.0 1.5-20 137.5 218.5 288.0 346.0 j 202.8 276.8 332.5 389.9 21-29 96.1 141.7 193.7 252.1 119.6 166.0 211.2 2.55.2 30-39 95.8 114.0 140.8 176.2 101.0 119.8 14G.7 181.7 40-49 63.5 77.9 89.7 98.9 73.8 97.0 116.3 131.7 50-59 37.7 44.5 51.5 58.7 50.8 60.4 72.2 S6.2 60-69 21.6 22.6 24.6 27.6 , 26.7 23.9 26.6 37.4 70-79 10.9 11.3 11.2 10.6 13.2 13.4 13.5 13.5 80-89 5.5 5.3 5.2 5.2 5.6 5.8 6.1 6.5 90 & over 2.9 2.9 2.8 2.6 2.7 3.0 3.1 .3.1 Values of k 25.82 27.75 28.81 31.48 35. 1 1 37.14 38.62 43.51 * See also Table in § 10. These ratios multiplied into the values of u' given in the preceding table, give the values for k (corrected for largeness of groups, see table of § 5, p. 86) shewn in the last line. If the male results are given the weight 1 and the female the weight 0.2368, i.e., the ratio of the probate-aggregates for males and females respectively, the results for " persons" are :— 1881, 27.60 ; 1891, 29.55 ; 1901, 30.69 ; and 1911, 1. More strictly the mean of the periods 1881-1890, 1891-1900, and 1901-1910. 128 The Estimatton of Wealu from Probate Returns. 33.78, while the results given in the table of § 25, p. 115, are respectively 24.05 ; 2.657 ; 29.35 ; and 32.74. If we use the general series shewn in § 25 as a basis, and by linear additions make the additions thereto so as to give values equal to these last- computed values, we obtain the results shewn in the table of § 36, p. 130, herein- after. These have a higher probability than the factors of the table in § 25. 34. Combined corrections. — Owing to the fact that the data as regards jDrobates: are complete only for " gross vakies," and that the limitations of the data preclude all possibility of attainmg to precision in the estimates of total private wealth from probates, the practical sokition may be simiDlified. Thus it will suffice to take the product of the individual corrections and apply this product to the total for Australia. The product of the corrections for assurance for settlements and for the reduction of gross to net values is 0.96 x 1.209 x 0.862 = 1.0005 ; hence, we may accept the gross values without correction and ap^ily the values of k thereto to obtain the aggre- gate of the wealth. 35. Empirical correction of probate results. — The question still remains to be settled whether probate results can be expected to agree with census results without further correction. As shewn on p. 28, the aggregate private wealth of Australia was £1,643,463,376. In a district whose population was 77,350, the total debt for males was about 0.00315 of the assets, for females about 0.00124, and for persons 0.00260, the ratio of the numbers in debt compared with those who (as declared) possessed assets being respectively 0.04340, 0.01433, and 0.02978. The total number of returns in this district was 25,932 out of a total population (all ages) of 77,350, i.e.,. very slightly over one-third. See p. 34 herein. The total nimiber of " not accounted for" in the whole War Census was : males, 1,147,623 ; females, 1,614,461 ; or persons, 2,762,084. Any correction for the amount of debt referred to would be insensible compared with the opposite correction for shortage of returns, and may therefore be wholly ignored. The k factor for the year 1915 is 34.07 (later calcvilation, 34.99); see § 25, p 115.. and the probate aggregate for that year (gross values) is £29,353,000 ; the product of the two is £1,000,057,000 (or £1,027,061,000); hence, to convert the probate estimate mto the census estimate of £1,643,463,376, it is necessary to multiply by 1.6425 (or 1.600161). We could therefore apply this factor to the values of i in the table in§ 25 (or 1.60016 to those in the later table), and thus obtam the values shewn in the table hereinafter ; see p. 130. 36. The growth of Australian wealth.^ — In the following table are shewn the gross values of both the Testate and Intestate estates in Australia for the years 1878 to 1915 inclusive. The figures for Western Australia were not available from 1878 ta 1892, but were estimated in the following manner : — The average value of all estates in the Commonwealth (less Western Australia) was found for the quinquennia 1878-1882 and 1896-1900. These values were £1844 and £2044 respectively. It was assumed that the average value of estates increased linearly from 1880 to 1898, the annualincrease in value being (2044- 1844)/18= £11.1. In Western Australia the average value of estates for the qumquennivim was found to be £1593. This was then reduced in the ratio of the linearly changing figures referred to, carrying on the change past 1880 to 1898. This method was deemed to be sufficiently accurate for the purpose in view. The figures for Intestate Estates. in Tasmania from 1878 to 1884 were computed in a similar mamier. Particulars of Testate and Intestate Estates in 1914 and 1915 were not given separately in the case of New South Wales, but the totals for all estates are given. The Rate of Devolution. Number and Value of Estates of Deceased Persons, 1878 to 1915. 129 Numbers. Year. N.S.W. Vic. Q'land. S.A. W.A. Tas. Commonwealth. P. + I. P. + I. P. + I. P. + I. 1 P. + I. P. + I. P. + I. 1 Total. 1878 1,087 - ^20: 1,341 +25c 191 + 15S 420+ 521 48+ 48 142+ 30 3,229 + 749 3,978 1879 1,051 19i 1,385 21£ 236 231 480 5£ 33 33 148 31 3,333 769 4,102 1880 1,173 212 1,235 204 ! 184 163 471 bi ! 37 37 133 28 3,233 702 3,935 1881 1,197 300| 1,548 1861 255 181 464 57 49 4S 174 36 3,687 810 4.497 1882 1,399 280 1.698 220! 318 27 C 543 67 1 49 49 182 38 4,189 93 ?t 5.118 1883 1,475 283 1,794 2381 312 27-1 553 6S 69 6S 165 35 4,368 96 "i 5335 1884 1,581 320 1.890 212| 406 4S4 624 77 64 64 266 56 4,831 1,163 5,994 1885 1,620 351 1,938 224! 509 351 556 6it 72 72 1 223 57 4,918 1,124 6,042 1886 1,732 271^ 2,126 254 1 488 36L 640 7£ 75 75 ' 246 39 5.307 1,078 6,385 1887 1,626 319:2,348 310 342 321 608 7c 70 7U 240 45 5,234 1,140! 6,374 1888 1,665 321 2,276 301! 493 288 564 6f 73 73 249 54 5,320 l,106l 6.426 1889 1,797 321 2,908 359 406 281 602 74 73 73 225 59 6.011 1,16 '1 7.178 1890 1,811 331 3,107 347 550 254 694 86 73 73 262 53 6,497 1,144 7.641 1891 1,959 419 2,711 331 529 197 732 9C 96 96 283 49 6.310 1,18. i 7.492 1892 2,129 436 3.208 243 577 248 742 91 112 101 281 39 7,049 1,158 8,207 1893 1,965 390 2.801 200 524 249 654 81 132 128 318 36 6,294 1,084 7,378 189-1 2.163 386 2,805 233 572 198 734 9C 112 148 201 48 6,587 1,103| 7,690 1895 2,154 422 3,153 184 539 251 778 96 224 283 180 43 7,028 1,279 8,307 1896 2,488 463 3,335 27t 562 350 811 lOU 211 413 216 52 7,623 1,648! 9,271 1897 2.210 433i 3.291 252 544 305 775 95 328 407 233 50 7,381 1,542' 8.923 1898 2,231 491 3.590 267 640 350 863 106 285 363 196 54 7.805 1,631 9.436 1899 2,505 461 3,641 223 620 366 876 108 253 261 192 60 8,087 1,479 9,566 1900 2.452 463 3.961 233 589 168 843 104 265 274 283 78 8.393 1,3201 9.713 1901 2.657 491! 3,846 278 594 149 927 114 313 242 229 85 8,566 1,35c 9,925 1902 2.782 552i 3.976 270 627 192 913 112 347 247 230 95 8,875 1,468 10,343 1903 2.767 582|3;884 30C 710 378 919 113 399 258 256 105 8.935 l,73e 10,671 1904 2.850 580 3.827 155 588 340 964 119 367 245 295 73 8.891 1,511 10.403 190."> 2.804 5401 3.853 191 584 382 902 111 406 264 270 68 8,819 1,5561 10.375 1906 2,852 46813,982 177 602 406 1.020 126 1 476 330 343 67 9,275 1,574 10,849 1907 3,084 .595 1 4. 1.56 172 599 497 975 103 423 300 414 70 9,661 1,737 11,398 1908 3.094 58314.105 240 706 492 1.011 120 455 301 346 98 9,717 1,834 11,551 1909 3,185 598 3.831 238 679 572 1.085 149 413 275 361 95 9.554 1,927 11,481 1910 3.336 62513,870 258 704 539 1,110 196 492 304 375 100 9,887 2,022 11,906 1911 3.589 656 4,265 349 729 623 1.057 127 584 300 399 88 10,623 2,143 12,766 1912 3.617 785,' 4,267 318 755 659 1.214 145 552 312 465 116 10.870 3,335 1 13,205 1913 4,279 835 4,185 298 765 782 1.373 147 580 292 459 61 11,641 2,415 14,056 1914 *4.438 4,070 381 831 646 1,418 181 577 330 402 84 13,358 1915 *5,088 4,011 438 896 673 1,515 157 682 268 455 64 14,247 Gross Value. Year. N.S.W. Vic Q'la 1(1. S.A W.A Tas Commonwea 1th. P. + I. P. + I. P. + I. P. + I. P. + I. P. + I. P. + I. Total. (£1,000.) ' (£1,000.) (£1.000.) (£1,000.) (£1.000.) (£1.000.) (£1,000.) (£1,000.)! (£1,0C0.) 1878 2,016 + 17| 2,919 + 37 2i8+ 8 411+ 4 66+2 254+ 5 5,884 + 73 5,957 1879 2.387 Hi 2.666 46 281 15 662 6 46 1 313 5 6,355 84 6.439 1880 1.534 24 1 1.890 28 144 13 342 3 52 1 260 5 4.222 74 4:296 1881 2,319 28! 2.935 78 163 9 719 7 69 2 303 6 6,508 130 6.638 1882 4,168 23 j 3.483 30 534 8 1,087 10 69 2 171 6 9,512 79 9.591 1883 4,117 35 3,748 35 460 14 869 8 98 3i 172 6 9,464 101 9,565 1884 4.248 29l 5.114 36 662 11 660 6 92 2 264 10 11,040 94 11,134 1885 4.323 24! 4.298 30 693 18 702 6 104 3I 249 9 10,369 90 10,459 1886 5.496 13 4.532 26 643 14 698 6 11(1 3 220 10 11.699 72 11,771 1887 4.263 211 5.201 44 835 11 584 5 103 3, 284 10 11.270 94 11,364 1888 4,291 16 7,027 36 1.087 14 365 3 108 3 241 7 13.119 79 13.198 1889 4.791 391 11,252 35 670 13 1,137 loi 109 3 297 7 18.256 107 18.363 1890 7.. -.28 72 8,667 36 1,081 12 1,071 10 110 3 528 7 18.985 140 19,125 1891 5.457 65 7,582 31 848 10 684 6 145 31 411 9 15.127 124 15,251 1892 5,769 26 9,670 26 860 14 1.138 10 171 6 269 9 17,877 91 17,968 1893 4,144 16 6,232 13 1,123 9 786 71 203 5| 236 9 12.724 59 12.783 1894 5.299 17 5,419 24 641 7 1,733 16 174 6 261 8 13.527 78 13,605 1895 4,858 24 5,340 24 1,105 6 1,560 14 349 13 217 5 13.428 86 13,514 1896 6,695 18 6,091 20 1.384 12 1,161 11! 291 14 205 7 15,827 82 15,909 1897 5,925 23 5,782 23 1.988 12 2,083 19 5.54 12 378 13 16,710 102 16,812 1898 5.936 251 6,269 32i 1.228 16 2,375 22[ 659 11 241 9 16,698 115 16,813 1899 5;064 271 5.920 22! 2,613 47 1,155 lit 274 !»! 556 5 15..582 122i 15.704 19C0 4,731 23 6,919 27 1,085 5 1,378 13 360 9 406 10 14.K79 87 14,966 1901 7.033 33 6,527 18 1,594 6 1,457 13 616 9 402 10 17.629 Sit 17,718 1902 1 5,807 34 7,571 22 1,079 10 1,790 16 488 11 299 17 17,034 110 17,144 19U3 7,180 25 6,088 3(1 2.617 15 2,464 22 703 11' 253 15 19.305 118 19,423 1904 6 156 41 5,783 14 1,513 20 2,057 19 423 16| 905 6 16;837 116, 16,953 1905 i 7,715 31 6,017 21 1.016 15 1,295 12 677 12 504 4 17,224 95 17,319 1906 7,529 22 6,434 30 1.795 16 2.041 19! 545 10 862 5 19.206 102 19,308 1907 7..563 .36 6,860 18 1,3.58 17 1.924 18! 1.154 8 841 8 19,700 105 19,805 1908 1 7.839 29 8.362 22 1.376 18 2,077 13 956 7 1,024 11 21,634 100, 21,734 1909 11,142 50, 7,790 16 1.509 19 1,929 19 939 8; 722 9 24.031 121 24,1.52 1910 1 8,835 40: 8,478 171 1,653 19 2,397 24 869 8 798 9 23,030 117! 23,147 19U 13,138 46 9.713 28 1 2,409 43 2,855 20, 844 8 597 7 29.556 152 29,708 1912 10,722 .54 9,697 26 2,730 36 2,291 25 842 13 984 3 27.266 157 27,423 1913 11,756 68 9,578 26 2.640 21 2,733 15 796 7 729 131 28,232 150 28,382 1914 *9,998 9,579 18 2,640 70 3,522 32 1,010 8 731 HI 27,619 1915 •10,814 9,982 27 2,731 92 3,372 45 1,272 13 1,005 10, .. 29,353 * Probate and Intestate Estates combined ; separate figures not available. 130 The Estimation or Wealth from Probate Returns. Re-seals and re-grants have been included in every State except Victoria, which includes value, but excludes the numbers, and South Australia, where second grants are excluded. Particulars relating to Intestate Estates in South Australia were not available till 1907. The figures from 1878 to 1906 were computed on the assumption that the proportion of Intestate to Testate Estates in each year from 1878 to 1906 was the same as the proportion of the aggregate figiu-es for 1907 to 1915. Applying to the quinquennial means of the aggregates the deduced factors referred to in § 33, and the corrections referred to in §§34 and 35, we obtain the following results, viz. : — Estimate of the Growth oi Private Wealth in Australia from 1878 to 1915- In- Total In- Total In- Total creased Value Wealth, creased Value Wealth, creased Value Wealth, Year. Total, of £l,0()!Jt Year. Total, of £l,000t Year. Total, of £l,000t £1,000.* k. (Means). £1,000.* k. (Means). £1,000.* k. (Means). 1878 9,532 27.06 257,940 1891 26,719 29.55 750,053 1904 28,849 31.49 912,319 1879 8,903 27.25 263.146 1892 25,198 29.65 745,287 1905 29,702 31.74 953,149 1880 10,535 27.42 295,713 1893 23,401 29.76 727,015 1906 30,440 ' 32.03 1,001,768 1881 11,691 27.60 328,978 1894 23,610 29.87 716,679 1907 32,744 32.31 1,069,557 1882 13,192 27.78 375,118 1895 23,240 29.98 719,479 1908 34,608 32.59 1,151,441 1883 15,163 27.98 415,858 1896 24.530 30.08 735,789 1909 37,938 32.88 1,244,216 1884 16,808 28.16 457,174 1897 25.203 30.20 754,506 1910 40,375 33.49 1,329,933 1885 17,375 28.35 503,755 1898 25,667 30.31 776,234 1911 42,500 33.78 1,417,901 1886 18,538 28 55 555,633 1899 26,243 30.44 795,540 1 1912 43.619 34.08 1,484,188 1887 20,853 28.74 606,824 1900 26,355 30.56 814,079 1913 45.600 34.38 1,542,448 1888 23,625 28.94 665,933 1901 27,188 30.69 835,446 1914 45,526 34.68 1,596,678 1889 25,027 29.14 717,994 1902 27,587 30.95 857,374 1915 46,970 34.99 1,643,464 1890 26,852 29.35 747,552 1903 28,340 31.22 884,844 1916 35.30 * Amount of probates multiplied by 1.60016. f Means for the quinquennium of which the year in question is the central year. The amounts for 1878 and 1915 are for the single year and 1. 37. Comparison with other estimates of private wealth. — Sir T. A. Coghlan, F.S.S. (then Mr. Coghlau), made, wlien Statisti(nan of New South Wales, estimates of the private wealth of Australia for various dates, and Mr. A. M. Laughton, F.I. A., F.F.A., F.S.S., Government Statist, Victoria, has also given estin^ates for recent years. They are as shewn hereunder, and for purposes of comparison the estimates now obtained are also given : — Year. Coghlan. Knibbs. Year. Coghlan. Knibbs. £1,000. •'r £1,000. £1,000. - ■ £1,000. r • 1813* 1 1890t 1019.2 747.6 1838* 26 1903t 982.0 884.8 1863* 163 Laughton. 1878 fi57.9 1911t 990. 1417.9 1888t 875 665.9 1911§ 1031. 1417.9 * T. A. (Coghlan.— The Ssven Colonies of Australasia, 1893. The figure for 1863 has been deduced from the rcsidt for Australasia, correcting In- tlie ratio of populations (,.\ustralia/ Australasia), t T A.Ooghlan.— The Seven Colonies of Australasia, 1903-4. t A. M. Laughton.— Vict. Year Book, 1911-12, p. 217 ; 1912-13, p. 271 : 1913-14. p. 591. § A. M. Laughton.— Vict. Year Book, 1914-15, p. 233 ; 1915-16, p. 295. 38. Probate and general distribution of wealth according to size of estate. — The distril)ution according to size of estates, of estates api^eariiig in probate-retiu-ns, is not identical with a distribution for the whole community : nevertheless it could be ascertained if only the distributions for age-groups (within small limits of age) were tabulated. Su])pose that m^., m' ^, m y., etc., be the ninnbers of persons of age x who are shewn on the ])robate-returns as possessing wealth between ranges to i\ ti to u , v' to i" , etc., and that /?„ be the ratio of the livuig to the dying ( H r= the reciprocal The Rate of Devolution. 131 of the death-rate at age x, eith r a year say, or a five or ten-year range of ages). Then the numbers for the corresponding ranges among the living (on the assumption that the dying are a fair sample of the living) are R ^m^., R.^m' ,_^, R ^m ^, etc. If we compile for all ages the numbers in each range, we have for the dying — m^ + m^^^ + m^^2 + etc.; m ^ -f tn\^^ + m\^^ + etc. ; + "^X + l + "*X+2 etc. But in the corresponding compilation for the living we have, on the assumption mentioned : — (34). ■ {R^mj, + R X + l"''X+l + ^X + 1 "^X+2 + ®^^) ' /?„._L, "i-',, _L. + R , m ,., + etc.); (R.J. in" R. m x + 1 + Rx 4-2 m. x + - -\- etc.); etc., etc. If the numbers between given ranges of net-values of estates for each age-group are kejJt, the grouping for all ages taken together can approximately be found. If, however, the group (for all ages) be formed from the probate-returns treated as a whole, one cannot obtain the general distribution by nnultiplying these by any general constant, as, for example, the weighted mean of R^, R^j^i, etc., say Rq, for this would give : — (35) {i^o»>.v r i?o"ia; + i + ^o'«a; + 2 + etf!.) ; {Rn»i'x + ^o"i'a;-|-i + ^o»i'a; + 2 + etc.); {Rom\ + i?o»«'"a; + i + ^a^^' x + i + ^^c.) ; etc., etc., which is obviously not identical with (34) above. The dissimilarity of the two distributions referred to in the previous demon- stration is revealed by making a comparison between the results as given by the War Census and in the probate-returns : — Distribution of Estates in Probate-returns and in War Census compared, for the State of Victoria. Range. .2 t.'ts*^ .2 S S >n Ills O tH Range. 'u. ;^ ro s .3 ^ S in Vict Prol Reti 1908 w U Not accounted for or in debt Under £100 . . 100-300* . . 3(io-r)00 r)00-i,oo() . . l,()(il)-2.()0() . . 2,001) -3,000* 3,000-4,000* 839,250 I 89,415 295,412 j 5,591 120,168 8,463 43,190 51,765 .36,746 12,181 8,051 5,015 5, .585 4,444 1,873 1,078 36,920 15,019 5,398 4,162 6,470 4,876 4,594 5,275 1,522 2,429 1,006 1,227 4,000-5,000 5,000-10,000 U»,()00-1.'),{)0(I l.'i, III 1(1-2.'), 00(1 ' 2.'),IK II H.')l 1,000 50,000-100,0001 Over 100,000 (Over £300) j Totals, etc. 3,923 7,935 2.113 1.403 798 313 170 (168,588) 685 1,442 430 247 168 63 40 490 992 264 175 100 39 Jl 717 1,325 407 305 207 140 (21,070) (21,070) (21,070) l,423,418!l24,539 602,243t * Interpolated values from the Census results. t 21,070 cases correspond to a population of 602,243 persons ; the total population was about 40,740,000. In the aVjove table the foiu-th cohnnns give the equivalent distribution of 21,070 estates according to the War Census results. The results for Prussia appear to agree rather with the proViato-distribution in Victoria tlian with the census-distribution. 39. Conclusions regarding the probate method. — (i.) Even when the data of a single year are (;t mplete, the probate method cannot be relied upon to give a satisfac- tory estimate of wealth existing at that year, because, whatever size the community, the appearance of large estates in probate-retiu-ns must necessarily bo irregular. 132 The Estimation or Wealth from Probate Returns. (ii.) Though the use of quinquennial averages diminishes this irregularity, it is insufficient to reduce it to an insensible amount : even the combination of the data for 10 years will not always effect this. (iii.) For precision the probate-records of each sex must be considered separ- ately : the use of a general multiplier is not rigorously exact. (iv.) To obtain results of high accuracy a record of all settlements, including all marriage settlements — which latter are rarely recorded — is an essential. If the proportion of settlements to probates be large, it is further necessary that the ages of donors and donees also be given, otherwise, the uncertainty of the result will be appreciable. The effect of settlements in distm-bing the normal distribution of wealth requires special investigation. (v.) To estimate the wealth in any age-group, the ratio of living to the dying should be the weighted average for the period considered, and inasmuch as this ratio sensibly changes from year to year, account should be taken of the change. (vi.) A correction is necessary in order to allow for the fact that, from the stand- point of averages, life insurance unduly increases the probate -return, and to that extent creates a wealth-differentiation between the living and dying. Existing statistics admit of only a rough correction. (vii.) Net values are necessary in all cases where precision is reqviired : it is not satisfactory to correct by a general factor of reduction (gross to net values). (viii.) Statistics are needed, to shew whether death-rates vary with the wealth of individuals : without this the rigour of the method is uncertain. Such statistics are not at present available. (ix.) An estimate made in respect of an average taken over a quinquennial or a decennial period may with advantage be ordinarily assigned to the middle of the period, but is not the value as at that particular date. (x.) In Australia the probate-method cannot lead to satisfactory results owing to the absence of the necessary data regarding settlements. This defect introduces great uncertainty into determinations from probates, a fact forcibly illustrated by the necessity of applying a correction-factor of about 1.6 to the resvilts obtained from probates, in order to bring them into agreement with the estimates obtained by the War Census. 40. Graphical representation. — The accompanying graphs furnish representa- tions of some of the leading features of the matter treated in the present part. The accompanying figure (Fig. Age Distribution of Wealth disclosed by Probate Returns, Victoria (1908-15). — — — — — — f?i ^ !\ _ - ^y / \\ ^ ~ ll \ t— ~ ^ L r / 3 \ p / =^ % / '\ — // ■7> ^ / ■> n ^ 10 4 — < 7 s L 1 1sl 90 10 100 Ag« Fig. 4. 4) furnishes for each sex the repre- sentation of the relative distribu- tion according to age of the wealth disclosed by probate returns in the experience of Victoria (1908-15). The heavy curved line marked M relates to males, the light line marked F to females. In each case the total area included between the curve and the base line is equal to 1. The area enclosed by any two ordinates and the portions of the ciu-ve and base cut off thereby represent the proportion of the total wealth for the sex in question attributable to testators between the ages represented by the selected ordinates (see page 109). The Rate of Devolution. 133 20 30 40 50 60 70 80 s 5 ^. .J L— .... ^ t '<^ ^ =^ -^ ?■ ,r^ 1 N~ ■\ _''A'_ _ , ■^ >N %- , / ^> '' \ '' J K- _ _ -^ [NT / / 1- 1 /■ / y ' <) ^ ^ . 100 Age Fig. 5. Fig. 5 furnishes a representation of the ratio to deaths of the number of estates subject to probate. The continuovis hues relate to Victorian experi- ence (1908-15), and the broken Ratio of Probates Estates to Deaths. lines to New South Wales experi- Victoria, 1908-15. N.S.W., 1911-13. ^^<'*' (1911-13). The two upper curves marked M relate to males, while the two lower marked F relate to females. As an alterna- tive representation for Victorian males a dot-and-dash line is shewn, which is probably a more correct indication of the trend than the closer-fitting, but wa\'y, continuous line. The curves are, in the main, based on decennial aggre- gates, while those shewn for Vic- toria in Fig. 10, on page 135, are based on returns for each year (see pp. 109, 110). The accompanying graph (Fig. 6) furnishes a representation of the average wealth per estate for each age, based upon the Victorian probate experience for the eight years 1908-15, and the New South Wales Average Wealth per Estate, experience for the three years Victoria, 1908-15. N.S.W., 1911-13. 1911-13. The Victorian re- sults are represented by con- tinuous lines, and the New South Wales results by dotted, the male and female results being denoted in each case by the letters M and F respectively. The small circles in the case of Vic- toria, and the dots in the case of New South Wales, indicate the position for the group jDlotted usually as at the central point (see pp. 109. 110). / \\ \ / ' ¥ .siw 5000 / kf / 4O0O 3 / 1 y I 3000 < ''\ -\ . — 1 1^ \^ 'Y- /' ^/ Tr^rr J iL A .'1^ I' -~^ ^ k ^ — ;— 4-J T _ ■^ ^ ^- 'X f n ^j^ i •» — _ 1 1 1 20 30 -to 50 60 80 90 100 Age Fig. 6. Ratio of Net to Gross Values of Estates subject to Probate. J(J *%! "T" ~ •9 9 -^ ^ fes h= =" ^ -F "-P" ^ r-^ ■ « N- ■ r' ^- ■8 ZO 30 /0( a 60( i * (z; fj\ 500 p \ 1/ \ 400 hA ' \ \ k I \\ «^ / f A ff V t/ \ 1 / / f / V I \ WO f y r N \ (A r- r ^ f^ 4 \ A uo ,u^ kT ■/■ V \\ r ^^ J ^ V \ k / ^ ''^ v^ lO 20 30 40 50 60 70 SO 30 100 Ages ^IfiO.OOO h 160 > \ / ^ \ 1^ f' ' / / I IDO / 1 8( ^ 60 / { / 1 40 J A ^ 1 / / / ^ \, 1 20 JO / y / \ \ y / ^ \ \ ^ ^ ^ -^ !v. 40 50 60 Fiff. 9. 70 80 30 100 irjes The Rate of Devolution. 135 Fig. 8 shews the numbers of estates subject to probate in Victoria during the period 1908-1915 per year of age ; the curve marlced M giving the numbers for males, and that marked F for females. Fig. 9 shews the aggregate net values of the estates subject to probate during the period 1908-1915 per year of age ; the curve marked M indicating the aggregate for males, and that marked F for females. (See pp. 122 to 125.) Average Net Wealth per Estate subject to Probate, according to Age, and the Ratios of such Estates to Total Deaths. Victoria, 1908-15. Ciu-ve A shews, according to age, the average net wealth per estate subject to probate for males ; and curve B for females. (See the text, page 121, for the significance of the dots, crosses, small circles, and small squares.) Curve C shews, for males, the ratios of the number of estates to the total deatlis at each age, and curve D furnishes a similar representation for females. (See the text, page 121, for the significance of the dots.) Curves C and D' are tlio general indication, for males and females respec- tively, of tho variation with ago of tiioso ratios. (See page 121.) PART VI.— THE INVENTORY METHOD OF ESTIMATING WEALTH. CHAPTER I.— ESTIMATE OF AUSTRALIAN PRIVATE WEALTH FOR 1915. 1. General. — Of the various methods of estimating the weaUh of the community the inventory method is that which furnishes most readily a comprehensive view of the various classes of wealth constituting the aggregate. In this respect it has ad- vantages which do not attach to either the succession (probate) method or the census method. The possibility of using it, however, is largely dependent on the existence of valuations of various kmds made for purposes other than the estimation of total wealth, as, for example, Local Government assessments, values of imports, values of plant and machinery engaged in various indxistries, etc. Further, in certain of the items direct valuation is not possible, and estimates based on indirect data and general knowledge must be employed, as, for example, an estimate of the value of clothing based on the known number of persons, and an assumed value per head, or a valuation of furniture based on the number of houses of various sizes or of various rental values. It is thus clear that, in common with all other estimates of wealth, the inventory method is involved in some measure of uncertainty, but it is doubtful whether this is more marked than in the case of other methods. On the other hand it has the advantages (i.) that it enables a fair idea to be obtained of the degree of uncertainty involved in each item, (ii.) that unlike a censvis it costs little to compile and can consequently be prepared at relatively short intervals, (iii.) that it relates approximately to a definite point of time, whereas a " succession" estimate at its best can only give the average for an extensive period if it is to be at all reliable. 2. Basis of estimate. — In the accompanying estimate provision has been made for the inclusion of all material private wealth existing in Australia, whether owned by persons domiciled in Australia or by those resident abroad, bvit public property whether national or cotnniunal has been omitted. Owing to this scheme it might possibly be considered necessary to mclude in the aggregate an item representing the securities for loans to Commonwealth and State Governments, and to public bodies, which are held in Australia, since such holdings will in all cases be included in succession returns and census results, and should thus be included to justify a comparison of the results obtained by the several methods. Although such inclusion might appear out of place in what is essentially a valuation of material objects, it might, perhaps, be possible to justify it on the view that the amount so included represents the portion of the national and communal property for which private investors resident in Australia hold certificates of title in the shape of bonds, debentures or stock. It is not clear, however, that a similar contention in favour of including the Australian public debt held outside the Commonwealth would not have equal validity. In view of all the circumstances it was decided to omit any reference to the public debt in the main estimate, but to refer to it later in making comparisons with the succession and War Census results. In broad outline the classes of private wealth contributing to the aggregate may be classed as follows : — Estimate of Australian Private Wealth for 1915. 137 (i.) Land and Improvements ; (ii.) Live Stock ; (iii.) Agricultural, Dairying and Pastoral Implements and Machinery ; (iv.) Manufacturing Plant and Machinery ; (v.) Mining Properties (including plant and machinery) ; (vi.) Coin and Bullion ; (vii.) Private Railways and Tramways ; (viii.) Shipping ; (ix.) Agricultural and Pastoral Products; (x.) Locally manufactured products; (xi.) Mining Products (other than gold) ; (xii.) Imported Merchandise ; (xiii.) Clothing and personal adornments ; (xiv.) Furniture and fittings, books, pleasure vehicles, etc. 3. Details of Estimations. — (i.) Land and Improvements. — The estimate in respect of this item is based on the municipal valuations of the several States and represents about two-thirds of the total estimated wealth. The form in which this information would be most serviceable is that of improved capital value, but unfortunately particulars of this nature are available for the whole State in the cases of Victoria and South Australia only. Similar information in the cases of New Soiith Wales and Western Australia is furnished for " municipalities" onlj% the assessments for " shires" in New South Wales and for the majority of the " road districts" in Western Australia being upon an unimproved basis. In Queensland all the assessments are based upon unimproved values, while in Tasmania and in a few of the Western Australian road districts the figures given relate to " annual values." It is thus necessary in several cases to apply certain factors for the purpose of con- verting " unimproved" and " annual values" into the corresponding '" improved capital values." (a) New South Wales. — The valuation of the municipalities of New South Wales for the year ended 31st December, 1915^ furnished the following results : — New South Wales. — Valuation of Municipalities for Year ended 31st Dec, 1915. Percentage Percentage Un- of Un- of Assessed Improved improved Assessed improved Annual Mvmicipalities. Capital Capital Annual on Value on Value. Value. Value. Improved Capital Improved Capital 1 Value. Value. £ ! £ £ ' o Sydney 78,580,300 27,22(),283 3,391,759' 34.65 4.32 Metropolitan Sul)ur)3s 91,198,244 33,403,223 6,686,058 3(5.63 7.33 Newcastle & Sul^urbs 8,417,087 3,193,866 534.948 37.94 6.36 Country Municipalities 49,532,471 19,649,329 3,660,862 39.67 7.39 Total, Municipalities 227,728,102 83,472,701 14,273,627 36.65 6.27 In the New South Wales Statistical Register for 1915 (p. 783), from which the valuation figures given above have been taken, the following definitions of the three classes of valuation are furnished : — " The Unimproved Capital Value of laud is the amoiuit which the fee simple estate in such land is worth under such reasoiuible conditions as a bona fide seller would require, assuming the actual improvements had not been made." ■" The Improved Capital Value is the amount which the fee simple estate of the land is worth, with all improvements and buildings thereon." " The Assessed Annual Value is nine-tenths of the fair average rental of land with improvements thereon." 138 The Inventory Method op Estimating Wealth. The total area embraced by these municipalities is 2913 square miles, or less than 1 per cent, of the total area of the State, while the population contamed therein represented more than 64 per cent, of the total population of the State. With the exception of a portion of the sparsely populated Western Land Division the remainder of the State is divided into shires, which cover a total area of 180,655 square miles, or somewhat more than 58 per cent, of the whole area of the State, the population of this portion representing nearly 35 per cent, of the total for the State. The unincorporated area of the Western Land Division covers an area of 125,893 square miles, or rather more than 40 per cent, of the area of the State. Its popula- tion, however, is rather less than 1 per cent, of the total population of New South Wales. As regards shire valuations for 1915, the unimproved capital value is available in all cases, and aggregates £104,745,633. Improved capital values which are available for eleven shires aggregate £21,412,096, the unimproved values for the same shires totallmg £9,599,892, or 44.83 per cent, of the corresponding improved values. There were ten cases in which improved capital vahies and assessed annual values were both given, the improved values aggregating £18,088,565, and the corres- ponding assessed annual values £822,201, or 4.88 per cent, of the impi'oved value. On the assvunption that the eleven shires, quoted above as giving a percentage of 44.83 for the ratio of unimproved to improved value, may be taken as a fair sample in this respect of the shires of New South Wales, the multiplier for converting the aggregate vmimproved value for shires into the corresponding improved value will be 100 -T- 44.83. Applying this factor the improved capital value for shires works out at £233,650,000. It may be noted that the ratio of unimproved to improved capital value obtained at the War Census of 1915 for owners domiciled in New South Wales was 44.91 per cent. In the case of the unincorporated portion of the Western Land Division an esti- mate of £10,000,000 unimproved value is quoted in the Official Year Book of New South Wales for 1915 (p. 587), as being within reasonable limits. This estimate is apparently based on the assumption that an unimproved value of 2s. 6d. per acre might be taken as applying to the whole of the area of slightly more than eighty million acres contained in the Western Division. Although this estimate might be appropriate for certain pui"poses, it appears somewhat high for adoption in the present case, and it was considered desirable to prepare an estimate on the basis of the popula- tion of the unincorporated area taken in conjunction with the average vuiimp roved value per head disclosed by the contiguous shires. These are the shires of Boomi, Walgett, Marthaguy, Bogan, Lachlan, Carathool, Waradgery and Wakool, which in 1915 had an aggregate population of about 21,200, and an aggregate unimproved valuation of £9,176,669, or £433 per head. As the population of the unincorporated areaof the Western Division in 1915 was about 16,000, the corresponding miimproved value would on this basis be £6,928,000. Particulars in respect of the ratio of " un- improved" to " improved values" are not available for this part of the State separately, but as it would be relatively high it has been taken at 60 per cent., giving an estimated improved value for the unincorporated area of £11,547,000. Combining these results, the total for the State works out as follows : — Estimated Improved Capital Value, New South Wales, 1915. Mtniicipalities. Shires. LTnincorporated Area. £227,728,000 £233,6.50,000 £11,547,000 Total. £472,925,000 Estimate of Australian Private Wealth for 1915. 139 This total represents an average of £253 per head of the mean population of the State for the year 1915. (b) Victoria. — In the case of Victoria the particulars available relate to improved capital values, and also to annual values for all local government areas. The figures for 1915 are as follows : — Victoria. — ^Local Government Valuations for Year 1915. Local Governing Districts. Improved Capital Value. Annual Value. Percentage of Annual Value on Improved Capital Value. Cities, Towns and Boroughs . . Shires Total £ 147,205,224 167,405,523 £ o/' 8,218.040 , 5^58 8,517,938 5.09 314,610,747 16,735.978 5.32 With the exception of French Island in Western Port Bay, the whole of Victoria is under local government. The total given above (in round numbers £314,611,000) may consequently be taken as fairly i-epresenting the total value of real property and improvements for 1915. It averages £221 per head of the mean population of the State for that year. (c) Queensland. — The municipal valuations for Queensland relate solely to unimproved capital values, and are separately available for the year 1915 for the 10 cities, 27 towns and 147 shires which amongst them comprise the whole area of the State. The particulars are as follows : — Unimproved Values, Queensland, 1915. Cities. Towns. Shires. 1 Total. £11,717,227 £4,683,948 £45,622,388 £62,023,563 In the absence of any valuation data for Queensland indicating the relation between " unimproved" and " improved" values, it is necessary to make use of the ratio for that State obtained from a comparison of the War Census data. The ratio so obtained for owners of freehold property who were domiciled in Queensland was 48.13 per cent. This ratio relates to the State as a whole, and in view of the varying ratios given above on p. 137 for municipalities and shires in New South Wales, it would clearly be inadmissible to apply the factor separately to the figures for cities, towns and shires in the preceding table. Applyhig it to the total of £62.023,563 gives the improved capital value for Queensland as £128,867,000, averaguig £187 per head of the mean population of the State for 1915. (d) South Au.'itralia.- — In the case of South Australia the improved capital values and the annual values of all ratable property for the year 1915 are given separately for the several corporations and district councils. The details are as follows : — 140 Thb Inventory Method of Estimating Wealth. South Australia. — Municipal Valuations, 1915. Local Governing Districts. Improved Capital Value. j Percentage of Annual Annual Value Value. on Improved ; Capital Value. Metropolitan — Corporations District Councils Country^ — Corporations District Councils £ 32,037,714 11,652,652 6,109,840 40,715,301 £ 1,597,957 588,632 320,299 2,012,666 o ,0 4.99 5.05 5.24 4.94 Total 90,515,507 4,519,554 4.99 Of the several Australian States, South Australia has by far the largest unin- corporated area. Thus, while corporations account for 81 square miles, and district councils for 45,586 square miles, the unincorporated area amounts to no less than 334,403 square miles, or 88 per cent, of the whole area of the State. This area is, however, very sparsely populated, and much of it is entirely vmoccupied. At the Census of 1911 the total population of the unincorporated portion of the State was only 11,908 persons, or less than 3 per cent, of the total population of the State. In the area under country district councils for 1915, the average capital value of ratable property per head of population was approximately £232. Assuming this average to be applicable to the unincorporated area, and taking the population of that area at about 12,000 for 1915, the estimated improved capital value for this portion of the State may be set down at £2,784,000. The total for South Australia may thus be given as follows : — Improved Capital Value, South Australia, 1915. Corporations. District Councils. Unincorporated Area. Total. £38,148,000 £52,368,000 £2,784,000 £93,300,000 This total gives an average of £212 per head of the mean population of tlie State for 1915. (e) Western Australia. — In this State the valuations of the municipalities are available in respect of what are termed " Capital value, including improvements," and " Net Annual Value." The totals for the year ended 31st October, 1915, are as follows : — Western Australia.— Municipal Valuations, 1915. Districts. • Improved Capital Value. Net Annual Value. Percentage of Net Annual Value on Improved Capital Value. Metropolitan Municipalities Extra-MetropoHtan ,, £ ] 9,945,078 4,976,344 £ 1,098,587 439,038 0/ /o 5.51 8.82 Total, Municipalities 24,921,422 1,537,625 6.17 Estimate of Australian Private Wealih for 1915. 141 In the case of the Road Districts which correspond approximately to the shires in some other States, rates are levied in part on " annual values," but mainly on " unimproved values," both bases being used in some districts. For the whole State the " annvial values" recorded for the year ended 30th June, 1915, were £327,709, while the " unimproved values" for the same year totalled £14,142,879. As in- dicated in the preceding table, the ratio of "net annual vakie" to "improved capital value" works out at 8.82 per cent, for extra-metropolitan municipalities in Western Australia, but such a ratio is certainly too high in the case of road districts. In the case of New South Wales the ratio for country municipalities was 7.39 per cent., while that ascertained for eleven shires for which the information was available was 4.88 per cent., or about one-third less. Assuming the same relation to hold between the extra-metropolitan municipalities and the road districts in W^estern Australia, the appropriate percentage would be two-thirds of 8.82, or 5.88. It was consequently decided to take 6 per cent, as fairly applying to the case. At the War Census of 1915 the ratio of " unimproved" to " improved" capital value in respect of property owners domiciled in Western Australia was 40.55; as this was based on a combination of town and country properties, it is probably too low for use in connection with country properties only. The factor to be applied in converting the " unimproved values" quoted above into " improved values" has consequently been based upon a ratio of 45 per cent. As a resxilt of these computations the " improved capital value" for road districts has been estimated at £36,891,000. Combining these results the total for Western Australia may be stated as follows, the whole of the State being incorporated : — Improved Capital Value, Western Australia, 1915. Municipalities. Road Districts. Total. £24,921,000 £36,891,000 £61,812,000 This total represents an average of £192 per head of the mean population of the State for 1915. (/) Tasmania. — In this case the municipal valuations available relate to '■ annual values" only, and total £1,654,654 for the year 1915. For the purpose of estimating the corresponding improved capital values, it is necessary to use a factor based on the experience of other States. As indicated above, the percentages of assessed annual values on improved capital values averaged as follows : — (i.) New South Wales municipalities, 6.27% ; (ii.) New South Wales shires, (11 only), 4.88% ; (iii.) Victorian cities, towns and boroughs, 5.58% ; (iv.) Victorian shires, 5.09% ; (v.) South Austi-alian local governing bodies, 4.99 °o ; (vi.) Western Australian municipalities, 6.17%. In view of these residts it appears that 5^'^, which is practically the ratio for South Australia, might reasonably be adopted as applicable to the Tasmanian data. On this basis the improved capital value works out at £33,093,000, and averages £166 per head of the mean population of the State for 1915. ((/) Territories. — Owing to their exceptional conditions the Northern and the Federal Territories furnish no data relative to local government corresponding to that quoted above in respect of the several States. Their omission from the estimate for Australia would not seriously affect the total, but for the sake of completeness it appears desirable to include them. It has consequently been deemed appropriate to compute a figure based upon the population in each case, and taking an average 142 The Inventory Method of Estimating Wealth. value per head indicated by the State estimates. In the Northern Territory the mean population for 1915 was 4403, while the corresponding figure for the Federal Terri- tory' was 2467. The average values per head of mean population disclosed above for the several States are as follows : — New South Wales, £253 ; Victoria, £221 ; Queens- land, £187 ; South Australia, £212 ; Western Australia, £192 ; and Tasmania, £166. In view of these averages it will probably be within the mark to assume an average of £150 per head for the Territories. This will give approximately £660,000 for the Northern Territory, and £369,000 for the Federal Territory. (h) Commonwealth . — Combining the results obtained in foregoing sub-sections, the results for the Commonwealth may be stated as follows in thousands of jjounds :— Improved Capital Value, Commonwealth, 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. £1,000 £1,000 472,925 314,611 £1,000 128,867 £1,000 £1,000 93,300 61,812 £1,000 33,093 £1,000 660 £1,000 369 £1,000 1,105,637 For the Commonwealth as a whole the average value per head of mean popula- tion for 1915 was £223 7s. (ii.) Live Stork. — Particulars concerning the value of live stock in the several States are not directly available, but the nvimbers of each of the principal classes and some of the minor classes are collected annually in each State and Territory'. The dates to which these records relate ai"e not uniform, but in each case the figures used for the present purpose refer to a point of time between 30th June, 1915, and 31st March, 1916, thus making appropriate allowance for the losses of the 1914-15 drought. The figures so taken for the principal classes of stock are as follows : — Numbers of Principal Classes of Australian Live Stock, 1915-16. Kind of Stock. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. Horses Cattle .. Sheep . . Pigs . . 731,735 2,472,631 32,874,359 286,478 493,779 1,043,604 10,545,632 192,002 686,871 4,780,893 15,950,1.54 117,787 253,333 226,565 3,674,547 66,237 163,016 821,048 4,803,850 58,231 41,422 169,575 1,624,450 37,778 19,957 483,961 57,827 500 1,310 5,666 102,683 289 2,391,423 10,003,943 69,633,502 759,302 For the valuation of this stock it was decided to adopt with slight amendments the standard values prescribed by the Federal Taxation Department for use in the preparation of income-tax returns. The amendments referred to above consisted in (i.) the substitution of a State rate for the standard district rates for sheep and cattle in Western Australia, (ii.) the insertion of rates for horses and pigs in Western Australia, (iii.) the insertion of a rate for pigs in the Northern Territory, (iv.) the insertion of rates for the Federal Territory identical with those for New South Wales. The values so adopted were as follows : — Values adopted for Valuation of Live Stock. Kind of Stock. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. Horses £8 £15 £4 £7 £20 £20 £5 £8 Cattle £6 £6 £3 £5 £2 10/- £3 £2 £6 Sheep 10/- 12/6 9/- 10/- 8/- 10/- 12/6 10/- Pigs .. £1 £2 10/- 15/- £2 £2 10/- 15/- £1 10/- £1 Estimate of Au.st^alian Privaie Wealth for 1915. 143 0.1 the Ijasis of these rates the vaUies obtained for the classes of stock quoted were as follows : — Valuation of Principal Classes of Australian Live Stock, 1915-16. Kind of Stock. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. Horses Cattle Sheep . . Pigs £ 5,853,880 14,835.786 16,437,180 286,478 £ £ 7,40o.685 2,747.484 6.261.624 14.342,679 6,591,020 7,177,.569 480,005 88,340 £ 1,773,331 1,132,825 1,837.273 132,474 £ 3,260,320 2,052,620 1,921,540 145,578 £ 828,440 508,725 812,225 28,333 £ 99,785 967,922 36,142 750 £ 10,48(1 33.9<»(. 51.342 289 £ 21.980,405 4(1.136,177 34,804.291 1,162,247 Total 37,413,32l'20,739,334!24,356,072 4,875,903' 7,380,058 i i i 1 2,177,7231104599 96,107 98,143,120 For the Commonwealth as a whole these values average £9 3s. lOd. per head for horses, £4 Os. 3d. per head for cattle, 10s. per head for sheep, and £1 lOs. 7d. per head for pigs. Of the minor classes of live stock, poultiy are the most important, but in this case the records are very incomplete. As the result of a census of poultry taken in Victoria in April, 1911, the numbers of fowls, ducks, geese and turkeys were ascer- tained, and these on the basis of the average market prices for that year were worth £581,766, or 36 per cent, of the average value of the poultry and eggs produced in the State for that year. As an estimate of such annual production is availalile for each State, it has been assumed that, in each case, the value of the poultrj'- as at 30th June, 1915, was 36 per cent, of the value of the prodiiction of poultry and eggs for 1915. On this basis the value obtained for the poultiy was as follows : — Estimated Value of Poultry as at 30th June, 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. F.T. C'wlth. £ 771,840 £ 628,920 £ 38,653 £ 186,771 £ 66,370 £ 72,000 £ 720 £ 1,765,274 The other kinds of domestic live stock in Australia are relatively unimportant, and consist mainly of goats, camels, mules and donkej-s. For the purposes of the present estimate the values of these have been taken at 10s. per head for goats, £25 per head for camels, £10 per head for mules, and £5 per head for donkeys. On this basis the values for the several States and Territories are as follows : — Estimated Value of Goats, Camels, Mules and Donkeys, 1915. N.S.W. Vie. Q'land. S.A. W.A. Tas. N.T. 1 F.T. C'wlth. £ 75,049 £ 3,264 £ 95,435 £ 134,534 £ 163,161 £ 1,283 £ 10,211 £ £ 35 1 482,972 A combination of the foregoing results gives a total for the Commonwealth slightly in excess of a himdred millions sterling, made up as follows, the figures being given to the nearest £1000 : — Estimated Total Value of Austrahan Live Stock. 1915-16. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. £1,000 38,260 £1,000 21,371 £1,000 24,490 £1,000 5,197 £1,000 7,610 £1,000 £1,000 2,251 1,115 £1,000 97 £1,000 100,391 144 The Inventory Method of Estimating Wealth. The total for the Commonwealth represents an average of £20 5s. 7d. per head of the mean population for 1915. (iii.) AyricuUural, dairying and pastoral implements and machinery. — In all the States except Victoria returns are furnished annually shewing separately the value of implements and machinery (i.) used mainly in general agriculture, (ii.) used mainly in dairying, (iii.) used mainly in pastoral pui'suits, (iv.) travelhng machinery. Figures are also furnished in respect of the Federal Territory annually, and a return for the Northern Territory was supplied for the year 1912. The figures so available, and the relation of these values (i.) to the area under cultivation, in the case of agricultural and travelling implements and machinery, (ii.) to the number of dairy cattle, in the case of dairying implements and machmery, and (iii.) to the number of sheep, in the case of pastoral implements and machinery, are given in the following table : — Values of Agricultural, Dairying and Pastoral Implements and Machinery, 1915. .\Kric ultural Dairying Pastoral Travelling Machinery. luipleuients Implements Implements and Machinery. and Machinery. and Machinery. state or Territory. Value per Value per Vahie per Value per Total 100 acres Total 100 head Total 1000 head Total 100 acres Value. under Value. of Dairy Value. of Value. under Crop. Cattle. Sheep.* Crop. £ £ s. d. £ £ s. d. £ £ s. d. £ £ .«. d. N.S.W. 5,357,019 92 8 5 570,871 76 16 6 2,012.539 43 19 9 117,045 2 5 Queensland . . 1,531,303 209 17 8 279,258 83 6 490,935 9 10 7 45,631 6 5 1 S. Australia 3,010,839 80 94,260 112 1 199,039 40 19 3 14,355 7 7 W. Australia 1,789,626 81 14 9 16,985 59 18 7 309,491 27 15 4 .53,959 2 9 3 Tasmania 317,117 95 2 10 62,703 131 17 11 18,907 7 5 5 79.668 23 18 Nor. Territory 3,000 1094 17 9 50 71 8 7 5,000 15 6 Fed. Territory 5,008 114 11 6 84 15 12 10 2,i>09 17 9 2 C'wlth, ex- clusive of Vic. 12 013,942 93 14 8 1,024,211 83 11 3,038,420 25 6 7 310,658 2 8 6 * For the purposes of this return cattle have been converted into their equivalent in sheep by multiplying by eight. The travelling machinery shewn in the foregoing table bemg mainly agricultural, its total value has been shewn in relation to the area under crop. As tlie conditions in respect of agricultural, dairying and pastoral pursuits in Victoria are probably more closely allied to those in New South Wales tlian to those in any other State, it has been assumed, for the purpose of estimating the total value for Victoria, that the values per 100 acres, etc., shewn above for New South Wales are applicable to the appropriate data available for Victoria. On this basis the Victorian values for 1915 have been estimated as follows : — Agricultural, £5,278,000 ; dairyuig, £347,000 ; pastoral, £072,000; travelling, £115,000.; total, £fi,412,000. The aggregage for the Commonwealth for 1915 may thus be estimated as follows : — Estimated Value of Agricultural, Dairying and Pastoral Implements and Machinery, 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. £1,000 8,057 £1,000 6,412 £1,000 2,347 £1,000 3,319 £1,000 2,170 £1,000 478 £1,000 8 £1,000 8 £1,000 22,799 The total for the Commonwealth represents an average of £4 12s. Id. per head of mean population for 1915. Estimate of Australian Private Wealth for 1915. 145 (iv.) Manufacturing plant and machinery. — In all the States returns are collected and tabulated annually in respect of all factories, a factoiy being defined as an in- dustrial establishment in which four or more persons are employed or in which power other than hand-power is used whatever number of persons are employed. These returns include one relating to the approximate value of plant and machinery employed in such factories, and the figures for 1915 have been used for the purposes of the present estimate. As, however, these figures include the value of plant and machinery to the amount of some £2,237,000, employed in railway and tramway workshops which are mainly Government establishments, a deduction has been made of the whole of the value so shewn in the annual returns. This deduction is probably somewhat in excess for this class of establishment, as some are private concerns, but the excess may be considered as a set-off to the values associated with other Government enterprises of a minor character. Approximate Value of Manufacturing Plant and Machinery, 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. C'wlth. £1,000 15,901 £1,000 10,761 £1,000 6,817 £1,000 3,225 £1,000 2,194 £1.000 1,142 £1,000 40,040 The total for the Commonwealth represents £8 Is. 9d. per head of the mean population for 1915. (v.) Mininrj Properties. — A reliable estimate of the value of mining properties in Australia is difficult to obtain. A careful examination of the paid-up capital and the dividends of such companies operating as at 30th June, 1915, disclosed the fact that the paid-up capital as at that date totalled £45,874,366, and that the dividends reported for the year ended 30th June, 1915, was £1,354,805. A similar investiga- tion in respect of the dividends for mines operating at 31st December, 1916, indicated that the total amount of the dividends paid during 1916 was £1,569,253. Writmg imder date December 1913, IVIr. R. L. Nash, in his " Australasian Joint Stock Com- panies Year-book, 1913-14," gives results for Australasia, which, on the deduction of the figiu-es stated or estimated as applicable to New Zealand, indicate for the Australian minhig companies a paid-up capital of about £50,000,000, and an annual dividend of about £3,300,000, but the period to which the data relate is not stated. The figures so given for paid-up capital is only about 10% in excess of that indicated above, but the amount of dividends shewn is much higher, exceeding bv nearlv 150°/ the amount computed for the year 1914-15, and by about 110°o that computed for 1916. Probably the reduction in the amount of dividends is due in large measure to the dislocating effects of the war. In view of these facts, it has not been deemed advi.sable to attempt a valuation based on the capitalisation of the dividends. It may be here noted that approximate values of the mining jilant and machinorv of all the States except Tasmania are furnished annually by their rcsjjective Depart- ments of Mines. The figures given for the year 1915 for these States and for the Northern Territory are as follows, an estimate being included for Tasmania based upon returns shewing the nuniV)er of men employed, and the value of the output for the vear : — 146 The Inventory Method of Estimating Wealth. Estimated Value of Mining Plant and Machiaerji , 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. C'wlth. £1,000 6,069 £1,000 1,597 £1,000 2,381 £1 ,000 750 £,100D 3,410 £1,000 850 £1,000 32 £1,000 15,089 After reviewing the evidence available, it appeared that for the purposes of the present estimate, the most suitable basis of computation would be one based on the paid-up capital, and that to allow for possible over capitalisation a deduction of say 10% should be made. On this basis the estimated values for 1915 work out as follows, the figures shewn for the Northern Territory being vakie of plant and machinery only : — Estimated Values of Mining Properties, 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. C'wlth. £1,000 10,875 £1,000 7,551 £1,000 6,170 £1,000 1,438 £1,000 11,311 £1,000 3,942 £1,000 32 £1,000 41,319 The total for the Commonwealth represents an average of £8 7s. per head of the mean population for 1915. (vi.) Coin and Bullion. — The principal supplies of coin and bullion in Aus- tralia are (a) those held by the banks, (6) those held by the Commonwealth Treasiiry as Australian Note Reserve, (c) those held by the Mint, (//) those in the hands of the public. As I'egards the bank holdings, returns are furnished qviarterly by all the cheque- paying banks, shewing for each State and the Northern Territory the average for the quarter of the weekly holdings of coin and bullion. For the purpose of the present return the mean has been taken of the averages for the quarter ended 30th June, 1915, and of that for the quarter ended 30th September, 1915. The figures so obtained represent approximately the position as at 30th June, 1915. In the case of gold this figure may be taken as it stands, but the face-value of silver and copper coinage will require to be reduced by the application of a factor representing the ratio of the buUion valvie of the com to its face-value. Returns furnished by tlie various banks as at 30th June, 1916, indicate that at that date the face-value of the coin held by them was distributed in the following proportions : gold, 95.54% ; silver, 4.31 °o ; bronze, 0. 15%. For the year 1915 the average price per ounce of silver in the London market was 23ild., and as the face-value of silver coin is 5s. 6d. per ounce, the factor for reduction in the case of silver is approximately 0.359. On the basis of the London prices of June, 1915, the metallic value of the bronze comage was about 9d. per lb. As bronze coins having a face- value of £1 weigh approximately 5| lbs., on the as- sumption that the amounts of pence and half-pence in circulation are approximately equal in face value, the appropriate reduction factor in the case of bronze is about 0.206. Takmg these factors in conjiuicl ion with the proportions of silver and bronze furnished above, it will be seen that the estimated banks' lioldings of coin as at 30th June, 1915, must be multiplied by 0.971 to reduce them to their metallic values. Estimate of Australian Private Wealth for 1915. 147 After making the requisite calculations, the results obtained are as follows : — Estimated Metallic Value of Coin and Bullion held by the Cheque-paying Banks at 30th June, 1915. x.s.w. Vic. Q'land. S.A. W.A. Tas. X.T. C'wlth. £ 13,667,081 £ 8,267,795 £ 3,342,470 £ 2,787,474 £ 3,928,046 £ 804,389 £ ' £ 7,488 32,804,743 Under the provisions of " The Australian Notes Act. 1910." the Commonwealth Treasurer was required to hold m gold coin (a) an amount not less than one-fourth of the amount of Australian Notes issued by the Treasurj^ up to £7,000,000 ; and {h) an amount equal to the amount of Australian Notes issued in excess of £7.000,000. By the " Austrahan Notes Act 1911," this provision was amended, and suice 1st July, 1912, the Treasurer has been requireil to " hold in gold coin a reserve of not less than one-fourth of the amount of Australian Notes issued." The amount so held in accordance with the Act on the last Wednesday in Jmie, 1915, was £11,034,703 10s. The amount held by the Mint at anj' given time is relatively unimportant. The accounts for the branches at Sydney, Melbourne, and Perth are made up to 31st December m each year, and shew in the " Bullion Account" the value of the bullion in store at the beguining and end of the year. For the pui-poses of the present estimate the mean of these for 1915 has been taken as representing approximately the position at the 30th June, 1915. The figures so obtained for the several branches are as follows : — Sjdney, £14,722 ; Melbourne, £2273 ; Perth, £4649. As regards the value of coin held by the general pul>lic. it has been assiuned that by the 30th June, 1915, gold had ceased to circulate, its place being taken bj- Aus- tralian notes. This is not strictly correct, as small amounts of gold coin were still in circulation at a later date. Further, there is little doubt that since the outbreak of war there has been a certain amount of hoardmg of gold coin. It is probable, however, that the amount omitted by ignoring these items is not large. In the case of silver and bronze coin it was estimated in 1906 by the deputy-master of the Perth branch of the Royal Mint that the amotuit then in circulation in the Commonwealth had a face value of £1,200,000. or. say, 5s. 1 Id. per head of population. This amount per capita was applied to the population of the several States and Territories as at 30th Jtme, 1915, and an allowance was made based on the relative amounts of silver and bronze coin held by the banks and the ratios of metallic to face values deter- mined above, the assumption being made that silver and bronze coin ii\ the hands of the public would be in the same proportion as regards face value as was foimd in the case of such coin held bj^ the banks. On this basis the values obtained were as follows : — Estimated MetaUic Value oS Silver and Bronze Coin held by the Public, 30th June, 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. £ 195,417 £ 149,264 £ 72,2.27 £ £ £ 45,793 33,739 20,756 £ 465 £ 271 £ 517,932 148 The Inventory Method of Estimating Wealth. Combining these particulars the value and distribution of coin and bullion work out approximately as follows : — Estimated Metallic Value of Coin and Bullion in Commonwealth, SOth June, 1915. Particulars. N.S.W. Vic. Q'lnd. S.A. W.A. Tas. N.T. F.T. C'wth. £1.000 £1,000 £1,000 £1,000 £1,000 £1,000 £1,000 £1,000 £1,000 Held by banks 13,667 8,268 3,342 2,787 3,928 804 8 32,804 Treasury note reserve 11,035 11,035 Held by Mint . . 15 2 5 22 In hands of public 195 149 72 46 34 21 1 518 Total 13,877 19,454 3,414 2,833 3,967 825 9 44,379 The total for the Commonwealth represents an average of £8 19s. 4d. per head of the mean population for 1915. (vii.) Private Railways and Tramways. — In all the States tlie principal lines of railway are owned and worked by the several Governments, and the majority of the tramways are under the control of either the government of the State or of municipal authorities. There are, however, in addition to the government railways upwards of 3000 miles of privately-owned lines in the Commonwealth, much of which is used solely for special industrial purposes, such, for example, as coal lines in New South Wales, svigar lines in Queensland, and timVjer lines in Western Australia. Of the private lines used for general trattic, the most extensive are the Midland Railway (177 miles) in Western Australia, the Etheridge Railway (142|^ miles), and the Chillagoe Railway (102| miles) in Queensland, the Emu Bay Railway (103^ miles) in Tasmania, the Silverton Tramway (36 miles), and the Deniliquin-Moama Railway (45 miles) in New South Wales. Electric tramways are run by private companies at Ballarat, Bendigo, North Melbourne and Geelong in Victoria, at Brisbane in Queensland, and at Kal- goorlie and Leonora in Western Australia. In the absence of any valuations of the several private lines, the cost of construction has been taken as the value for the ptu-poses of the present return. Estimated Value of Private Railways and Tramways, 1915. Particulars. N.S.W. Vic. Q'land. S.A. W.A. Tas. C'wlth. Private Railways — General Traffic Special Piu-poses Private Tramways £1,000 1,211 250 £1,000 45 50 405 £1,000 1,464 1,667 1,477 £1000 68 £1,000 2,037 1,375 458 £1,000 1,163 65 £1,000 5,920 3,475 2,340 Total 1,461 500 4,608 68 3,870 1,228 11,735 The total for the Commonwealth represents an average of £2 7s. 5d. per head of the mean population for 1915. (viii.) Shipping. — Particulars in respect of the vessels on the Registers of the Commonwealth are available as at 31st December in each year. A simimary of the information so furnished in respect of the number and net tonnage for 1914 and 1915 is given in the following table : — Estimate of Australian Private Wealth for 1915. 149 Vessels on Australian Registers at 31st December, 1914 and 1915. 31st Dec, 1914. 31st Dec, 1915. Average Average No. Net Tonnage No. Net Tonnage Tonnage. per Tonnage. per Vessel. Vessel. Steam — tons. tons. tons. tons. Dredges and Tugs 135 8,640 64.00 137 8,717 63.63 Other Vessels . . 1,030 320,465 311.13 1,029 316,059 307.15 Sailing — Fitted with auxiliary power 179 3,751 20.96 196 4,156 21.20 Other Vessels . . 1,167 50,558 43.32 1,141 48,242 42.28 Barges, Hulks, Dredges, etc., (not self-propelled) 286 66,223 231.55 277 68,771 248.27 Total 2,797 449,637 160.76 2,780 445,945 160.41 For the purposes of the present estimate, a request was made to some of the leading shipowners for an approximate value per net ton as at 30th June, 1915, appHcable to the vessels on the register. This information was courteously furnished by those applied to, the average values given per net ton being as follows : — Steam Dredges £95, Steam Tugs £300, Other Steam Vessels £32, Sailing Vessels fitted with auxiliary power £27, Other Sailing Vessels £10, Barges, Hulks, Dredges, etc, not self-propelled, £12. On the basis of these averages the value of the shipping on the register was computed, en the assumption that the appropriate number for 30th June, 1915, was the mean between the numbers on the register at 31st December,. 1914, and 31st December. 1915. For the purposes of local allocation, the vessels registered in the several States and in the Northern Territory have been treated as domiciled therein. Estimated Value of Shipping Registered, 30th Jime, 1915. N.S.W. Vic. Qland. S.A. W.A. Tas. N.T. C'wlth. £1,000 4,215 £1,000 4,844 £1,000 £1,000 1,102 , 2,009 i £1,000 838 £1,000 £1,000 316 I 7 £1.000 13,331 The total for the Commonwealth represents an average of £2 13s. lOd. per head of the mean population for 1915. (ix.) Agricultural and Pastoral Products. — Whatever the point of time in respect of which an estimate of wealth is being prepared, there will, hi any agricultural and pastoral community, always be a proportion of the previous season's production in the hands of the producers and dealers. In addition, there will usually at such a time be a greater or less amount of work performed, seed sown, etc., in respect of the succeeding harvest. In the case of Australia there is also a large value attachable to the wool clip, which is being shorn as at the 30th June in any year. To allow for these several factors, it has been assumed that the value of agricultural and pastoral products in the liands of producers and dealers at 30th June, 1915, plus the value of 150 The Inventory Method of Estimating Wealth. work done, etc., for the ensuing season, may be taken at one-half the value of the agricultural production for 1915 plus 90% of the wool clip for that year. The estimate which has been made in (ii.) above in respect of sheep is so low that it must be treated as value " off the shears." No allowance has been made for stocks of tallow, skins, hides, etc., held locally. The value obtained is as follows : — Estimated Value of Agricultural and Pastoral Products as at 30th June, 1915. Particulars. N.S.W Vic. Q'lnd. S.A. W.A. Tas. N.T. F.T. C'wlth Agriciiltiu-al Pastoral . . £1,000 11,816 10,970 £1,000 11.706 3,746 £1.000 2,510 5,471 £1,000 5,990 1,220 £1,000 3,155 755 £1,000 1,694 370 £1,000 2 14 £1,000 11 35 £1,000 36,884 22,581 Total 22,786 15,452 7,981 7,210 3,910 2,064 16 46 59,465 The Commonwealth total represents an average of £12 Os. 3d. per head of the mean population for 1915. (x. ) Locally Manufactured Products. — The value of the output of manufacturing establishments is collected and tabulated annually in the several States, and for th^i year 1915 totalled £169,086,700 for the whole of Australia. Of this, however, the railway and tramway workshops which are largely owned by various Govern- ments are responsible for £6,046,521 in all (see item iv. above). This amount has consequently been deducted to reduce the total to a "private" basis in each State. For the piu-poses of the present estimate it has been assumed that one-sixth of the year's output would be in the hands of merchants and dealers at 30th June, 1915, and that the same proportion of the year's total would be in the hands of the manu- facturers in the form of (a) completed articles, (b) partly manufactured goods, or (c) raw materials. Tlie estimate for the holdings of all parties will thus be as follows : — Estimated Value of Locally Manufactured Products held at 30th June, 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. C'wlth. £1,000 21,942 £1,000 16,546 £1,000 8,285 £1,000 4,428 £1 .000 1,766 £1,000 1,380 £1,000 54,347 The Commonwealth total represents an average of £10 19s. 7d. per head of the mean population for 1915. (xi.) Minim/ Products (other than Gold). — Many of the products of mining in Australia are in the hands of maniifacturers and banks, or are exported at a relatively early date after their extraction. This is particularly the case with gold. Probably the mineral most extensively held after extraction and before manufactiu-e, con- sumjJtion, export, etc., is coal. In the United States estimate for the year 1912, it was assumed that at 31st December, 1912, a quantity of coal equalto the wholeof that mined during 1912 was in hand. Such an estimate would be much too high for Australia. For the purpose of the present estimate, it has been assumed that at 30th June, 1915, no gold was in the hands of the mining companies, and that the value of the other minerals so held was one-sixth of the total production of such minerals for the year 1915. Returns of the quantity and value of all minerals produced are t;ollected and published annually by the Mines Departments of the several States. Estimate of Australian Private Wealth for 1915. The values ascertained in the manner indicated above are as follows : — Estimated Value of Mineral Stocks (other than Gold), 30th June, 1915. 151 N.S.W. 1 Vic. Q'land. S.A. W.A. Tas. N.T. C'wlth. £1,000 1,506 £1,000 £1,000 57 377 £1,000 162 £1,000 56 £1,000 £1,000 191 5 £1,000 2,354 The total for the Commonwealth represents an average of 9s. 6d. per head of the mean population for 1915. (xii.) Imported Merchandise. — During the year ended 30th June, 1915, the total oversea importations of merchandise into Australia were valued at £63,563,781. For the purposes of the present estimate it has been assumed that at 30th June, 1915, the vahie of such merchandise in bonded warehouses, and in the hands of traders, was one-half of the total value, or in round numbers £31,782,000. Owing to the absence of interstate trade statistics, it is impossible to accurately allocate these importations to their States of ultimate destination. Figures are available shewing the values of oversea merchandise directly delivered in each of the States, but as certain of the States, more particularly New South Wales and Victoria, import extensively for the purpose of subsequent distribution to other States, it is clear that an estimate based on direct importation oversea would misrepresent the ultimate distribution. The total of £31,782,000 mentioned above has consequently been allocated to the several States and Territories on a population basis, the results being as follows : — Estimated Value of Imported Merchandise on Hand, 30th June, 1 915. N.S.W. Vic. 1 Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. £1,000 11,997 £1,000 9,159 £1,000 £1,000 4,410 1 2,822 £1,000 2,070 £1,000 1,280 £1,000 28 £1,000 16 £1,000 31,782 The Commonwealth total represents an average of £6 8s. 5d. per head of the mean population for 1915. (xiii.) Clothing and Personal Adornment. — ^Under this head may be included all articles of wearing apparel, watches, jewellery, etc., in the hands of the public. Articles of this nature in bonded warehouses or in the hands of traders have been already accounted for under preceding heads. The item is one of some importance, but unfortunately there are no means readily available for making a reliable estimate of the value involved. It has consequently been assumed that an average of £3 per head of the mean population for 1915 might be taken as a figiu-e which at all events does not exaggerate the position. The result so obtained is as follows : — Estimated Value of Clothing and Personal Adornment, 30th June, 1915. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. £1,000 5,606 £1,000 4,280 £1,000 2,061 £1,000 1,319 £1,000 967 £1,000 £1,000 £1,000 | £1,000 598 13 14,851 152 The Inventory Method of Estimating Wealth. (xiv.) Furniture and fittings, books, pleasure vehicles, &c. — Under this head an estimate is given in respect of (i.) household furniture and fittings, (ii. ) books, (iii.) motor cars and other vehicles used for purposes of pleasure, (iv. ) musical instruments, (v.) sewmg machines, (vi.) kitchen utensils, (vii. ) fanoygoods, etc., etc. As in the <;ase of the preceding item, the materials available for an estimate are meagre. It is evident, however, that the wealth represented by the items coming under this head must be considerable. The estimate was made in the following manner : — The Census of 3rd April, 1911, furnished the number of dwellings, "private" and "other than private," according to the number of rooms, and according to the rental paid. The numbers were as follows : — State. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. Private Dwellings (a) Other than private (6) Unspecified as to — Rooms (a) Do. (b) Rent (a) Do. (b) 319,766 11,210 1,340 455 55,741 1,708 263,634 9,049 1,119 359 41,264 1,306 121,753 4,083 486 342 23,179 905 82,108 2,071 303 88 9,585 295 66,553' 38,950 2,317 1,075 291 382 129 23 17,404' 5,757 446' 147 1,194 54 6 23 414 34 431 11 6 262 6 Total Dwellings 330,976 272,683 125,836 84,179 68,870| 40,025 1,248 442 One estimate was made of the average amount of fiu-nitvu-e, etc., necessary for ■" private" and " other than private" dwellings, according to the number of rooms in the dwelling, and a second estimate was made on the basis of the rental paid. These estimates were applied to the data for each State, and means were taken. ^ It was assumed that the value could on the whole be taken as two-thirds of the value of new furnitiu'e. On dividing by the number of houses at the time of the census, and also by the population, the results obtained as indicated were as follows : — State. N.S.W Vic. Q'land S.A. W.A. Tas. N.T. F.T. Value per house ..£ Per head of population £ Population*at Census No. Population* in 1915 Mo. 83.60 16.8 1,647 1,869 78.18 16.2 1,316 1,427 61.16 12.7 606 687 73.85 15.2 409 440 58.14 14.2 282 322 60.13 12.6 191 199 30.80 11.6 3.3 4.4 61.19 15.8 1.7 2.5 * In thousamla. As the number of dwellings in 1915 was not available, the amount per head shewn above was multiplied into the population, giving the folkvving results, viz. : — Estimated Value of Furniture, etc , as at 80th June , 1915. N.S.W. Vic. Q'land. S.A W.A. Tas. N.T. F.T. ! C'wlth. 1 £1,000 31,392 £1,000 23,111 £1,000 8,724 £1,000 6,681 £1,000 4,577 £1,000 2,512 £1.000 51 £1,000 £1,000 39 77,087 1. Simple lUf^aiis except in the ease of Western Australia, in which case the weight 2 was allowed to the istiMiatioii on the basis of roonis, and the weisht 1 to that on the basis of rentals, these wei«hts expressing the relative degrees of confidence which it was believed should be attributed to the result. Estimate of Aistralian Private Wealth for 1915. 153 The total for the Commonwealth represents an average of £15 lis. 6d. per head of the mean population for 1915, or £74 8s. 9d. per occupied dwelling on the 1911 census average of 4.78 inmates per occupied dwelling. 4. Aggregate of detailed estimates. — On combining the detailed estimates given in the preceding section, tlie total value of private wealth existing in Australia, ex- clusive of private interests in national and comInm^al property, is found to be ap- proximately 1620 millions sterling, or £.327 per head of the mean population of the Commonwealth for 1915. As pointed ovit in section 2 of the present Chapter,, a comparison of this estimate with one based on a wealth census or on probate re- turns is not satisfactory unless there be added to the inventory estimate an allowance for the local holdings of Commonwealth, State and Municipal securities, all of which are brought to accoiuit in the census and probate methods. At the 30th Jrnie, 1915, the total amoimt so held was approximately 140 millions sterling, making with the smn quoted above, a total of 1760 millions as compared with the war census total of 1643 millions, and an estimate on the probate basis of little more than 1000 millions. In view (i.) of the emergency nature of the war census, (ii.) of the evidence of incom- pleteness furnished by the returns, and (iii.) of the tendency for persons ftirnishing such returns to suspect taxation, and hence to furnish a conservative estimate, it is probable that the War Census total is an imderstatement of the position. It will thus be seen that the result obtained by the inventory method, although much in excess of any previous estimates, is in the main corroborated by the wealth census result. A summary of the values obtained is fiirnished in the following table :- — ■ Estimate of the Private Wealth of Australia as at 30th June, 1915, Based on the Inventoiy Method of Estimation. Class of Property. N.S.W. Vic. Q'land. S.A. W.A. Tas. N.T. F.T. C'wlth. £1,000 £1,000 £1,000 £1,000 £1,000 £1,000 £1,000 £1,000 £1,000 (i.) Land and Improvements (ii.) Live Stock 472,925 38,260 314,611 128,867 21,371 24.490 93,300 5,197 61,812 7,610 33,093 2,251 660 1,115 369 97 1,105,637 100,391 (iii.) Atrripultiiral. Dairying and Pastoral Implements and Machinery 8,057 6,412 2,347 3,319 2,170 478 8 8 22,799 (iv.) Manufacturing Plant and Machinery 15,901 10,761 6,817 3,225 2,194 1,142 40,040 (v.) Mining Properties (includ- ing Plant * Macliinery) 10,875 7,551 6,170 1,438 11,311 3,942 32 41,319- (vi.) Coin and Bullion 13,877 19,454 3,414 2,833 3,967 825 9 44,37* (vii.) Private Railways and Tramways 1,461 500 4,608 68 3,870 1,228 11,735 (viii.) Shipping . . 4,215 4,844 1,102 2,009 838 316 7 13,331 (ix.) Agricultural and Pastoral Products 22,786 15,452 7,981 7,210 3,910 2,064 16 46 59,465 (x.) Locally Manufactured Pro- ducts 21,942 16,546 8,285 4,428 1,766 1,380 54,347 (xi.) Mining Products (other than Gold) 1,506 57 377 162 56 191 5 2,354 (xii.) Imported Merchandise . . 11,997 9,159 4,410 2,822 2,070 1,280 28 '16 31,782 (xiii.) Clothing and Personal Adornments 5,606 4,280 2,061 1,319 967 598 13 7 14,851 (xiv.) Furniture and Fittings, Books, Pleasure Vehicles, etc. 31,392 660,800 23,111 8,724 6,681 4,577 2,512 51 39 77,087 Total 454,109 209,653 134,011 107,118 51,300 1,944 582 1,619,517 Mean Pop\ilation for 1915 (in thousands) . . 1,868.6 1,426.6 686.9 439.5 322.4 199.3 4.4 2.5 4,950.2 Private Wealth per Head £354 £318 £305 £305 £332 £258 £442 £233 £327 154 The Inventory ISIethod or Estimating Wealth. For the sake of avoiding any possible misunderstanding of the significance of the above figures, it may be well to again state here that what they represent is an esti- mate of the value of all the private material wealth existing in Australia at :iOth June, 1915, whether such wealth was owned by Australian residents or not. Pro- perty situated outside Australia but owned by Australian residents is not included, and immaterial wealth such as title deeds, mortgage deeds, debentures, etc., is not, as such, included at all, the estimate being based entirely on the material private wealth itself, not in any way upon the individual titles thereto. National wealth in the sense of the property of Commonwealth and State Governments, and communal wealth in the sense of the property of the variovis local governing bodies, are not included, nor has any allowance been made for the fact that private investors are to a very large extent monetarily interested in such property in consequence of advances made by them by way of public and municipal loans. An estimate of the value of national and commmial property has not, on the present occasion, been undertaken. One of the large items is the Government Railways and Tramways, and the Municipal Tramways, whose cost of construction and equipment to 30th Jime, 191.5, was about £200,000,000. These, together with public buildings and their sites. State and mvmicipal industrial undertakings, and some other branches of national and com- munal property, are of covirse capable of approximate valuation, but there are in addition such items as (i.) unalienated crown lands, (ii.) streets, roads and bridges, (iii.) harbours, etc., for which it would be difficult to devise a suitable valuation basis. CHAPTER II.— EARLIER AUSTRALIAN INVENTORY ESTIMATES. 1. Estimate for 1890 and earlier years. — The earliest estimate of this nature made in respect of Australia appears to be that made in 1892 by Mr. (now Sir) T. A. Coghlan, who, at the time, was Government Statistician of the State of New South "sVales. Particulars of this estimate were embodied in a paper read before the Aus- tralasian Association for the Advancement of Science at its Hobart session in 1892, and were svabsequently published in the 1892 issue of Coghlan's " Seven Colonies of Australasia." The estimate relates not only to Australia, but includes figures for New Zealand, and also furnishes aggregates but not details in respect of Australasia for 181.3, 1838, and 1 8()3. As the settlement of New Zealand in a permanent manner dates from 1840, the figures for 1813 and 1838 are necessarily purely Australian, while for 1890 the estimate for New Zealand is shewn in detail. In the case of 1863, however, the only figures furnished are those relating to " Australasia." For the purpose of comparing the Australian figures for the several years mentioned, it has been assumed here that in the estimate for 1863 the private wealth per head of population was the same in New Zealand as in Australia. With this adjustment Coghlan's estimate of private wealth in Australia for the years in question may be stated as follows, the average amount per head of mean population being also shewn : Earlier Aistralian Inventory Estimates. 155 Coghlans Estimate of Australian Private Wealth, 1813 to 1890. Year. 1813. 1838. 1 1863. 1890. Aggregate amoiuit . . Mean Population . . Average per head of Mean Population . . £1,000,000 13,293 £75 £26,000.000 143,178 £182 £160,000,000* 1,233,106 £130 £1,019,242,000 3,106,917 £.32S * Adjusted. See preceding paragraph. In later issues of " The Seven Colonies of Aiistralasia," the figures for 1890 have been omitted, and an estimate for 1888 has been substituted, presumably with the object of making equal intervals of 25 years between the successive estimates. The figures, however, are given for " Australasia," not for the Commonwealth and New Zealand separately. The total shewn is £1,015,000,000, or £154,434,000 less than the •" Australasian" total for 1890. Assuming this rate of reduction to have applied equally to Australia and New Zealand, the Commonwealth figure for 1888 would work out at about £885,000,000, or £302 per head of mean population. The following table shews the estimate under eight classes of private wealth for Australia as a whole, particulars having been added shewing the relative size of each class, and the amount per head of mean population : — Coghlan's Estimate of Private Wealth in Australia in 1890. Classification of Wealth. I Average Percentage! Amount Aggregate ^^ \ per Head Amount. Total. °^ IMean Popiilation. £ 0/ ,0 £ s. d. Land, Houses & Permanent Improvements 721,303,000 70.77 232 3 2 Live Stock . . 102,952.000 10.10 33 2 9 Coin and BxiUion . . 28.809.000 2.82 9 o o Merchandise 44.722,000 4.39 14 / 11 Household Furniture & Personal Property 52,863,000 5.19 17 3 Shipping 5,210,000 .51 1 13 / Mines and Mining Plant . . 33,823,000 3.32 10 1/ 9 Plant Employed in Agricultural, Manu- factm-uig and other Industries not elsewhere included 29,560,000 2.90 9 10 3 Total 1,019,242,000 : 1 100.00 328 1 1 2. Estimates for 1903 and earlier years. — Furtlier estimates of the private wealth of A\istralasia were prepared by Coghlan in respect of the years, 1899, 1901 and 1903, and published in his "Seven Colonies of Australasia," and his " Statistical Account of Australia and New Zealand." The particulars in respect of the method of estimating are less complete than is the case with the estimate for 1890, but evidently they were made upon principles very similar in character. For the purposes of the present review it will bo sufficient to consider in detail the latest of these, viz., that for 1903. The classes of wealth adopted differ slightly from those used in the 1890 estimate, the main alteration being the separation of " Land" from " Houses and Permanent Improvements," and the separation of " Personal Effects" from " Furniture and Household (Joods and Effects," thus increasing the number of classes to ten in place of the eight classes used in the estimate for 1890. The other classes were in some 156 The Inventory Method of Estimating Wealth. instances slightly altered in title, but were apparently little changed otherwise. The aggregate obtained for the Commonwealth is that shewn in the succeeding table, columns having lieen added to shew relative distribution and values per head : — Coghlan's Estimate of Private Wealth in Australia for 1903. Classification of Wealth. Aggregate Amount. Percentage I on Total. Land Houses and Permanent Improvements . . Live Stock . . Furniture & Household Goods & Effects Personal Effects Machinery and Implements of Trade (ex- cluding Mining Machinery) Shipping Mining Properties and Plant Merchandise and Produce on Hand Coin and Bullion . . Total 373,679,000 310,26.5,000 96.91.5.000 30,899,000 12,464,000 33,495,000 6,359,000 32,199,000 .59,640,000 26,064,000 981,979,000 Average Amount per Head of Mean Population. 38.04 31.60 9.86 3.15 1.27 3.45 .65 3.27 6.06 2.65 100.00 £ s. d. 95 19 7 79 13 10 24 17 10 7 18 9 3 4 8 12 1 1 12 8 8 5 5 15 6 4 6 13 11 4 5 CHAPTER III.— COMPARISON OF EARLIER ESTIMATES WITH THOSE FOR 1915. 1. Aggregate amounts. — For the purpose of comparing the estimates made in respect of the years 1890, 1903 and 1915, the following table, based on the classifica- tion adopted in 1890, has been prepared : — Comparison of Estimates for 1890, 1903, 1915. Classification of Wealth. Aggregate Amount of Private Wealth. Increase ( + ) or Decrease ( — ) 1890. 1903. 1915. 1890 1903 1890 (Coghlan) (Coghlan) (Knibbs) to 1903. to 1915. to 1915. £1,000 £1,000 £1,000 £1,000 £1,000 £1,000 Land, Houses and Permanent Iniprovenicnts 721,303 683,944 1,105,637 —37,359 -1-421,693 + 384,334 Live Stock 102,952 96,915 100,391 — 6,037 + 3,476 — 2,561 Coin and JJullion . . 28,809 26,064 44,379 — 2,745 + 18,315 + 15,570 Merchandise and Produce on Hand 44,722 59,640 147,948 -f 14,918 -f 88,308 + 103,226 Household Furniture and Personal Property 52,863 43,363 91,938 — 9,500 -f 48,575 + 39,075 .Shippina 5,210 6,359 13,331 4- 1,149 + 6,972 + 8,121 Mines and Mining Plant, . . 33,823 32,199 41,319 — 1,624 -t- 9,120 + 7,496 Plant. Machinerv, etc., not elsewhere included 29,560 33,495 74,574 + 3,935 -f41,079 + 45,014 Total 1,019,242 981,979 1,619,517 —37,263 -1-637,538 + 600,275 '\Vith the (>xception of three items, viz., (a) Merchandise, etc., (h) Ship])ing, and (c) Plant, Machinery, etc., the aggregate estimates for 1003 fell short of the cor- responding items for 1890, the princiyial shortage being a decline of £37,359,000 in the estimated value of "land, liouses and permanent improvements." For all classes ■of wealth combined the estimate for 1903 fell short of that for 1890 by £37,263,000. Comparison of Earlier Estimates with those for 1915. 157 On the other hand the estimate for 1915 shews in every item a substantial advance on that for 1903. The largest increase is that of £421,693,000 in the value of " land, houses and permanent improvements," while for all classes of wealth an advance of £637,538,000 is shewn. Comparing the estimate for 1915 with that for 1890 there is in evidence an in- crease in every item except that of live stock, the total increase shewn for the 25 years being £600,275,000. As a partial explanation of the decline in estimated values between 1890 and 1903, it may be pointed out that the year 1890 occurred near the apex of a period of exceptional and to some extent perhajDs fictitiovis prosperity, and that in conseqtience prices, and especially the prices of real estate, were in an inflated condition. The subsequent collapse, followed and accentuated by the banking crisis of 1893, and supplemented by a series of unfavourable seasons, produced a condition of depression which was only slightly relieved by the discovery and development of the Western Australian Goldfields during the years 1893-1897. The outcome was that the prices of commodities fell rapidly, and the fall in the prices of real estate was even more marked. A further unfavourable influence in the case of 1903 was the fact that in the season 1902-3 Australia experienced one of its most severe droughts. In the case of 1915 it should be noted that since 1896 there has been a fairly continuous upward trend in the world's prices for practically all commodities, accompanied in Australia by a marked recovery in the values of real estate. This rise in the prices of commodities has been very marked since 1905, and has in recent years been accentuated by the outbreak of war in 1914. 2. Relative distribution of private wealth according to class. — The following table furnishes a comparison of the relative distribution of wealth according to class for the estimates made in respect of 1890, 1903 and 1915 : — Relative Distribution of Private Wealth, 1890, 1903 and 1915. Increase ( + ) or Percentage on Decrease ( — ) in Pro- Estimated Total. portion per cent. Classification of Wealth. 1890. 1903. 191.5. 1890 to 1903 to 1890 to . Coghlan Coghlan Knibbs [ 1903. 1915. 1915. Land, Houses and Per- O' /O 0' /o o/ /o o O' /O o manent Improvements 70.77 69.64 68.27 —1.13 —1.37 —2.50 Live Stock 10.10 9.86 6.20 ! —0.24 —3.66 —3.90 Coin and Bullion 2.82 2.65 2.74 —0.17 + 0.09 —0.08 Merchandise and Produce on Hand 4.39 6.06 9.14 + 1.67 + 3.08 + 4.75 Household Fvu-niture and Personal Property . . 5.19 4.42 5.68 —0.77 + 1.26 + 0.49 Shipping 0.51 0.65 0.82 + 0.14 + 0.17 + 0.31 Mines & Mining Plant 3.32 3.27 2.55 —0.05 —0.72 —0.77 Plant, Machiiiery, etc.. not elsewhere included 2.90 3.45 4.60 + 0.55 + 1.15 + 1.70 Total 100.00 100.00 100.00 i 1 158 The Inventory Method of Estimating Wealth. An interesting feature of this comparison is the very high proportion in each case which is represented by property in the form of " land, houses, and permanent improvements," ranging from 70.77 per cent, in the 1890 estimate, to 68.27 per cent, in that for 1915. Threeof the items, viz., (i.) land, etc., (ii.) live stock, and (iii.) mining properties, occupied positions of diminishing relative importance at the successive estimates. On the other hand, three items, viz., (i.) merchandise, etc., (ii.) shipping, and (iii.) plant, machinery, etc., occupied positions of increasing relative importance. In the case of the two remaining items, viz., (i.) coin and bullion, and (ii.) household furni- ture, etc., the estimates indicated an initial decrease, and subsequent increase in relative importance, the variation in the case of coin and bullion being very smalL In the main it may be said that the figures indicate a decline in the relative import- ance of the primary sources of wealth, and an increase in the relative importance of the accumulated products of industry in the shape either of goods available for con- sumption or of mechanical and other aids to production. With the excaption, however, of the relative increases in the items "merchandise,, etc.," and "plant, etc.," and the relative decreases in the item "live stock," the variations were not verv marked. 3. Private wealth per head in each class. — ^ Another comparison of importance in this matter is the amount per head of mean population for the years in question,, represented by the several items. This is furnished in the succeeding table : — Private Wealth per Head of Mean Population, 1890, 1903 and 1915. Avera ge Wealth per Head. Increase ( + ) or Decrease ( — ) in Average Wealth per Head. Classifloation of Wealth. 1890 1903 1915 1890 1903 1890 (Coghlan) (Coghlan) (Knibbs) to 1903. to 1915. to 1915. £ s. d. £ s. d. £ s. d. £ s. d.; £ s. d. £ s. d. Land, Houses, and Pennan ent Improvements 232 3 2 175 13 5 223 7 — 56 9 9 +47 13 7 — 8 16 2 Live Stock . . 33 2 9 24 17 10 20 5 7 — 8 4 11- 4 12 3 -12 17 2 Coin and Bullion . . 9 5 5 6 13 11 8 19 4 — 2 11 6-1-2 5 5 — 061 Merchandise and Produce on I Hand 14 7 11 15 6 4 29 17 9 + 18 5 -f 14 11 5 + 15 9 10 Household Furniture and Personal Property 17 3 11 2 9 18 11 6 — 5 17 6 + 78 9 + 1 11 3 Shipping 1 13 7 1 12 8 2 13 10 — 11 + 11 2 + 10 3 Mines and Mining Plant 10 17 9 8 5 5 8 7 — 2 12 4 + 01 7 — 2 10 9 Plant, Machinery, etc., not elsewhere included 9 10 3 8 12 1 15 1 3 — 18 2 + 69 2 + 5 11 Total 328 1 1 252 4 5 327 3 3 — 75 16 8 +74 18 10 — 17 10 In all the items except that of " merchandise, etc.," tlie estimate per head for 1903 is below that for 1890, the most extensive decline being in the case of "" houses, etc." "Livestock," "coin and bullion," "household furniture, etc.," and "mines," also shew substantial shortages, the total per head for 1903 falling short of the 1890 estimate by £7.5 16s. 8d. On the other hand the 191.5 estimate per head exhibits advances on that for 1903 in all the items except Hve stock, the total per head giving an advance of £74 18s. lOd. Compared with the estimate per liead for 1890, that for 1915 shews decreases in four items, viz., " land, etc.," " live stock," " coin and Ijullion," and " mines," while it exhibits increases in the other four items. For a reference to the causes tending to produce these fluctuations see p. 157. Estimates of National Wealth of United States of America. 159 CHAPTER IV.— ESTIMATES OF THE NATIONAL WEALTH OF THE UNITED STATES OF AMERICA. 1. General. — The following particulars exhibiting the methods and the results of estimates of the wealth of the United States of America have, in the main, been taken from the publications of the Bureau of the Census, Washington, D.C. 2. Census of 1850. — The first effort of the Government to obtain a statement of the valuation of the property of the comitry was made under the Census Act of 1850. The instructions on the schedules issued to United States marshals, through whom the census statistics for that year were collected, required those officers to obtain statistics of the valuation of real and personal property as assessed for taxation, and ill addition thereto the true valuation of such property. For obtaming this latter, the schedules contained the following instructions : — '■ The true valuation of all jiroperty should be estimated at what is its cash value in the place where it is situated. In some places, however, it is valued by appraisers at two-thirds or one-half of its just value, and the assessment made upon such valuation. If in the estimate of an estate it is valued at other than its true worth, the trvie valuation should be stated, which may easily be done by adding the proper per centiun to the recorded valuation."' No valuation statistics of the above character were published in the final report of the Census of 1850, but a preliminary report by the Superintendent, which was published as a Congress Paper, contained a table of such values under the heading ■' real and personal estate," with the following remark : — '■ The table of real and personal estate owned by individuals is made up from official returns of property for taxation. Where the assessment has been made on a sum less than the intrinsic worth, the assistant marshals were in- structed to add the necessary percentage. For the purposes of taxation the full amount is not generally given, in rural districts especially. Stocks or bonds owned by the States or by the General Government are not represented. The value of slaves is included." The table mentioned is headed "' valuation of real and personal estate of the inhabitants of the United States for the year ending 1st Jime, 1850," and the total true or estimated value is giv^en as $7,135,780,228 (= £1,466,000,000 approximately, i.e., on the basis of 84.86?* to the £). 3. Census of 1860. — At the Census of 1860 the marshals of the United States were directed to obtain from the records of the States and Territories respectively, an account of the value of real and personal estates as assessed for taxation. In- structions were given these officers to add the proper amounts to the assessment, so that the return should shew the true value as well as the inadequate .lum generally attached to the property for taxation purposes. The aggregation of these returns indicated that the value of individual property in the States and Territories amounted to 816,159,616,068 (= £3,320,000,000 approximately, at $4.86-5 to the £). In the returns for 1850 and 1860 the value of all taxable property was retiu-ned, including that of foreigners and non-residents, as well as that of natives and residents, while all property belonging to the State or Federal Government was excluded. 160 The Inventory Method of Estiviati.vg Wealth. i. Census of 1870.^Iii 1870 the duty of ascertaining the assessed and true valuation of property was again entrusted to the United States marshals. The point? particularly dwelt upon in the instructions from the Census Office were : — (i.) the undervaluation of real estate in assessments for taxation ; (ii.) the large class of personal property lawfully exempt from taxation ; (iii.) the class disregarded by assessors ; (iv.) the class which by evasion or fraud escapes taxation. In the report dealing with this census, it is stated that " for the majority of the States and for the vast majority of the property of the country, the additions to be made to assessed values on account of the undervaluation of real estate has been calculated with great nicety by competent investic/ators.'" The report admits, however, that no such accurate methods could be applied to make good the shortages due to exemp- tions or escape of personal property from taxation in 1870, and states that the result reached must be characterised rather as an impression than an opinion. The estimated true value of all taxable property was given for 1870 on a gold basis as $24,054,814,806 (= £4,940,000,000 approx., at $4.86| to the £). o. Census of 1880. — At the Census of 1880 a special effort was made to intro- duce an initial correction into the statistics of the assessed valuation of real estate. With this object a circular letter was addressed from the Census Office to a very large number of bankers, real estate agents, and business men, as well as public officials connected more or less directly with the valuation of property for the piu-poses of taxation. The letter enclosed a form of report drafted for the piu-pose of obtaining an explicit statement of the methods of procedure adopted in the various localities in connection with the valuation of real estate. The main object of the inquiry was that of ascertaining for the different classes of real estate the percentage of assessed value to real value in the different localities. Over 25,000 replies to the circular were received, the majority of them exliibiting both a disposition to assist, and also a fair comprehension of the purpose of the inquiry. From an analysis of the data so obtained, it was ascertained that the ratios of assessed to true valuation of real estate ranged from 40 to 100 per cent., with an average for the country as a whole of 65 per cent. The percentage was in general found to be highest in those States having a large urban population, and least in the rapidly-growing States of the Upper Mississippi Valley. On previous occasions the estimates had related to taxable property only, but at the Census of 1880, and those taken subsequently, an estimate was also made of the value of property exempt from taxation, consisting mainly of the property of Federal, State and Local Governments, and of religious, charitable and educational institutions. In the reports dealing with the censuses subsequent to that of 1880, the esti- mated values of taxable and exempt property are shewn separatelj% but in that of the 1880 Census the figures given relate to taxable and exempt property combined. In 1890 the estimate for exempt property represented 5.9% of the combined total, the corresponding percentage in 1900 being 7, while in 1904 it was 6.4%, and in 1912, 6.6%. The combined total value for taxable and exempt property ascer- tained at the Censas of 1880 was $43,642,000,000 (= £8,968,000,000 at $4. 86s to . the £). Estimates of National Wealth of United States of America. 161 6. Census of 1890. — At the Census of 1890 inquiries were sent to county and municipal officers asking them to state what, in their opinion, was the relation be- tween the assessed and the true vahie of the real estate as respectively assessed V>y them. To corroborate the reports fiu-nished by these officers, upwards of 25,000 inquiries were sent throughout the country to persons believed to be familiar with the values of real estate, asking their opinion as to the relation between the assessed and true value in their respective localities. The replies received were considered in connection with the reports of the assessors. The value of farm lands as reported by the censiis enumerators was also taken into consideration. The estimated vahie of property for the Census of 1890 was $65,037,091,197, comprising taxable property $61,203,755,972, and exempt property $3,833,335,225. Again, taking $4.86fs to the £, these may be represented approximately by taxable property £12,577,000,000, and exempt property £788,000,000, giving a combined total of £13,365,000,000. 7. Census of 1900. — (i.) General. — The volume relative to wealth, debt and taxation issued by the Bureau of the Census, Washington, in connection with the Censtis of 1900, contains the results of two estimates of wealth, one in respect of the year 1900, the other in respect of the year 1904. The former of these was authorised by the Act of 3rd March, 1899, providing for the Twelfth Census, the latter by the Act of 6th March, 1902, establishing the permanent Census Office. In both cases the particulars published relate to continental United States, that is, they are exclusive of Alaska, Hawaii, Porto Rico, and the Philippines. (ii.) Farm and Factory Property. — For the year 1900 Congress specifically authorised and directed that the value of property employed in agriculture and manu- factures as appraised by owners, occupiers or managers thereof should be ascer- tained through the agency of census eniunerators. The values so determined for this class of property are shewn in the following table :■ — • Estimated Value of Farm and Factory Property, U.S.A., 1900. Farm Property — Land and Improvements (other than Buiklings) Buildmgs Live Stock Implements and Machinery Factory Property — - Land Buildmgs Machinery, Tools and Implements Total Farm and Factory $ £1,000,000 13,058,007,995 = 2.683 3,556,639,496 = 731 3,075,477,703 = 632 749,775,970 = 154 1,027,368,280 — 211 1,449,403,782 = 298 2,541,046.6.39 = 522 25,457,719,865 = 5,231 The conversion in this table from American to British currency has been made on the basis of $4,863 to the £. The farm and factory total, however, constituted but a small part of the tangible wealth of the United States, and represented less than 29 per cent, of the total estimated wealth of all kinds for 1900. (iii.) Taxable Real Property. — For the value of property other than that con- nected with farms and factories, estimates of various kinds were employed. The most important single class of property outside those mentioned above was taxable property used for residential and business purposes, and for mines and quarries. 162 The Inventory Method of Estimating Wealth. No complete appraisal of taxed real property had ever been made in the United States except by assessors for purposes of taxation, and as the Census Act did not authorise the collection by census enumerators of such information for property other than that connected with farms and factories, the lists prepared by the taxation assessors were used as the basis for estimating the other kinds of real estate. For the purposes of this estimate an endeavour was made to ascertain the percentage of true value represented in each case by the assessed valuation, and the Bureau of the Census sought to utilise all the available information relating to the subject. The means adopted comprised (i.) the comparison of farm values collected by the census enumerators with assessed values for the same properties ; (ii.) the comparison of selling prices with assessed values ; (iii.) inquiries made by agents of the Bureau of the Census in practically all cities, villages and county seats from persons com- petent to give information relating to the ratio between the assessed valuation and the true value of real property ; (iv.) reports of such ratios given in financial pub- lications ; (v.) reports of State tax commissions and State equalisation boards. (iv.) Exempt Real Property. — In estimating the value of real property exempt from taxation, great difficulty was experienced in all cases except New York, Massa- chusetts, New Jersey, and Pennsylvania. In the majority of cases the estimates of the value of exempt real property were prepared by using information secured from a number of sources, comprising amongst others :■ — (i.) Special inquiries by census agents ; (ii.) special returns supplied by city authorities ; (iii.) special returns from churches, schools and kindred institu- tions ; (iv.) a uniform rate of $1.25 ( = 5s. 2id.) per acre assigned to the imappropriated and reserved domain of the United States outside of Indian Territory and Oklahoma ; (v.) in the two Territories mentioned a value equal to that assigned by farmers who, as lessees, used it for agricultural purposes. (v.) Live Stock. — On 1st June, 1900, the census eniunerators recorded the number and value of the various classes of domestic stock on farms, and the value of poultry and bees on farms. They also recorded the numl^er, but not the value, of domestic stock not on farms. These latter were valued on the assiunption that the average value of each class of stock was the same as that ascertained for farms. Poultry and bees not on farms were not recorded. (vi.) Farm Implements and Machinery. — The figures given under this head for 1900 are those reported by the census eniunerators in respect of farm implements and machinery on farms at 1st June, 1900. (vii.) Manufacturing Machinery, Tools, and Implements. — The values of manu- faoturing machinery, tools, and implements for 1900 were reported by the Census of Manufactures for that year. The census was practically for the calendar year 1899, and the value returned for manufacturing machinery, tools, and implements is therefore the value at the close of that year, or about 1st January, 1900, not 1st June, 1900. No allowance for this fact was made in the final table, which conse- quently, owing to increases between 1st January and 1st June, tends to under- estimate the value. (viii.) Oold and Silver Coin and Bullion. — The estimate used for these was based upon the reports of the Director of the Mint, and of the Comptroller of the Currency for the year 1900. (ix.) Railroads and their Equipment. — An extensive valuation of the railroads and their equipment was made for the year 1904 by capitalising the net earnings of individual railways and railway systems. To obtain figures for 1900, computations were made to ascertain approximately the increase from 1900 to 1904, and the figures for 1904 were reduced in accordance therewith. Estimates of National Wealth of United States of America. 163 (x.) /Street Railways, etc. — The value of street railways was obtained by methods substantially the same as those adopted for estimating the commercial value of rail- roads, and the same is true in a general way of the estimated value of telegraph and telephone systems. The value of canals was assumed to be the same as that reported at the Census of 1890. The value of shipping was obtained by multiplying the ton- nage afloat by the building cost per ton as reported by the 1900 Census of Manu- factures, and deducting one-third for depreciation. To this was added the reported cost of the ships of the United States Navy in active commission. The values of electric light and power stations are based upon the cost of con- struction as estimated for the year 1902, with a deduction of twice the cost of new construction during 1902. As privately -owned gas-works had already been included with factories, no special estimates were made for them. (xi.) Products of Agriculture, Manufactures, and Mitiing.- — The value assigned to agricultural products was one-half the value of the crops reported by the Census of Agriculture as raised in the year 1899 (being the quantity estimated as still in hand at 1st June, 1900), plus the value of the labo\ir which had been expended to 1st June, 1900, on the crops of that year, and which was included in the value of the growing crops at that date. The value of the products of manufactures was based wholly on the report of the 1900 Census of Manufactures. For the value of materials and products in the possession of the factories, an amount was (apparently arbitrarily) allowed equal to two months' " gross products" of 1900. For the manufactured goods in the posses- sion of merchants, an amount was allowed equal to one-half the annual " net products " of the factory output, exclusive of hand trades. The value of the products of mines and quarries was based upon the census report for mines and quarries for 1902, taken in conjimction with the reports of Geological Survey for the years 1900 and 1902. In the case of imported merchandise it was assumed that the value of the im- ports either in bonded warehouses or in the hands of traders on 1st June, 1900, was equal to one-half the value of all such goods imported into the United States during the year ended 30th June, 1900. (xii.) Clothing, Furniture and Kindred Personal Property. — The estimated value of clothing and personal adornments, including watches, jewellery, etc., con- sisted substantially of the amounts which, on the basis of the 1900 Census of Manu- factures and the import returns for 1900, it was estimated that the people of the country expended for clothing and personal adornment for that year. An addition of one-third was made to allow for the increase in value due to the cost of transporta- tion and for the profit of the middleman. A small fiu-ther addition was made to allow for the value of the work in homes in converting cloth into clothing. In estimating the value of such articles as furniture for houses and public build- ings, books in libraries, carriages, bicycles, automobiles, harness, saddles and all kindred articles other than clothing, it was loosely estimated that the value of all these articles in the possession of the people or in public buildings was equal to four years' purchases of the same articles. The probable cost of four years' purchases was then estimated from the value of the manufactured products and imports which entered into the aggregate, one-third being added for the middleman's profits. In this connection the following account of the method adopted for valuing the cor- responding items at the Census of 1880 is of interest. It is taken from the report on that census : — 164 The Inventory Method of Estimating Wealth. " The number of families in each State was taken, and these were dis- tributed, according to the statistics of occupation, into certain characteristic classes. The average value of the household goods in the families of each class was then estimated as thoughtfiilly as possible, item by item, the values given to the goods representing what they were worth to the owner, or what it would cost to replace them, with fair allowance for wear and tear ; not what they would be worth to sell as second-hand goods. These results, secondly, were checked by an independent computation, in which the annual product or importation of ea. 1. 172 Miscellaneous Estimates of Wealth. The income assessed for taxation which was not brought to account for capital- isation in this estimate comprised (i.) fovir-fifths of income from trades and profes- sions (luider Schedule D), £140,000,000, (ii.) the permanent charge on the national debt for 1875-6, viz., £21,737,000, and (iii.) Schedule E, made \ip of salaries, pensions and annuities not earned by capital, totalling £32,540,000. These three items of income totalled £194,277,000. The total wealth shewn above, viz., £8,548,120,000, represents about £259 per head of the population of some 33,000,000. It may be noted that this method of estimating is, in essence, a variant of the inventory method, the vahies of the various assets bemg in the main based upon a capitalisation of the income which they realise. In the samie paper Giffen makes an estimate for the United Kingdom on similar lines for 1865, and obtains a total of £6,114,063,000, or £204 per head of the then population of 30,000,000. ' 8. Giffen's estimate Jor 1885.- — In his work on "The Growth of Capital,"* Giffen gives an estimate for the United Kingdom for 1885, based upon data and cal- culations of the same natvire as those indicated in the preceding section as having been used for the 1865 and 1875 estimates. The total obtained for 1885 was £10,037,436,000, or £279 per head of the then popxilation of 36,000,000. In the preparation of the 1885 estimate some minor alterations were made in the number of years' purchase adopted for the capitalisation of incomes. In some cases the number was increased, and in others diminished, the aggregate for 1885 being affected less than a half of one per cent, by the change. 9. Giffen's Estimate for 1903. — A further estimate was made by Sir Robert Giffen for a paper contributed by him to the Economics and Statistics Section of the British Association in September, 1903. * This estimate, however, which was not the main object of the paper, was not prepared with the same analysis of detail as characterised his estimates for 1865, 1875, and 1885, and caimot be regarded as more than a very rough approximation made to furnish a convenient working basis for the consideration of modes of expenditure. In addition to an estimate for the United Kingdom the paper contains similar estimates in respect of Canada, Australasia^ India, South Africa, and the remainder of the Empire. The figure so given for the wealth of the United Kingdom is £15,000,000,000, or £355 per head of the population, which in 1903 was about 42,250,000. The figures given in the paper for the British Empire are as follows : — Giffen's Estimate of the Wealth of the British Empire, 1903. United Kingdom. Canada. Australasia India. South Africa. Remainder of Empire. Total British Empire. £1,000,000 15,000 £1,000,000 1,350 £1,000,000 1,100 £1,000,000 3,000 £1,000,000 600 £1,000,000 1,200 £1,000,000 22,250 1. "The Growth of Capital," by Robert (iilfcn. George Bell & Sons, London, 1889. 2. Journal of the Royal Statistical Society, Vol. LXVI., p. 582. Estimates of Wealth in France. 173 These figures have been somewhat extensively quoted, e.f/., by Augustus D. "\Vebb, F.S.S., in " The New Dictionary of Statistics" for 1911, and by the Bureau of the Census, Washington, but it is clear from the context of the paper in which they appear that they were not put forward by the author as representing in most cases anything more than what may be termed " well-informed guesses." 10. Harris and Lakes estimate, 1903-6. — In a paper read before the Royal Statistical Society^ on 18th December, 1906, Messrs. Harris and Lake discxissed the compilation of wealth estimates on the basis of probate returns (see Part V. hereof). As the result of the calculations so made supplemented by estimates in respect of property not subject to death dvities, the total wealth of the United Kingdom at or about the end of 1904 was estimated at £9,207,000,000, thus falling short of Giffen's rough estimate, quoted in Section 9, by nearly £6,000,000,000. In view of the analysis of the limitations of the probate method given in Part V. hereof, there is little doubt that the estimate of Messrs. Harris and Lake is very much in defect. 11. Mallet's estimate, 1905 and 1906. — In a paper read before the Royal Statis- tical Society, 2 on 18th February, 1908, Mr. (now Sir) Bernard Mallet further discxissed the question of estimates based on probate returns, and in the course of his paper gave an estimate for England and Wales of £5,500,000,000, on the basis of the 1905 returns, and £6,098,000,000, on the basis of the 1906 returns, irrespective of any allowance on account of property not subject to death duties. For the reasons already referred to, it is probable that these estimates are much below the truth (see Part V. hereof). 12. Cbiozza Money's estimate, 1908.^ — In an estimate based largely on the method of capitalising incomes, Mr. L. (4. Chiozza Money* gave as a total for the Wealth of the United Kingdom m 1908 a sum of £13,762,000,000, or £313 per head on a population of some 44,000,000. CHAPTER n.— ESTIMATES OF WEALTH IN FRANCE. 1. Various early estimates. — On p. 127 of his work, already mentioned (" The Growth of Capital"), (riffen quotes M. de Foville as having fiirnished in his " La France Economique " particulars cf several estimates of the value of property in France, and gives the following summary of some of the more important of these : — Estimate of the Value of Property in France. Real Personal Authors. Date. Property. Property. Total. £1,000,000 £1,000,000 £1,000,000 M. de Girardin 1853 3,680 1,320 5,000 M. Wolowski . . 1871 4,800 2,200 7,000 M. C. Due d'Ayen . . 1872 4,000 3,800 7,800 M. C. D. Vacher 1878 8,640 1,760 10,400 M. Amelin 1878 5,400 4,200 9,600 M. S. Mony 1881 4,600 4,040 8,640 1. Journal of the Royal Statistical Society, Vol. LXIX., p. 709. 2. Journal of the Koyal Statistical Society, Vol. LXXI., p. 65. 3. " Riches and Poverty," by L. '^ J UNIVERSITY OF CALIFORNIA LIBRARY