University of California 
 College of Agriculture 
 Agricultural Experiment Station 
 Berkeley, California 
 
 STATISTICAL ANALYSIS OF TKS AFNUAL AVERAGE F.O.B. PRICES 
 OF ZmmQ ASP/iRAGUS, 1925-26 TO 1948-49 
 
 by 
 
 Sidney Hoos 
 
 '•WVERSVTY OF CAUFORNIA 
 
 LIBRAR 
 
 COULEX-E OP AGKICULTURE 
 DAVIS 
 
 April, 1949 
 Contribution from the 
 Gianninl Foundation of Agricultural Economics 
 Mimeographed Report No, 95 
 
statistical Analysis of the Annual Average F.O.B, Prices of 
 Canned Asparagus, 1925-26 to 1948-49 
 
 Sidney Hoos y 
 
 Dtiring a number of the years before World War II, the Giannini Foundation of 
 Agricultural Economics annually issued a report presenting the results of sta- 
 tistical analyses of canned asparagus prices. Those reports were made available 
 for the benefit of the canned asparagus industry, growers, packers, shippers and 
 purchasers. During the war years, the reports were suspended because of the ab- 
 normal conditions which prevailed then, such as federal price control. 
 
 In September 1947, the California Agricultural Experiment Station issued two 
 publications on asparagus.^ Those publications were made available for the 
 purpose of presenting in general terms an analysis of the economic trends under- 
 lying canned asparagus, and providing background information on the industry and 
 its economic status. The prewar, wartime, and immediate postwar developments 
 were reviewed to give a coBiprehensive basis for the industry's outlook. 
 
 This report undertakes to resume the type of statistical analyses of the 
 F.O.B, prices of canned asparagus which were issued in the prewar years, as noted 
 above . With the experience of three postwar pack-years available now, we are 
 beginning to get the basis fbr determining the postwar pattern of statistical 
 
 1/ Associate Professor of Agricultuiral Economics, Associate Economist in the 
 Experiment Station and on the Giannini Foiandation. 
 
 2/ Sidney Hoos and H. Fisk Phelps, California Asparagus, Economic Status 1948, 
 Calif, Agr, Exp. Sta. Circ, 373 (Sept. 1947). 
 
 Sidney Hoos and H, Fisk Phelps, Statistical Supplement to Calif, Agr. Exp« 
 Sta. Circ, 373 (Sept, 1947). 
 
 3/ For additional recent statistical data see: Sidney Hoos and Irvih Dubov. 
 Selected Statistics Pertaining to California Asparagus, Calif, Agr. Exp, Sta. 
 Contribution from the Giannini Foundation (April 1949) , 
 
' ■ ■ ■ 
 
2. 
 
 relations. Analysis of the available evidence indicates the existence of a 
 pattern which bears some similarity to but also has some characteristics different 
 from the prewar statistical relations. . A major difference concerns the effects 
 of consumers' money income as reflected by the index of nonagricxiltural income 
 payments. In the prewar years, the net relation between the prices and con- 
 sumers' income was best measured by a straight-line; that is, a change of income 
 from one level had the same effect on price as a change of income from another 
 level, within the range of experience. But when the postwar years are included 
 in the analysis, it appears that the net relation between the prices and con- 
 sumers' income can be adequately reflected by a curve; that is, the effect which 
 a change of income has on price is influenced by the income level from which the 
 change is considered. In other terms, an increase of 10 points in the income 
 index, if money income is high as in postwar years, ivS associated with a smaller 
 increase in the price than if the income index increases 10 points in relatively 
 low income years such as the middle 1930' s. 
 
 Below we present the results of an analysis of the major factors which have 
 influenced the annual average F.O.B. prices received for canned asparagus by 
 canners in California from 1925-26 through 1948-49, but excluding the war years 
 1941-42 through 1945-46^, The war years were omitted from the analysis because 
 of the reasons noted above. 
 
 Three formulations of the statistical demand relations for canned asparagus 
 are summarized in this report. All three formulations cover the period 1925-26 
 through 1948-49, excluding the war years 1941-42 through 1945-46, 
 
 The first formulation concerns the average relationships between F«O.B, 
 prices of California canned asparagus and (l) domestic shipments of Cali- 
 fornia canned asparagus, (2) the index of nonagricultural income payments 
 in the United States, and (3) factors included under "time." For this 
 first formulation: 
 
_ ■■<;:.: ; y,i-.i^^ '"^i®'?. IsSwv,,^:^ .Sfi-^ -ill; 
 
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I 3. 
 
 Equation 1 in table 2 summarises the statistical results ^ 
 obtained when the F*0<B. price is considered as the dependent 
 variable and the other three variables are used as the inde- 
 pendent ones; 
 
 Equation 2 in table 2 summarizes the statistical results 
 when the volume of domestic shipments of California canned 
 asparagus is considered as the dependent variable and is re- 
 lated to the F.O.B. price, index of nonagricvd-tviral income, 
 and the time-trend of demand. 
 The second formulation is similar to the first, except that income is 
 expressed in terms of its logarithms which is a convenient procedure 
 for meastxring the relations of relative changes in the income index. 
 Also, the "time" variable is reflected in a modified manner. For the 
 second formulation; | 
 Equation 3 in table 2 summarizes the statistical resiJ.ts 
 lAien the F.O.B. price is considered as the dependent variable; 
 and equation 4 in table 2 summarizes the results when domestic 
 shipments of Calif orijia canned asparagus is considered as the 
 dependent variable. 
 In the two formulations noted above, "time" is used as a proxy for and is 
 presumed to reflect the combined influence of factors which change smoothly and 
 persistently with time. It appears that a very important factor of that type is 
 the volime of asparagus canned in states other than California. 
 
 The third formiilation concerns the average relations between the F.O.B, 
 prices of California canned asparagus and (l) domestic shipments of 
 California canned asparagus, (2) the logarithm of the index of nonagri- 
 cultural income payments in the United States, and (3) the volume of 
 asparagus canned in states other than California^ For the third formulation: 
 
; v*', 
 
4. 
 
 Equation 5 in table 2 stunmarizes the statistical results 
 when the F.O.B, price is considered as the dependent variable; 
 and equation 6 in table 2 sioimnarizes the resxilts when domestic 
 shipments of California canned asparagus is considered as the 
 dependent variable. 
 
 When the F.O.B. prices are viewed as the dependent variable, the results of 
 all three formvilations (equations 1, 3 and 5 in table 2) are about equally accept- 
 able on statistical grounds; the third formulation (equation 3) is very slightly 
 better than the other two, but not significantly better. IJhen the domestic ship- 
 ments of California canned asparagus aro considered as the dependent variable, 
 the first formulation (eqviation 2) is less acceptable than the other two; but 
 the third formulation (equation 6) is only very slightly better (not signifi- 
 cantly so) than the second formulation (equation 4) . From the combined view- 
 points of economics, marketing and statistics, the third formulation appears to 
 be the most acceptable. Hence, that formulation is further considered, with 
 F.O.B, price viewed as the dependent variable. j 
 
 The average relationships which prevailed from 1925-26 through 1948-49 (ex- 
 cluding 1941-42 through 194-5-46) betv/een the F.O.B, prices of California canned 
 asparagus and three major factors were measured. The three price-influencing 
 factors include (l) domestic shipments of California canned asparagus, (2) non- 
 agricultxiral income payments in the United States, and (3) volume of asparagus 
 canned outside of California. 
 
 Figure 1 shows graphically the average relations between the F.O.B, price 
 and each of the independent variables, as determined by equation 5 in table 2. 
 Expressed in numerical term.s, these average relations are as follows for the 
 period of years under consideration: 
 
 (a) VJith both the nonagri cultural income payments and the volme of 
 asparagus canned outside of California held constant, a change 
 
; ft;? ' 
 
 ,'5 «jflE* ifsnV 
 
 
 ■ > 
 
of 100,000 cases in domestic shipments of California canned 
 asparagus was on the average accompanied by a change in the 
 opposite direction of 13 cents a case in the F.O.B, price of 
 California canned asparagus. This relation is shown graphically 
 in panel A of figure 1, 
 
 (b) With both domestic shipments of California canned asparagus and 
 the volume of outside pack held constant, a change of 10 per cent 
 in the index of nonagricultural income payments was on the average 
 accompanied by a change in the same direction of 40 cents a case 
 in the F.O.B, price of California canned asparagus. This re- 
 lation is shown graphically in panel B of figiure 1. 
 
 (c) With both domestic shipments of California canned asparagus and 
 nonagricultural income payments held constant, a change of 100,000 
 cases in the volume of asparagus canned outside of California was 
 on the average accompanied by a change in the opposite direction 
 
 of 10 cents a case in the F.O.B, price of California canned asparagus. 
 This relation is shown graphically in panel C of figvire 1. 
 Differences between the actual prices and those estimated by equation 5 are 
 given in table 3, column 3. The differences are plotted as deviations from the 
 respective net regression lines in figure 1. 
 
f. 
 
 I 
 
Figure 1: Net Regression of F»O.B. Prices of California Canned Asparagus, 
 1925-26 to 1948-49, on: A, Domestic Shipments of California 
 Canned Asparagus; B, Index of Nonagri cultural Income Payments; 
 and C, Pack of Asparagus Canned Outside of California 
 
 8,00 
 
 7.00 
 
 6.00 
 
 5.00 - 
 
 4.00 
 
 ICQ 
 
 10.00 
 
 8.00 
 
 6.00 
 
 4.00 
 
 2.00 
 
 50 
 
 150 200 
 Xg : California Domestic Shipments (10,000 oases) 
 
 46-470 
 
 ^1.3 
 
 14,680068 + 9,672110 log 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 Xg: Index of Konagricultural Income (1935-1939 = 100) 
 
7. 
 
8. 
 
 TA.BLE 1 
 
 Annual Average. .F«0»B. Prices of California Canned Asparagus 
 and Important Factors Affecting Them, 1925-26 to 1948-49 
 
 lear 
 
 
 Domestic ship- 
 
 Index of non- 
 
 Canned asparagus 
 
 March 
 
 r •u.Da price 
 
 ments of Cali- 
 
 agricultural 
 
 pack of s 
 
 :ates 
 
 through 
 
 of California 
 
 fornia canned 
 
 income 
 
 other than 
 
 February 
 
 canned asparagus 
 
 asparagus 
 
 (1935-39=100) 
 
 California 
 
 
 J. 
 
 ► ■ - <> - ■ - 
 
 c 
 
 O 
 
 4 
 
 
 
 dollars per case 
 
 iu,uuu cases 
 
 ver cent 
 
 1,000 cases 
 
 1 no c oe 
 
 p. AT 
 D • Ui 
 
 io4 
 
 iXU 
 
 4{ 
 
 } , 
 
 1926-27 
 
 5.69 
 
 171 
 
 114 
 
 37i/ 
 
 1927-28 
 
 5.44 
 
 172 
 
 115 
 
 26 . 
 
 L jC O — w y 
 
 O • DO 
 
 lyo 
 
 1 1 Q 
 
 402/ 
 
 lycy— Ow 
 
 
 j.yo 
 
 1 ox 
 
 51 
 
 t 
 
 1 y ou— 0 i 
 
 
 ioy 
 
 110 
 
 lOOa/ 
 
 1931-32 
 
 5.54 
 
 130 
 
 94 
 
 14S 
 
 
 1932-33 
 
 4.10 
 
 159 
 
 72 
 
 2( 
 
 
 J. yoo — o*± 
 
 AO 
 
 JLoO 
 
 I 1 
 
 184 
 
 
 X jO*± — OU 
 
 t .ou 
 
 1 A t; 
 
 X4-0 
 
 OA 
 
 23e 
 
 
 iyoo— oo 
 
 4 .00 
 
 100 
 
 Q7 
 
 O 1 
 
 281 
 
 
 1936-37 
 
 4.75 
 
 160 
 
 103 
 
 436 
 
 
 1937-38 
 
 5.22 
 
 159 
 
 106 
 
 631 
 
 
 X i/OO — 
 
 A AR 
 
 loo 
 
 
 eo-i 
 
 
 X yo y— f V 
 
 A AA 
 
 
 1 AO 
 
 671 
 
 
 1940-41 
 
 4.68 
 
 184 
 
 117 
 
 921 
 
 
 X C7*±X— ft) 
 
 p . 0 c 
 
 lOD 
 
 
 1,44£ 
 
 
 1942-43 
 
 (n.a . ) 
 
 229 
 
 183 
 
 1,651 
 
 f 
 
 1943-44 
 
 (n.a. ) 
 
 209 
 
 221 
 
 1,482 
 
 
 1944-45 
 
 (n.a . ) 
 
 244 
 
 242 
 
 1,396 
 
 
 1945-46 
 
 6.38 
 
 246 
 
 247 
 
 1,44C 
 
 ) 
 
 1946-47 
 
 6.86 
 
 238 
 
 258 
 
 1,65£ 
 
 ) 
 
 1947-48 
 
 7.21 
 
 192 
 
 285 
 
 1,65£ 
 
 
 1948-49±/ 
 
 8.32 
 
 187 
 
 307 
 
 1,71E 
 
 
 a/ Preliminary, subject to 
 
 revision; (n.a,). 
 
 not available. 
 
 
 
 Sources of data: 
 
 Col. 1: Years 1925-26 to 1935-36 compiled from records of canners. Years 
 1936-37 to 1948-49 from reports of Asparagus Advisory Board and 
 records of canners. , 
 
 Col. 2: From table 4, col. 6. I 
 
 Col. 3: All figures obtained from the following sources-, converted to 1935-1939 
 base by dividing by 62.22. 1925-26 to 1928-29; TJ.S.3.A.E. mimeo. dated 
 2/2/42. 1929-30 and all subsequent years; National Supplement to Surv^ 
 of Current Business, July 1947, table 48; Survey of Current Business, 
 Jan. 1949 and weekly supplements — Feb. 11 and March 11, 1949. 
 
 Col. 4: Years 1925-26 to 1932-33 from U.S. Dept. of Commerce, Biennial Census of 
 Manufactures, v/ith 1926-27, 1928-29, and 1930-31 estimated; years 1933- 
 34 to 1941^42 compiled from Canned Food Pack Statistics, National 
 Canners Association; years 1942-43 to 1948-49 derived from data in 
 Canners League of California, Special Bulletin, December 28, 1948, 
 San Francisco. 
 

 
 
 
 
 
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TABLE 2 
 
 California Canned Asparagus 
 Regression Coefficients and Auxiliary Constants for Multiple Regression Analyses 
 Covering 1925-26 through 1948-49 (excluding 1941-42 through 1945-46) 
 
 Equation 
 
 Dependent 
 variable 
 
 Constant 
 term 
 
 Net regression coef f icients 
 (figures in parentheses are t-ratios) 
 
 Adjusted co- 
 efficient of 
 multiple cor- 
 relation: R 
 
 Xl 
 
 X2 
 
 X3 
 
 log 10 (X3) 
 
 X4 
 
 t 
 
 t2 
 
 1 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 1 
 
 Xl 
 
 S. 558 254 
 
 
 -0.011268 
 (5.395960) 
 
 0.031402 
 (6. -411849) 
 
 
 
 -0.1184 20 
 (5.103034) 
 
 -0,008271 
 (1.765824) 
 
 0.9728 
 
 1 
 
 
 208.808293 
 
 -40.084387 
 (3.395960) 
 
 
 1.533069 
 (3.740093) 
 
 
 
 -5.259179 
 
 (2.809868) 
 
 -0,508232 
 (1.831976) 
 
 0,7628 
 
 3 
 
 Xl 
 
 -10.023225 
 
 
 -0.012622 
 (4.187852) 
 
 
 8.463105 
 (17 1430529) 
 
 
 -0.059260 
 (5.187517) 
 
 
 0.9773 
 
 4 
 
 ^2 
 
 -418.909099 
 
 -42.704453 
 (4.187852) 
 
 
 
 395.139516 
 (4.884515) 
 
 
 -2.308664 
 (2.463400) 
 
 
 0.8173 
 
 5 
 
 Xl 
 
 -11.999990 
 
 
 -0 .-012736 
 (4.377667) 
 
 
 9.672110 
 (15.763148) 
 
 -0 .-000998 
 (5.464351) 
 
 
 
 0.9788 
 
 6 
 
 X2 
 
 -514.393086 
 
 -44.043169 
 (4.377667) 
 
 
 
 454 ."^69413 2 
 (4.770193) 
 
 -0.040718 
 (2.658475) 
 
 
 ,, ,. 
 
 0.8265 
 
 a/ = Annual average f,o.b, price of California canned asparagus; in dollars per case (see table l».col, 1). 
 X2 = Domefatic shipments ef California canned asparagus; in units of 10,000 cases (see table 1, col, 2). 
 X3 = Index of nonagricultural income payments in the United States, 1935-39=100 (see table 1, coi. 3). 
 X4 «= Canned asparagus pack of states other than California; in units of 1,000 cases (see table 1, col. 4), 
 t >»= Time in years; origin at 1935-36. 
 
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10. 
 
 TABLE 3 
 
 Actual and Estimated F.O.B. Prices of 
 California Canned Asparagus, 1925-26 through 1948-49 
 (excluding 1941-42 through 1946-46) 
 
 Year 
 
 
 
 
 
 
 March 
 
 
 
 Difference: 
 
 Percentage differ- 
 
 through 
 
 Actual 
 
 Estimated 
 
 col. 1 minus 
 
 ence; col. 3 
 
 as 
 
 February 
 
 price 
 
 price 
 
 col. 2 
 
 per cent of col. 1 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 
 
 dollars per 
 
 case 
 
 per cent 
 
 1925-26 
 
 6.01 
 
 5.99 
 
 0.02 
 
 0.33 
 
 
 1926-27 
 
 5.69 
 
 5.68 
 
 0.01 
 
 
 
 1927-28 
 
 5.44 
 
 5.71 
 
 -0,27 
 
 -4.96 
 
 
 1928-29 
 
 5.63 
 
 5,58 
 
 0,05 
 
 0.89 
 
 
 1929-30 
 
 5.69 
 
 5.68 
 
 0.01 
 
 0.18 
 
 
 1930-31 
 
 5.64 
 
 5.62 
 
 0,02 
 
 0,35 
 
 
 1931-32 
 
 5.54 
 
 5.29 
 
 0,25 
 
 4.51 
 
 
 1932-33 
 
 4.10 
 
 3.92 
 
 0.18 
 
 4.39 
 
 
 1933-34 
 
 3.49 
 
 3.39 
 
 0.10 
 
 2.87 
 
 
 1934-35 
 
 4.30 
 
 4.33 
 
 -0.03 
 
 '•U« f U 
 
 
 1935-36 
 
 4.55 
 
 4.47 
 
 0.08 
 
 1.76 
 
 
 1936-37 
 
 4.75 
 
 4.99 
 
 -0.24 
 
 -5.05 
 
 
 1937-38 
 
 5.22 
 
 4.93 
 
 0.29 
 
 5,56 
 
 
 1938-39 
 
 4.48 
 
 4.77 
 
 -0.29 
 
 -6.47 
 
 
 1939-40 
 
 4.44 
 
 4.72 
 
 -0,28 
 
 -6.31 
 
 
 1940-41 
 
 4,68 
 
 4.74 
 
 -0,06 
 
 -1.28 
 
 
 • 
 
 (war years) 
 
 
 
 
 
 
 « 
 
 1946-47 
 
 6.86 
 
 6.64 
 
 0.22 
 
 3,21 
 
 
 1947-48 
 
 7.21 
 
 7.64 
 
 -0.43 
 
 -5.96 
 
 
 1948-49 
 
 8.32 
 
 7.96 
 
 0.36 
 
 4.33 
 
 
 Sources of data: 
 
 Col. 1: From table 1, col. 1. 
 
 Col. 2: Based on equation 5, table 2, 
 
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u. 
 
 TABLE 4 
 
 Pack, Carry-over, Shipments and Domestic Movement 
 of California Canned Asparagus, 
 1925-26 to 1948-49 
 
 j Year 
 
 California 
 
 
 
 
 Ma T*oVi 
 
 
 Carry-over 
 
 Available 
 
 Total 
 
 United 
 
 California 
 
 through 
 
 Pack 
 
 from 
 
 for 
 
 shipments 
 
 States 
 
 domes'' 
 
 ;ic 
 
 February 
 
 
 preceding 
 
 shipment 
 
 
 exports 
 
 shipments 
 
 
 
 year 
 
 
 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 in ] 
 
 L.OOO cases. 
 
 1925-26 
 
 1,745 
 
 170 
 
 1,915 
 
 1,664 
 
 325 
 
 1,33c 
 
 ) 
 
 1926-27 
 
 2,236 
 
 251 
 
 2,487 
 
 2,080 
 
 367 
 
 \,1U 
 
 
 1927-28 
 
 2,190 
 
 407 
 
 2,597 
 
 2,195 
 
 474 
 
 1,72] 
 
 
 1928-29 
 
 2,338 
 
 402 
 
 2,740 
 
 2,471 
 
 540 
 
 1,931 
 
 
 1929-30 
 
 2,673 
 
 269 
 
 2,942 
 
 2,619 
 
 671 
 
 1,94? 
 
 ! 
 
 1930-31 
 
 2,663 
 
 323 
 
 2,986 
 
 2,028 
 
 435 
 
 1,592 
 
 5 
 
 1931-32 
 
 1,747 
 
 958 
 
 2,705 
 
 1,646 
 
 350 
 
 1,296 
 
 1 
 
 1932-33 
 
 1,313 
 
 1,059 
 
 2,372 
 
 1,918 
 
 32 G 
 
 1,592 
 
 
 1933-34 
 
 2,135 
 
 454 
 
 2,589 
 
 2,313 
 
 485 
 
 1,82£ 
 
 ! 
 
 1934-35 
 
 1,914 
 
 276 
 
 2,190 
 
 1,980 
 
 633 
 
 1,447 
 
 f 
 
 
 2,238 
 
 210 
 
 2,448 
 
 2,143 
 
 568 
 
 1,57J 
 
 
 1936-37 
 
 2,350 
 
 305 
 
 2,655 
 
 2,133 
 
 530 
 
 1,60: 
 
 5 
 
 1937-38 
 
 2,072 
 
 522 
 
 2,594 
 
 2,018 
 
 431 
 
 1,58"; 
 
 r 
 
 1938-39 
 
 1,796 
 
 576 
 
 2,372 
 
 1,922 
 
 340 
 
 1,582 
 
 
 1939-40 
 
 1,849 
 
 450 
 
 2,299 
 
 2,126 
 
 338 
 
 1,786 
 
 ) 
 
 1940-41 
 
 2,182 
 
 173 
 
 2,355 
 
 1,956 
 
 116 
 
 1,84C 
 
 ) 
 
 
 1,578 
 
 399 
 
 1,977 
 
 1,670 
 
 115 
 
 1,55J 
 
 
 1942-43 
 
 2.258 
 
 307 
 
 2,565 
 
 2,345 
 
 51 
 
 2,294 
 
 \ 
 
 1943-44 
 
 2,071 
 
 220 
 
 2,291 
 
 2,114 
 
 20 
 
 2,094 
 
 [ 
 
 1944-45 
 
 2,436 
 
 177 
 
 2,614 
 
 2,462 
 
 20 
 
 2,442 
 
 
 1945-46 
 
 2,480 
 
 152 
 
 2,632 
 
 2,506 
 
 47 
 
 2,45£ 
 
 
 1946-47 
 
 2,783 
 
 126 
 
 2,909 
 
 2,720 
 
 344 
 
 2,37{ 
 
 
 1947-48 
 
 2,259 
 
 189 
 
 2,448 
 
 2,274 
 
 352 
 
 1,922 
 
 
 1948-49a/ 
 
 1,983 
 
 174 
 
 2,157 
 
 2,027 
 
 156b/ 
 
 1,87] 
 
 
 1949-50a/ 
 
 
 130 
 
 
 
 
 
 a/ Preliminary, subject to revision. 
 
 b/ March through December 1948. 
 Sources of data: 
 
 Cols. 1-4; Canners League of California and Asparagus Advisory Boards. Carry- 
 over figures are total stocks on hand, sold and unsold. 
 
 Col. 5; Compiled from reports of United States Bur'oau of Foreign and 
 
 Commerce. Pounds converted to cases on the basis of 34 pounds 
 per case. 
 
 Col. 6; Col. 4 minus col. 5. 
 
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