Wv \%\ ^11 University of California College of Agriculture Agricultural Experiment Station Berkeley, California STATISTICAL ANALYSIS OF THE Sa'.SOMAL AVER'.GE F. 0. B. PRICES OF CALIFORNIA WINTER .'KD SUl'i.ER ORj'j^GES, 1922-23 to 1939-40 \^ H. R« Wellman and G. M. Kuznets March, 1942 UNIVERSITV OF CALIFORNIA LIBRARY COLLEGE OF AGRICULTURE DAVIS Contribution from the Giannini Foundation of Agricultural Economics Mimeographed Report No. 77 STATISTICAL AIIALY3IS OF THE SEASONAL AVERAGE F. 0. B. PRICES OF CALIFORNIA WHITER AITO SUIER ORANGES, 1922-25 to 1939-40 by 1/ 2/ H. R. Wellman — ' and G. ?I. Kuznets — The purpose of this report is to present the res^ults of an analysis of the major factors which have influenced the seasonal average f.o.b. prices of Cali- fornia winter and suniner oranges from 1922-23 through 1939-40. Winter oranges are ^ those shipped during the six months November through April, which for California consist mainly of VJashington navels. Summer oranges are those shipped during the six months ilay through October. For California, summer oranges consist mainly of Valencias. During the six months, May through October, California normally con- tributes 80 to 90 per cent of the Ihited States shipments of oranges; during the six months November through April shipments from California constitute only 45 to 55 per cent of United States shipments of oranges. For each of the two classifications — winter oranges and summer oranges — the average relationships which prevailed from 1922 to 23 through 1939-40 between the seasonal average f.o.b. prices of California oranges and three factors were measured. These factors are: (1) Lhited States supply of oranges, (2) non- agricultural income payments, and (3) trend of demand for oranges. For the eighteen-year period covered by the analysis these three factors account for about 92 per cent of the variation in the f.o.b. prices of California winter oranges and for about 93 per; cent of the variation in the f.o.b. prices of California summer oranges. £./ While the use of these variables results in a large reduction of the variance of the dependent variable, it is not to be supposed that they are the only ones that have affected the f.o.b. prices from 19*22-23 through 1939-40, or that they are the only factors which will affect f.o.b. prices during the coming years. Neither is it certain that the relationships between the seasonal average f.o.b. prices of California oranges and the factors considered will be the same in the future as they were, on the average, during the period covered by the analysis. i The characteristics of deinand functions under two different h37potheses are sumr^iariaed in table 2 for winter oranges and in table 6 for summer oranges. From an a priori standpoint both formulations are legitimate hj'potheses concerning the relation between price and the associated variables. The essential feature of the first hypothesis (arithmetic form; is that the net regressions retain their slope irrespective of their positions. Equations 1 and 2 of table 2 and equations — ' Professor of Agricultural Economics, Agricultural Economist in the Experi- ment Station and Agricultural Economist on the Giannini Foundation. 2/ — Instructor in Agricultural Economics, Junior Agricultural Economist in the Experiment Station and Junior Agricultural Economist on the Giannini Foundation. 3/ — See tables 2 and 6 for values of the adjusted coefficients of multiple correlation. The values given above are the averages of their squares. 2. 1 and 2 of table S give the results of applying this hypothesis to winter and summer oranges respectively. The basic characteristic of the second hypothesis (logarithmic form) is that the absolute amount of shift of a given net regression, with a specified change in the other independent variables, is influenced by the point on the net regression from which the change is measured. Equations 3 and 4 in table 2 and equations 3 and 4 in table 6 embody this hypothesis for winter and summer oranges respectively. In each formulation both price and quantity were used as dependent variables. Shifts in the demand for oranges during the period \inder review have been reflected both in changes in prices paid and in quantities taken. In general those changes in demand from year to year that were occasioned by changes in the incomes of consumers have appeared mainly in the form of price movements; whereas the gradual change in the demand over the years that was caused by factors sub- sumed under time has appeared mainly in the form of quantity movements. By presenting statistical measurements of shifts in the demand for oranges in terms of quantities taken as well as in terms of price, a more comprehensive picture of the actual situation is obtained than by using either alone. The results secured with these different treatments were found to be in substantial agreement. All of the equations employed show the demand for winter and summer oranges to be inelastic. The net relation of price and quantity to i/^' come was foiind to be well approximated by a straight line for both winter and summer oranges under both hypotheses. In all of the formulations considered in connection with winter and summer oranges, introduction of curvilinearity into the regression on time improved total fit. The results secured suggest that dur- ing a large part of the period 1922-25 to 1939-40 the demand for winter and summer oranges in this country relative to the buying power of consumers shifted upward but at a diminishing rate. The peak in this upward shift of demand for winter oranges was apparently reached between 1935 and 1938. Whether the demand for winter and especially summer oranges relative to incomes of consumers during the last part of the period rera:iined stationary or turned downward is not cleai'ly revealed by the analysis. The average relations between f.o.b. prices of v/inter oranges and each of the three independent variables imder the first hypothesis are shown graphically in figure 1. Expressed in numerical terms the relations indicated in panels A and B of figure 1 are as follows: (a) With both the nonagricultural income payments and the trend of demand held constant a change of one million boxes in the United States supply of winter oranges was, on the average, accompanied by a change in the opposite direction of 16 cents a box in the f.o.b. price of California winter oranges; and (b) with both the IMited States supply of winter oranges and the trend of demand held constant, a change of 10 points in the index of nonagricul- tural income was, on the average, accompanied by a change in the same direction of 48 cents a box in the f.o.b. price of California winter oranges. Figure 2 presents similar information for summer oranges. Expressed in numerical terms the relations portrayed in panels A and B are as follows : (a) With both the nonagricultural income payments and the trend of demand held constant, a cliange of one million boxes in the LMted States supply of summer oranges was, on the average, accompanied by a change in the opposite direction of 33 cents a box in the f.o.b. price of California summer oranges; and (b) with both the liiited States supply of summer oranges and the trend of demand held con- stant, a change of 10 points in the index of nonagricultural income was, on the average accompanied by a change in the same direction of 49 cents a box in the f.o.b. price of California summer oranges. 3 TABLE 1 Seasonal Average F.O.B. Prices of California w'inter Oranges and iTiportant Factors .'effecting Them, 1922-23 to 1939-40 Year Index of non- November F.o»b. United States agricultural through y.pril pri ce ;;upply inc ome 1 2 3 vi U X J. ax £3 100 000 per box boxes 100 1922-23 2 . 71 189 83 \JxJ 1923-24 Q? 1924-25 3.60 198 *? o 1925-26 3.50 206 100 192o-27 1927-28 4.39 1928-29 290 V/ W 1929-30 4 .45 1930-31 2.17 296 91 1931-32 1.80 274 75 1932-33 1.43 255 61 1933-34 l.o5 271 69 1934-35 1.80 314 74 1935-36 1.95 272 32 1936-37 2.53 2bl 93 1937-38 1.46 313 88 1938-39 1.38 360 90 1939-40 1.60 344 97 Sources of data: Col.l: From the California Fruit Growers Exchang,e, Prices are the weighted average prices per packed box received for oranges shipped during the six months Noveraber through x^pril. Since November 1, 1929 Arizona oranges are included. Since May 1, 1930 prices include loose fruit on a packed-box basis. Government purchases for relief distribut- ion are not included. Col. 2: From table 4, col. 7. Col. 3: Simple average of the monthly indices of national income, excluding, agricultural income, average 1924-1929 equals 100, compiled from the United States Department of Agriculture, Bureau of Agricultural Economics, The Agricultural Situation, current issues. TABLE 2 Winter Oranges: Regression Coefficients and Auxiliary Constants, Arithmetic and Logarithmic Forms, 1922-23 to 1939-40 (Figures in parentheses are standard errors) Equation Dependent variable Constant term Net regression coefficients* Adjusted coefficient of multiple correlation R Flexibility of price 63 r Elasticity of demand 'I «1 ^2 t; .1 2 T 4- 5 6. 7 8 9 10 11 1 2 ^1 ^2 2.6660 189.3100 -45.4719 (7.6434) -0.0161 (0.0027) 0.0480 (0.0059) 2.1941 (0.4781) 0.0243 (0.0134) 2.2406 (0.4993) -0.0022 (0.0007) -0.0862 (0.0450) 0.95ol 0.9543 -1.6953 (0.2827) -0.4314 (0,0728) Equation Dependent variable Constant term Log Xj^ Log Xg Log X3 t t2 R 3 4 Log Log Xg 0 .9644 1.1209 -0.5208 (0.0847) -1.4288 (0.2323) 1 1 1.4875 (0.1665) 0.7734 (0.1617) 0.0017 (0.0019) 0.0027 (0.0009) -0.0005 (0.0001) -0.00023 (0.00008) 0.9668 0.9550 -1.4288 (0.2323) -0.5208 (0.0847) X3_ Seasonal average f.o.b. price of California winter oranges (in dollars per box). Xg United States supply of winter oranges (in units of 100,000 boxes), X3 Index of nonagricultural income payments in the United States, November-April (1924-1929 = 100). t Time in units of half-years (origin between 1930-31 and 1931-32)^ i ; ; 1 , i i set''' Fig. 1. — Net Regression of F«O.B. Prices of California Vifinter oranges. Arithmetic Form, 1922-23 to 1939-40 on: A, United States Supply of Winter Oranges; B, Index of fiKonagri cultural Income Payments; C, Time Index of nonacrl cultural Incoiiie ! ■, ' ■ i I ] I 6. TABLE 3 Actual and Estimated F.O.B. Prices of Cpliforria Winter Oran-i Arithmetic Forn, 1922-23 to 1839-40 Year, Fovei^her Actual Estimated Re t^i dnfl 1 throui^h April price price col. 1 r.inv.s col. 2 1 2 ~^ 3 1922-23 2, 71 2,57 0.14 1923-24 2.12 2.56 -0, 44 1924-25 5.60 3.26 0.34 1925-26 3. 50 3.62 -0.12 1926-27 3.4-5 3.49 -0.04 1927-28 4.59 4.10 0.29 1928-29 2.80 2.91 -0.11 1929-30 4.45 4.35 0.10 1930-31 2.17 2.25 -o.oe 1951-32 l.SO 1.88 -0.08 1932-33 1.4-3 1.55 -0.12 1933-34 1.65 1.69 -0.04 1934-55 i.no 1.23 0.57 1935-36 1.95 2.27 -0.32 1936-57 2.53 2.61 -0.08 1937-38 1.46 1.' J. -0.35 1958-39 1.38 1.07 0.31 1939-40 1.60 1 !:;o •!-.>- 0.02 Sources of data: I Col. 1: From tahle 1, col. 1. Ccl, 2: Based on equation 1, table 2, j 7. TABLE 4 United States Supply of V/inter Oranges, 1922-23 to 1939-40 Year United States Shi pments Receipts Total : United United States November Calif- Other Total : from Rierto col. 3 States supply: col. 5 thr ough ornia- states ool . 1 Rico and plus cJol.4 exports minus col. 6 April Arizona [jIus ool . 2 imports 1 2 3 4 5 6 7 Thousand boxes 1922-23 10,353 8,712 19,365 557 19,922 1,070 18,852 1923-24 12,546 11,452 23,998 171 24,169 1,402 22,767 1924-25 11,135 9,603 20,76& 2 65 21,033 1,194 19,839 1925-23 12,838 8,679 21,517 360 21,877 1,308 20,569 1926-27 15,107 9 ,215 24,322 252 24,574 1,656 22,918 1927-28 13,119 7,670 20,789 431 21,220 1,418 19,802 1928-29 L f fO OO XO , DC 1 O i. f cc*± ^ 1 Q7 c a g \jc f 1 929-30 12,542 8,861 21,403 219 21,622 1,306 20,316 1930-31 15,982 15,706 31,688 68 31,756 2,217 29,539 1931-32 16,216 12,522 28,738 29 28,767 1,376 27,391 1932-33 13,816 12,916 2^,732 31 26,763 1,223 25,540 1933-34 13,001 15,498 28,499 34 28,533 1,406 27,127 1934-35 18,713 14,177 32,890 36 32,926 1,588 31,338 1935-36 14,338 14,886 29,224 44 29,238 2,043 27,225 1936-37 11,740 17,809 29,549 24 29,573 1,494 28,079 1937-38 15,551 18,724 34,275 27 34,302 3,037 31,265 1936-39 15,035 25,243 40,278 30 40,308 4,321 35,987 1939-40 16,844 19 ,ood 36,710 24 3b, 734 2 ,363 34,371 Sources of data; Col. 1: The figures pertain to both packed and loose fruit. For the years 1922-23 throuj^h 1933-34 estimates of the industry packed fruit shipments were based upon the ratio of the California Fruit Growers Exchange rail shipments to total industry rail shipmer-ts applier to the California Fruit Grov/ers Exchange packed orange shipments. Estimates of the industry loose orant.e shipments were based upon the ratio of the loose fruit sales by local associations affiliated v/ith the California Fruit Grov/ers 'exchange to theit* packed fruit sales applied to the industry pa 'ked fruit shipments. Years 1934-35 through 1939-40: From sumiT:aries of xveekly shipments of oranges reported by the Cal if orn ia-i.riz; na Orai^ge and Grapefruit ;.gency. Shipments for weeks which fell in two months were prorated between the months on the basis of daily shipments of California oranges by rail and boat as reported h\' the United States Department of Agriculture, Market Nexvs Service. Government purcnases for relief distribution are net included. Col. 2: From Division of fruits and Ve5etables, Surplus i^arKetinj^ Admin- istration, United States Department of Agriculture. j Cols. 4 and 6; United States DepartnB.it of Commerce, Bureau of Foreign and Domestic Commerce, Division of foreign Trade Statistics. TABLE 5 Seasonal Average F.O.B. Prices of California Summer Oranges and Important Factors Affecting tnem, 1923 to 1940. Index of non— r #0 •b • uniuQu o osoes a j/^r i c ult ur a 1 "t" r\ n ft pr ice supply 1 nc o:ne X o c 3 dollars 100,000 1924-1929 = per box boxes 100 1923 2 .73 105 88 1924 3.12 lo2 69 1925 5.26 69 97 1926 3.59 105 100 1927 4.11 119 102 1928 5 .74 93 105 1929 2.69 181 108 1930 5.87 96 98 1931 2.27 160 84 1932 1.82 156 65 1933 1.78 170 53 1934 2 .73 155 71 1935 2.01 176 77 1936 2.61 178 88 1937 3.64 138 96 1938 1.57 218 87 1939 1.78 220 94 1940 1.89 228 100 Sources of data: Col. 1: From the California Fruit Growers Exchan^,©. Prices are the v/eighted aTeraj.-,e prices per packed box received for oranges shipped durin; the six months kay through October. Since ITay 1, 1930, i.rizona oranges are included and prices include loose fruit on a packed-box basis. Government purchases for relief distribution are not included. Col. 2: From table 8, col. 7. Col. 3: Si:Tiple average of the m^onthly indices of national income, excluding agricultural income, average 1924-1929 equals 100, ccmpiled from the United States Department of Agriculture, Bureau of jigricultural Economics, T;he xigricultural Situation, current issues. S' " TABLE 6 Summer Oranges: Regression Coefficients and Auxiliary Constants, Arithmetic and Logarithmic Forms, 1923 to 1940 (Figures in parentheses are standard errors) Equation Dependent Constant Net regression coefficients* Adjusted Flexibility of Elasticity variable term X2 X3 t t2 coef f 3 cient of multiple correlation R price of demand 1 2 3 4 5 6 7 8 9 10 11 1 ^1 3,9006 -0.0333 (0.0040) 0.0491 (0.0081) 0.0709 (0.0175) -0.0027 (O.OOll) 0.9567 -1.6118 (0.1996) 2 Xp .25.1630 -25.3088 (3.0195) 1.1954 (0.2832) 2.3737 (0.3037) -0.0586 (0.0320) 0.9728 -0.5235 \ U •UdoI ) Equation Dependent variable Constant term Log Xl Log Xg Log Xj t t2 R If 3 Log Xi .9017 -1.2488 (0.1265) 1 .1742 (0.1662) 0.0059 (0.0017) -0.0005 (0.0001 ) 0.9731 -1.2488 (0.1265) 4 Log Xg .9563 -0.7065 (0.0716) 0.7949 (0.1644) 0.0055 (0.0009) -0.0004 (O.OOOl) 0.9771 -0.7065 (0.0716) X-|_ Seasonal average f.o.b. price of California Summer Oranges (in dollars per box). Xg United States supply of summer oranges (in units of 100,000 boxes). Xj Index of nonagriculturai income payments in the United States, May-October (1924-1929 = lOO). t Time in units of half-years (origin between 1931 and 1932). t 1 i 1 i 1 i j 1 ! 1 ■ * . ■ ■ ■ r - - ■ ■ • . . :; M ;;.'0'-:.: - ; -. . . ; . ■.. ■: ; i • > ■ - . ■ ■ ; -.--.-i L. . -.--1 i 4 10. Fig. 2,— Net Regression of F.C.B. Prices of California Summer Oranges, Arithmetic Form, 1923 to 1940 on: A, United States Supply of Summer Oranges; B, Index of Hoiiiagricultural Income Payments; C, Time. o CD cti O 04 O 6.40 r 5.60 ^ 4.80 4.00 - 3.20 - " 2,40 a. 1.60 .80 .00 10 15 20 U.S. Supply - Millions of Boxes 25 4.20 X o £> O) n. m nJ o ■a O •H u a, o g 3.80 - ^ 3,40 60 70 90 100 110 1,00 _l 1 I i , I I I I L. ' I I I L. Index of Nonagri cultural Income 23 25 27 29 31 33 35 37 39 Year TABLE 7 Actual and Estimated F.C.B. Prices of California Svtmmer Oran--es, Arithmetic Form, 1925 to 1940 Year, May i Actual ! Estimated He si duals throuf;;h October price price col. 1 minus col. 2 1 2 3 1923 2.73 2.74 -O.OJ 1924- 3.12 3.21 -0.09 1925 5.26 4.99 0.27 1926 4.21 -0.62 1927 4. 11 4.09 0.02 1928 5.74 5.33 0.41 1929 2.75 -0.06 1930 5.87 5.28 0, 59 1931 2.27 2.62 -0.35 1932 1.82 1.96 -0.14 1933 1.73 1.52 0.26 1934 2.73 2.-1 0.22 1935 2.01 2.18 -0.17 1936 2.61 2.71 -0 10 1937 3.64 4.47 -0.83 1938 1.57 1.37 0.20 1939 1.78 1.64 0.14 1940 1.89 1.64 0.25 Sources of data: Cel. 1: From table 5, col. 1. Col. 2: Based on equation 1, table 6. 12. TABLE 8 United States Supply of Summer Oranges, 1923 to 1940 Year Unite c States shipments Receipts Total: United United . ay throu^ C a li f- Other Total: from Puerto col . 3 States states October ornia- states doi. 1 Rico and plus col . 4 exports supply: Arizona plus ^ imports col. 5 minus 00 1. 2 col. 6 1 2 3 4 5 6 7 Thousand boxes 10,376 1,143 11,519 89 11, 608 1,057 1924 10,316 1,018 11,334 91 11,425 1, 218 10,207 1925 6,969 572 7,541 117 7, 658 784 6,874 1923 11,272 494 11,766 69 11,835 1,335 10,500 1927 12,815 863 13,678 124 13,802 1,956 11,346 9,729 644 10,373 28 lu,401 1,124 1929 19,681 1,762 21,443 16 21,459 3,385 16,074 1930 9,455 938 10,393 61 10,454 883 9,571 1931 16,646 2,083 18,729 14 18,743 2,719 16,024 1932 16,435 1,046 17,481 3 17,484 1,826 15,658 1933 16,245 2,877 19,122 2 19,124 2,171 16,953 15,426 1,922 17,348 6 17,354 1,890 ±U 1935 19,661 1,776 21,457 2 21,459 3,338 17,621 193o 17,523 2,413 19,936 19 19,955 2,167 17,788 1937 11,063 3,778 14,841 2 14,843 994 13,849 1928 21,765 4,620 26,335 1 26,386 4,561 21,825 1939 17,133 7,025 24,158 24,158 2,150 22,008 1940 22,392 1,880 24,272 24,272 1,465 22,807 Sources of data: Col. 1: The figures pertain to both packed and loose fruit. For the years 1923 throu^^h 1933 estimates of the industry packed fruit shipments were based upon the ratio of the California Fruit Growers Exchange rail shipments to total industry rail shipments applied to the California Fruit Growers Exchange packed orange shipments. Estimates of the industry loose orange shipments were based upon the ratio of the loose fruit sales by local associations affiliated mth the California Fruit Growers Exchange to their packed fruit sales applied to the industry packed fruit shipments. Years 1934 through 1940: r'rom summaries of v/eekly shipments of oranges reported by the Calif ornia-.-.riaona Orange and Grapefruit Agency. Shipments for weeks which fell in tavo months were prorated between the months on the basis of daily shipments of California oranges by rail and boat as reported by the United States Department of Agriculture, Market F.ews Service. Government purchases for relief distribution are not included. Col. 2: From Division of Fruits and Vegetables, Surplus Marketing Administration, United States Department of Agriculture . Cols. 4 and 6: United States Department of Commerce, Bureau of Foreign and Domestic Commerce, Division of Foreign Trade Statistics. t rt V \ ■ ... • ■ • - i f ^ . i 1 t j • i :