University of California College of Agriculture Agricultural Experiment Station Berlreley, California STATISTICAL ANALYSIS OF TIE ANNUAL AVERAGE F.O.B. PRICES OF CANNED ASPARaGUS, 1925-26 TO 1940-41 by G. M. Kuznets and 11, R* Wellnan April, 1942 Contribution frori the annini Foundation of agricultural Economics Llimoographed Report No. 80 UN|VBf»»tTY OF CALIFORNIA J.IBRARY OOL.LF.GS OF <S ■ ' 'CULTURE STATISTICAL ANALYSIS OF THE ANNUAL AVERAGE F.O.B. PRICES OF CANNED ASPARAGUS, 1925-26 TO 1940-41 by G. M. Kuznets Vand H. R. Vlellman The purpose of this report is to 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 1940-41. Two formulations of characteristics of demand for canned asparagus are presented in this report. For the period 1925-26 through 1939-40 the average relationships between f.o.b. prices of California canned asparagus and (1) domestic shipments of California canned asparagus* (2) nonagricultural income payments in the United States, and (3) factors included under "time" were measured. Equation 1 of table 2 gives the results obtained when the f.o.b. price of California canned asparagus is taken as the dependent variable and the three factors mentioned above are employed as independent variables. In equation 2 of table 2 the volume of domestic shipments of California canned asparagus is taken as the dependent variable and is related to the f.o.b. price of California canned asparagus, the index of nonagricultural income, and the trend of demand. The fit of the regression surface is not nearly as good in this case as with equation 1. The adjusted coefficient of multiple correlation is only 0.897 as against 0.978 when, price is taken as the dependent variable. In the above formulation "time" is used as a proxy for and is presumed to exhibit the combined influence of factors which change slowly and smoothly with time. It is probable that among such factors the volume of asparagus canned in states other than California exerts the most important single influence. For the period 1925-26 through 1940-41 equations 3 and 4 of table 2 give the results secured when the trend of demand is replaced by the volume of asparagus canned outside of California as the third independent variable. As was the case in the first formulation a distinctly better fit ( R^^a) " 0.968) is obtained with f.o.b. price of California canned asparagus as the dependent variable than with volume of domestic shipments as the dependent variable 0*2(134) = 0*867), However, the fit of the surface described by equation 3 is almost as good as the fit of the surface described by equation 1, the difference between -the adjusted coefficients of multiple correlation being only 0.010. Ileither is the fit of the surface described by equation 4 markedly inferior to the fit of the surface described by equation 2, — ' Instructor in Agricultural Economics, Junior Agricultural Economist in the Experiment Station and Junior Agricultural Economist on the Giannini Foundation. Professor of Agricultural Economics, Agricultural Economist in the Experi- ment Station and Agricultural Economist on the Giannini Foundation. ■it ■■ 2. The average net relations between the f.o.b. prices of California canned asparagus and (1) domestic shipments of California canned asparagus, (2) nonagricultural income payments in the United States, and (3) volume of asparagus canned outside of California are shown graphically in figure 1. Expressed in numerical terms these relations are as follows: (a) with both the nonagricultural income payments and the volume of asparagus canned out- side of California held constant, a change of 100,000 cases in domestic ship- ments of California canned asparagus was on the average accompanied by a change in the opposite direction of 17 cents a case in the f.o.b. price of California canned asparagus; (b) with both domestic shipments of California canned asparagus and the volume of outside pack held constant, a change of 10 points in the index of nonagricultural income payments was on the average accompanied by a change in the same direction of 51 cents a case in the f.o.b. price of California canned asparagus; and (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. Differences between the actual prices and those estimated by means of equation 3 are given in table 3, column 3. The differences are plotted as deviations from the net regression lines in figure i. Data for the year 1941-42, which are in part preliminary, are also shown in the tables. The actual f.o.b. price of California canned asparagus in 1941-42 was 12 cents a case above that expected on the basis of the correlation analysis. §p l Imp? 9^V09?&< <m$w P0 $m &0mg>q mewl tm&imteesmmn *ir 1 :' :' . - ! . • -." : • - ■ : - ' • ■ ~J i rjj ... . ., .., ^ , . i »,j >ljy : ■•■ ( .\. . ; - ; 3. TABLE 1 Annual Average F.o.b. Prices of California Canned Asparagus and Important Factors Affecting Them, 1925-26 to 1940-41 Domestic r • U • u « pi J. ot? c Vi t ran o n "f- c? Ilarch of California of California Index of asparagus through canned canned nonagricul- pack of February asparagus asparagus tural income other state JS 1 2 3 4 dollars 10,000 per cent 1,000 pel LdSU /•% f*> ri s*\ CciSCS cases 1925-26 6.01 134 97 48 1926-27 5.69 171 101 37* 1927-28 5.44 172 102 26 1928-29 5.63 193 105 40* X J C-i Zl — xj \J o .oy xyo -LU / Do 1930-31 5.64 159 97 100* 1931-32 5.54 130 82 142 1932-33 4.10 159 65 20 1933-34 3.49 183 64 184 1934-35 4.30 145 72 235 1935-36 4.55 158 78 281 1936-37 4.75 160 89 438 1937-38 5.22 159 93 631 1938-39 4.48 158 88 607 1939-40 4.44 179 95 671 1940-41 4.68 184 102 927 1941-42 5.52 161 1 120i~ 1,449 * Estimated. ■f Preliminary, subject to revision. Sources of data: Col. 1: Years 1925-26 to 1935-36 compiled from records of canners. Years 1936-37 to 1941-42 compiled from reports of asparagus Advisory Board. Col. 2: From table 4, col. 6. Col. 3: Simple average of monthly indexes of national income, excluding agricultural income, average 1924-1929 equals 100, compiled from the United States Bureau of Agricultural Economics, The Agricultural Situation, current issues. Col. 4: Years 1925-26 to 1932-33 from United States Department of Commerce, Biennial Census of lianufactures; years 1933-34 to 1941-42 compiled from Canned Food Pack Statistics, national Canners Association. / ' . " .h < ,! ■^gr US*** i 1 «$* ' : . .'.'*»■- ' •■ . ■ ■ ! ! ; i3 Si! 'it so-:: TABLE 2 California Canned Asparagus: Regression Coefficients and Auxiliary Constants (Figures in parentheses are standard errors) Dependent Constant Net regression coefficients* Adjusted coefficient Period Equation variable term X l X 2 X 3 X 4 t t 2 of multiple correlation R 1 2 3 4 5 6 7 8 9 10 11 1925-26 to 1939-40 1 h 3.3404 -0.0169 (0.0024) 0.0517 (0.0045) -0.0479 (0.0109) -0.0094 (0.0031) 0.9776 2 h 180.5229 -48 ,9039 (7.0887) 2.6661 (0.3456) -2.1924 (0.7235) -0.5207 (0.1621) 0.8968 1925-26 to 1940-41 3 h 3.4561 -0.0167 (0.0027) 0.0507 (0.0037) -0,0010 (0.0002) 0.9680 4 x g : 186,0118 -45.8683 (7.3448) 2.4452 (0.3560) -0.0445 (0.0117) 0.8668 * X^ = Annual average f.o.b. price of California canned asparagus in dollars per case. Xg = Domestic shipments of California canned asparagus in units of 10,000 cases. X 3 = Index of nonagricultural income payments, 1924-1929 = 100. X 4 = Canned asparagus pack of states other than California in units of 1,000 cases, t = Time in years, origin at 1932-33. T" : . ... ! \ \ : ' I I 1 ! - - * ,-Jr ! 1 smm j 1 jf~ ""^^^^^^S^S&tfiv — i "~ ~ — "4 . ...r^;™..:r^.~;-^.:.„r. i Fig. 1.— Net Regression of F.o.b. Prices of California Canned Asparagus, 1925-26 to 1940-41, on: A, Domestic Shipments of California Canned Asparagus; B, Index of Nonagricul tural Income Payments; C, Pack of Asparagus Canned! Outside of California. 5. 5.90 5.50 CD CO (d o k 0) D. CO 3 5.00 CD O Q 4.50 13 6.00 - 5.50 5.00 - 14 15 16 17 18 19 California domestic shipments - 100,000 cases 5.50,- 5.00 - 4.50 4.20 70 80 90 100 110 Nonagricul tural income index 0 2 4 6 8 10 Pack of other states - 100,000 cases 15 — 6 • 3 3S> Go.O- 8S 03 y j OS. I / #0 ■ / 02. £ 8| 000,001 01 J KU3LE 3 Actual and Estimated F.o.b. Prices of California Canned Asparagus, 1925-26 through 1940-41 Year Residuals COX . X "fell TTinrh K/i-Ll I J Lit—XL ijs ujuccwsu price minus COX. C " "1 ' ■ JL 0 dollars per dollars per dollars case case per case 1925-26 U • UX —u.uo 1926-27 ^ RQ O • OJ o »oo u.ux 1927-28 □ . f o — u.iiy 1928-29 5.63 5.52 0.11 1929-30 5.69 5.57 0.12 1930-31 5.64 5.62 0.02 1931-32 5.54 5.30 0.24 1932-33 4.10 4.08 0.02 1933-34 3.49 3.46 0.03 1934-35 4.30 4.45 -0.15 1935-36 4.55 4.49 0.06 1936-37 4.75 4.86 -0.11 1937-38 5.22 4.89 0.33 1938-39 4.48 4.67 -0.19 1939-40 4.44 4.61 -0.17 1940-41 4.68 4.63 0.05 1941-42 5.52 5.40 0.12 Sources of data: Col. 1: From table 1, col. 1. Col* 2: Based on equation 3, table 2. c. T 550.' BfetfF v : • I:...:- JOB 7. IA.BLE 4 Pack, Carryover, Shipments, and Domestic Movement of California Canned Asparagus, 1925-26 to 1941-42 California Year Carryover March X I Vlil A TTQ "1 1 O V» I /—> ji Vui ± tx 0 — e i o tax United Calij ?ornia through Pack preceding for shipments dom< jstic February year shipment exports shipments 1 2 3 4 5 ( 1 1,000 1,000 1,000 1,000 1,000 1,000 cases cases cases cases cases cases 1925-26 1,745 170 1,915 1,664 325 1,339 1926-27 2,236 251 2 487 (J , uou 367 1,713 1927-28 2,190 407 2 .^97 474 1,721 1928-29 2,338 402 2 .740 ? 471 540 1,931 1929-50 2,673 269 c , OX 671 i#J 348 1930-31 2,663 323 2,986 2,028 435 Id 593 1951-32 1,747 958 2 .70^ x , o*±o 350 1,296 1932-33 1,313 1,059 2,372 1,918 326 1,592 1933-34 2,135 454 2,589 2,313 485 1,828 1934-35 1,914 276 2,190 1,980 533 1,447 1935-36 2,238 210 2,448 2,143 568 M 575 1936-37 2,350 305 2,655 2,133 530 M .03 1937-38 2,072 522 2,594 2,018 431 87 1938-39 1,796 576 2,372 1,922 340 .82 1939-40 1,849 450 2,299 2,126 338 M r 88 ; 1940-41 2,182 173 2,355 1,956 116 140 | 1941-42 1,578 399 1,977 1,670 57* 1,613 f * March through September, 1941* •f Preliminary, subject to revision. Sources of data: Cols. 1-4: Canners League of California and Asparagus Advisory Boards. The carryover figures are total stocks on hand sold and unsold. Col. 5: Compiled from reports of United States Bureau of Foreign and Domestic Commerce. Pounds converted to cases on the basis of 34 pounds per case. Col. 6: Col. 4 minus col, 5,