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,