University of California College of Agriculture Agricultural Experiment Station Berkeley, California Statistical Analysis of Annual Average Returns to Growers of ADjnonds, 1924-25 to 1948-49 Ivain M, Lee gNlVneiTY OF CAUFORNIA LIBRARY OOLLECE OF AGRlCULTURr DAVIS February, 1950 Contribution from the Giannini Foundation of Agricultural Economics Mimeographed Report No, 103 I i statistical Analysis of Annual Average Returns to Growers of Almonds, 1924-25 to 1948-49 Ivan M, Lee-'^ This report suniuarizes the results of multiple regression analyses of season's average returns to almond growers and several related factors dviring the period 1924-25 through 1948-49. The years 1943-44, 1944-45, and 1945-46 were excluded from the analyses due to the abnorml conditions prevailing during these years, arising primarily from federal price control. The related factors introduced into the equations are volume of almonds sold by domestic growers, volmne of almonds imported, nonagri cultural income pajonents, and prices of competing domestic nuts» The basic series used in the analyses are contained in table 1, while the resulting regression equations are presented in table 2, A weakness of the series "voliune of almonds sold by growers" for the tj'pe of analysis herein presented should be mentioned,- This series represents production adjusted for estimated consumption on farms where produced. No ad-p justment is made for changes in carry-over from year to year. Hence, the series is not completely adequate for reflecting variation in sales. Data on carry- over from other sources were not adequate to permit adjusting this series for the entire period covered by the analyses; A supplementary analysis using carry-over data for a part of the period indicated that the statistical fit of the multiple regression equations would have been improved if changes in carry- over could have been taken into account.-. i 2/ Assistant Professor of Agricultural Economics, Assistant Agricultural Economist in the Experiment Station and on the Giannini Foundation, rife ..f-fi-?i *f> . ^fr-* >3- r^.b/*-.\. .f ^;"^T-J>i;i^. r^pA,, o t : '=ujt n ; ; p^;^ ^ -iii , r-ii • ^fi^j; T ^ "•i-^^^.; fiJi;. i;©*ito«e«j. «1A< 8fl^jUBit««->«-. -;it8^.-.»^Jif}av.: grj^K-N^J.-^ff*; 9C^: "^^^^H/ tlj_ M^Jtfi*:; ■'if-- ■^^•f ??t«t* ■-ifs!^^>!?|>jj v:*^ ':-'-^f^ .. . •.; a?r:^Apsi t;g4^' xii^. ^K}-t0:lb l£ fteVoxqaJt nsarf sajrat] a\;:M'V ^nr-f+sfrp^ j1f?K^^»-»--- sft{-t4fi.-:-w i?ff' 2. In eqtiations and t| (table 2) all variables are employed in arithmetic form. In equations Tg and the series' "nonagricultural income payments" is introduced in logarithmic form while all others remain in arithmetic form. Equations Tg and differ from the other two pairs of equations in that each variable enters in logarithmic form and fiirther in that two of the variables used in the other equations, volume of imports and prices of competing domestic nuts, are omitted from the analysis. It will be observed that in each of the T equations season's average returns to growers serves as the "dependent" variable while in the T* equations volume sold serves as the "dependent" vari- able. One of the purposes of this analysis is to obtain an approximate measure of the net relation between season's average returns and volume sold during the period under review. For this purpose two equations of the same form, one employing season's average returns as the "dependent" variable and the other using volume sold as "dependent," may be considered as giving equally acceptable approximations to this net relation. Furthermore, in this analysis neither economic nor statistical criteria provide a strong basis for preferring any one pair of the equations indicated above over any other pair. Therefore, all three pairs are presented. To illustrate the interpretation which may be placed on the coefficients in these eqmtions, equation T2 is interpreted as follows: (1) With volume of almond imports, nonagricultural income payments, emd prices of competing domestic nuts held constant, a change of 1,000 tons in the volume of almonds sold by growers was on the average, for the period under review, associated with a change in the opposite direction of around 15 dollars per ton in season's average returns to growers, (2) With volume of almonds sold by growers, nonagricultural income, and . ■;. . .. . : KJ^f,^.y'i^;.,^i^-^ .a'^J£ si! .- V- ^- ' ; { ':^"-u< '! . •; •.. •. .r<;... • ... . ^•/;. -f^:^,. 4. sold by growers is treated as the "dependent" variable.. Interpretation may- be illustrated with reference to the coefficient of season's average returns in equation t|.. Here a change of 15 dollars per ton in season's average returns to growers, with almond imports, nonagricultioral income payments, and prices of competing nuts held constant, was on the average associated with a change in the opposite direction in the voliime sold by growers of about 670 tons. In table 5 actual average returns to growers and actual volume sold each year may be compared with returns and volume sold estimated from equations and Tg, respectively. The differences between actual and estimated returns are plotted as residuals about the net regressions of equation Tg in panels A, B, C, and D of figiire 1, In addition to the net regression coefficients, measures of price flexi- bility (for the T equations) and demand elasticity (for the equations) have been calculated. These measures pertain to the net relation between volume sold by growers and season's average returns. The coefficient of price flexibility represents the ratio of a small percentage change in the season's average returns to growers to the small percentage change in volume sold by growers with which it is associated. The coefficient of demand elasticity represents the ratio of a small percentage change in volvune sold by growers to the small percentage change in season's average returns with which it is associated. In equations T and T^, which employ logarithms of the variables, price o o flexibility and demand elasticity are constant along the net sales-returns regression lines. As will be observed in table 2, the regression coefficient of volvime sold in equation Tj is the measure of price flexibility while the regression coefficient of season's average returns in equation Tg is the measure of demand elasticity. In the other equations, the net relations between y I- i S - M *■ "t r-r>A;r- Lu.bK £Sip.fIc .•.•^;..;'4s?V9'3ts,o ifj^mforf.. , ., .. ^^... : . ^ Jl^ al^^» *>- .V- ^ • . .^^i!^J.c:,x ':':^'.>ri'r-'-^ ^]^:.:^^^ r'^\ il-''-*p'X^ ^ r>37-f:;.t:'g:«.5- i.r.*_-f: .-.tr.i? nn-. " ... . r • : . . -v.;. , arithmetic values of voliJine sold and season's average returns are lineari It is characteristic of such a relation that the coefficient of price flexibility or demand elasticity is different at different points on the net regression line. Estimates of flexibility or elasticity at the centroid are presented in table 2 for each of the equations, T^^, T^, Tg, and Tg. To indicate the variation in price flexibility and demand elasticity over the range of volume sold and season's average returns covered by the period included in our analyses, annml coeffi- cients of price flexibility and demand elasticity based on equations ^ and Tg, respectively, are presented in table 4, ..... ... ii./^a -^^.-^--^ 6. Table 1 Almonds: Basic Series Used in the Price Analysis, 1924-25 through 1948-49 (excluding 1943-44, 1944-45, 1945-46) Season's Index of Index c )f average Volume Volume United States prices c )f returns to sold by of almonds nonagricultural competing Year growers^/ growersS/ imported^ xncomeS/ domestic nuts^ (Unshelled basis) (Shelled basis ^ J. 3 4 5 dollars 1,000 100,000 1935-1939 = 1935-193: \ per ton tons pounds - 100 100 1924-25 300 7.8 224,9 101.7 241.2 1925-26 400 7,3 196,9 110.0 229.8 1926-27 300 15,8 158^9 112 i 5 iC J.O. 1927-28 320 11.8 184.0 113.2 1928-29 340 13^8 186.7 118.3 198,4 1929-30 480 4.5 199.6 117.1 160.1 1930-31 200 13.3 132,6 102.5 187.4 1931-32 176 14.6 83.4 82.6 101.4 1932-33 165 13.8 49.1 66.2 80.3 Xfc7 00— U*x 186 12.7 103.1 1934-45 180 10.7 29.9 79.7 112.1 1935-36 280 9.1 107,6 90il 91.5 1936-37 402 7.4 114*4 103.0 119,6 1937-38 275 19.8 30.7 99.6 83.3 1938-39 258 14.8 15.1 99,9 107.4 1939-40 209 21.4 13.8 107.3 93.2 1940-41 324 11.8 19.9 120.8 108.2 1941-42 704 5.8 37.2 150.3 121.3 1942-43 442 23.6 10.2 194,3 166 .-9 1946-47 486 37.6 93.2 258.5 310.6 1947-48 558 29,0 118.5 284.5 209,8 1948-49 425 33.8 103.2 300.6 178.1 §/ October-September year. b/ July-Jxme year. ; i jj/ Simple average of July- June monthly indexes. \ d/ Fixed weight index of prices received by domestic growers for walnuts, filberts, and pecans. Weights based on volume sold, 1935-36 to 1939-40, (continued on next page.) i I L- .» ■■ •• - •4-t.-. . i ■ ■ -■ >■ r : ■-.'IS ; 005 ! fT#Si : ' ■ ■ _ ■ f i _. i . .V--*.* ^ ■■ ■ -s -t^ -^t- \^ D9Vj:9C!3a ssoiiq xp&r'x •frtniew bsicrH \^ .. 7. Table 1 continued. Sources of data: Columns 1, 2, 5: 19S4-25 to 1945-46: U. S, Bureau of Agricultin-al Economics, Tree Nuts. Acreage, Production, Farm Disposition, Valu e and Utiliza tion of Sales, 1909- 1945, V/ashington, D, C. October, 1947, Processed, 1946-47 to 1948-49: U. S. Bureau of Agricultural Economics, T ree Nuts^ Acreage, Production, Farm Disposition, Value and Utilization of Sal es, Annual issue, August, 1949, Processed, Column 3: U. S, Bureau of Foreign and Domestic Commerce, Monthly Summary of Foreign Commerce of the United States , Wash- ington, D. C. January and June issues, (Unshelled con- verted to shelled by multiplying by. ,30.) 1925-1949. Column 4: 1924-25 to 1928-29: U. S. Bureau of Agricultural Economics, Mimeo, Dated April 11, 1944, 1929-30 to 1941-42: U. S. Department of Commerce, National Income Supplement to Sui-vey of Current Business , Wash- ington, D. C. July, 1947, 1942-43 to 1947-48: U. S. Department of Commerce, Survey of Current Business . July, 194^9, 1948-49: U, S, Department of Commerce, Survey of Current Business, Current issues. Table 2 Almonds: Regression Coefficients of Multiple Regression Analyses, 1924-25 through 1948-49 (excluding 1943-44, 1944-45, and 1945-46) (Figures in parentheses are t ratios) Regression coef f icientsa/ Adjusted Equa- tion Depen- . dent variable Constant term ^1 ^2 ^3 ^4 ^5 multiple correlation coefficient R Coefficient of demand elasticity Coefficient of price flexibility ^1 ^1 193.0683 (5.6523) (1.8967) P QQ7 1 . (7.4390) 0.6750 (1.5050) 0.8755 -0.8499^ 1 2 7.8363 -0.0353 (5.6523) -0.0457 (3.3276) 0.1343 (8.4267) 0.0408 (2.2262) 0.9432 -0.7679^ ^1 ^2 ^3 Log^Q X4 ^5 ^1 -1,621.6007 -14.6794 (5.6787) -0.4516 (1.3911) 1,054.1813 (8.6930) 0.2549 (6.6229) 0.9042 -0.6739^ t' ^2 ^2 -86.5487 -0.0446 (5.6787) -0.0439 (2.8106) 56.0392 (7.3201) 0.0316 (1.4687) 0.9287 -0»9716^ Log^Q Log^Q Log^Q X4 0.7436 -0,4945 (7.2657) 1.1104 (12.2679) 0.9361 -0.4945 ^°^10 ^2 0.9957 -1.4870 (7.2657) 1.8476 (9.2264) 0.8937 -1.4870 a/ = Season's average returns to growers (dollars per ton). Xg = Volume sold by growers (1,000 tons); o (Continued on next page») ♦ j i,. li V- ... . . ... • . ; .■ • - ■ • ■ . ■ — •-. . . : r — • i \ ' 1 • t r 1' ■. ■ ■ < • ! • * t„. . .-. j. 1 \ ■ • » •: > ... . r 1; i ■ • ; ■ •■■■'"r.*'isir)i ■ 'rm 1 1 A c»i.i.cTfff Toa ■ -j Table 2 continued. Footnote a continued: Xj = Volume of almonds imported (100,000 pounds). = Index of nonagricultural income (1935-1939 = 100). Xg = Index of prices of competing nuts (1935-1939 = lOO),. b/ At the centroid. to 10.. Table 3 Almonds: Actual and Estimated Returns and Volume Sold,, 1924-25 through 1948-49 (excluding 1943-44, 1944-45, and 1945-46) Differ- Differ- 1 1 t Diff ei^ 1 Diff er- ence : ence 1 i 1 Esti- i ence : e mce Esti- col, 2 as per j Actual i mated 1 col, 6 as 5 per Actual mated minus cent of 1 volume volume ' minus cent of returns returns col, 1 actual 1 i sold 1 ' • ■ ' sold col, 5 actual 1 3 , 5 6 7 8 dollars -oer ton -.000 tons 300 340 40 13,33 7.8 10,3 2.5 52.05 400 393 - 7 - 1.75 7.3 8,6 1.3 ] L7..81 . Q — »7 - 3.00 15.8 — x.u 6,33 1 1 H xo 4-.69 11.8 u, O 2,54 340 327 - 13 - 3,82 13.8 12.5 -1.3 9.42 480 444 - 36 - 7,50 4.5 4.3 -0.2 _ 4.44 200 291 91 45,50 13.3 17.3 4.0 30.08 176 173 - 3 - 1.70 14.6 12.6 -2,0 -13.70 165 94 - 71 -43.03 13.8 8,5 -5,3 -38.41 186 172 - 14 - 7.53 12.7 11.7 -1.0 7.87 180 241 61 33,89 10,7 14.2 3.5 32.71 280 280 0 0 9.1 8.7 -0,4 4.40 402 370 - 22 - 7.96 7,4 7,1 -0.3 4,05 275 203 - 72 -«;d,1o 19, o 14.6 -5.2 -2 16,26 258 290 32 12.40 14.8 16,7 1.9 ] -2,84 1 209 222 13 6,22 21.4 20.3 -1.1 5,14 i 324 419 95 29,32 11.8 18.2 6.4 c 54,24 704 602 -.102 -14.49 5,8 6.2 0.4 6,90 442 482 40 9,05 23.6 26,8 3.2 ] .3,56 486 407 - 79 -16,26 37,6 32.7 -4.9 -] .3,03 558 540 - 18 - 3.23 29,0 27.5 -1.5 5.17 425 493 68 16,00 33.8 34,5 0.7 2,07 Year 1924- 25 1925- 26 1926- 27 1927- 28 1928- 29 1929- 30 1930- 31 1931- 32 1932- 33 1933- 34 1934- 35 1935- 36 1936- 37 1937- 38 1938- 39 1939- 40 1940- 41 1941- 42 1942- 43 1946- 47 1947- 48 1948- 49 Sources of data: Column 1; From table 1, column 1. Column 2: Estimated by equation Tg, table 2, Column 5: From table 1, column 2, Column 6; Estimated by equation Tg, table 2, 11. Fig. 1: Net regressions* of Season's Average Returns to Growers of Almonds on: (A) Volume of Almonds Sold by Growers, (B) Volume of Almond Imports. (C) Nonagricultural Income Payments, and (D) Prices of Comoeting Domestic Nuts, 1924-25 through 1948-49 (excluding 1943-44. 1944-45, and 1945-46). U £ o bO o •p (3 O (•> -P 0) u a, V bO es u r-4 > i-t fli O T3 (0 c o a « « 09 « 600 1- 42 30' ■ ! '\.* 37 26 I 400 \- 200 r 33 25- 36^ -,^29 35 41 • . 39 31 40 43 48 ® 47 49 563.8146 - 14.6794 Xg 10 20 30 Xp - Volume sold by growers (lOOO tons) 40 (0 (h & o u o -p to ^ c fc* o 3 -P P (D U Ih 0) cu hfl CO u a! (1> r-l > r-l CS O XI (0 "a o 10 H O 3 -p -p 4> u ttO (0 as u OS 9) i-H > rH OS o to — ' B o » CO t 800 600 400 200 i ^I'log x' -1852.9704 + 1054.1813 log-^^X^ 47 48! 30 38' 2627*' 37% "-SS - ' "40 .. 25 32 39 I 31 •41 0 60 35 42 43 100 140 180 220 260 300 - Nonagricultural income (1935-39 = lOO) M U o •p w ^ c c u o 3 -p •p a, V hO (0 03 li ki o U) rH > .-• OS o w ■ "cl o a .* CQ 500; 400t 300 200. X, ^» 297.3033 + 0.2549 X^. 1-5 5 47 42 38 33 37 34 32.1 - 33. 40 . 39 35 *41 100 30 29- • 28 26 '27 25 43 « 140 51 180 ® 220 260 Xg - Prices of competing domestic nuts (1935-39 300 100) H o » s f . IS. Table 4 Almonds: Annual Coefficients of Price Flexibility and Demand Elasticity, 1924-25 through 1948-49 (excluding 1943-44, 1944-45, and 1945-46) Year Price / flexibility^ Demand elasti citv^ Ia -j^^-wj^'yiiij}- v;j.>j^".j<:;i ...v....'- ! I "V; , »• -• i.J ■ I • I