University of California College of Agriculture Agricultural Experiment Station Berkeley, California Statistical Anal ysi s of t he A nnua 1 Farm Prices for Seasonal Types of Co-^nmercial Head Lettuce, 1918-19 47 Sidney Hoos UNIVERSITY OF CAUFORNp* LJBRARr COil£Qi: Of AGPJCULTURE DAVIS May, 1948 Contribution from the Giannini Foundation of Agricultui^l Economics I-Iineographed Report No. 92 I I University of California College of Agriculture Agricultural Experiment Station Berkeley, California Statistical Analysis of the Annual Fa rm Prices f or Seasonal Types of Commercial Head Lettuce, 1918-1947 Sidney Hoos May, 1948 Contribution from the Giannini Foundation of Agricultural Economics Mimeographed Report No. 92 I statist ical Ana l ysis of the Annual Farm Price s for Seasonal. Types of Commercial H ead Lett uce. 1918-1947 Sidney Hoos" 1/ In February 1948, the California Agricultural Escperiment Station issued the following two publications on commercial head lettuce: The circular reviewed and analyzed historical trends in the commercial head let- tuce industry and summarized its current economic status. The statistical sup- plement to the circular presented the detailed data on the industry. This report may be viewed as a continuation of the work reflected in the two previous publications on commercial head lettuce. In particular, the purpose of this report is to present the results of an analysis of the major factors' which have influenced and are correlated with the prices and shipments of commercial head lettuce from 1918 through 1947. As oranges and lemons are considered to be segregated according to "summer" and "winter," depending on the time of picking and shipping, commercial head let- tuce is separated into seasonal periods. The annual lettuce season is divided into the following marketing periods: winter; early-spring; late-spring; summer; and fall. Although there actually is no clear-cut separation of these seasonal types of lettuce, for purposes of convenience as well as reflecting to a great ex- tent production and marketing practices, the following classification has been es- tablished : "Commercial Head Lettuce, Economic Status 1947," (Calif. Agr. Exp. Sta. Circ. 378, February 1948) j and "Statistical Supplement to Agricultural Experiment Station Circular 378," (February 1948), Processed Winter : acreage planted after September 1 for harvest during December 15-March 15, Sprin g t in general, acreage planted prior to March 1 for harvest until July 1. Early-Spring : planted during January for harvest to May 1, Late-Spring ; planted during February for harvest to July 1, Summer; acreage planted during the period March 1- June 1 for harvest during July 1-September 1. Fall; acreage planted between June 1 and September 1 for harvest after September 1, 1/ Associate Professor of Agricultural Economics, Associate Economist in the Experiment Station and on the Giannini Foundation, <- ■ .,.,.*firv.. In the analyses underlying this report, early-spring and late-spring lettuce are combined. Hence, the resulting four seasonal types are considered to be mar- keted during the following months; "All types combined," therefore, cover the twelve-month period from January through December, In the statistical analysis presented in this report, the results for the re- spective seasonal types pertain to the corresponding marketing periods noted in the preceding paragraph. Although California is the dominant commercial lettuce producing state, this report concerns itself with the national situation. Cali- fornia growers and shippers of commercial lettuce face competition from growers and shippers in other parts of the country during all four of the seasonal mar- keting periods. The basic data used in the analyses are given in tables 1, 2, and 3, With respect to the basic data, the following comments are pertinent. For the supply series, the most appropriate .data would be total commercial shipments; however, an adequate series of that nature is not available. Therefore, we have used har- vested production of commercial lettuce, which is highly correlated with the quan- tities taken by the market. For the income variable, unrevised data were used in the analyses sizmiiiarized in table 4 and the revised income series were used in the analyses summarized in table 5, The two series differ effectively only in the last several years. Table 3 shows the revised income series. In some of the regression analyses, "time" was introduced as one of the inde- pendent variables. In those cases, "time" is used as a proxy for and is presumed to exhibit the combined influence of factors which change slowly and smoothly with time. In commercial head lettuce, such factors probably include tastes and atti- tudes of consumers affected by changing ideas of nutrition and changing relative importance of the several seasonal types of lettuce. These may be combined under the factor of "shifts in the demand" for commercial head lettuce, reflected by the "time" variable. Table 4 presents the multiple regression results for the period 1918-1945. For each of the seasonal types, as well as for all types combined, price and quan- tity, respectively, are considered as fionctions of the indicated independent var- iables. Hence, two formulations of statistical demand characteristics are given for each of the seasonal typos and for all types combined, respectively. All of the empirical demand formulations are not equally acceptable on statistical grounds, as may be noted by examination of the various coefficients of multiple correlation and the t- ratios of the net regression coefficients. In all cases the signs of the net regression coefficients are consistent with what would be expected from the viewpoints of economic theory and marketing experience. As an example of the usual interpretation of the statistical demand results, we can consider equation No, 1 of table 4, which expresses the average net rela- tions between the supply of commercial lettuce taken by the United States market Seasonal Type "Winter" "Spring" "Summer" "Fall" January -March April -June July -August September-December Marketing Period 3. during January-December (l) the United States farm price, (2) nonagricultural in- come level in the United States, and (3) the "time" trend. Expressed in numerical terms, these relations are as follows: (a) with both the nonagricultural income and the "time" trend held constant, a change of ^1,00 per crate in the United States farm price for commercial head lettuce was, on the average , accompanied by a change in the opposite direction of 5 million crates of commercial head lettuce taken by the United States market; (b) with both the price and the "time" trend held constant, a change of 10 points in the Income index was, on the avera ge ,1 ac- companied by a change in the same direction of 800,000 crates of commercial let- tuce taken by the United States market; and (c) with both the price and income held constant, a change of one time unit in the "time" trend was, on the average ^ acconpanied by a change in the same direction of 600,000 crates of commercial lettuce taken by the United States market. The combined influence of price, in- come, and the "time" trend variables statistically accounts for about 93 per cent of the obsei-ved year-to-year variation in the quantity of commercial head lettuce taken by the United States market. These results are average relations for the period under consideration, 1918-1946, The other equations in table 4 (equations 2 through 10) are interpreted in the same manner as for equation 1 considered in the preceding paragraph, with at- tention given to the respective dependent and independent variables, . Differences between the actual values of the dependent variable and those estimated by equation 1 are plotted as deviations from the net regression lines in figure 1. Also, the differences between the actual values of the dependent variable and those estiiiiated by equation 2 arc plotted as deviations from the net regression lines in figure 2, Similar net regression charts were constructed for the other equations in the course of the study in order to discern hints as to whether other formulations of the demand characteristics would yield improved statistical fits. It is noted that the statistical results presented in table 4, and briefly discussed in the preceding paragraphs, are based on the period 1918-1946 which in- cludes the v/ar years during which there was federal price control on commercial head lettuce. Hence, statistical demand formulations were studied for the period 1918-1947, but excluding the war years 1942-1945, These results are summarized in table 5, It is of some interest that, in general, the resialts of the two sets of analyses agree reasonably well. But such correspondence may be expected; 25 of the same years in the 30-year period from 1918 through 1947 were used in both sets of analyses. 4. X TABLE 1 United States Commercial Head Lettuce Harvested Production (in Millions of Crates) Von v» 1 ear 0\u!uUt>I X e o L< U O tJ "Pal 1 " ! Annual (Jan. -Dec. ) 1 \ 1918 l.o4 ♦ Di PQ • C •1' 3.79 1919 1 .<;3 1 • by . DO • f O 4.33 1920 3.50 o o o c *cd . y.L X • u / 7.70 TOOT 19i0l • 54 o o c C mCb J. • iy X • 7.21 T r\ o o 1922 3.01 O AO i .DO 9.29 T O O OP 4 •ci C. • CO 1 . oo X • Ou 10.37 O • 04 1 • Ot: P %9 12.42 T O O C 1925 4 .o^ 4 •4i 9 17 c . O 1 p no 13.70 A Q 9 c • 0 1 P 7Q 15.10 1927 C T ^ 5.16 A a A 4 « o4 O . O'i O • " t: 16.98 1928 5.85 5.55 t CO 5. DO O • 40 18.46 1929 6.26 4 .45 4.yu • OO 19.99 1930 5 .74 5.Po 4.60 1931 5.35 5.76 3.83 4.41 19.34 1932 4.83 5.00 3.67 3.88 17.38 1933 4.49 5.01 3.77 4.02 17.29 1934 3.83 5.95 4.23 4.78 18.81 1935 4.07 6.07 4.44 4.68 19.25 193S 4.45 7.23 4.56 4.37 20.60 1937 4.65 6.51 4.66 4.80 20.63 1938 4.45 5.93 3.96 4.57 18.81 1939 5.19 6.93 4.85 5.00 21.96 1940 4.61 7.07 4.86 4.82 21.36 1941 5.30 7.49 5.40 4.86 23.05 1942 5.73 7.70 5.00 4.99 23o43 1943 5.80 7.37 5.44 5.81 24.42 1944 7.31 8.80 6.14 6.16 28.40 1945 7.55 9.12 6.60 6.45 29.71 1946 8.92 9.43 7.45 7.88 33.69 1947 34.05 Source of data: Detailed sources noted in Statistical Supplement to California Agricultural Experiment Station 'Circular 378, Commercial Head Lattuce, Economic Status 1947, February 1948. ..•3r:r-.-.-Ti:Tr.;7— 5 TABLE 2 United States Commercial Head Lettuce Farm Price (Dollars per Crate) 1 Year "Winter" | lettuce 1. "Spring" lettuce "Summer" lettuce "Fall" lettuce Annual (Jan. -Dec.) 1918 1.21 1.71 2.33 2.20 1. 63 1919 1.45 1.94 2.52 2.07 1.91 1920 1.30 1.32 2.51 1.86 1.53 1921 1.48 1.83 3.01 1.77 1. 89 1922 1.90 2.17 1.79 1.62 1. 88 1923 1.51 1.52 1.87 1.66 1.60 1924 1.53 1.52 1.83 1.54 1.57 1925 1.58 1.23 1.54 1.60 1. 46 1926 1.93 1.50 1.63 1.57 1. 68 1927 1.34 1.36 1.40 1.27 1. 34 1928 1.43 1.52 1.95 2.21 1. 70 1929 1.89 2.04 1.69 1.74 1. 84 1930 1.87 1.62 1.52 1.85 1.72 1931 1.42 1.17 1.86 1.64 1. 48 1932 1.55 1.32 1.00 1.21 1.29 1933 1.26 1.13 1.45 1.41 1. 30 1934 1.35 1.66 1.26 1.23 1,40 1935 1.28 1.71 1.21 1.54 1. 46 1936 1.10 1.35 1.85 1.57 1.46 1937 2.04 1.76 1.41 1.06 1,58 1938 1.08 1.98 1.35 1.50 1 .52 1939 1.47 1.23 1.36 1.51 1.38 1940 1.33 1.83 1.28 1.30 1,48 1941 1.40 1.87 1.78 1.54 1. 67 1942 2.19 1.86 3.25 3.27 2. 54 1943 3.64 3.84 2.81 2.78 3. 31 1944 2.65 2.65 2.38 2.72 2. 61 1945 2.73 3.01 3.13 2.85 2. 93 : 1946 2.84 2.58 2.44 2.67 2. 64 j 1947 3, 18 i Source of data: Detailed sources noted in Statistical Supplement to California Agricultural Experiment Station Circular 378, Commercial Head Lettuce, Economic Status 1947, February 1948. 6. TABLE 3 United States Nonagricultural Income (1935-1939 = 100) 1 ■ oprmg rail average average ouuMner average Toy* TT^iVt , Annual Year Mar . June J uiy-Aug , Nov.— Dec. Jan.— Dec • lyio CO r\ bo ,U nn r\ ( I ,U 77 C 71; c 7/1 7 lyiy /b,y 76,1 Q O O OO, (C Q 7 O o < PT O ol . (C Ci A C y5. o yb.B yi . 4 y4.i Q A O o«:.y o 0,L) R "5 T O O.l oO,5 od.y Q 7 >1 RK ft DO .0 yo.i yb , 5 T An 7 T AO Q lUc , 0 yy , J iyy .1 oU.U pn c oU.O pn ^ ou. t fin n 1935 83.9 85.6 86.4 89.2 86,5 1936 93,8 103.2 105.6 103.5 101.4 XUD , 107 1 1938 98.9 97.4 98.0 100,6 98,9 1939 103.3 104.1 106.4 109,4 106.0 1940 111.6 112.5 115,0 119.3 115,0 1941 126.9 134.0 142.0 148.0 138,2 1942 156.8 167.5 179.2 191.2 174,6 1943 205.4 212.8 217.9 224.6 215.7 1944 233.8 23G.6 240.9 244.8 239.4 1945 251.0 251.6 250,6 242.2 248,1 1946 242.5 248 .7 255.6 264.2 253.5 1947 270,8 272.6 277.6 294.8 280.4 Source of data: U.S. Bureau of Agricultural Economics mimeo. dated 4-11-44, National Income Supplement to Survey of Current Business, July 1947, table 48. Survey of Cirrrent Business, Dec. 1947. II TABLE 4 United States Commercial Head Lettuce Regression Coefficients and Auxiliary Constants for Statistical Regression Analysis Covering 1916-1946 1 Seasonal t type of Equation number Dependent variable Constant term a/ Net regression coefficients—' (figures in parentheses are t-ratios) ■ Adjusted coefficient of multiple correlation ■ R ' lettuce H j ^3 ^3 I X ■3: o 4 ! 5 6 7 8 1 All types 1 combined 1 1 Xl 16.7864 -5.1791 (3.4743) .0861 (4.4774) .5987 (9.5376) .965 { 2 X2 1.3765 -.0629 (3.4743) .0128 (10.3185) ,0275 (1.9886) ,915 Winter 3 ^1 2.6518 -.5981 (1, 1353) .0275 (3.5143) .0538 (1.9770) .840 4 .6226 -.0931 (1.4272) .0132 (5.9638) ' 7845 ' j Spring 5 Xl 5.4123 -.9670 (4.4209) .0148 (4.5452) . 2274 (16.3163) .980 ' 1 6 ^2 2.8050 -.4537 (4.4209) ,0123 (7.0085) .1004 (3.9134) .85t 1 Summer 1 . . 7 Xl 3.5611 -.6546 (2.9105) ,0118 (3.0434) .1561 (8.2716) .960 8 1.2414 -.2753 (4.7373) .0141 (6.6791) .777 Fall 9 Xl 3,8730 -.5426 (1.6785) .0078 (1,6421) .1826 (9.6197) ,955 lo ^2 .9037 -.1450 (3.2219) .0121 (7.5211) .830 _ . ..... . a/ Xj^^United States harvested production of lettuce in units of millions of crates. Xg^United States farm price of lettuce in dollars per crate. X3=Index of United States nonagricultural incomes, 1935-1939=100. X^^Time in years, origin at 1932. Winter lettuce is marketed during January-March; Spring lettuce during April-June; Summer lettuce during July • August; and Fall lettuce during September-December. The quantity and price series for the different seasonal types reflect transactions during the respective months in the season. The income index for the different seasonal types is the average of the monthly values for the respective months ;^ in the setso'i. Figure 1, United States Lettuce — Quantity Taken by the Market Related to: (A) Seasonal Farm Prices, (b) Index of United States Nonagricu].tural Income , and (c) Time Trend (Based on Equation 1, Table 4) 28 - o r — 2- 20 ^ 18 ^ V, IS >^ 12. 4- lO 8 6 G' . '30 'SI 18 X 17.837586 ,5^8710 IS M 15 -to - 5 O 5 innc 'Ti'c-.nd (Origin at i^32) lO 15 1.5 i.o 2.5 3.0 US Farrn Price (DoHot^s per Cfo+e ) 3.5 Figvire 1 (Continued) 9, c % A) .0 t Figure 2, United States Lettuce — Seasonal Farm Prices Related to (A) Quantity Taken by tke Market, (B) Index of United States NonagrlCultural Ihcolne; and (C) Time Trend (Based on Equation 2> Table 4) 10, ^ 2.5 0 0 *0 2.0 O I.S .111 . '30 2^ .^'.,,'3^ •21 M8 •23 •15 •i? X^^ = l.786ao7 4-.Oe75£6 -IS •5 , c» . 5 to (5 uo.iHtv "^akan by Ihe U5 Mcu-Uel ( M". 1 1 . Croias) i'tS' i; Figure 2 (Continued) 11. Ihdcx of Klonagr'iculturo! Income C 55 - 5*^= lOO ) [ o TABLE 5 United States Commercial Head Lettuce Regression Coefficients and Auxiliary Constants for Statistical Regression Analysis Covering 1918-1947 Excluding 1942-1945 Seasonal type of j lettuce Equation number 1 Dependent variable Constant Net regression coef f icients^./ (figures in parentheses are t-rati-)s) A T 1 1 c: "t* (3 coefficient of term Xl ^2 ^3 h ^ i 1 2 3 4 5 6 7 8 i All types 1 1 16.0876 -4. 5544 (2.0455) .0838 (3.6821) .6109 (8.5391) .966 combined 2 ^2 .9699 -.0269 (3.9237) ,0104 (9.9736) .915 Winter 3 Xl 2.1723 - .0662 (.0092) .0248 (2,7433) .0630 (2.2641) .866 4 ^2 .6308 -.0446 (.7814) .0108 (5.1614) .860 Spring 5 Xl 1 X — 5.3349 (3.3401^ (4.6756) (15.6960) .978 i 6 H 2.3151 -.3354 (3.3401) .0109 (6.4376) .0738 (2.9463) .821 1 1 1 Summer 7 Xi 3.2350 - .5392 (1.9649] .0134 (3.2574) .1619 (7.6444) .963 8 X2 1.2827 -.2739 (5.1357) .0134 (6.5256) .769 .958 1 Fall 9 Xl 3.6756 1 - .2140 ( .4754; .0048 (1.0921) .1926 (9.1557) .785 1 10 X2 1.2599 -.1369 (3.8336) .0080 (6.4745) 1 a/ X]^=United States harvested production of lettuce in units of millions of crates. X2=United States farm priceof lettuce in dollars per crate, X3= Index of United States nonagricultural income , 1935-1939=100. X4=Time in yeare, origin at 1932. Winter lettuce is marketed during January -March; Spring lettuce during April-June; Summer lettuce diiring July- August; and Pall lettuce during September-December • ■ The quantity and price series for the different seasonal types reflect transactions during the respective months of the season. The income indej: for the different seasonal types is the average of the monthly values for the respective months in the sepson. ■ -.y ■ --' — — i i„. — — ■ ---- ■ 0 1 .. - . ...J ,^ t^: -.J.....?. -i