The major policy implication from Figure 6A; however, is that the real grower price, adjusted for inflation, has been steadily decreasing over the 1970-2001 period. The 2001 real grower price of almonds was barely over 50 cents per pound down from the peak real price of about $3.00 per pound in 1973. A causal glance at Figures 1A-6A in Appendix A indicates that the almond market is continually changing and a lot of world marketing forces affect California’s production and sales of almonds. Supply and demand models are developed and estimated for almonds and the results are given in the next section. Some theoretical and data issues must be addressed before the models and estimations are presented. First, should a researcher use a singe-equation approach or a system approach? In this report both approaches are presented, although single equation estimations are usually considered to be less efficient. There are several reasons for considering this model. Based on previous research work by the authors, alternative nuts were found to be weak substitutes for almonds in the United States domestic market. Similar results were also found by Alston et al . Thus, the advantages of imposing theoretical restrictions such as Slutsky symmetry conditions may be of little value in a demand system or subsystem for nuts. In addition,grow hydroponic retail prices for almonds do not exist since they are used as ingredients in confectionaries. This has two important implications. First, are the demand functions retail or farm-level demands? Wohlgenant and Haidacher developed the theoretical relationships for the retail to farm linkages for a complete food demand system.

Their approach, however, assumes that both retail and farm-level prices exist. In our case retail prices do not exist so we cannot employ their approach. This limitation of the demand models needs to be considered when interpreting the elasticity estimates. For example, farm-level own-price elasticities are generally more elastic than retail own-price elasticities for food commodities. Second, this may imply that nuts are not weakly separable from other food commodities.2 This would rule out estimating a nut demand subsystem. The model that we employed uses CPI to account for the prices of other food items and commodities. Given the alternate bearing phenomenon of almonds, there is a demand for consumption and a demand for storage. Alston et al did not find evidence of a stock holding effect. Thus, we followed their approach and assume that the demand function reflects consumption responses and not storage effects. Finally, there is a calendar year versus a crop year problem involved with data collection. Alston et al , when they estimated the domestic demand for almonds, used total availability minus US calendar year net exports minus stocks carried out plus carryins as their dependent variable. All of the estimations in the report are carried out using SHAZAM, version 10. The linear and double logarithmic forms are special cases of the Box-Cox specification. The linear and double-log functional forms in the almond demand equation were tested against the more flexible Box-Cox functional form and in both cases the linear and double-log specifications were strongly rejected. The values of the likelihood ratio statistics were 43.7 for the linear and 14.85 for double-log model. The chi-squared critical value with one degree of freedom is 3.841 at the five percent significance level. Table 1 presents the estimations. The homogeneity condition of degree zero in all prices and income does not hold globally in the Box-Cox specification unless the functional form is double log.

The linear, double-log, and Box-Cox estimated functional forms for almond demand equations are presented in Table 3. In order to make the different models comparable, homogeneity was imposed in the double-log models and the other models were deflated by CPI. The models were estimated using annual data from 1970 to 2001, a total of 32 observations. The Durbin-Watson values were 1.23 and 1.12 in the linear and double-log functional forms. The critical values are 1.244 and 1.650 at the five percent significance level, thus in the double-log and Box-Cox specifications the models were also estimated with an AR error process. The estimated auto correlation coefficients were 0.49 and 0.56 with an estimated asymptotic standard error of 0.15 and 0.14 . The estimated own-price elasticity of domestic demand for almonds ranged from –0.48 to -0.35. The estimated elasticity was -0.38 in the Box-Cox functional form with an AR error process. The estimates were highly significant with small p-values. Also, the estimated cross-price elasticity with walnuts was positive in four of the five models, but none of the coefficients were statistically significant; the smallest p-value being 0.39. The results confirm the absence of gross substitution effects between almond and walnuts. All of the estimated income coefficients were positive and ranged from 0.46 to 0.97 with small p-values. A sequential Chow and Goldfeld-Quandt test was conducted to determine if any structural changes had taken place during this period. No evidence was found of any structural changes. Additional models were estimated using the dependent variable, US total consumption of almonds plus California exports minus US imports. The dependent variable captures the international demand for US almonds as well as the domestic demand. The ordinary least squares estimated double-log regression had an R2 of 0.92. The estimated own-price elasticity of demand for almonds was -0.270 with an associatedp-value of 0.022.

The estimated model had a positive time trend coefficient of 0.05 income elasticity was 2.10 with a p-value of 0.07.Data for the years 1970-2001 are presented in Appendix B for walnuts. California marketable production, total domestic consumption, exports and imports, per capita consumption, acreage, yield, and grower prices, both nominal and real for walnuts are given in Figures 1B-6B in Appendix B. An overview of the walnut industry can be seen by an examination of the Figures. Marketable production of walnuts has slowly increased from just below 100 million pounds in 1970 to over 250 million pounds in 2001. Exports of walnuts exhibit a similar pattern of that to production . Per capita consumption of walnuts has remained relatively stable at 0.4 pounds over the period 1970-2001 . Acreage has slowly increased over the period starting with about 150 thousand acres in 1970 to about 200 thousand in 2001.Yields of walnuts are more volatile over the period than acreage but with a steady trend upward over the period 1970-2001 . Real grower prices have decreased over the period from 1970 to 2001 . Real grower prices reached a peak in about 1978 of $2.00 per pound and have declined ever since to about 60 cents per pound in 2001. Demand, acreage, yield,grow table hydroponic and production equations were estimated for walnuts using annual data from 1970 to 2001. The United States domestic demand for walnuts is estimated and reported first. The restriction of homogeneity of degree zero in all prices and income was imposed. When the model for all the years, 1970 to 2001, was estimated by ordinary least squares, the Durbin-Watson value was small indicating a possible misspecified model. Consequently, sequential Chow and Goldfeld-Quandt tests were performed and they indicated a structural break in 1983. Two demand functions were estimated, one using data from 1971 to 1983 and one employing data from 1983 to 2001. The estimated models, double-log and Box-Cox functional forms, are presented in Table The R2 values range from 0.71 to 0.76. The fit of the models to the data was not as good as for the almond demand equations. The Durbin-Watson staThistics did not indicate any problems with auto correlation. The estimated own-price elasticity of demand for walnuts ranged from –0.266 to -0.284 for the time period prior to 1983 and from -0.251 to -0.267 after the year 1983. The p-values were 0.068 and 0.63 for the double-log models and 0.113 to 0.051 for the Box-Cox functional forms. The Box-Cox equation post 1983 was estimated with a time trend. Its estimated coefficient was -0.03 with an associated p-value of 0.014. Three of the four estimated income elasticities were positive with only the post 1983 for the double-log specification negative . Only one of the estimated almond cross-price elasticities was significant at any reasonable level. Thus, the sample evidence finds little substitution effects between almonds and walnuts. Based on the sample evidence the estimated own-price elasticity of demand for walnuts is inelastic. What are some economic factors that can explain the structural break around 1982-83? From Figure 6B, real walnut prices dropped dramatically in 1983. There was a large supply of walnuts that year and inventory levels increased significantly. In addition, the United States imposed a tariff on pasta and Italy, one of the largest importers of U.S. walnuts, retaliated by placing an embargo on U.S. walnuts. Exports dropped causing increases in inventory levels. Another model was estimated where the dependent variable was US total consumption of walnuts plus California exports minus US imports.

The dependent variable captures domestic plus net export demand. Again, sequential structural tests indicated a structural break around 1983. The results from this estimated equation yielded a total own-price elasticity of demand for walnuts of –0.354 prior to 1983 and an estimated value of –0.061 after 1983. The estimated coefficient of determination for this equation was 0.923. The wide difference between the estimated own-price elasticities of demand between the two time periods may be due, in part, to structural changes mentioned above. The primary policy implications are that the demand for walnuts is inelastic with little evidence that almonds are an important substitute for walnuts. The coefficient of determination is 0.72. The Durbin-Watson calculated value of 1.78 does not support evidence of negative correlation. The “see-saw” pattern exhibited by walnut yields is more consistent that than for almond yields and thus the dummy variable included in the systematic part of the equation picks up the alternative bearing phenomenon . The estimated coefficient on D is positive and highly significant as expected and the coefficient on March temperature is positive as expected but not significant. There is a little evidence of a positive time trend. The lagged price coefficient is unexpectedly negative but not significant.Based on the models estimated for almonds and walnuts the own-price elasticity of US domestic demand for almonds was found to be between –0.35 and -0.48.. These estimates are inelastic and imply that almond producers are vulnerable to large swings in prices of almonds due to supply shifts. Similar estimates of the own-price elasticity of US domestic demand for walnuts were obtained. The estimated own-price elasticities for walnuts ranged from –0.25 to –0.28. Walnut producers face the same marketing situation as almond producers, that is, prices of walnuts fluctuate widely due to shifts in the supply function of walnuts. The estimated acreage response equation for almonds indicated that producers respond positively to lag prices. The estimated short-run price elasticity of acreage for almonds was 0.12 and significant. This is relatively small but does indicate that producers are responsive to increases in prices over time. For walnuts the estimated short-run price elasticity of acreage was 0.02 and significant. Again, the value is small but positive. The estimated yield equations for both almonds and walnuts reflected a significant alternate-year phenomenon. For almonds the phenomenon was capture by a significant and negative auto correlation coefficient. For walnuts it was captured by a dummy variable. Yields for almonds are significantly affected by a time trend. Yields of almonds are increasing over the time period 1979-2001, based on the estimated yield equation. For walnuts, yields were positively affected by temperature in March and a time trend, but neither coefficient was significant.A SUR demand system was estimated for walnuts and almonds. The domestic own-price elasticity of demand for walnuts was estimated to -0.14 and that of almonds – 0.20 with almonds being significant. The estimated income elasticity of demand for walnuts was 0.82 and that for almonds was 1.05 with the estimated income elasticity in the almond equation being significant.The primary policy implication based on these results is that almond and walnut producers are facing an inelastic domestic demand for their products. Combine this with the volatility of the supply function due to temperature and rainfall changes, wide variations in prices exist which lead to wide variations in profits from year to year. Storage, improved technology, and an expanding export market are factors that may mitigate the volatile market conditions facing US producers of almonds and walnuts.