Estimating Functional Forms with Special Reference to Agriculture: Discussion

Gallant, Wohlgenant, and Chalfant each have presented challenging papers. Readers would benefit from the extended versions of the papers which were available to the reviewers and are available from the authors. What insights and conclusions are given which will improve the economic analysis of agriculture? Gallant points out that flexible functional forms such as the translog retain the augmenting hypothesis induced by model specification. He argues for the seminonparametric methodology of the Fourier flexible form. The ties with theory are in treating the Fourier flexible form as if it were the "true" function and ties with nonparametric approaches are by increasing numbers of parameters with sample size. Gallant has developed elsewhere the desirable properties of this estimator and also notes some limitations, such as possible wild oscillations at discontinuity points. He argues that further work may uncover means to correct this problem. It sounds promising. How does it work? In the applied work of both Wohlgenant and Chalfant, the elasticities cycle over the time period. Wohlgenant finds such results plausible, whereas Chalfant finds the cycling signs and magnitudes of elasticities to be unacceptable. It is not surprising to find that the introduction of sine and cosine terms of a Fourier function "cause" cyclical behavior. A question: Is it possible that the estimating equation is consistent with two quite different theories? Waugh and Norton used sine and cosine terms to estimate seasonal demand for fish. Using graphics and usual measures of seasonal demand as preliminary analysis, they then found that the sine and cosine terms nicely replicated the cyclical pattern of prices over the season. Coefficients were statistically significant. Thus, the true demand curve did have a cyclical component captured by the trigonometric function. They reference the work of Harold Davis of the Cowles Commission, who had used the approach in studying cyclical economic time series. It would appear that we may have the not uncommon situation of an estimating equation that is identical for two quite dissimilar economic models: the Gallant-type model where the goal is global approximation and the Waugh-type model where cyclical behavior is postulated. The difference is in the interpretation of the coefficients as in extrapolative versus adaptive expectations. Wohlgenant argues that the Fourier-flexible form provides a reasonable pattern of direct price and income coefficients over time. His expanded paper allows one to calculate the nonfood cross elasticities that change from negative to positive values, which might warrant additional analysis or explanation. The statistical comparisons favor the Fourier over the translog and the generalized Leontief. However, one notes that only one of four sine-cosine terms differ significantly from zero. One would like more and different data to explain these changes over time. Are we expecting too much from one data set? As to the results from the almost ideal demand system, an eleven-commodity model reported by Blanciforti and Green resulted in negative and reasonable food elasticities. Perhaps the level of aggregation (i.e., food versus nonfood) did not allow sufficient disaggregation for reasonable estimates. As to the magnitude of the expenditure elasticity, it includes both a quantity and quality component, and if services and so forth are positively related to income, the expenditure elasticity will exceed the quantity elasticity. In our 1971 study, a quantity conc pt was used. Overall, Wohlgenant has raised some challenging issues on demand patterns over time which deserve further exploration. Chalfant presents results for an aggregate cost function for U.S. agriculture. This is a well-reasoned paper that emphasizes tradeoffs among models. He points out that properties of precision or stability in elasticities are Gordon A. King is a professor of agricultural economics, University of California, Davis.