Choice of Functional Form for Agricultural Production Analysis

Abstract

Economic theory is useful in many aspects of model specification, such as identifying relevant variables for a supply equation or suggesting homogeneity restrictions, curvature requirements, or symmetry restrictions across equations. Theory is seldom sufficient, though, to determine functional form, either a hypothesized true form or a reasonable approximation. Because the validity of statistical tests and inferences are conditional on model specification, the functional form should be appropriate for the specific research use or hypotheses to be tested, capture applicable theoretical concerns, and also allow the data to speak. In addition to theoretical considerations, empirical priors (e.g., knowledge about the technology or industry characteristics) and/or model pretesting are often considered by the analyst in choosing a functional form. The choice of functional form is not a trivial matter. Empirical estimates, including own-price elasticities, elasticities of substitution, returns to scale, and model specification test conclusions are often sensitive to choice of functional form (i.e., Berndt and Khaled; Chalfant; Swamy and Binswanger; Shumway and Lim). Perhaps of greatest importance is the fact that predicted responses of policy analyses using an inferior functional form may be biased and inaccurate, thus posing serious problems for policy impact analysis. Identifying suitable functional forms before estimating parameters of concern is clearly important. The most frequently used functional forms in production (and consumption) analyses are second-order Taylor-series expansions, also termed locally or just flexible functional forms.' These forms have a sufficient number of parameters to represent comparative statics at a point without imposing any restrictions across effects (Fuss, McFadden, and Mundlak). Three flexible functional forms dominate the recent empirical production economics literature translog, generalized Leontief, and quadratic. An examination of the 113 published articles cited by Fox and Kivanda and Shumway that estimated static dual models of agricultural production between 1972 and 1993 revealed that one-half used the translog (TL) functional form, one-fourth used the normalized quadratic (NQ), one-eighth used the generalized Leontief (GL), and one-eighth used a variety of other functional forms. Empirical priors for specifying functional form for an agricultural production model are often limited, both because of the small number of functional form tests conducted and because of differences in findings among them. For example, using different data sets for U.S. agriculture, Gottret failed to reject any of these three functional forms for a restricted profit function, Ornelas, Shumway, and Ozuna failed to reject only the NQ for a restricted profit function, and Chalfant rejected both functional David P. Anderson is an Agricultural Economist, Livestock Marketing Information Center; Andrew Tan Khee Guan is a lecturer, Universiti Sains Malaysia; and the remaining authors are, respectively, Research Assistant, Graduate Student, Research Assistant, and Professor of Agricultural Economics, Texas A&M University. The authors are listed alphabetically. Senior authorship is shared equally. The constructive comments of anonymous RAE reviewers on earlier drafts of this manuscript are gratefully acknowledged. The manuscript reports research conducted by the Texas Agricultural Experiment Station, Texas A&M University System. 'They can be expansions of a monotonic transformation of the underlying function, not necessarily of the function itself.