Functional form, model specification, and analytic simplification in multiple-output production analysis

Abstract

Aggregate output supply and input demand models of agricultural production were specified for each of four geographically diverse states (California, Iowa, Texas, and Florida) using three locally flexible functional forms (translog, generalized Leontief, and normalized quadratic). Tests of nonjointness and homothetic separability were conducted to identify opportunities for analytic simplification. Results indicated that some model simplification was clearly justifiable in all states but the extent of justified simplification was affected both by state and by choice of functional form. Designed for consistency with competitive theory, the above nonrejected simplifying hypotheses, and multi-stage choice, aggregate dual models were employed to examine multiple-output production relationships in each state. Homogeneity, convexity, and symmetry were maintained in all estimations. Convexity was tested and not rejected for any model. Monotonicity was checked at every observation and was significantly rejected only in Iowa for two functional forms. All three functional forms were employed to estimate systems of output supply and input demand (or share) equations, derive Marshallian elasticites, and determine the extent to which these policy-relevant results were dependent on choice of functional form and state. Similarities in selected own-price elasticities were observed across all functional forms in California, Iowa, and Florida, and across all states for the generalized Leontief and normalized quadratic. Common patterns across functional forms and states were indicated by a few cross-price elasticities. Multistage modeling was then performed to obtain fully disaggregated parameter estimates utilizing the normalized quadratic functional form. Curvature properties were tested and were not significantly violated in any of the states for any suboptimization model...