Entropy Estimation of Disaggregate Production Functions: An Application to Northern Mexico

Abstract

This paper demonstrates a robust maximum entropy approach to estimating flexible-form farm-level multi-input/multi-output production functions using minimally specified disaggregated data. Since our goal is to address policy questions, we emphasize the model’s ability to reproduce characteristics of the existing production system and predict outcomes of policy changes at a disaggregate level. Measurement of distributional impacts of policy changes requires use of farm-level models estimated across a wide spectrum of sizes and types, which is often difficult with traditional econometric methods due to data limitations. We use a two-stage approach to generate observation-specific shadow values for incompletely priced inputs. We then use the shadow values and nominal input prices to estimate crop-specific production functions using generalized maximum entropy (GME) to capture individual heterogeneity of the production environment while replicating observed inputs and outputs to production. The two-stage GME approach can be implemented with small data sets. We demonstrate this methodology in an empirical application to a small cross-section data set for Northern Rio Bravo, Mexico and estimate production functions for small family farms and moderate commercial farms. The estimates show considerable distributional differences resulting from policies that change water subsidies in the region or shift price supports to direct payments