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

Richard Howitt,Siwa Msangi

doi:10.3390/e16031349

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.

Highlights

This paper develops a method to estimate disaggregated production function models from minimal data sets
This paper shows that a generalized maximum entropy (GME) approach makes it is possible to construct flexible-form production function models from a data set of modest size
A researcher can construct similar, theoretically consistent, flexible-form production models using data ranging from small samples with minimal degrees of freedom to full econometric data sets with standard degrees of freedom

Summary

Introduction

This paper develops a method to estimate disaggregated production function models from minimal data sets. Disaggregated models of bio-economic systems serve two main purposes. They allow the distributional effects of policies to be measured across farm size or location. The distributional effects of a policy have a greater political impact than efficiency gains. Heterogeneity is often present in the sample, which results in spatial differences in policy impacts and input use that are important to model. Throughout the paper, we assume that sample size is fixed and strive to maximize the policy information derivable from such a data set. We focus our attention on predicting the impacts of a policy on farmers in terms of their net income and use of natural resources in production

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