Endogeneity in Stochastic Production Frontier With One and Two-Step Models: An Application With Municipal Data From the Brazilian Agricultural Census

Abstract

Stochastic production frontier models are widely used in microeconometrics and, in the last decades, have been proven to be versatile in their range of applications. However, there are few studies concerning endogeneity in stochastic production frontier models. Here we present two stochastic production frontier models with endogenous variables based on the main distributions for the technical inefficiency. We also derive analytic gradient vectors to obtain the best performance at a reasonable computational time cost. The methodology presented here is based on one and two-step maximum likelihood estimation, allows for endogeneity and heteroscedasticity in relation to one or both error terms, and is implemented in R language. Finally, we illustrate an application with municipal data from the Brazilian agricultural census. The results show that capital dominates the production function, credit access and technical assistance are endogenous, and income concentration seems to impede productive inclusion through the more intensive use of technology.