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.

摘要 随机生产前沿模型（stochastic production frontier models）被广泛应用于微观计量经济学领域，近数十年来，其应用范畴已被证实愈发多元丰富。然而，针对随机生产前沿模型中内生性问题的相关研究仍较为稀缺。本文提出两种基于技术无效率（technical inefficiency）主流分布形式、包含内生变量的随机生产前沿模型。同时，我们推导了解析梯度向量，以在合理的计算时间成本下获得最优性能。本文所提出的方法论基于单步与两步极大似然估计框架，可针对单个或两个误差项处理内生性与异方差性问题，并已在R语言中实现。最后，我们借助巴西农业普查的市级数据集展示了该方法的应用实例。结果显示：资本在生产函数中占据主导地位，信贷获取与技术援助均为内生变量，而收入集中度似乎会通过更密集的技术使用阻碍生产包容性的提升。