Estimating Stochastic Production Frontiers: A One-stage Multivariate Semi-Nonparametric Bayesian Concave Regression Method

Abstract: This paper describes a method to estimate a production frontier that satisfies the axioms of monotonicity and concavity in a non-parametric Bayesian setting. An inefficiency term that allows for significant departure from prior distributional assumptions is jointly estimated in a single stage with parametric prior assumptions. We introduce heteroscedasticity into the inefficiency terms by local hyperplane-specific shrinkage hyperparameters and impose monotonicity using bound-constrained local nonlinear regression. Our minimum-of-hyperplanes estimator imposes concavity. Our Monte Carlo simulation experiments demonstrate that the frontier and efficiency estimations are competitive, economically sound, and allow for the analysis of larger datasets than existing nonparametric methods. We validate the proposed method using data from 2007-2010 for Japan's concrete industry. The results show that the efficiency levels remain relatively high over the time period.