Stochastic Frontier Models with Bounded Inefficiency

Abstract

This paper introduces a new model of the stochastic production frontier that incorporates an unobservable bound for inefficiency, which is naturally instituted by market competition forces. We consider doubly truncated normal, truncated half-normal, and truncated exponential distributions to model the inefficiency component of the error term. We derive the analytical form of density function for the error term of each specification, expressions of the conditional mean of inefficiency levels, and provide proofs of local identifiability of these models under differing assumptions about the deep parameters of the distributions. We examine skewness properties of our new estimators and provide an explanation for the finding of positive (“wrong”) skewness in many applied studies using the traditional stochastic frontier model. We extend the model to the panel data setting and specify a time-varying inefficiency bound as well as time-varying efficiencies. A Monte Carlo study is conducted to study the finite sample performance of the maximum likelihood estimators in cross-sectional settings. Lastly, we illustrate the use of our model to the analysis of efficiencies in the US banking industry from 1984 to 2009 using a recently developed panel of over 4,000 banks and also compare our findings to those based on a set of competing specifications of the stochastic frontier model. We find substantial increases in efficiency after the regulatory reforms of the 1980s but also substantial backsliding during the 2005–2009 period presaging the financial meltdown experienced in the US and worldwide.