A penalization approach for estimating inefficiency in stochastic frontier panel models

Abstract

Efficiency analysis is essential for evaluating the performance of entities that deliver essential or standardized services. The estimator proposed by Jondrow et al. (1982) is widely used in this context, but it has been criticized for several shortcomings: it tends to bias inefficiency estimates toward the mean, distorts the distribution, and misrepresents the conditional distribution of inefficiency—especially in cross-sectional data.

Zeebari et al. (2023) propose a regularization-based alternative that aligns sample and theoretical moments; however, this method is primarily designed for cross-sectional applications and does not extend naturally to panel data.

In response, this paper introduces a penalized mode estimator for unit inefficiency in panel data. The estimator accounts for heteroskedasticity in both inefficiency and idiosyncratic errors. A closed-form expression is derived, and Monte Carlo simulations demonstrate its superior performance compared to existing methods. An empirical application using data from electricity providers in Australia, Canada, and New Zealand highlights the practical advantages of the proposed approach.