A Gamma-distributed stochastic frontier model

TLDR

The authors extend the Aigner–Lovell–Schmidt stochastic frontier model by replacing the half‑normal inefficiency term with a two‑parameter Gamma distribution and introduce a corrected OLS estimator based on moments. They employ maximum‑likelihood estimation, which requires evaluating intractable integrals, and propose two numerical methods for computing these integrals, applying the resulting model to illustrative data. In their application, the Gamma‑based model produces results that differ markedly from those obtained with three alternative formulations.

Abstract

We modify the stochastic frontier model of Aigner, Lovell, and Schmidt to allow the one-sided part of the disturbance to have a two-parameter Gamma distribution rather than the less flexible half-normal distribution. Maximum-likelihood estimation and the estimation of firm-specific inefficiency estimates require the evaluation of integrals which have no closed form and for which there are no polynomial approximations available. We consider two methods of computing these integrals. We also present a corrected OLS estimator based on the methods of moments. An application is presented for illustration. We find that for these data, the gamma distribution produces results which differ noticeably from those of three alternative formulations.