Stochastic Production Frontier and Technical Inefficiency: A Sensitivity Analysis

Abstract

The present paper focuses attention on the sensitivity of technical inefficiency to most commonly used one-sided distributions of the inefficiency error term, namely the truncated normal, the half-normal, and the exponential distributions. A generalized version of the half-normal, which does not embody the zero-mean restriction, is also explored. For each distribution, the likelihood function and the counterpart of the estimator of technical efficiency are explicitly stated (Jondrow, J., Lovell, C. A. K., Materov, I. S., Schmidt, P. ([1982]), On estimation of technical inefficiency in the stochastic frontier production function model, J. Econometrics19:233-238). Based on our panel data set, related to Tunisian manufacturing firms over the period 1983-1993, formal tests lead to a strong rejection of the zero-mean restriction embodied in the half normal distribution. Our main conclusion is that the degree of measured inefficiency is very sensitive to the postulated assumptions about the distribution of the one-sided error term. The estimated inefficiency indices are, however, unaffected by the choice of the functional form for the production function.Stochastic frontier, Farrell's technical inefficiency, Unbalanced panel data, Composed disturbance error, One-sided distribution,

Nonparametric frontier estimation via local linear regression

“…These parametric assumptions may lead to misspecification of rðÁÞ and invalidate any optimal derived properties of the proposed estimators (generally maximum likelihood), and consequently lead to erroneous inference. In addition, as recently pointed out by Baccouche and Kouki (2003), estimated inefficiency levels and firm efficiency rankings are sensitive to the specification of the joint density of ðY t ; X t Þ. Hence, different density specifications can lead to different conclusions regarding technology and efficiency from the same random sample.…”

The impact of TennCare on hospital efficiency

“…Recently, Baccouche and Kouki [52] examined the sensitivity of SFA cost efficiency estimates to the choice of the distribution of the inefficiency error term when using a panel of firms. 4 They found that the generalized halfnormal and truncated normal provide more reliable inefficiency estimates than the exponential and the half normal.…”

Likelihood ratio tests for model selection of stochastic frontier models

“…Some of the literature has shown that measures of the inefficiencies based on models with misspecified distributions on the one-sided error u i can be misleading. For instance, Baccouche and Kouki (2003) pointed out that estimated inefficiency indices are sensitive to the most commonly used one-sided distributions of u i , but are insensitive or unaffected by the choice of the parametric functional form of the production frontier. A similar result is also found in Caudill and Ford (1993), where heteroscedasticity in the one-sided error component leads to overestimation of the intercept and underestimation of the slope and the variance of the two-sided error component in the linear parametric frontier production function.…”