A Post-Truncation Parameterization of Truncated Normal Technical Inefficiency

In this paper we consider a stochastic frontier model in which the distribution of technical inefficiency is truncated normal. In standard notation, technical inefficiency u is distributed as N^+ (μ,σ^2). This distribution is affected by some environmental variables z that may or may not affect the level of the frontier but that do affect the shortfall of output from the frontier. We will distinguish the pre-truncation mean (μ) and variance (σ^2) from the post-truncation mean μ_*=E(u) and variance σ_*^2=var(u). Existing models parameterize the pre-truncation mean and/or variance in terms of the environmental variables and some parameters. Changes in the environmental variables cause changes in the pre-truncation mean and/or variance, and imply changes in both the post-truncation mean and variance. The expressions for the changes in the post-truncation mean and variance are quite complicated. In this paper, we suggest parameterizing the post-truncation mean and variance instead. This leads to simple expressions for the effects of changes in the environmental variables on the mean and variance of u, and it allows the environmental variables to affect the mean of u only, or the variance of u only, or both.