Endogeneity in Stochastic Frontier Models

Stochastic frontier models are typically estimated by maximum likelihood (MLE) orcorrected ordinary least squares. The consistency of either estimator depends on exogeneity of the explanatory variables (inputs, in the production frontier setting). We will investigate the case that one or more of the inputs is endogenous, in the simultaneous equation sense of endogeneity. That is, we worry that there is correlation between the inputs and statistical noise or inefficiency. In a standard regression setting, simultaneity is handled by a number of procedures that are numerically or asymptotically equivalent. These include 2SLS; using the residual from the reduced form equations for the endogenous variables as a control function; and MLE of the system that contains the equation of interest plus the unrestricted reduced form equations for the endogenous variables (LIML). We will consider modifications of these standard procedures for the stochastic frontier setting. The paper is mostly a survey and combination of existing results from the stochastic frontier literature and the classic simultaneous equations literature, but it also contains some new results.