In this paper we consider a fixed-effects stochastic frontier model. That is, we have panel data, fixed individual (firm) effects, and the usual stochastic frontier analysis (SFA) composed error.
Maximum likelihood estimation (MLE) of this model has been considered by Greene, 2005a and Greene, 2005b. It is subject to the “incidental parameters problem”, that is, to possible inconsistency due to the number of parameters growing with the number of firms. In the linear regression model with normal errors, it is known that the MLE of the regression coefficients is consistent, and the inconsistency due to the incidental parameters problem applies only to the error variance. Greene’s simulations suggest that the same is true in the fixed effects SFA model.
In this paper we take a somewhat different approach. We consider MLE based only on the joint density of the deviations from means. In the linear regression model with normal errors, this estimator is the same as the full MLE for the regression coefficients, but it yields a consistent estimator of the error variance. For the SFA model, the MLE based on the deviations from means is not the same as the full MLE, and it has the advantage of not being subject to the incidental parameters problem.
The derivation of the joint density of the deviations from means is made possible by results in the statistical literature on the closed skew normal family of distributions. These results may be of independent interest to researchers in this area.
Simulations indicate that our within MLE estimator performs quite well in finite samples.