Estimating production uncertainty in stochastic frontier production function models

One of the main purposes of the frontier literature is to estimate ineffici ency. Given this objective, it is unfortunate that the issue of estimating "firm-specific'' inefficiency in cross sectional context has not received m uch attention. To estimate firm-specific (technical) inefficiency, the stan dard procedure is to use the mean of the inefficiency term conditional on t he entire composed error as suggested by Jondrow, Lovell, Materov and Schmi dt (1982). This conditional mean could be viewed as the average loss of out put (return). It is also quite natural to consider the conditional variance which could provide a measure of production uncertainty or risk. Once we h ave the conditional mean and variance, we can report standard errors and co nstruct confidence intervals for firm level technical inefficiency. Moreove r, we can also perform hypothesis tests. We postulate that when a firm atte mpts to move towards the frontier it not only increases its efficiency, but it also reduces its production uncertainty and this will lead to shorter c onfidence intervals. Analytical expressions for production uncertainty unde r different distributional assumptions are provided, and it is shown that t he technical inefficiency as defined by Jondrow et al. (1982) and the produ ction uncertainty are monotonic functions of the entire composed error term . It is very interesting to note that this monotonicity result is valid und er different distributional assumptions of the inefficiency term. Furthermo re, some alternative measures of production uncertainty are also proposed, and the concept of production uncertainty is generalized to the panel data models. Finally, our theoretical results are illustrated with an empirical example.