Stochastic production frontiers and panel data: A latent variable framework

This paper deals with the issues of estimating production frontier and measuring efficiency from a panel data set. First, it proposes an alternative method for the estimation of a production frontier on a short panel data set. The method is based on the so-called mean-and-covariance structure analysis which is closely related to the generalized method of moments. One advantage of the method is that it allows us to investigate the presence of correlations between individual effects and exogenous variables without the requirement of some available instruments uncorrelated with the individual effects as in instrumental variable estimation. Another advantage is that the method is well suited to a panel data set with a short number of periods. Second, the paper considers the question of recovering individual efficiency levels from the estimates obtained from the mean-and-covariance structure analysis. Since individual effects are here viewed as latent variables, they can be estimated as factor scores, i.e. weighted sums of the observed variables. We illustrate the proposed methods with the estimation of a stochastic production frontier on a short panel data of French fruit growers.