Inferring technological parameters from incomplete panel data

This paper contributes to production economics by providing a procedure to estimate cost models with incomplete panel data and by illustrating how this procedure can be implemented using a panel data set of trucking firms. Most panel data sets of firms presently available are incomplete for numerous reasons, including mergers, acquisitions, bankruptcies, incomplete surveys, etc. Hence, in this type of sample, when a firm is missing for at least one period, all the variables relevant to this firm are missing for the same period. Our method jointly considers the cost-input demand system and a bivariate probit selection model of entry to and exit from the sample. Random firm-specific effects are included in both the cost and selection models. The inclusion of random effects in the models makes their joint estimation more delicate. However, some restrictions are imposed on the distribution of the random variables in order to simplify the analysis. For instance, we assume that the variances and covariances of the random variables are constant over time. The method is applied to an incomplete panel of Ontario (Canada) trucking firms. A test for selectivity bias on this panel reveals potential bias related to exit but not to entry. Estimation results indicate that the bias can be reduced and even eliminated with an appropriate specification of the cost model, at least for the sample used.