The Journal of Productivity Analysis, 3, 45-65 (1992) 0 1992 Kluwer Academic Publishers, Boston. Manufactured in the Netherlands. Allowing for Inefficiency in Parametric Estimation of Production Functions for Urban Transit Firms BERNARD THIRY Universite’ de Li&e and CIRIEC, Lit& HENRY TULKENS CORE, Universitb Catholique de Louvain and Facul& Universitaires Saint-Louis, Bruxelles Abstract Efficient versus inefficient observations are first identified and evaluated numerically by the nonparametric free disposal hull (FDH) method. Next, parametric production frontiers are obtained by means of estimating translog production functions through OLS applied to the subset of efficient observations only. Technical progress is included at both stages. Monthly data from three urban transit firms in Belgium, to which this two-stage technique is ap- plied, show widely varying degrees of efficiency over time and across firms, and much less technical progress than standard (i.e., non frontier) econometric estimates suggest. 1. Motivation, methodology and antecedents In this article, we wish to experiment with, and further develop, a method designed to account for the possibility of technically inefficient behavior, in the process of estimating the parameters of production functions with technical progress. Our motivation comes from both institutional and historical characteristics of three urban transit firms in Belgium that we have encountered in the course of a wider study of these firms’ economic performance (Thiry and Tulkens [1988]). The three companies under review are public enterprises run by autonomous local management under the supervision of the Ministry of Communications. For many years, this supervision has been rather loose and substantially increasing deficits were incurred, covered by the overall State budget without much public discussion. Towards the end of 1982, however, the Belgian government dras- tically changed its policy, imposing severe financial constraints on these firms and reorgan- izing their top management. These facts suggest that for these firms, at least until the imposed changes, the usual assumption that they operated on their production function, that is, on the boundary of their production set, can be questioned. However, prevailing methods of estimating produc- tion functions do rest on this assumption. Hence, the parameter estimates they yield are bound to be biased. Moreover, if one is willing to hypothesize that the 1982 changes may have had an impact on the degree of efficiency on the firms’ operations, the production function estimation procedure should allow for possible changes over time in this respect. Considerations of this nature are clearly at the origin of the literature on production fron- tiers.’ This literature proposes several parametric estimation methods allowing for ineffi- ciency that differ not only in their statistical properties, but more fundamentally, in the 41