On the econometric estimation of the distance function representation of a production technology

Recent developments in the econometric estimation of multi-output, multi-input distance functions have provided a promising new solution to the single-output restriction implicit in the standard production function. However, a suspicion that regressor endogeneity may introduce possible simultaneous equations bias has concerned some econometricians. In this paper we show that, under profit maximising behaviour, distance functions face no greater danger from such bias than their production function cousins. Furthermore, we prove that ordinary least squares (OLS) provides consistent estimates of an input distance function under an assumption of cost minimising behaviour. We also prove that OLS provides consistent estimates of an output distance function under an assumption of revenue maximising behaviour. These results are established for the Cobb-Douglas and translog functional forms, which are the two most commonly used functional forms in applied analyses. Our results provide strong support for the direct estimation of distance functions, and indicate that the instrumental variables (IV) methods, proposed by some authors, may not be required in many cases.