Orthogonality conditions for identification of joint production technologies
Axiomatic nonparametric approach to the estimation of stochastic distance functions
The classic econometric approach treats productivity as a residual term of the standard microeconomic production model. Critics of this approach argue that productivity shocks correlate with the input factors that are used as explanatory variables of the regression model, which causes an endogeneity problem. This paper sheds some new light on this issue from the perspective of the production theory. We first examine the standard cost minimization problem to demonstrate that even if the observed inputs and outputs are endogenous, consistent estimation of the input distance function is possible under certain conditions. This result reveals that the orthogonality conditions required for econometric identification critically depend on the specification of the distance metric, which suggests the directional distance function as one possible solution to the endogeneity problem. We then introduce a stochastic data generating process of joint production where all inputs and outputs correlate with inefficiency and noise. We show that an appropriately specified direction vector can provide the orthogonality conditions required for identification of the directional distance functions. A consistent nonparametric estimator of the directional distance function is developed, which satisfies the essential axioms of the production theory. Specification of the direction vector is examined through an application to electricity distribution firms.