Estimation of Input Distance Functions: A System Approach

This article offers a methodology to address the endogeneity of inputs in the input distance function (IDF) formulation of the production processes. We propose to tackle endogenous input ratios appearing in the normalized IDF by considering a flexible (simultaneous) system of the IDF and the first-order conditions from the firm's cost minimization problem. Our model can accommodate both technical and (input) allocative inefficiencies amongst firms. We also present the algorithm for quantifying the cost of allocative inefficiency. We showcase our cost-system-based model by applying it to study the production of Norwegian dairy farms during the 1991--2008 period. Among other things, we find both an economically and statistically significant improvement in the levels of technical efficiency among dairy farms associated with the 1997 quota scheme change, which a more conventional single-equation stochastic frontier model appears to be unable to detect.