Estimation of input-oriented technical efficiency using a nonhomogeneous stochastic production frontier model

Technical inefficiency can be modeled as either input-oriented (IO) or output-oriented (OO). However, in the estimation of parametric stochastic production frontier models which use maximum likelihood method only the OO measure is used. In this article we consider a simple nonhomogeneous production function and estimate it with both IO and OO specifications. A sample of 80 Spanish dairy data (1993-1998) is used to estimate both models. We consider one output (liters of milk) and four variable inputs (viz., number of cows, kilograms of concentrates, hectares of land, and labor [measured in man-equivalent units]). We find that returns to scale (RTS) and technical efficiency results derived from these models are different because either estimated technologies are different, or they are evaluated at different points. Using a Monte Carlo analysis we show that if RTS is close to unity differences in the estimates of RTS and technical efficiency are smaller. This holds true for estimates of both RTS and technical efficiency.