Technical efficiency and inefficiency: SFA misspecification

Abstract

The effect of external factors z on technical inefficiency (T I) in stochastic frontier (SF) production models is often specified through the variance of inefficiency term u. In this setup the signs of marginal effects of z on T I and technical efficiency T E identify how one should control z to increase T I or decrease T E. We prove that these signs for T I and T E are opposite for typical setups with normally distributed random error v and exponentially or half-normally distributed u for both conditional and unconditional cases.On the other hand, we give an example to show that signs of the marginal effects of z on T I and T E may coincide, at least for some ranges of z. In our example, the distribution of u is a mixture of two distributions, and the proportion of the mixture is a function of z. Thus if the real data comes from this mixture distribution, and we estimate model parameters with an exponential or half-normal distribution for u, the estimated efficiency and the marginal effect of z on T E would be wrong. Moreover for a misspecified model, the rank correlations between the true and the estimated values of