Technical efficiency and inefficiency: Reassurance of standard SFA models and a misspecification problem

This paper formally proves that if inefficiency ($u$) is modelled through the variance of $u$ which is a function of $z$ then marginal effects of $z$ on technical inefficiency ($TI$) and technical efficiency ($TE$) have opposite signs. This is true in the typical setup with normally distributed random error $v$ and exponentially or half-normally distributed $u$ for both conditional and unconditional $TI$ and $TE$. We also provide an example to show that signs of the marginal effects of $z$ on $TI$ and $TE$ may coincide for some ranges of $z$. If the real data comes from a bimodal distribution of $u$, and we estimate model with an exponential or half-normal distribution for $u$, the estimated efficiency and the marginal effect of $z$ on $TE$ would be wrong. Moreover, the rank correlations between the true and the estimated values of $TE$ could be small and even negative for some subsamples of data. This result is a warning that the interpretation of the results of applying standard models to real data should take into account this possible problem. The results are demonstrated by simulations.