It is formally proven that if inefficiency (u) is modelled through its variance, considered as a function of exogenous variables z, then the marginal effects of z on technical inefficiency (TI) and technical efficiency (TE) have opposite signs in the typical setup with a normally distributed random error and an exponentially or half-normally distributed u. This is true for both conditional and unconditional TI and TE. An example is provided to show that the 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 a model is estimated with an exponential or half-normal distribution for u, the estimated efficiency and the marginal effect of z on TE could 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 the data. This is a warning that in the case when the true (real life) distribution of the inefficiency is bimodal, commonly used standard SFA models could lead to wrong policy recommendations. The kernel density plot of the residuals is suggested as a diagnostic plot. The results are illustrated by simulations.
- Model misspecification
- Productivity and competitiveness
- Stochastic frontier analysis