Abstract: 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.
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