Specification tests for normal/gamma and stable/gamma stochastic frontier models based on empirical transforms

Goodness-of-fit tests for the distribution of the composed error term in a Stochastic Frontier Model (SFM) are suggested. We focus on the case of a normal/gamma SFM and the heavy-tailed stable/gamma SFM. In the first case we use the moment generating function as tool while in the latter case the characteristic function of the error term and formulate our test statistics as weighted integrals of properly standardized data. The new tests are consistent, and for the normal/gamma SFM are shown to have an intrinsic relation to moment-based tests. The finite-sample behavior of a resampling version of the new test for the normal/gamma SFM is investigated by Monte Carlo simulations, while the corresponding test for the stable/gamma SFM is applied on several real-data sets.