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. The focus is on the case of a normal/gamma SFM and the heavy–tailed stable/gamma SFM. In the first case the moment generating function is used as tool while in the latter case the characteristic function of the error term is employed. In both cases our test statistics are formulated as weighted integrals of properly standardized data. The new normal/gamma test is consistent, and is shown to have an intrinsic relation to moment–based tests. The finite–sample behavior of resampling versions of both tests is investigated by Monte Carlo simulation, while several real–data applications are also included.