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

TL;DR

This paper proposes new goodness-of-fit tests for the error distribution in stochastic frontier models, using empirical transforms based on moment generating and characteristic functions, with demonstrated consistency and finite-sample effectiveness.

Contribution

It introduces novel test statistics for normal/gamma and stable/gamma SFMs based on empirical transforms, enhancing model validation methods.

Findings

The normal/gamma test is consistent.

Resampling methods improve finite-sample performance.

Applications demonstrate practical utility.

Abstract

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.