Abstract
•Empirical skewness and kurtosis can serve as useful diagnostics.•Present maximal bounds for skewness/kurtosis of error from stochastic frontier model.•Construct test of correct distributional assumptions.•Provide several empirical applications of test.
The distributional specifications for the composite regression error term most often used in stochastic frontier analysis are inherently bounded as regards their skewness and excess kurtosis coefficients. We derive general expressions for the skewness and excess kurtosis of the composed error term in the stochastic frontier model based on the ratio of standard deviations of the two separate error components as well as theoretical ranges for the most popular empirical specifications. While these simple expressions can be used directly to assess the credibility of an assumed distributional pair, they are likely to over reject. Therefore, we develop a formal test based on the implied ratio of standard deviations for the skewness and the kurtosis. This test is shown to have impressive power compared with other tests of the specification of the composed error term. We deploy this test on a range of well-known datasets that have been used across the efficiency community. For many of them we find that the classic distribution assumptions cannot be rejected.
