Type II failure and specification testing in the Stochastic Frontier Model

Posted: January 7, 2021 in Research, Research papers
Tags: , , , ,

This has just been accepted in European Journal of Operational Research and the Author’s accepted version has been uploaded here. It has been written together with Christopher Parmeter of Miami University.

There are some nice theoretical results related to Skewness and Excess Kurtosis for the composite distributions used in Stochastic Frontier Analysis, but to me the main contribution is a specification test that uses only OLS residuals and it appears the most powerful such test to date. With this test, one can first test for the error specification after just an OLS regression, and then code the maximum likelihood estimator.

Abstract. 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.

  1. Clive Nicholas says:

    Hello Alecos,

    When might a social scientist analysing social or political data use stochastic frontier models, because I can’t think of any?


    • In any situation where bargaining takes place, one can use the two-tier stochastic frontier model. For applications in International Relations check Wang Y (2016a). Bargaining matters: an analysis of bilateral aid to developing countries. Journal of International Relations and Development. https://doi.org/10.1057/jird.2016.8 and
      Wang Y (2016b). The effect of bargaining on US economic aid. International Interactions, 42(3):479-502.
      Another example: think incarcerations. A researcher will have certain variables that can be used as explanatory variables for number of incarcerations, but it is likely that for some causal factors data won’t exist. The effect of these factors on the outcome variable can be estimated using a stochastic frontier model (single-tier or 2TSF as the case may be). Maybe you would want to read Papadopoulos, A. (2020). “The Two-tier Stochastic Frontier Framework (2TSF): Measuring Frontiers wherever they may exist”. in Parmeter C.F. and Sickles R. (eds) Advances in Efficiency and Productivity Analysis, Springer.

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