Dependence of the technical efficiency on the uncertainty of the inefficiency error
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Stochastic frontier analysis (SFA) production models usually imply heteroscedasticity of the inefficiency. A technical efficiency depends on inputs of the model and the uncertainty of an inefficiency error, which in turn depends on heteroscedasticity factors. The dependence of the technical efficiency on the uncertainty of the inefficiency error is unclear, as the functional relations between them in SFA is complex. We show that these dependencies for most-used exponential and half normal distribution of the inefficiency error are negative: more uncertainty leads to a lower technical efficiency. Our results also provide the sign and the value of the dependence between the technical efficiency and the heteroscedasticity factors. In addition, we show, that for common assumptions for the distribution of the inefficiency error, the marginal effect can be of a different sign. We accompany our theoretical results with analysis of Russian manufacturing industry. The experiments support the evidence that the effect of the uncertainty of the inefficiency error on the technical efficiency is negative and significant for the exponential and the half normal distribution of inefficiency error.
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