Измерение ранжирующей способности модели стохастической границы с усечённым нормальным распределением неэффективности

Экономика и математические методы. 2025. Т. 61. № 1. С. 109–117.

Ахмедов Э., Furmanov K. K.

A stochastic frontier model is a regression model where an explained variable is either output of a firm or its costs, and unexplained variation of this variable is divided into two components: inefficiency and stochastic shock. These components are modeled by random variables with different families of distributions. The model allows estimation of inefficiency at firm level and at industry level refined from the effects of stochastic shocks. At present it is the basic instrument for analyzing the efficiency and productivity. We consider a problem of assessing the accuracy of inefficiency estimators, obtained via stochastic frontier model with truncated normal distribution of inefficiency components. We propose using Harrell’s C-index as a measure of concordance between true inefficiencies and their estimates. We derive the expression for the asymptotic C-index as a function of distribution parameters of model’s random components (stochastic shocks and inefficiencies). The derived expression can be used by practitioners for assessing the ranking ability of a stochastic frontier model. The value of C-index has clear interpretation: it is the probability of choosing a more efficient firm from two randomly selected ones. For demonstration purposes, we provide historical data on cotton refining plants in the Soviet Union. The obtained result may be useful both for academic researchers and for regulatory agencies.

Keywords: ранжирование, stochastic frontier, стохастическая граница, ranking, inefficiency, Harrell's C, неэффективность, коэффициент Харрелла