TY - JOUR

T1 - Technical efficiency and inefficiency

T2 - Reliability of standard SFA models and a misspecification problem

AU - Kumbhakar, Subal C.

AU - Peresetsky, A.

AU - Shchetynin, Y.

AU - Zaytsev, A.

N1 - Funding Information:
We are grateful for many invaluable comments provided by participants at the Sixteenth European Workshop on Efficiency and Productivity Analysis in London, 2019, and CFE-CMStatistics 2020 conference, 2020. We thank two anonymous referees for careful and constructive comments that helped to improve the paper. Alexey Zaytsev acknowledges financial support fromthe Russian Science Foundation (project 20-71-10135 )
Publisher Copyright:
© 2021 The Authors

PY - 2022

Y1 - 2022

N2 - It is formally proven that if inefficiency (u) is modelled through its variance, considered as a function of exogenous variables z, then the marginal effects of z on technical inefficiency (TI) and technical efficiency (TE) have opposite signs in the typical setup with a normally distributed random error and an exponentially or half-normally distributed u. This is true for both conditional and unconditional TI and TE. An example is provided to show that the signs of the marginal effects of z on TI and TE may coincide for some ranges of z. If the real data comes from a bimodal distribution of u, and a model is estimated with an exponential or half-normal distribution for u, the estimated efficiency and the marginal effect of z on TE could be wrong. Moreover, the rank correlations between the true and the estimated values of TE could be small and even negative for some subsamples of the data. This is a warning that in the case when the true (real life) distribution of the inefficiency is bimodal, commonly used standard SFA models could lead to wrong policy recommendations. The kernel density plot of the residuals is suggested as a diagnostic plot. The results are illustrated by simulations.

AB - It is formally proven that if inefficiency (u) is modelled through its variance, considered as a function of exogenous variables z, then the marginal effects of z on technical inefficiency (TI) and technical efficiency (TE) have opposite signs in the typical setup with a normally distributed random error and an exponentially or half-normally distributed u. This is true for both conditional and unconditional TI and TE. An example is provided to show that the signs of the marginal effects of z on TI and TE may coincide for some ranges of z. If the real data comes from a bimodal distribution of u, and a model is estimated with an exponential or half-normal distribution for u, the estimated efficiency and the marginal effect of z on TE could be wrong. Moreover, the rank correlations between the true and the estimated values of TE could be small and even negative for some subsamples of the data. This is a warning that in the case when the true (real life) distribution of the inefficiency is bimodal, commonly used standard SFA models could lead to wrong policy recommendations. The kernel density plot of the residuals is suggested as a diagnostic plot. The results are illustrated by simulations.

KW - Efficiency

KW - Inefficiency

KW - Model misspecification

KW - Productivity and competitiveness

KW - Stochastic frontier analysis

UR - http://www.scopus.com/inward/record.url?scp=85122486250&partnerID=8YFLogxK

U2 - 10.1016/j.ecosta.2021.12.006

DO - 10.1016/j.ecosta.2021.12.006

M3 - Article

AN - SCOPUS:85122486250

JO - Econometrics and Statistics

JF - Econometrics and Statistics

SN - 2452-3062

ER -