Technical efficiency and inefficiency: Reassurance of standard SFA models and a misspecification problem

Kumbhakar, Subal C. and Peresetsky, Anatoly and Shchetynin, Yevgenii and Zaytsev, Alexey (2020): Technical efficiency and inefficiency: Reassurance of standard SFA models and a misspecification problem. Forthcoming in: Econometrics and Statistics (23 December 2021)

Abstract

This paper formally proves that if inefficiency ($u$) is modelled through the variance of $u$ which is a function of $z$ then marginal effects of $z$ on technical inefficiency ($TI$) and technical efficiency ($TE$) have opposite signs. This is true in the typical setup with normally distributed random error $v$ and exponentially or half-normally distributed $u$ for both conditional and unconditional $TI$ and $TE$.

We also provide an example to show that 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 we estimate model with an exponential or half-normal distribution for $u$, the estimated efficiency and the marginal effect of $z$ on $TE$ would 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 data. This result is a warning that the interpretation of the results of applying standard models to real data should take into account this possible problem. The results are demonstrated by simulations.

• Item Type: MPRA Paper
• Language: English
• Keywords: Productivity and competitiveness, stochastic frontier analysis, model misspecification, efficiency, inefficiency
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C21 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; D - Microeconomics > D2 - Production and Organizations > D22 - Firm Behavior: Empirical Analysis; D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M1 - Business Administration > M11 - Production Management

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