Study Reveals Critical Flaws in Standard Methods for Assessing Firm Efficiency

An international research team including Subal C. Kumbhakar, A. Peresetsky, Y. Shchetynin, and A. Zaytsev has published a paper “Technical efficiency and inefficiency: Reliability of standard SFA models and a misspecification problem” in Econometrics and Statistics journal. The study uncovers a fundamental issue in Stochastic Frontier Analysis (SFA) models used to evaluate the performance of firms and industries.

The problem emerges when the true inefficiency distribution is bimodal — for instance, when a dataset contains firms with fundamentally different management quality. In such scenarios, standard models not only severely distort efficiency estimates but can also reverse conclusions about the impact of external factors. Notably, company efficiency rankings can become completely inverted, as evidenced by negative correlations between true and estimated values.

As a practical solution, the authors propose a straightforward diagnostic tool — analyzing the distribution of model residuals, where bimodality indicates the need for model respecification. This is particularly crucial for regulators and analysts using SFA models for decision-making in public policy and corporate governance.

Abstract:
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.