"Wrong" skewness and endogenous regressors in stochastic frontier models: an instrument-free copula approach with an application to estimate firm efficiency in Vietnam

Stochastic frontier models commonly assume positively skewed inefficiency. However, if the data speak against this assumption, sample-failure problems are often cited, but less attention is paid to economic reasons. We consider this phenomenon as a signal of distinctive population characteristics stemming from the inefficiency component, emphasizing its potential impact on evaluating market conditions. Specifically, we argue more generally that "wrong" skewness could indicate a lack of competition in the market. Moreover, endogeneity of model regressors presents another challenge, hindering the identification of causal relationships. To tackle these issues, this paper proposes an instrument-free estimation method based on Gaussian copulas to model the dependence between endogenous regressors and composite errors, while accommodating positively or negatively skewed inefficiency through simultaneous identification. Monte Carlo simulation experiments demonstrate the suitability of our estimator, comparing it with alternative methods. The contributions of this study are twofold. On the one hand, we contribute to the literature on stochastic frontier models by providing a comprehensive method for dealing with "wrong" skewness and endogenous regressors simultaneously. On the other hand, our contribution to an economic understanding of "wrong" skewness expands the comprehension of market behaviors and competition levels. Empirical findings on Vietnamese firm efficiency indicate that endogeneity hinders the detection of "wrong" skewness and suggests a lack of competitive market conditions. The latter underscores the importance of policy interventions to incentivize firms in non-competitive markets.