Asymptotic properties of endogeneity corrections using nonlinear transformations

Breitung, Jörg; Mayer, Alexander; Wied, Dominik

doi:10.1093/ectj/utae002

The Econometrics Journal

2024

DOI: 10.1093/ectj/utae002

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Asymptotic properties of endogeneity corrections using nonlinear transformations

Jörg Breitung,

Alexander Mayer,

Dominik Wied

Abstract: This paper studies the asymptotic properties of endogeneity corrections based on nonlinear transformations without external instruments, which were originally proposed by Park and Gupta (2012) and have become popular in applied research. In contrast to the original copula-based estimator, our approach is based on a nonparametric control function and does not require a conformably specified copula. Moreover, we allow for exogenous regressors, which may be (linearly) correlated with the endogenous regressor(s). … Show more

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Cited by 4 publications

References 40 publications

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Endogeneity in stochastic frontier models with 'wrong' skewness: copula approach without external instruments

Haschka

2024

Stat Methods Appl

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Stochastic frontier models commonly assume positive skewness for the inefficiency term. However, when this assumption is violated, efficiency scores converge to unity. The potential endogeneity of model regressors introduces another empirical challenge, impeding the identification of causal relationships. This paper tackles these issues by employing an instrument-free estimation method that extends joint estimation through copulas to handle endogenous regressors and skewness issues. The method relies on the Gaussian copula function to capture dependence between endogenous regressors and composite errors with a simultaneous consideration of positively or negatively skewed inefficiency. Model parameters are estimated through maximum likelihood, and Monte Carlo simulations are employed to evaluate the performance of the proposed estimation procedures in finite samples. This research contributes to the stochastic frontier models and production economics literature by presenting a flexible and parsimonious method capable of addressing wrong skewness of inefficiency and endogenous regressors simultaneously. The applicability of the method is demonstrated through an empirical example.

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Endogeneity in stochastic frontier models with 'wrong' skewness: copula approach without external instruments

Haschka

2024

Stat Methods Appl

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

Haschka

2024

J Prod Anal

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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.

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Dealing with regression models’ endogeneity by means of an adjusted estimator for the Gaussian copula approach

Liengaard,

Becker,

Bennedsen

et al. 2024

J. of the Acad. Mark. Sci.

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Endogeneity in regression models is a key marketing research concern. The Gaussian copula approach offers an instrumental variable (IV)-free technique to mitigate endogeneity bias in regression models. Previous research revealed substantial finite sample bias when applying this method to regression models with an intercept. This is particularly problematic as models in marketing studies almost always require an intercept. To resolve this limitation, our research determines the bias’s sources, making several methodological advances in the process. First, we show that the cumulative distribution function estimation’s quality strongly affects the Gaussian copula approach’s performance. Second, we use this insight to develop an adjusted estimator that improves the Gaussian copula approach’s finite sample performance in regression models with (and without) an intercept. Third, as a broader contribution, we extend the framework for copula estimation to models with multiple endogenous variables on continuous scales and exogenous variables on discrete and continuous scales, and non-linearities such as interaction terms. Fourth, simulation studies confirm that the new adjusted estimator outperforms the established ones. Further simulations also underscore that our extended framework allows researchers to validly deal with multiple endogenous and exogenous regressors, and the interactions between them. Fifth, we demonstrate the adjusted estimator and the general framework’s systematic application, using an empirical marketing example with real-world data. These contributions enable researchers in marketing and other disciplines to effectively address endogeneity problems in their models by using the improved Gaussian copula approach.

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Asymptotic properties of endogeneity corrections using nonlinear transformations

Cited by 4 publications

References 40 publications

Endogeneity in stochastic frontier models with 'wrong' skewness: copula approach without external instruments

Endogeneity in stochastic frontier models with 'wrong' skewness: copula approach without external instruments

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

Dealing with regression models’ endogeneity by means of an adjusted estimator for the Gaussian copula approach

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