Estimation of semi- and nonparametric stochastic frontier models with endogenous regressors
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Estimation of semi- and nonparametric stochastic frontier models with endogenous regressors Artem Prokhorov1,2 · Kien C. Tran3 · Mike G. Tsionas4 Received: 28 February 2020 / Accepted: 8 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper considers the problem of estimating a nonparametric stochastic frontier model with shape restrictions and when some or all regressors are endogenous. We discuss three estimation strategies based on constructing a likelihood with unknown components. One approach is a three-step constrained semiparametric limited information maximum likelihood, where the first two steps provide local polynomial estimators of the reduced form and frontier equation. This approach imposes the shape restrictions on the frontier equation explicitly. As an alternative, we consider a local limited information maximum likelihood, where we replace the constrained estimation from the first approach with a kernel-based method. This means the shape constraints are satisfied locally by construction. Finally, we consider a smooth-coefficient stochastic frontier model, for which we propose a two-step estimation procedure based on local GMM and MLE. Our Monte Carlo simulations demonstrate attractive finite sample properties of all the proposed estimators. An empirical application to the US banking sector illustrates empirical relevance of these methods. Keywords Constrained semiparametric limited information MLE · Efficiency · Endogeneity · Local limited information MLE · Smooth coefficient · Stochastic frontier
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Artem Prokhorov [email protected] Kien C. Tran [email protected] Mike G. Tsionas [email protected]
1
Business School, University of Sydney, Sydney, NSW, Australia
2
St. Petersburg State University, St. Petersburg, Russia
3
Department of Economics, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada
4
Lancaster University Management School, Lancaster LA1 4YX, UK
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A. Prokhorov et al.
JEL Classification C13 · C14 · C36
1 Introduction In most applications in stochastic frontier model, researchers typically assume that the functional form of the frontier takes a specific parametric form (e.g., Cobb–Douglas, translog, constant elasticity of substitution, etc.) for the data they want to analyze. However, economic theories rarely predict specific functional form for the frontier, and consequently, misspecification of the functional form can lead to biased and inconsistent parameter estimators as well as to misleading inference on inefficiencies. In such cases, researchers may wish to adopt a semi- or nonparametric specification.1 Nonparametric stochastic frontier models have been previously considered by Fan et al. (1996), Martins-Filho and Yao (2007), Kumbhakar et al. (2007), among others. However, to the best of our knowledge, all of the above papers assumed that the regressors are exogenous. When some or all of the regressors are endogenous, their proposed estimation approaches are no longer valid and need to be modified.
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