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Sample selection models with monotone control functions
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DOI：10.1016/j.jeconom.2021.01.010.png)
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The celebrated Heckman selection model yields a selection correction function (control function) proportional to the inverse Mills ratio, which is monotone. This paper studies a sample selection model that does not impose parametric distributional assumptions on the latent error terms, while maintaining the monotonicity of the control function. We show that a positive (negative) dependence condition on the latent error terms is sufficient for the monotonicity of the control function. The condition is equivalent to a restriction on the copula function of latent error terms. Using the monotonicity, we propose a tuning-parameter-free semiparametric estimation method and establish root n-consistency and asymptotic normality for the estimates of finite-dimensional parameters. A new test for selectivity is also developed in the presence of the shape restriction. Simulations and an empirical application are conducted to illustrate the usefulness of the proposed methods. (C) 2021 Elsevier B.V. All rights reserved.
Keyword:
Copula
Sample selection models
Isotonic regression
Semiparametric estimation
Shape restriction
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