Sample Selection Models with Monotone Control Functions
59 Pages Posted: 17 Jul 2019
Date Written: May 23, 2019
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 which 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. Utilizing 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 exploring the shape-restricted estimation. Simulations and an empirical application are conducted to illustrate the usefulness of the proposed methods.
Keywords: Copula, Sample Selection Models, Isotonic Regression, Semi- parametric Estimation, Shape Restriction
JEL Classification: C14, C21, C24, C25
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