A sample selection model with a monotone selection correction function

2020 Fiscal Year Final Research Report

• Project/Area Number: 19K13666
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 07030:Economic statistics-related
• Research Institution: University of Tsukuba
• Principal Investigator: YU ZHENGFEI 筑波大学, 人文社会系, 助教 (40774758)
• Project Period (FY): 2019-04-01 – 2021-03-31
• Keywords: Shape restriction / Isotonic regression / Isotonic regression / Tuning parameter free / Sample selection model / Ordered response model / Accelerated failure time

Outline of Final Research Achievements

Motivated by the celebrated Heckman selection model which implies a parametric and monotone selection function, this project studies a sample selection model that does not impose parametric distributional assumptions on the latent errors, while maintaining the monotonicity of the control function. It shows that a positive dependence condition on the latent errors is sufficient for the monotonicity. The condition is equivalent to a restriction on the copula function of latent error terms. Using the monotonicity, this project proposes a tuning-parameter-free semiparametric estimation method and establishes root n-consistency and asymptotic normality for the estimates of finite-dimensional parameters. Simulations and an empirical application are conducted to illustrate the usefulness of the proposed methods. The shape-restricted estimation methods are also applicable to other semiparametric models including the ordered response model and accelerated failure time model.

Free Research Field

計量経済学

Academic Significance and Societal Importance of the Research Achievements

This project shows that the monotonicity of the control function implied by the celebrated Heckman selection model is shared by a much larger family without parametric assumptions. It proposes a more convenient semiparametric estimation method for the sample selection model.