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Rate-Optimal Estimation of the Intercept in a Semiparametric Sample-Selection Model

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  • Chuan Goh

Abstract

This paper presents a new estimator of the intercept of a linear regression model in cases where the outcome varaible is observed subject to a selection rule. The intercept is often in this context of inherent interest; for example, in a program evaluation context, the difference between the intercepts in outcome equations for participants and non-participants can be interpreted as the difference in average outcomes of participants and their counterfactual average outcomes if they had chosen not to participate. The new estimator can under mild conditions exhibit a rate of convergence in probability equal to $n^{-p/(2p+1)}$, where $p\ge 2$ is an integer that indexes the strength of certain smoothness assumptions. This rate of convergence is shown in this context to be the optimal rate of convergence for estimation of the intercept parameter in terms of a minimax criterion. The new estimator, unlike other proposals in the literature, is under mild conditions consistent and asymptotically normal with a rate of convergence that is the same regardless of the degree to which selection depends on unobservables in the outcome equation. Simulation evidence and an empirical example are included.

Suggested Citation

  • Chuan Goh, 2017. "Rate-Optimal Estimation of the Intercept in a Semiparametric Sample-Selection Model," Papers 1710.01423, arXiv.org, revised Sep 2018.
  • Handle: RePEc:arx:papers:1710.01423
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    3. Arabmazar, Abbas & Schmidt, Peter, 1982. "An Investigation of the Robustness of the Tobit Estimator to Non-Normality," Econometrica, Econometric Society, vol. 50(4), pages 1055-1063, July.
    4. Schafgans, Marcia M. A., 2000. "Gender wage differences in Malaysia: parametric and semiparametric estimation," Journal of Development Economics, Elsevier, vol. 63(2), pages 351-378, December.
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    Cited by:

    1. Kanaya, Shin & Taylor, Luke, 2020. "Type I and Type II Error Probabilities in the Courtroom," MPRA Paper 100217, University Library of Munich, Germany.
    2. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2021. "Intercept Estimation in Nonlinear Selection Models," IZA Discussion Papers 14364, Institute of Labor Economics (IZA).

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