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A Simple Data-Driven Estimator for the Semiparametric Sample Selection Model

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  • Juan Carlos Escanciano
  • Lin Zhu

Abstract

This paper proposes a simple fully data-driven version of Powell's (2001) two-step semiparametric estimator for the sample selection model. The main feature of the proposal is that the bandwidth used to estimate the infinite-dimensional nuisance parameter is chosen by minimizing the mean squared error of the fitted semiparametric model. We formally justify data-driven inference. We introduce the concept of asymptotic normality, uniform in the bandwidth, and show that the proposed estimator achieves this property for a wide range of bandwidths. The method of proof is different from that in Powell (2001) and permits straightforward extensions to other semiparametric or even fully nonparametric specifications of the selection equation. The results of a small Monte Carlo suggest that our estimator has excellent finite sample performance, comparing well with other competing estimators based on alternative choices of smoothing parameters.

Suggested Citation

  • Juan Carlos Escanciano & Lin Zhu, 2015. "A Simple Data-Driven Estimator for the Semiparametric Sample Selection Model," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 734-762, December.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:734-762
    DOI: 10.1080/07474938.2014.956577
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    References listed on IDEAS

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    1. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    2. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    5. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    6. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    7. Li, Dong & Li, Qi, 2010. "Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters," Journal of Econometrics, Elsevier, vol. 157(1), pages 179-190, July.
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    Cited by:

    1. Juan Carlos Escanciano, 2020. "Uniform Rates for Kernel Estimators of Weakly Dependent Data," Papers 2005.09951, arXiv.org.
    2. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.

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