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Semiparametric Selection Models with Binary Outcomes

  • Klein, Roger


    (Rutgers University)

  • Shen, Chan


    (University of Texas MD Anderson Cancer Center)

  • Vella, Francis


    (Georgetown University)

This paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary. Since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting, we develop estimators for both the marginal effects and the underlying model parameters. The marginal effect estimator only uses observations which are members of a high probability set in which the selection problem is not present. A key innovation is that this high probability set is data dependent. The model parameter estimator is a quasi-likelihood estimator based on regular kernels with bias corrections. We establish their large sample properties and provide simulation evidence confirming that these estimators perform well in finite samples.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 6008.

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Length: 45 pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:iza:izadps:dp6008
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  1. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
  2. Lee, Lung-fei, 1995. "Semiparametric maximum likelihood estimation of polychotomous and sequential choice models," Journal of Econometrics, Elsevier, vol. 65(2), pages 381-428, February.
  3. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, 05.
  4. Klein, Roger & Shen, Chan, 2010. "Bias Corrections In Testing And Estimating Semiparametric, Single Index Models," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1683-1718, December.
  5. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  6. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, 05.
  7. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
  8. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  9. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
  10. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  11. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, 05.
  12. Andrews, Donald W K & Schafgans, Marcia M A, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 497-517, July.
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