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Semiparametric selection models with binary outcomes

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  • Roger Klein
  • Chan Shen
  • Francis Vella

Abstract

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 Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP30/11.

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Date of creation: Sep 2011
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Handle: RePEc:ifs:cemmap:30/11

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  1. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905.
  2. Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. 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.
  4. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
  5. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  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. 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.
  8. 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.
  9. 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.
  10. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
  11. 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.
  12. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, 05.
  13. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  14. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318.
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