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Viewpoint: Comparing features of convenient estimators for binary choice models with endogenous regressors

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  • Arthur Lewbel
  • Yingying Dong
  • Thomas Tao Yang

Abstract

We discuss the relative advantages and disadvantages of four types of convenient estimators of binary choice models when regressors may be endogenous or mismeasured or when errors are likely to be heteroscedastic. For example, such models arise when treatment is not randomly assigned and outcomes are binary. The estimators we compare are the two-stage least squares linear probability model, maximum likelihood estimation, control function estimators, and special regressor methods. We specifically focus on models and associated estimators that are easy to implement. Also, for calculating choice probabilities and regressor marginal effects, we propose the average index function (AIF), which, unlike the average structural function (ASF), is always easy to estimate.

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Bibliographic Info

Article provided by Canadian Economics Association in its journal Canadian Journal of Economics.

Volume (Year): 45 (2012)
Issue (Month): 3 (August)
Pages: 809-829

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Handle: RePEc:cje:issued:v:45:y:2012:i:3:p:809-829

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References

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  1. Magnac, Thierry & Maurin, Eric, 2003. "Identification and Information in Monotone Binary Models," IDEI Working Papers 180, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2004.
  2. Arthur Lewbel, 1997. "Coherence and Completeness of Structural Models Containing a Dummy Endogenous Variable," Boston College Working Papers in Economics 456, Boston College Department of Economics, revised 04 Sep 2006.
  3. Richard Blundell & James Powell, 2001. "Endogeneity in semiparametric binary response models," CeMMAP working papers CWP05/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Magnac, Thierry & Maurin, Eric, 2004. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," IDEI Working Papers 280, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jan 2005.
  5. Lewbel, Arthur & Schennach, Susanne M., 2007. "A simple ordered data estimator for inverse density weighted expectations," Journal of Econometrics, Elsevier, vol. 136(1), pages 189-211, January.
  6. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
  7. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, 05.
  8. Jacho-Chávez, David T., 2009. "Efficiency Bounds For Semiparametric Estimation Of Inverse Conditional-Density-Weighted Functions," Econometric Theory, Cambridge University Press, vol. 25(03), pages 847-855, June.
  9. Yingying Dong & Arthur Lewbel, 2004. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Boston College Working Papers in Economics 604, Boston College Department of Economics, revised 15 Jun 2012.
  10. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
  11. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
  12. Blundell, Richard W & Smith, Richard J, 1989. "Estimation in a Class of Simultaneous Equation Limited Dependent Variable Models," Review of Economic Studies, Wiley Blackwell, vol. 56(1), pages 37-57, January.
  13. Shaikh, Azeem M. & Vytlacil, Edward, 2008. "Endogenous binary choice models with median restrictions: A comment," Economics Letters, Elsevier, vol. 98(1), pages 23-28, January.
  14. Charles F. Manski, 2007. "Partial Identification Of Counterfactual Choice Probabilities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1393-1410, November.
  15. Stefan Hoderlein, 2009. "Endogenous semiparametric binary choice models with heteroscedasticity," CeMMAP working papers CWP34/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  16. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
  17. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, 07.
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Citations

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Cited by:
  1. Yasar, Mahmut, 2013. "Political Influence of Exporting and Import-Competing Firms: Evidence from Eastern European and Central Asian Countries," World Development, Elsevier, vol. 51(C), pages 154-168.
  2. TAKEDA Yosuke & UCHIDA Ichihiro, 2013. "Make or Buy, and/or Cooperate? The Property Rights Approach to Auto Parts Procurement in Japan," Discussion papers 13066, Research Institute of Economy, Trade and Industry (RIETI).
  3. Arthur Lewbel & Thomas Tao Yang, 2013. "Identifying the Average Treatment Effect in a Two Threshold Model," Boston College Working Papers in Economics 825, Boston College Department of Economics.

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