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Identification and Information in Monotone Binary Models

  • Magnac, Thierry
  • Maurin, Eric

This paper considers binary response models where errors are uncorrelated with a set of instrumental variables and are independent of a continuous regressor v, conditional on all other variables. It is shown that these exclusion restrictions are not sufficient for identification and that additional identifying assumptions are needed. Such an assumption, introduced by Lewbel [Semiparametric qualitative response model estimation with unknown heteroskedasticity or instrumental variables. Journal of Econometrics 97, 145-177], is that the support of the continuous regressor is large, but we show that it significantly restricts the class of binary phenomena which can be analysed. We propose an alternative additional assumption under which β remains just identified and the estimation unchanged. This alternative assumption does not impose specific restrictions on the data, which broadens the scope of the estimation method in empirical work. The semiparametric efficiency bound of the model is also established and an existing estimator is shown to achieve that bound. The efficient estimator uses a plug-in density estimate. It is shown that plugging in the true density rather than an estimate is inefficient. Extensions to ordered choice models are provided.

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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 180.

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Date of creation: 2003
Date of revision: Oct 2004
Publication status: Published in Journal of Econometrics, vol. 139, n°1, juillet 2007, p. 76-104.
Handle: RePEc:ide:wpaper:3063
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  1. Denis Cogneau & Eric Maurin, 2001. "Parental Income and School Attendance in a Low-Income Country : A semi-parametric analysis," Working Papers DT/2001/16, DIAL (Développement, Institutions et Mondialisation).
  2. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
  3. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-96, May.
  4. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  5. 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.
  6. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 835-864.
  7. Crepon, Bruno & Kramarz, Francis & Trognon, Alain, 1997. "Parameters of interest, nuisance parameters and orthogonality conditions An application to autoregressive error component models," Journal of Econometrics, Elsevier, vol. 82(1), pages 135-156.
  8. Bo E. Honore & Arthur Lewbel, 2002. "Semiparametric Binary Choice Panel Data Models Without Strictly Exogeneous Regressors," Econometrica, Econometric Society, vol. 70(5), pages 2053-2063, September.
  9. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers 1166, Econometric Society.
  10. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-82, May.
  11. Arthur Lewbel & Oliver Linton & Daniel McFadden, 2001. "Estimating features of a distribution from binomial data," CeMMAP working papers CWP07/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  12. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
  13. Newey, W.K., 1989. "The Asymptotic Variance Of Semiparametric Estimotors," Papers 346, Princeton, Department of Economics - Econometric Research Program.
  14. 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.
  15. 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.
  16. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-60, November.
  17. 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.
  18. Thierry Magnac & Eric Maurin, 2003. "Identification et Information in Monotone Binary Models," Working Papers 2003-07, Centre de Recherche en Economie et Statistique.
  19. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
  20. Anton, A Alonso & Sainz, A Fernandez & Rodriguez-Poo, J, 2001. " Semiparametric Estimation of a Duration Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(5), pages 517-33, December.
  21. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
  22. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  23. Hong, Han & Tamer, Elie, 2003. "Endogenous binary choice model with median restrictions," Economics Letters, Elsevier, vol. 80(2), pages 219-225, August.
  24. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  25. Maurin, Eric, 2002. "The impact of parental income on early schooling transitions: A re-examination using data over three generations," Journal of Public Economics, Elsevier, vol. 85(3), pages 301-332, September.
  26. Ruud, Paul A, 1983. "Sufficient Conditions for the Consistency of Maximum Likelihood Estimation Despite Misspecifications of Distribution in Multinomial Discrete Choice Models," Econometrica, Econometric Society, vol. 51(1), pages 225-28, January.
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