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Identification and Information in Monotone Binary Models

Listed author(s):
  • Thierry Magnac

    (IDEI - Institut d'économie industrielle - UT1 - Université Toulouse 1 Capitole, LERNA - Economie des Ressources Naturelles - UT1 - Université Toulouse 1 Capitole - INRA - Institut National de la Recherche Agronomique - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

  • Eric Maurin

    (PSE - Paris School of Economics, PSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

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 HAL in its series Post-Print with number halshs-00754218.

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Date of creation: Jul 2007
Publication status: Published in Journal of Econometrics, Elsevier, 2007, 139 (1), pp.76-105. <10.1016/j.jeconom.2006.06.005>
Handle: RePEc:hal:journl:halshs-00754218
DOI: 10.1016/j.jeconom.2006.06.005
Note: View the original document on HAL open archive server: https://hal-pjse.archives-ouvertes.fr/halshs-00754218
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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  1. 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.
  2. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-1460, November.
  3. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  4. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
  5. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  6. 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.
  7. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 655-679.
  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. 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.
  10. 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.
  11. Denis Cogneau & Eric Maurin, 2001. "Parental Income and School Attendance in a Low-Income Country : A Semi-parametric Analysis," Working Papers 2001-08, Centre de Recherche en Economie et Statistique.
  12. Thierry Magnac & Eric Maurin, 2003. "Identification et Information in Monotone Binary Models," Working Papers 2003-07, Centre de Recherche en Economie et Statistique.
  13. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, 07.
  14. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
  15. Lewbel, Arthur & McFadden, Daniel & Linton, Oliver, 2011. "Estimating features of a distribution from binomial data," Journal of Econometrics, Elsevier, vol. 162(2), pages 170-188, June.
  16. 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.
  17. 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.
  18. 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.
  19. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
  20. Hong, Han & Tamer, Elie, 2003. "Endogenous binary choice model with median restrictions," Economics Letters, Elsevier, vol. 80(2), pages 219-225, August.
  21. 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 517-533, December.
  22. 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.
  23. 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.
  24. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
  25. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
  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 225-228, January.
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