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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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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 139 (2007)
Issue (Month): 1 (July)
Pages: 76-104

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Handle: RePEc:eee:econom:v:139:y:2007:i:1:p:76-104
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  1. Eric Maurin, 1999. "The Impact of Parental Income on Early Schooling Transitions : A Re-examination Using Data over Three Generations," Working Papers 99-69, Centre de Recherche en Economie et Statistique.
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  4. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-96, May.
  5. 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.
  6. 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.
  7. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers 1166, Econometric Society.
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  17. 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.
  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. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-60, November.
  20. Hong, Han & Tamer, Elie, 2003. "Endogenous binary choice model with median restrictions," Economics Letters, Elsevier, vol. 80(2), pages 219-225, August.
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  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. 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.
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