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Identification et Information in Monotone Binary Models


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  • Thierry Magnac


  • Eric Maurin



Let, y, a binary outcome, v a continuous explanatory variable and x someother explanatory variables. Assume that the population distribution of the random variablew = (y, v, x) satisfies Monotone (1) and Large Support (2) assumptions: (1) E(y | v, x) ismonotone in v and (2) E(y | v, x) varies from 0 to 1 when v varies over its support. Withinthis framework, this paper studies inference on the parameters of the semiparametric binaryregression model y = 1(xß + v + > 0). It shows that the moment restrictions that Lewbel(2000) proposed lead to exact identification of the parameter of interest, ß. In other words, anuncorrelated-error restriction (E(x) = 0) combined with a partial-independance assumption(F( | v, x) = F( | x)) are sufficient and necessary for identification. We also show thatLewbel’s moment estimator attains the semi-parametric efficiency bound in the set of latentmodels that he considers. Yet, uncorrelated-error and partial-independence assumptionsare not sufficient to identify ß when the support of v is not sufficiently rich. We proposeintuitive additional identifying assumptions under which ß remains just identified. Monte-Carlo experiments show that the estimation performs well in moderately small samples. Anextension to ordered choice models is also provided.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2003-07.

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Date of creation: 2003
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Handle: RePEc:crs:wpaper:2003-07

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Cited by:
  1. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, Elsevier, vol. 139(1), pages 76-104, July.
  2. Lewbel, Arthur & Schennach, Susanne M., 2007. "A simple ordered data estimator for inverse density weighted expectations," Journal of Econometrics, Elsevier, Elsevier, vol. 136(1), pages 189-211, January.
  3. Arthur Lewbel, 2000. "Endogenous Selection Or Treatment Model Estimation," Boston College Working Papers in Economics 462, Boston College Department of Economics, revised 13 Jun 2007.
  4. Songnian Chen & Shakeeb Khan & Xun Tang, 2013. "Informational Content of Special Regressors in Heteroskedastic Binary Response Models," PIER Working Paper Archive 13-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Stewart, Mark B., 2005. "A comparison of semiparametric estimators for the ordered response model," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 49(2), pages 555-573, April.


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