0) when ² is assumed uncorrelated with a set of instruments z, ² is independentof v conditionally on x and z, and the conditional support of ² is su¢ciently smallrelative to the support of v. We characterize the set of observationally equivalentparameters ¯ when interval data only are available on v or when v is discrete. Whenthere exist as many instruments z as variables x, the sets within which lie the scalarcomponents ¯k of parameter ¯ can be estimated by simple linear regressions. Also, inthe case of interval data, it is shown that additional information on the distribution ofv within intervals shrinks the identification set. Namely, the closer to uniformity thedistribution of v is, the smaller the identification set is. Point identification is achievedif and only if v is uniform within intervals."> 0) when ² is assumed uncorrelated with a set of instruments z, ² is independentof v conditionally on x and z, and the conditional support of ² is su¢ciently smallrelative to the support of v. We characterize the set of observationally equivalentparameters ¯ when interval data only are available on v or when v is discrete. Whenthere exist as many instruments z as variables x, the sets within which lie the scalarcomponents ¯k of parameter ¯ can be estimated by simple linear regressions. Also, inthe case of interval data, it is shown that additional information on the distribution ofv within intervals shrinks the identification set. Namely, the closer to uniformity thedistribution of v is, the smaller the identification set is. Point identification is achievedif and only if v is uniform within intervals."> 0) when ² is assumed uncorrelated with a set of instruments z, ² is independentof v conditionally on x and z, and ">
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Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data

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  • Thierry Magnac

    (Crest)

  • Eric Maurin

    (Crest)

Abstract
We investigate inference in semi-parametric binary regression models, y = 1(x¯ +v+² > 0) when ² is assumed uncorrelated with a set of instruments z, ² is independentof v conditionally on x and z, and the conditional support of ² is su¢ciently smallrelative to the support of v. We characterize the set of observationally equivalentparameters ¯ when interval data only are available on v or when v is discrete. Whenthere exist as many instruments z as variables x, the sets within which lie the scalarcomponents ¯k of parameter ¯ can be estimated by simple linear regressions. Also, inthe case of interval data, it is shown that additional information on the distribution ofv within intervals shrinks the identification set. Namely, the closer to uniformity thedistribution of v is, the smaller the identification set is. Point identification is achievedif and only if v is uniform within intervals.

Suggested Citation

  • Thierry Magnac & Eric Maurin, 2004. "Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data," Working Papers 2004-11, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2004-11
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    References listed on IDEAS

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    1. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
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    3. 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.
    4. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 2-16, January.
    5. Bierens, H.J., 1988. "Nonlinear regression with discrete explanatory variables," Serie Research Memoranda 0061, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    6. 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.
    7. Manuel Arellano & Costas Meghir, 1992. "Female Labour Supply and On-the-Job Search: An Empirical Model Estimated Using Complementary Data Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 537-559.
    8. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, September.
    9. Bierens, Herman J. & Hartog, Joop, 1988. "Non-linear regression with discrete explanatory variables, with an application to the earnings function," Journal of Econometrics, Elsevier, vol. 38(3), pages 269-299, July.
    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. Leamer, Edward E, 1987. "Errors in Variables in Linear Systems," Econometrica, Econometric Society, vol. 55(4), pages 893-909, July.
    12. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 27-28, January.
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