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A Note on Regressions with Interval Data on a Regressor

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  • Daniel Cerquera
  • François Laisney
  • Hannes Ullrich

Abstract

Motivated by Manski and Tamer (2002) and especially their partial identification analysis of the regression model where one covariate is only interval-measured, we present two extensions. Manski and Tamer (2002) propose two estimation approaches in this context, focussing on general results. The modified minimum distance (MMD) estimates the true identified set and the modified method of moments (MMM) a superset. Our first contribution is to characterize the true identified set and the superset. Second, we complete and extend the Monte Carlo study of Manski and Tamer (2002). We present benchmark results using the exact functional form for the expectation of the dependent variable conditional on observables to compare with results using its nonparametric estimate, and illustrate the superiority of MMD over MMM.

Suggested Citation

  • Daniel Cerquera & François Laisney & Hannes Ullrich, 2014. "A Note on Regressions with Interval Data on a Regressor," Discussion Papers of DIW Berlin 1419, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp1419
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    References listed on IDEAS

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    1. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 835-864.
    2. Cerquera, Daniel & Laisney, François & Ullrich, Hannes, 2012. "Considerations on partially identified regression models," ZEW Discussion Papers 12-024, ZEW - Leibniz Centre for European Economic Research.
    3. 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.
    4. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    5. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
    6. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    7. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
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    More about this item

    Keywords

    Partial identification; true identified set; superset; MMD; MMM;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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