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Considerations on partially identified regression models


  • Daniel Cerquera
  • François Laisney
  • Hannes Ullrich


Motivated by Manski and Tamer (2002) and especially their partial identification anal- ysis of the regression model where one covariate is only interval-measured, we offer several contributions. 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 contri- bution 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 estimates, and illustrate the superiority of MMD over MMM. For MMD, we propose a simple shortcut for estimation.

Suggested Citation

  • Daniel Cerquera & François Laisney & Hannes Ullrich, 2012. "Considerations on partially identified regression models," Working Papers of BETA 2012-07, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  • Handle: RePEc:ulp:sbbeta:2012-07

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    References listed on IDEAS

    1. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    2. Markus Frölich, 2006. "Non-parametric regression for binary dependent variables," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 511-540, November.
    3. 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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    Cited by:

    1. Angela Blanco-Fernández & Peter Winker, 2016. "Data generation processes and statistical management of interval data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 475-494, October.
    2. 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.

    More about this item


    partial identification; true identified set; superset; MMD; MMM; estimation.;

    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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