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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.

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Paper provided by Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg in its series Working Papers of BETA with number 2012-07.

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Date of creation: 2012
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Handle: RePEc:ulp:sbbeta:2012-07
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  1. Markus Fr�lich, 2006. "Non-parametric regression for binary dependent variables," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 511-540, November.
  2. Christian Bontemps & Thierry Magnac & Eric Maurin, 2011. "Set identified linear models," CeMMAP working papers CWP13/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
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