Considerations on Partially Identified Regression Models

Working Papers of BETA (Bureau d'Economie Théorique et Appliquée) No. 2012-07

ZEW - Centre for European Economic Research Discussion Paper No. 12-024

42 Pages Posted: 20 Dec 2011 Last revised: 30 Jul 2014

Daniel Cerquera

Centre for European Economic Research (ZEW)

Francois Laisney

Centre for European Economic Research (ZEW)

Hannes Ullrich

University of Zurich - Faculty of Economics, Business Administration and Information Technology; German Institute for Economic Research (DIW Berlin) - Innovation, Management, Service

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Date Written: March 30, 2012

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 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 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 estimates, and illustrate the superiority of MMD over MMM. For MMD, we propose a simple shortcut for estimation.

Keywords: partial identification, true identified set, superset, MMD, MMM, estimation

JEL Classification: C01, C13, C40

Suggested Citation

Cerquera, Daniel and Laisney, Francois and Ullrich, Hannes, Considerations on Partially Identified Regression Models (March 30, 2012). Working Papers of BETA (Bureau d'Economie Théorique et Appliquée) No. 2012-07; ZEW - Centre for European Economic Research Discussion Paper No. 12-024. Available at SSRN: https://ssrn.com/abstract=1975022 or http://dx.doi.org/10.2139/ssrn.1975022

Daniel Cerquera

Centre for European Economic Research (ZEW) ( email )

P.O. Box 10 34 43
L 7,1
D-68034 Mannheim, 68034
Germany

Francois Laisney (Contact Author)

Centre for European Economic Research (ZEW) ( email )

P.O. Box 10 34 43
L 7,1
D-68034 Mannheim, 68034
Germany

Hannes Ullrich

University of Zurich - Faculty of Economics, Business Administration and Information Technology ( email )

Plattenstrasse 14
Zurich, 8032
Switzerland

German Institute for Economic Research (DIW Berlin) - Innovation, Management, Service ( email )

Mohrenstraße 58
Berlin, 10117
Germany
+493089789521 (Phone)

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