A Note on Regressions with Interval Data on a Regressor

32 Pages Posted: 21 Oct 2014

See all articles by Daniel Cerquera

Daniel Cerquera

ZEW – Leibniz Centre for European Economic Research

Francois Laisney

ZEW – Leibniz Centre for European Economic Research

Hannes Ullrich

University of Copenhagen - Department of Economics; German Institute for Economic Research (DIW Berlin) - Innovation, Management, Service

Multiple version iconThere are 2 versions of this paper

Date Written: October 2014

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.

Keywords: Partial identification, true identified set, superset, MMD, MMM

JEL Classification: C01, C13, C40

Suggested Citation

Cerquera, Daniel and Laisney, Francois and Ullrich, Hannes, A Note on Regressions with Interval Data on a Regressor (October 2014). DIW Berlin Discussion Paper No. 1419, Available at SSRN: https://ssrn.com/abstract=2512195 or http://dx.doi.org/10.2139/ssrn.2512195

Daniel Cerquera

ZEW – Leibniz Centre for European Economic Research ( email )

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

Francois Laisney

ZEW – Leibniz Centre for European Economic Research ( email )

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

Hannes Ullrich (Contact Author)

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5, Bygn 26
Copenhagen, 1353
Denmark

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

Mohrenstraße 58
Berlin, 10117
Germany
+493089789521 (Phone)

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