A Note on Regressions with Interval Data on a Regressor

25 Pages Posted: 31 Jul 2014 Last revised: 29 Mar 2015

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: March 26, 2015

Abstract

We reconsider the partial identification analysis of the regression model in Manski and Tamer (2002) where one covariate is only interval-measured and present two additional sets of results. 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. We illustrate the superiority of MMD over MMM, as well as the advantage of adopting a geometric estimation approach in both cases.

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 (March 26, 2015). Available at SSRN: https://ssrn.com/abstract=2473768 or http://dx.doi.org/10.2139/ssrn.2473768

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 (Contact Author)

ZEW – Leibniz Centre for European Economic Research ( email )

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

Hannes Ullrich

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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