Interpretation of Regressions with Multiple Proxies

MacArthur Network on Poverty and Inequality in a Broader Perspective Working Paper

32 Pages Posted: 25 Sep 2001

See all articles by Darren H. Lubotsky

Darren H. Lubotsky

University of Illinois at Chicago

Martin Wittenberg

University of the Witwatersrand - School of Economics and Business Sciences

Date Written: August 2001

Abstract

We consider the situation in which there are multiple proxies for one unobserved explanatory variable in a linear regression and provide a procedure by which the coefficient of interest can be extracted "post hoc" from a multiple regression in which all the proxies are used simultaneously. This post hoc estimator is strictly superior in large samples to coefficients derived using any index or linear combination of the proxies that is created prior to the regression. To use an index created from the proxies that extracts the largest possible signal from them requires knowledge of information that is not available to the researcher. Using the proxies simultaneously in a multiple regression delivers this information, and the researcher then simply combines the coefficients in a known way to obtain the estimate of the effect of the unobserved factor. This procedure is also much more robust than ad hoc index construction to departures from the assumption of an underlying common factor. We provide some Monte Carlo simulations and applications to existing empirical problems to show that the reduction in attenuation bias can be non-negligible, even in finite samples.

Keywords: Proxy variables, Measurement error, index construction

JEL Classification: C1, C31

Suggested Citation

Lubotsky, Darren H. and Wittenberg, Martin, Interpretation of Regressions with Multiple Proxies (August 2001). MacArthur Network on Poverty and Inequality in a Broader Perspective Working Paper, Available at SSRN: https://ssrn.com/abstract=284165 or http://dx.doi.org/10.2139/ssrn.284165

Darren H. Lubotsky (Contact Author)

University of Illinois at Chicago ( email )

University Hall Room 724
Chicago, IL 60607
United States

HOME PAGE: http://lubotsky.people.uic.edu/

Martin Wittenberg

University of the Witwatersrand - School of Economics and Business Sciences ( email )

Private Bag 3
P.O. Wits 2050
Johannesburg
South Africa

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