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Interpretation of Regressions with Multiple Proxies

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Author Info

  • Darren Lubotsky

    (Princeton University)

  • Martin Wittenberg

    (University of the Witwatersrand)

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.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0110005.

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Length: 32 pages
Date of creation: 14 Oct 2001
Date of revision:
Handle: RePEc:wpa:wuwpem:0110005

Note: Type of Document - Latex; prepared on Unix latex; to print on HP; pages: 32 ; figures: included
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Web page: http://128.118.178.162

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Keywords: Proxy variables; measurement error; index construction;

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  8. Mauro, Paolo, 1995. "Corruption and Growth," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 681-712, August.
  9. Aigner, Dennis J. & Hsiao, Cheng & Kapteyn, Arie & Wansbeek, Tom, 1984. "Latent variable models in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 23, pages 1321-1393 Elsevier.
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