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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Paper provided by EconWPA in its series Econometrics with number
0110005.
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 Contact details of provider: Web page: http://129.3.20.41
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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.
[Downloadable!] (restricted)
Edward L. Glaeser & David I. Laibson & José A. Scheinkman & Christine L. Soutter, 2000.
"Measuring Trust,"
The Quarterly Journal of Economics,
MIT Press, vol. 115(3), pages 811-846, August.
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