Interpretation of Regressions with Multiple Proxies
Darren Lubotsky and
Martin Wittenberg ()
Econometrics from University Library of Munich, Germany
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 (search for similar items in EconPapers)
JEL-codes: C1 C31 (search for similar items in EconPapers)
Pages: 32 pages
New Economics Papers: this item is included in nep-ecm
Note: Type of Document - Latex; prepared on Unix latex; to print on HP; pages: 32 ; figures: included
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Journal Article: Interpretation of Regressions with Multiple Proxies (2006)
Working Paper: Interpretation of Regressions with Multiple Proxies (2001)
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:0110005
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