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Interpretation of Regressions with Multiple Proxies

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  • Darren Lubotsky

    (Princeton University)

  • Martin Wittenberg

    (University of the Witwatersrand South Africa)

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.

Suggested Citation

  • Darren Lubotsky & Martin Wittenberg, 2001. "Interpretation of Regressions with Multiple Proxies," Working Papers 836, Princeton University, Department of Economics, Industrial Relations Section..
    • Handle: RePEc:pri:indrel:457
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    More about this item

    Keywords

    Proxy variables; measurement error; index construction;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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