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Interpretation of Regressions with Multiple Proxies

  • Darren Lubotsky

    (Princeton University)

  • Martin Wittenberg

    (University of the Witwatersrand)

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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File URL: http://econwpa.repec.org/eps/em/papers/0110/0110005.pdf
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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
Contact details of provider: Web page: http://econwpa.repec.org

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  1. 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.
  2. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
  3. Anne Case & Darren Lubotsky & Christina Paxson, 2002. "Economic status and health in childhood: the origins of the gradient," Working Papers 262, Princeton University, Woodrow Wilson School of Public and International Affairs, Center for Health and Wellbeing..
  4. 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.
    • Glaeser, Edward Ludwig & Laibson, David I. & Scheinkman, Jose A. & Soutter, Christine L., 2000. "Measuring Trust," Scholarly Articles 4481497, Harvard University Department of Economics.
  5. Leamer, Edward E., 1983. "Model choice and specification analysis," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 5, pages 285-330 Elsevier.
  6. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
  7. Filmer, Deon & Pritchett, Lant, 1998. "Estimating wealth effects without expenditure data - or tears : with an application to educational enrollments in states of India," Policy Research Working Paper Series 1994, The World Bank.
  8. Sendhil Mullainathan & Marianne Bertrand, 2001. "Do People Mean What They Say? Implications for Subjective Survey Data," American Economic Review, American Economic Association, vol. 91(2), pages 67-72, May.
  9. David M. Blau, 1999. "The Effect Of Income On Child Development," The Review of Economics and Statistics, MIT Press, vol. 81(2), pages 261-276, May.
  10. Griliches, Zvi, 1986. "Economic data issues," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 25, pages 1465-1514 Elsevier.
  11. Mauro, Paolo, 1995. "Corruption and Growth," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 681-712, August.
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