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Interpretation of Regressions with Multiple Proxies

  • Darren Lubotsky
  • Martin Wittenberg

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://arks.princeton.edu/ark:/88435/dsp01fq977t77z
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Paper provided by Princeton University, Department of Economics, Industrial Relations Section. in its series Working Papers with number 836.

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Date of creation: Sep 2001
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Handle: RePEc:pri:indrel:dsp01fq977t77z
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  1. 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.
  2. Glaeser, Edward Ludwig & Laibson, David I. & Scheinkman, Jose A. & Soutter, Christine L., 2000. "Measuring Trust," Scholarly Articles 4481497, Harvard University Department of Economics.
  3. 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.
  4. 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.
  5. 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.
  6. Anne Case & Darren Lubotsky & Christina Paxson, 2002. "Economic Status and Health in Childhood: The Origins of the Gradient," American Economic Review, American Economic Association, vol. 92(5), pages 1308-1334, December.
  7. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
  8. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
  9. 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.
  10. 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.
  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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