Interpretation of Regressions with Multiple Proxies
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 0110005.
Length: 32 pages
Date of creation: 14 Oct 2001
Date of revision:
Note: Type of Document - Latex; prepared on Unix latex; to print on HP; pages: 32 ; figures: included
Contact details of provider:
Web page: http://188.8.131.52
Proxy variables; measurement error; index construction;
Other versions of this item:
- Darren Lubotsky & Martin Wittenberg, 2006. "Interpretation of Regressions with Multiple Proxies," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 549-562, August.
- Darren Lubotsky & Martin Wittenberg, 2001. "Interpretation of Regressions with Multiple Proxies," Working Papers 836, Princeton University, Department of Economics, Industrial Relations Section..
- 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
This paper has been announced in the following NEP Reports:
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.:
- Scheinkman, Jose A. & Soutter, Christine L. & Glaeser, Edward Ludwig & Laibson, David I., 2000.
4481497, Harvard University Department of Economics.
- 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.
- Mauro, Paolo, 1995. "Corruption and Growth," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 681-712, August.
- 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.
- Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
- 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.
- Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
- 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.
- Anne Case & Darren Lubotsky & Christina Paxson, 2001. "Economic Status and Health in Childhood: The Origins of the Gradient," NBER Working Papers 8344, National Bureau of Economic Research, Inc.
- 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..
- 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.
- 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.
- 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.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).
If references are entirely missing, you can add them using this form.