Quantile Uncorrelation and Instrumental Regression

26 Pages Posted: 30 Nov 2010

See all articles by Tatiana Komarova

Tatiana Komarova

Department of Economics, University of Manchester

Thomas Severini

affiliation not provided to SSRN

Elie T. Tamer

Harvard University

Date Written: September 2010

Abstract

We introduce a notion of median uncorrelation that is a natural extension of mean (linear) uncorrelation. A scalar random variable Y is median uncorrelated with a kdimensional random vector X if and only if the slope from an LAD regression of Y on X is zero. Using this simple definition, we characterize properties of median uncorrelated random variables, and introduce a notion of multivariate median uncorrelation. We provide measures of median uncorrelation that are similar to the linear correlation coefficient and the coefficient of determination. We also extend this median uncorrelation to other loss functions. As two stage least squares exploits mean uncorrelation between an instrument vector and the error to derive consistent estimators for parameters in linear regressions with endogenous regressors, the main result of this paper shows how a median uncorrelation assumption between an instrument vector and the error can similarly be used to derive consistent estimators in these linear models with endogenous regressors. We also show how median uncorrelation can be used in linear panel models with quantile restrictions and in linear models with measurement errors.

JEL Classification: D91;I18

Suggested Citation

Komarova, Tatiana and Severini, Thomas and Tamer, Elie T., Quantile Uncorrelation and Instrumental Regression (September 2010). LSE STICERD Research Paper No. EM552, Available at SSRN: https://ssrn.com/abstract=1717446

Tatiana Komarova (Contact Author)

Department of Economics, University of Manchester ( email )

Arthur Lewis Building
Oxford Road
Manchester, M13 9PL
United Kingdom

Thomas Severini

affiliation not provided to SSRN

No Address Available

Elie T. Tamer

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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