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Quantile uncorrelation and instrumental regression

Komarova, Tatiana, Severini, Thomas and Tamer, Elie (2010) Quantile uncorrelation and instrumental regression. Econometrics Discussion Papers, EM/2010/552. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.

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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.

Item Type: Monograph (Discussion Paper)
Official URL: http://sticerd.lse.ac.uk
Additional Information: © 2010 The Authors
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Journal of Economic Literature Classification System: C - Mathematical and Quantitative Methods > C0 - General
Sets: Departments > Economics
Collections > Economists Online
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: EM/2010/552
Date Deposited: 20 Feb 2012 12:47
URL: http://eprints.lse.ac.uk/41949/

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