@article {192371,
	title = {Quantile Uncorrelation and Instrumental Regression},
	volume = {1},
	number = {1},
	year = {2012},
	pages = {2-14},
	abstract = {Abstract. We introduce a notion of median uncorrelation that is a natural extension\&nbsp;of mean (linear) uncorrelation. A scalar random variable Y is median\&nbsp;uncorrelated with a k-dimensional random vector X if and only if the slope from\&nbsp;an LAD regression of Y on X is zero. Using this simple definition, we characterize\&nbsp;properties of median uncorrelated random variables, and introduce a notion of multivariate\&nbsp;median uncorrelation. We provide measures of median uncorrelation that\&nbsp;are similar to the linear correlation coefficient and the coefficient of determination.\&nbsp;We also extend this median uncorrelation to other loss functions.\&nbsp;As two stage least squares exploits mean uncorrelation between an instrument vector\&nbsp;and the error to derive consistent estimators for parameters in linear regressions\&nbsp;with endogenous regressors, the main result of this paper shows how a median uncorrelation\&nbsp;assumption between an instrument vector and the error can similarly\&nbsp;be used to derive consistent estimators in these linear models with endogenous\&nbsp;regressors. We also show how median uncorrelation can be used in linear panel\&nbsp;models with quantile restrictions and in linear models with measurement errors.
},
	url = {http://www.degruyter.com/dg/viewjournalissue.articlelist.resultlinks.fullcontentlink:pdfeventlink/$002fj$002fjem.2010.1.issue-1$002f2156-6674.1001$002f2156-6674.1001.pdf?t:ac=j$002fjem.2010.1.issue-1$002fissue-files$002fjem.2010.1.issue-1.xml},
	author = {Elie Tamer and Tatiana Komarova and Thomas Severini}
}
