# Abstract for:

## Quantile Uncorrelation and Instrumental Regression

Tatiana Komorova,
Thomas Severini,
Elie Tamer,
September 2010

Paper No' EM/2010/552:
Full paper

## 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.