Quantile Uncorrelation and Instrumental Regressions

Q3 Mathematics Journal of Econometric Methods Pub Date : 2010-09-01 DOI:10.1515/2156-6674.1001
T. Komarova, T. Severini, E. Tamer
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引用次数: 5

Abstract

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 k-dimensional 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.
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分位数不相关和工具回归
摘要我们引入了中位数不相关的概念,它是均值(线性)不相关的自然扩展。标量随机变量Y与k维随机向量X的中位数不相关当且仅当Y在X上的LAD回归的斜率为零。利用这个简单的定义,我们描述了中位数不相关随机变量的性质,并引入了多元中位数不相关的概念。我们提供了类似于线性相关系数和决定系数的中位数不相关度量。我们还将这种中值不相关扩展到其他损失函数。由于两阶段最小二乘法利用工具向量和误差之间的平均不相关来推导出具有内生回归量的线性回归中参数的一致估计,因此本文的主要结果表明,如何类似地使用工具向量和误差之间的中位数不相关假设来推导出具有内生回归量的线性模型中的一致估计。我们还展示了中位数不相关如何用于具有分位数限制的线性面板模型和具有测量误差的线性模型。
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来源期刊
Journal of Econometric Methods
Journal of Econometric Methods Economics, Econometrics and Finance-Economics and Econometrics
CiteScore
2.20
自引率
0.00%
发文量
7
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