Weighted-average quantile regression

TL;DR

This paper introduces a new weighted-average quantile regression framework, providing a consistent and asymptotically normal estimator, and demonstrates its application in financial and wage inequality studies.

Contribution

The paper develops a novel estimator for weighted-average quantile regression that is $\

Findings

Estimator is $\

Applied to financial data to analyze industry portfolio shortfalls.

Used in wage data to explore inequality and social welfare dependence.

Abstract

In this paper, we introduce the weighted-average quantile regression framework, $\int_0^1 q_{Y|X}(u)\psi(u)du = X'\beta$, where $Y$ is a dependent variable, $X$ is a vector of covariates, $q_{Y|X}$ is the quantile function of the conditional distribution of $Y$ given $X$, $\psi$ is a weighting function, and $\beta$ is a vector of parameters. We argue that this framework is of interest in many applied settings and develop an estimator of the vector of parameters $\beta$. We show that our estimator is $\sqrt T$-consistent and asymptotically normal with mean zero and easily estimable covariance matrix, where $T$ is the size of available sample. We demonstrate the usefulness of our estimator by applying it in two empirical settings. In the first setting, we focus on financial data and study the factor structures of the expected shortfalls of the industry portfolios. In the second setting, we focus on wage data and study inequality and social welfare dependence on commonly used individual characteristics.