  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.
