Unconditional Quantile Regressions

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We propose a new regression method to evaluate the impact of changes in the distri- bution of the explanatory variables on quantiles of the unconditional (marginal) distrib- ution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explana- tory variables. The influence function, a widely used tool in robust estimation, is easily computed for quantiles, as well as for other distributional statistics. Our approach, thus, can be readily generalized to other distributional statistics.

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