We propose an alternative (“dual regression”) to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the quantile regression process while largely avoiding the need for “rearrangement” to repair the intersecting conditional quantile surfaces that quantile regression often produces in practice. Dual regression can be appropriately modified to provide full structural distribution function estimates of the single equation instrumental variables model; this and similar extensions have implications for the analysis of identification in econometric models of endogeneity.

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