Marginal Unit Interpretation of Unconditional Quantile Regression and Recentered Influence Functions Using Centred Regression

Unconditional quantile regressions, as introduced by Firpo, Fortin, and Lemieux (2009), are a special case of Recentered Influence Functions (RIF) Regressions that can be used to relate how small changes in the distributions of explanatory variables affect an unconditional statistic of interest. While there is general understanding with regards to the analysis and interpretation of changes in continuous variables, difficulties remain when interpreting changes in qualitative characteristics (dummies). Firstly, the implicit inter-relationship among binary variables is usually ignored, and secondly, standard RIF regressions only capture effects at the margins, not distributional treatment effects. This paper suggests the use of restricted least squares regression analysis based on Haisken-DeNew and Schmidt (1997), combined with the use of centered continuous variables, and re-scaling, to isolate the intercept cleanly as the distributional statistic of interest and more appropriately interpret the results of RIF-regressions in the presence of dummy variables