John P. de New, Melbourne Institute - Marginal Unit Interpretation of Unconditional Quantile Regression and Recentered Influence Functions using Centered Regression

Title: Marginal Unit Interpretation of Unconditional Quantile Regression and Recentered Influence Functions using Centered Regression

Abstract:  Unconditional quantile regressions, as introduced by Firpo, Fortin, and Lemieux (2009), is 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 distribution statistic of interest.  While there is general understanding with regards to the analysis and interpretation of changes in continuous variables, difficulties remain when understanding and interpreting dummies that describe qualitative characteristics. On the one hand, the implicit inter-relationship among binary variables is usually ignored, and on the other hand, that standard RIF regressions only capture effects at the margins, not distributional treatment effects. This paper suggests the use of restricted least squares regression analysis (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 better interpret the results of RIF-regressions in the presence of dummy variables. A Stata ADO implements this methodology.

Presenter: John P. de New, Melbourne Institute

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