New Tools, Novel Consequences: Testing Unconditional Quantile Regression Using Simulated Data
Recently, however, researchers have raised concerns over using conventional conditional quantile regression (CQR) modelling. Especially one issue has been highlighted: whether adding control variables changes the interpretation of the predictors, with even more devastating consequences when using fixed effects (e.g. Killewald and Bearak, 2014). To remedy these shortcomings, Killewald and Bearak (2014) argue that a new unconditional quantile regression model resolves these issues. A study showed higher motherhood wage penalty among low-wage women using individual-level fixed effects (Budig and Hodges, 2014); Killewald et al.(2014), however, demonstrate that new unconditional quantile regression give different results.
This new unconditional quantile model (UQR) was developed by Firpo et al. (2007, 2009). In Firpo et al (2007), they show how this method can be used to generalize conditional Oxacaca-Blinder decompositions, a counterfactual model devised for means, to other distributional statistics.
Conditional and unconditional quantile regressions should yield the same estimates when only one predictor is used. In this study, we test this key assumption. We use simulated data to test the performance of CQR and UQR. Our findings reveals that (1) CQR and UQR with one predictor sometimes produce different results – especially for skewed dichotomous variables; (2) the discrepancies worsen with specific types of measuring the predictor; (3) and also with the sample size. These findings do not necessarily undermine UQR, but we believe they are crucial guidelines to when and under which circumstances this new method can be safely deployed.