A New Framework for Estimation of Unconditional Quantile Treatment Effects: The Residualized Quantile Regression (RQR) Model

The opportunities for understanding how treatment effects vary across different segments of the population have led to a rise in the use of quantile regressions for identifying unconditional quantile treatment effects (QTEs). However, existing quantile regression models fall into two categories: those that are unsuitable for identifying unconditional QTEs, and those that often struggle with the complex data structures common in sociology and other social sciences. Therefore, existing methods to identify unconditional QTEs are incomplete: the propensity score framework of Firpo (2007) allows for only a binary treatment variable, and the generalized quantile regression model of Powell (2020) faces difficulties with large data sets and high-dimensional fixed effects. This paper introduces a two-step approach to estimating unconditional QTEs, which is easy to use and aligns with the needs of sociologists. First, the treatment variable is decomposed into a systematic and random part, and then, the random variation in the treatment status is used in a bivariate quantile regression model. Through a series of simulations and three empirical applications, we demonstrate that the RQR approach provides unbiased estimates of unconditional QTEs. Moreover, the RQR approach offers greater flexibility and enhances computational speed compared to existing models, and it can easily handle high-dimensional fixed effects. In sum, the RQR approach fills a pressing void in quantitative research methodology, offering a much-needed tool for studying treatment effect heterogeneity.