Quantile continuous treatment effects

Continuous treatments (e.g., doses) arise often in practice. Methods for estimation and inference for quantile treatment effects models with a continuous treatment are proposed. Identification of the parameters of interest, the dose-response functions and the quantile treatment effects, is achieved under the assumption that selection to treatment is based on observable characteristics. An easy to implement semiparametric two-step estimator, where the first step is based on a flexible Box-Cox model is proposed. Uniform consistency and weak convergence of this estimator are established. Practical statistical inference procedures are developed using bootstrap. Monte Carlo simulations show that the proposed methods have good finite sample properties. Finally, the proposed methods are applied to a survey of Massachusetts lottery winners to estimate the unconditional quantile effects of the prize amount, as a proxy of non-labor income changes, on subsequent labor earnings from U.S. Social Security records. The empirical results reveal strong heterogeneity across unconditional quantiles. The study suggests that there is a threshold value in non-labor income that is high enough to make all individuals stop working, and that this applies uniformly for all quantiles. It also shows that the threshold value is monotonic in the quantiles.