An IV Model of Quantile Treatment Effects1

This paper develops a model of quantile treatment effects with treatment endo-geneity. The model primarily exploits similarity assumption as a main restriction that handles endogeneity. From this model we derive a Wald IV estimating equation, and show that the model does not require functional form assumptions for identification. We then characterize the quantile treatment function as solving an “inverse ” quan-tile regression problem and suggest its finite-sample analog as a practical estimator. This estimator, unlike generalized method-of-moments, can be easily computed by solv-ing a series of conventional quantile regressions, and does not require grid searches over high-dimensional parameter sets. A properly weighted version of this estimator is also efficient. The model and estimator apply to either continuous or discrete variables. We apply this estimator to characterize the median and other quantile treatment effects in a market demand model and a job training program