Inference On Counterfactual Distributions

In this paper we develop procedures to make inference in regression models about how potential policy interventions affect the entire distribution of an outcome variable of interest. These policy interventions consist of counterfactual changes in the distribution of covariates related to the outcome. Under the assumption that the conditional distribution of the outcome is unaltered by the intervention, we obtain uniformly consistent estimates for functionals of the marginal distribution of the outcome before and after the policy intervention. Simultaneous confidence sets for these functionals are also constructed, which take into account the sampling variation in the estimation of the relationship between the outcome and covariates. This estimation can be based on several principal approaches for conditional quantile and distributions functions, including quantile regression and proportional hazard models. Our procedures are general and accommodate both simple unitary changes in the values of a given covariate as well as changes in the distribution of the covariates of general form. An empirical application and a Monte Carlo example illustrate the results.