Multivariate Distribution Regression

This paper introduces multivariate distribution regression (MDR), a semi-parametric approach to estimate the joint distribution of outcomes. The method allows studying complex dependence structures and distributional treatment eects without making strong parametric assumptions. I show that the MDR coecient process converges to a Gaussian process and that the bootstrap is consistent for the asymptotic distribution of the estimator. Methodologically, MDR contributes by oering the analysis of many functionals of the CDF. For instance, this includes counterfactual distributions. Compared to copula models, MDR achieves the same accuracy but is (i) more robust to misspecication and (ii) allows to condition on many covariates, thus ensuring a high degree of exibility. Finally, an application analyzes shifts in spousal labor supply in response to a health shock. I find that if low-income individuals receive disability insurance benets, their spouses respond by increasing their labor supply. Whereas the opposite holds for high-income households, likely because they are well insured and can aord to work fewer hours.