Multivariate distribution regression

Abstract

This article introduces multivariate distribution regression (MDR), a semi-parametric approach to estimate the joint distribution of outcomes conditional on covariates. The method allows for studying complex dependence structures and distributional treatment effects while maintaining high flexibility. I show that the MDR coefficient process converges to a Gaussian process and that the bootstrap is consistent for the asymptotic distribution of the estimator. Methodologically, MDR contributes by offering the analysis of many functionals of the multivariate CDF, including counterfactual distributions. Compared to existing models, the contribution of MDR is its flexibility – it requires weak assumptions, is not affected by the curse of dimensionality, and does not require setting tuning parameters. Simulation studies show that MDR’s flexibility helps reduce potential biases at the moderate costs of increased variances. Finally, I analyze shifts in spousal labor supply in response to a health shock. I find that if low-income individuals receive disability insurance benefits, their spouses respond by increasing their labor supply. The opposite holds for high-income households, likely because they can afford to work fewer hours and look after their partner.