Bivariate Distribution Regression; Theory, Estimation and an Application to Intergenerational Mobility

TL;DR

This paper introduces Bivariate Distribution Regression (BDR), a method for estimating joint distributions of two outcomes conditioned on covariates, with applications to intergenerational mobility and analysis of dependence structures.

Contribution

It develops the theoretical properties of BDR, proposes inference procedures, and applies the method to analyze intergenerational income mobility using panel survey data.

Findings

Decomposition of joint distribution differences into composition, marginal, and sorting effects.

Analysis of gender differences in intergenerational mobility transition matrices.

Empirical results highlight the roles of observable and unobservable factors.

Abstract

We employ distribution regression (DR) to estimate the joint distribution of two outcome variables conditional on chosen covariates. While Bivariate Distribution Regression (BDR) is useful in a variety of settings, it is particularly valuable when some dependence between the outcomes persists after accounting for the impact of the covariates. Our analysis relies on a result from Chernozhukov et al. (2018) which shows that any conditional joint distribution has a local Gaussian representation. We describe how BDR can be implemented and present some associated functionals of interest. As modeling the unexplained dependence is a key feature of BDR, we focus on functionals related to this dependence. We decompose the difference between the joint distributions for different groups into composition, marginal and sorting effects. We provide a similar decomposition for the transition matrices which describe how location in the distribution in one of the outcomes is associated with location in the other. Our theoretical contributions are the derivation of the properties of these estimated functionals and appropriate procedures for inference. Our empirical illustration focuses on intergenerational mobility. Using the Panel Survey of Income Dynamics data, we model the joint distribution of parents' and children's earnings. By comparing the observed distribution with constructed counterfactuals, we isolate the impact of observable and unobservable factors on the observed joint distribution. We also evaluate the forces responsible for the difference between the transition matrices of sons' and daughters'.