Dynamic Heterogeneous Distribution Regression Panel Models, with an Application to Labor Income Processes

TL;DR

This paper develops a dynamic distribution regression panel model with heterogeneous coefficients, enabling analysis of how individual income distributions respond to shocks, with a bootstrap method ensuring robust inference, demonstrated through labor income data.

Contribution

It introduces a novel dynamic distribution regression panel model with heterogeneous coefficients and a bootstrap inference method, applied to labor income dynamics.

Findings

Substantial coefficient heterogeneity in income data

Negative income shocks significantly affect future income distribution

Methodology enables analysis of distributional impacts of shocks

Abstract

We introduce a dynamic distribution regression panel data model with heterogeneous coefficients across units. The objects of primary interest are functionals of these coefficients, including predicted one-step-ahead and stationary cross-sectional distributions of the outcome variable. Coefficients and their functionals are estimated via fixed effect methods. We investigate how these functionals vary in response to counterfactual changes in initial conditions or covariate values. We also identify a uniformity problem related to the robustness of inference to the unknown degree of coefficient heterogeneity, and propose a cross-sectional bootstrap method for uniformly valid inference on function-valued objects. We showcase the utility of our approach through an empirical application to individual income dynamics. Employing the annual Panel Study of Income Dynamics data, we establish the presence of substantial coefficient heterogeneity. We then highlight some important empirical questions that our methodology can address. First, we quantify the impact of a negative labor income shock on the distribution of future labor income.