Identification and estimation of dynamic random coefficient models

TL;DR

This paper develops methods to partially identify and estimate heterogeneity in dynamic panel models with individual-specific coefficients, addressing issues of non-point identification.

Contribution

It characterizes the identified sets for coefficient distributions in heterogeneous panel models and provides computationally feasible estimation procedures.

Findings

Unobserved heterogeneity affects earnings persistence among U.S. households.

The model accommodates discrete, continuous, and unbounded data.

Results reveal significant heterogeneity in earnings risk.

Abstract

I study linear panel data models with predetermined regressors (such as lagged dependent variables) where coefficients are individual-specific, allowing for heterogeneity in the effects of the regressors on the dependent variable. I show that the model is not point-identified in a short panel context but rather partially identified, and I characterize the identified sets for the mean, variance, and CDF of the coefficient distribution. This characterization is general, accommodating discrete, continuous, and unbounded data, and it leads to computationally tractable estimation and inference procedures. I apply the method to study lifecycle earnings dynamics among U.S. households using the Panel Study of Income Dynamics (PSID) dataset. The results suggest the presence of unobserved heterogeneity in earnings persistence, implying that households face varying levels of earnings risk which, in turn, contribute to heterogeneity in their consumption and savings behaviors.