Identification and estimation of dynamic random coefficient models

Authors: Wooyong Lee

Date of publication: October 2022

Working paper number: 03

Abstract: 

I study panel data linear models with predetermined regressors (e.g. lagged dependent variables) that allow the coefficients as well as the intercept to be individual-specific, permitting unobserved heterogeneity in the effects of regres- sors 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 sharp identified sets of the mean, variance, and CDF of the coefficient distributions. The characterization is general, allowing discrete, continuous, and unbounded data. A computationally efficient estimation and inference procedure is pro- posed, based on a fast and precise global polynomial optimization algorithm. The method is applied to study lifecycle earnings dynamics in U.S. households in the Panel Study of Income Dynamics (PSID) dataset. The results suggest substantial unobserved heterogeneity in earnings persistence, which implies that households face different levels of earnings risk that lead to heterogeneity in their consumption and savings behaviors.

Keywords: Panel data; Heterogeneous effects; Partial identification

Acknowledgement of Country

UTS acknowledges the Gadigal people of the Eora Nation, the Boorooberongal people of the Dharug Nation, the Bidiagal people and the Gamaygal people, upon whose ancestral lands our university stands. We would also like to pay respect to the Elders both past and present, acknowledging them as the traditional custodians of knowledge for these lands.