Bi-integrative analysis of two-dimensional heterogeneous panel data model

TL;DR

This paper introduces a novel bi-integrative regression model for two-dimensional heterogeneous panel data, capturing group and cohort effects simultaneously, with proven theoretical properties and demonstrated empirical effectiveness.

Contribution

It develops a new bi-integrative procedure with an ADMM algorithm for two-dimensional heterogeneous panel data, incorporating group and cohort structures with proven consistency and oracle properties.

Findings

The proposed estimator is asymptotically normal and consistent.

Simulation studies show good finite sample performance.

Application to real data demonstrates practical utility.

Abstract

Heterogeneous panel data models that allow the coefficients to vary across individuals and/or change over time have received increasingly more attention in statistics and econometrics. This paper proposes a two-dimensional heterogeneous panel regression model that incorporate a group structure of individual heterogeneous effects with cohort formation for their time-variations, which allows common coefficients between nonadjacent time points. A bi-integrative procedure that detects the information regarding group and cohort patterns simultaneously via a doubly penalized least square with concave fused penalties is introduced. We use an alternating direction method of multipliers (ADMM) algorithm that automatically bi-integrates the two-dimensional heterogeneous panel data model pertaining to a common one. Consistency and asymptotic normality for the proposed estimators are developed. We show that the resulting estimators exhibit oracle properties, i.e., the proposed estimator is asymptotically equivalent to the oracle estimator obtained using the known group and cohort structures. Furthermore, the simulation studies provide supportive evidence that the proposed method has good finite sample performance. A real data empirical application has been provided to highlight the proposed method.