Identifying Heterogeneity in Dynamic Panel Models with Individual Parameter Contribution Regression

Abstract

Dynamic panel models are a popular approach to study interrelationships between repeatedly measured variables. Often, dynamic panel models are specified and estimated within a structural equation modeling (SEM) framework. An endemic problem threatening the validity of such models is unmodelled heterogeneity. Recently, individual parameter contribution (IPC) regression was proposed as a flexible method to study heterogeneity in SEM parameters as a function of observed covariates. In the present paper, we derive how IPCs can be calculated for general maximum likelihood estimates and evaluate the performance of IPC regression to estimate group differences in dynamic panel models in discrete and continuous time. We show that IPC regression can be slightly biased in samples with large group differences and present a bias correction procedure. IPC regression showed generally promising results for discrete time models. However, due to highly nonlinear parameter constraints, caution is indicated when applying IPC regression to continuous time models.