An Analytical Evaluation of Model Selection Criteria in the Context of Nested Panel Data Specifications with Correlated Errors

Abstract

This paper presents an analytical evaluation of model selection criteria specifically designed for nested panel data specifications characterized by correlated error structures. The investigation focuses on the theoretical foundations and empirical performance of information criteria including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC) when applied to hierarchical panel data models with complex error correlation patterns. Through extensive mathematical derivations and simulation studies, we demonstrate that traditional model selection approaches often fail to adequately account for the multilevel structure inherent in nested panel data, leading to suboptimal model choices and biased parameter estimates. Our analysis reveals that the presence of correlated errors at multiple levels significantly affects the asymptotic properties of standard information criteria, necessitating the development of modified selection procedures. We propose a novel framework that incorporates penalty adjustments based on the correlation structure of the error terms and the degree of nesting in the data hierarchy. The methodology accounts for both within-cluster and between-cluster correlations while maintaining computational feasibility. Simulation results indicate that our proposed approach achieves superior performance in terms of model selection accuracy, with improvement rates ranging from 15\% to 30\% compared to conventional methods across various data generating processes. The findings have important implications for empirical research in economics, finance, and social sciences where nested panel data structures are prevalent.