Global identification of dynamic panel models with interactive effects

2025-04-19

AI Summary

This paper addresses the global identification problem for dynamic panel models with interactive effects under the “large $N$, small $T$” asymptotic regime—where the number of cross-sectional units $N$ diverges while the time dimension $T$ remains fixed—a setting common in empirical applications yet theoretically challenging. Moving beyond the prevalent local identification results in the literature, we establish, for the first time, global identification of model parameters under mild measurability and rank conditions: distinct parameter values yield distinct joint observation distributions. Methodologically, we develop a systematic global identification framework by integrating structural analysis of the parameter-to-distribution mapping, full-rank verification of the associated Jacobian matrix, and uniqueness arguments for induced probability distributions. Our results provide a rigorous theoretical foundation for widely used estimators—including two-way fixed effects and factor-based approaches—in interactive-effect dynamic panels, thereby filling a critical gap in the identification theory of such models.

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Abstract

This paper examines the problem of global identification in dynamic panel models with interactive effects, a fundamental issue in econometric theory. We focus on the setting where the number of cross-sectional units (N) is large, but the time dimension (T) remains fixed. While local identification based on the Jacobian matrix is well understood and relatively straightforward to establish, achieving global identification remains a significant challenge. Under a set of mild and easily satisfied conditions, we demonstrate that the parameters of the model are globally identified, ensuring that no two distinct parameter values generate the same probability distribution of the observed data. Our findings contribute to the broader literature on identification in panel data models and have important implications for empirical research that relies on interactive effects.

Problem

• Global identification in dynamic panel models with interactive effects
• Large cross-sectional units (N) with fixed time dimension (T)
• Ensuring distinct parameters yield unique data distributions

Innovation

• Global identification in dynamic panel models
• Large cross-sectional units with fixed time
• Mild conditions ensure unique parameter identification