Wider Panels, Higher Hausman Test Specificity: A Monte Carlo Study Under Missing Data

This study aims to determine how panel architecture, model complexity, and missing data conditions jointly affect the specificity of the Hausman specification test. A Monte Carlo analysis was conducted using 192,000 simulations (192 scenarios, 1000 replications each). Wide panels achieved the highest specificity at every model complexity level tested, declining only 2.9 percentage points (94.3% to 91.4%) from simple to high-dimensional models. Long panels declined far more steeply (87.1% to 73.7%), corresponding to an actual Type I error rate as high as 26.3% under a nominal 5% test, over five times the nominal level. Panel architecture, model complexity, and their interaction were all highly significant determinants of specificity (all p ≤ 10−122). All four missing-data mechanisms examined remained computationally viable under every condition tested, including 40% missingness, with zero computational failures throughout. Mechanism and missingness rate both reached statistical significance at this sample size, but their effect sizes were negligible (η2 = 0.0001 each), nearly 300 times smaller than panel architecture (η2 = 0.028). These results indicate that panel architecture and model dimensionality, not the missingness mechanisms examined here, are the dominant practical determinants of specification-test validity. Wide panels tolerate model complexity considerably better than conventional design heuristics suggest. This design identifies the pattern but cannot separate the contributions of cross-sectional and temporal sample size to it, motivating a specific, testable follow-up that varies N and T independently.