Spectral Omnibus test for cross-sectional dependence in panel models

Abstract

The Spectral Omnibus test (SPECO) is introduced as a diagnostic for assessing departures from cross-sectional independence in panel model residuals. SPECO operates on the eigenvalue spectrum of the residual correlation matrix and aggregates six complementary spectral indicators—capturing dominance, separation, concentration, and disorder—into a single omnibus decision. For each indicator, empirical significance values are obtained from a Monte Carlo null cache indexed by panel dimension and combined using the Cauchy method, yielding reliable finite-sample inference without relying on large-sample edge approximations. Extended simulations spanning global (linear and nonlinear), structured (sparse and block), and robustness (temporal and non-Gaussian) dependence structures show that all procedures achieve nominal size after empirical calibration. In power comparisons, SPECO attains near-unit power under linear and monotonic dependence and delivers substantial gains under oscillatory, sign-varying alternatives, where standard moment-based and pairwise diagnostics can exhibit substantially reduced power. SPECO also remains stable under heavy-tailed errors, Gaussian mixtures, heterogeneous panels, and moderate temporal dependence. Overall, SPECO provides a computationally efficient, broadly applicable diagnostic when the form of cross-sectional dependence is unknown.