Finite-Sample Properties of Model Specification Tests for Multivariate Dynamic Regression Models
Koichiro Moriya, Akihiko Noda
TL;DR
The paper develops a multivariate specification-test framework by generalizing Durbin regression to SUR systems and recasting it as a GLS estimator that explicitly models cross-equation covariance and joint regressor–disturbance dynamics. It proves that the generalized Durbin estimator remains consistent under the broad EBD exogeneity class and achieves GLS efficiency when the cross-equation structure is correctly specified, while competing OLS/GLS and CO-type methods can fail in dynamic multi-equation settings. A Wald statistic based on the generalized Durbin estimator is proposed, with a bootstrap bias-corrected version (BC-GD) to improve finite-sample size control, including a fast double bootstrap algorithm. Monte Carlo experiments show near-nominal size and competitive power for BC-GD across BD, GEXOG, and EBD designs, and an empirical application to Fama–French factor models demonstrates more stable inference and sensitivity to test choice in higher-dimensional setups. Overall, the approach offers a principled, robust tool for multivariate specification testing in asset-pricing and related multiequation frameworks, outperforming traditional GRS/HAR tests when cross-equation dependence and regressor–error dynamics are present.
Abstract
This paper proposes a new multivariate model specification test that generalizes Durbin regression to a seemingly unrelated regression framework and reframes the Durbin approach as a GLS-class estimator. The proposed estimator explicitly models cross-equation dependence and the joint second-order dynamics of regressors and disturbances. It remains consistent under a comparatively weak dependence condition in which conventional OLS- and GLS-based estimators can be inconsistent, and it is asymptotically efficient under stronger conditions. Monte Carlo experiments indicate that the associated Wald test achieves improved size control and competitive power in finite samples, especially when combined with a bootstrap-based bias correction. An empirical application further illustrates that the proposed procedure delivers stable inference and is practically useful for multi-equation specification testing.