Finite-Sample Properties of Model Specification Tests for Multivariate Dynamic Regression Models

TL;DR

This paper introduces a new model specification test for multivariate dynamic regression models that remains valid under weaker exogeneity conditions, improving finite-sample performance with bootstrap methods.

Contribution

It develops a generalized Durbin estimator and bootstrap-based Wald tests that are consistent under minimal exogeneity assumptions and demonstrate better finite-sample properties.

Findings

Bootstrap Wald test improves size control in finite samples.

The proposed estimator remains consistent under the weakest exogeneity conditions.

Application to Fama-French models shows the test's practical relevance.

Abstract

We propose a new model specification test for multiple-equation systems with cross-equation error and dynamic regressor--error dependences. Conventional tests often rely on exogeneity conditions strong enough to ensure consistency of the OLS estimator. These exogeneity conditions are violated when regressors and errors are dynamically dependent, rendering conventional model specification tests invalid. To address these limitations, we clarify the relationship among alternative exogeneity conditions, characterize the consistency of competing multiple-equation estimators, and propose a generalized Durbin estimator for multiple-equation systems with an intercept, cross-equation error and regressor--error dependences. We show that our estimator remains consistent under the weakest exogeneity condition. We then derive its asymptotic distribution and construct Wald tests. Our Monte Carlo experiments confirm that the bootstrap-based Wald test substantially improves finite-sample size control. An application of the bootstrap-based Wald test to the Fama--French multifactor models leaves the null hypothesis unrejected in cases where competing FGLS-based tests reject it.