🤖 AI Summary
This study addresses the issue of size distortion in weak exogeneity tests within dynamic linear models, which often arises due to omitted variables inducing reverse causality. To resolve this, the paper proposes a novel asymmetric Portmanteau test that avoids joint dynamic parametrization by constructing an asymmetric quadratic form statistic based on the sequential cross-correlation structure. This statistic effectively distinguishes between violations of weak exogeneity and genuine reverse causal effects, and under the null hypothesis, it follows an asymptotic normal distribution, thereby circumventing the size distortions inherent in conventional symmetric tests. An empirical application to economic policy uncertainty shocks reveals rejection of weak exogeneity; upon introducing control variables, the inflation response shifts from negative to positive, lending support to a supply-shock interpretation and demonstrating the practical utility of the proposed method.
📝 Abstract
This paper studies specification testing in dynamic linear models in the presence of omitted variables. The null hypothesis of interest is weak exogeneity: shocks have zero conditional expectation given their own past and the past of omitted variables. Existing tests based on quadratic forms of serial cross-correlations suffer from size distortions because their variance incorporates symmetric dependence in both directions, including causality from past shocks to present omitted variables (inverse causality). This paper proposes an asymmetric Portmanteau test that isolates violations of weak exogeneity from inverse causality, is asymptotically normal under the null, and does not require a parametric specification of the joint dynamics. An empirical application examines the Economic Policy Uncertainty shock series and rejects its weak exogeneity. Addressing this failure by controlling for omitted variables changes the estimated inflation response from negative to positive, suggesting a supply-side shock interpretation.