Testing for the Interconnection channel

When modeling the dynamics of a large cross section of interdependent variables, the employment of small scale Vector Autoregressive (VAR) models augmented by few factors, extracted as linear combination of the variables under analysis, is the typical solution to avoid the proliferation of parameters in large heterogeneous VARs. The factors’ loadings/weights can be estimated or derived from economic literature, and are usually interpreted as interconnection channels. We propose a novel Likelihood Ratio Test procedure to empirically evaluate the chosen set of weights, and show that testing is fundamental for valid inferences. We exploit the intuition that, if the factors employed are empirically valid, no remaining information from the cross section remains statistically significant. The proposed test is intuitive, easy to implement, and presents very good finite sample properties. In the empirical exercise, we test several interconnection channels for the sovereign bond market in the euro area.