Misspecifications in vector autoregressions and their effects on impulse responses and variance decompositions

This paper investigates the consequences of model misspecifications in vector autoregressions (VARs). We specifically consider the effects of misspecifications on estimated impulse responses and variance decompositions. Assuming the underlying economic system has an ARMA representation, we derive closed-form expressions for the inconsistency in VAR-parameter estimates caused by omitted variables, ignored moving average terms, incorrectly specified lag lengths, or incorrect orthogonalization of innovations. Using these results we derive the inconsistencies for implied impulse responses and variance decompositions. Employing a trivariate economic model, we examine the potential seriousness of these misspecifications in applied work.