Valeria Gargiulo

This paper proposes a novel approach to the estimation of threshold VARs in which the regimes govern the conditional variance as well as the conditional mean. We introduce the decoupled threshold VAR, in which the two sets of regimes are driven by different observable state variables with separate thresholds, both estimated from the data; the standard joint-switching model, in which the two thresholds coincide, is a special case, consistently selected and estimated under our general framework. Existing threshold estimators locate the regimes from the conditional mean alone. We show that this is inconsistent when there is a regime change in the variance – a common feature of macroeconomic data – and inefficient when both moments change, and we develop a likelihood-based estimator that uses both. We establish consistency, derive the nonstandard limiting distributions of the thresholds, and show that their super-consistent rate leaves inference on the regime parameters unaffected. The framework delivers a new reading of U.S. government spending multipliers. Wars and major fiscal events form a separate high-variance regime. Once it is isolated, significant state dependence emerges even at the thresholds imposed in earlier work, and post-WWII multipliers are larger in expansions than in recessions. The result reconciles apparently conflicting findings in the literature.