Mean and Variance Regimes in Threshold VARs: Revisiting Regime-dependent Fiscal Multipliers
This paper develops the estimation theory for threshold VARs in which regimes govern not only the conditional mean but also the conditional variance, with regime boundaries determined endogenously by the data. We introduce the decoupled threshold VAR, in which mean and variance regimes are driven by different observable state variables and separate thresholds, and show that the joint-switching model is its constrained special case. Existing threshold estimators identify regimes from the conditional mean alone; we show that this is inconsistent when the regime change is in the variance – a common feature of macroeconomic data – and inefficient when it is in both, and provide a likelihood-based estimator that uses both moments. We establish consistency, derive the nonstandard limiting distribution of the thresholds, and show that their super-consistent rate leaves inference on the regime parameters unaffected. We apply the framework to U.S. government spending multipliers, where wars and major fiscal events constitute a separate high-variance regime. Once these episodes are isolated, significant state dependence emerges even at the thresholds imposed in earlier work, and post-WWII multipliers are larger in expansions than in recessions, reconciling apparently conflicting findings in the literature.