Nonlinear Drivers of Macroeconomic Tail Risk: A Threshold Stochastic Volatility-in-Mean VAR with Regime-Dependent Leverage

Haroon Mumtaz and Sofia Velasco

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Abstract: The tails of macroeconomic outcomes can respond differently from the centre of their distribution: shocks with modest effects on median growth or inflation can shift downside growth or upside inflation risk. We develop a threshold stochastic-volatility-in-mean VAR with regime-dependent leverage to study their structural drivers. The model allows endogenous interactions between outcomes and volatility, contemporaneous level-volatility dependence, and regime-specific propagation. In nearly 150 years of U.S. data, predictive model selection supports three inflation-defined regimes. We identify business-cycle, financial, macroeconomic-uncertainty, and financial-uncertainty shocks and decompose their contributions to growth- and inflation-at-risk. The structural composition of tail risk differs from that of the predictive median. Business-cycle shocks dominate the median response of GNP growth but account for a substantially smaller share of growth-at-risk. Macroeconomic uncertainty makes a material contribution to both growth- and inflation-at-risk, with its share of growth-at-risk increasing with the magnitude of a positive macroeconomic-uncertainty impulse, despite its limited role at the median. In high-inflation states, the contribution of financial uncertainty to inflation-at-risk rises with the magnitude of positive financial-uncertainty impulses.

Date: 2026-09
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