The Fiscal Impulse Metric & r − g Sovereign Debt Sustainability
Measuring whether government fiscal policy is actively stimulating or draining GDP, debt dynamics under the r − g equation, and the primary deficit boundary.
1. The Fiscal Impulse: Beyond Headline Deficits
Headline government deficits do not explain whether fiscal policy is adding to or subtracting from economic momentum. An economy running a static 6% deficit provides zero incremental fiscal push to GDP compared to the previous year. To measure the true macroeconomic stimulus, institutional economists compute the Fiscal Impulse:
A positive fiscal impulse indicates that tax policy and government discretionary outlays are expanding faster than automatic stabilizers, injecting net purchasing power into corporate cash flows and consumer balance sheets.
2. Sovereign Debt Dynamics & The Classical $r - g$ Equation
The mathematical sustainability of a nation's sovereign Debt-to-GDP ratio ($b = B/Y$) is governed by the difference between the government's average nominal borrowing cost ($r$) and the nominal economic growth rate ($g$):
Where $pb_t$ is the primary budget balance as a percentage of GDP (revenues minus non-interest spending). This relationship dictates two critical debt regimes:
| Regime | Mathematical Condition | Sovereign Debt Trajectory |
|---|---|---|
| Self-Stabilizing Growth | $r < g$ | GDP expands faster than interest compounds. A country can run modest primary deficits without increasing its Debt-to-GDP ratio. |
| Debt Snowball Spiral | $r > g$ | Interest costs compound faster than economic output. Debt-to-GDP increases exponentially unless a primary budget surplus is achieved. |
3. Fiscal Dominance & Monetary Policy Constraints
When the debt-to-GDP ratio exceeds critical thresholds and $r > g$, the central bank faces Fiscal Dominance: a state where raising interest rates to suppress inflation increases sovereign interest expense so rapidly that the resulting fiscal deficit injects more liquidity into the economy, undermining the intended monetary tightening.