Country A has a debt-to-GDP ratio of 120%, an interest rate of 2%, and GDP growth of 3%. Country B has debt at 60% of GDP, an interest rate of 5%, and growth of 1%. Which country faces a more problematic fiscal trajectory?
ACountry A, because its absolute debt ratio is twice Country B's
BCountry B, because r > g means its debt-to-GDP ratio will rise without primary surpluses, creating explosive dynamics
CCountry A, because high debt always signals fiscal irresponsibility regardless of growth rates
DBoth equally — any country with debt above 60% of GDP is on an unsustainable path
The critical diagnostic is r − g. In Country A, r (2%) < g (3%), so the denominator of the debt ratio grows faster than interest compounds the numerator — debt dynamics are self-correcting even with a small primary deficit. In Country B, r (5%) > g (1%), so debt compounds faster than the economy grows, and the debt ratio explodes without sustained primary surpluses. Country A's higher absolute debt level is much less alarming than Country B's unfavorable r − g dynamics. Fiscal sustainability is about trajectories, not snapshots.
Question 2 Multiple Choice
The intertemporal government budget constraint (IGBC) says a government is solvent if:
AIts annual deficit stays below 3% of GDP in every year
BIts debt-to-GDP ratio remains below 60% at all times
CThe present value of all future primary surpluses equals the current outstanding debt stock
DIt can roll over maturing debt in financial markets without triggering a liquidity crisis
The IGBC is a long-run solvency condition, not a short-run liquidity rule. It says: Debt today = PV(future revenues) − PV(future non-interest spending). A government that runs large deficits now can still be solvent if it credibly commits to sufficiently large future primary surpluses. Conversely, a government running small deficits in a high-debt, slow-growth environment may violate the IGBC. The 3% and 60% rules (EU Stability and Growth Pact) are arbitrary political thresholds, not theoretically derived solvency conditions.
Question 3 True / False
A government can sustain a primary deficit indefinitely as long as the economy's growth rate exceeds the interest rate on its debt.
TTrue
FFalse
Answer: True
When g > r, the debt-to-GDP ratio's denominator grows faster than its numerator compounds. This means the ratio can remain stable or even fall even while the government runs a primary deficit — the economy 'grows its way out' of the debt. This was broadly true in many advanced economies during the post-WWII boom and arguably in the 2010s with near-zero interest rates. The r − g comparison is the fundamental reason why some high-debt countries are sustainable and some low-debt countries are not.
Question 4 True / False
A government running a large fiscal deficit is necessarily on an unsustainable debt path.
TTrue
FFalse
Answer: False
Sustainability depends on r − g dynamics and the long-run trajectory projected by the intertemporal budget constraint — not on the current deficit level alone. A rapidly growing economy with g > r can sustain a primary deficit indefinitely. A government may also run a temporary large deficit during a recession or emergency (like a war or pandemic) and return to primary surplus afterward, satisfying the IGBC over the long run. The question is always whether current policy, projected forward with realistic assumptions, converges to a stable debt ratio — not whether today's deficit is large.
Question 5 Short Answer
Why is the comparison of r and g (interest rate minus growth rate) the primary diagnostic for fiscal sustainability rather than the absolute level of debt or the size of the current deficit?
Think about your answer, then reveal below.
Model answer: Fiscal sustainability is fundamentally a question about debt dynamics over time, not a snapshot comparison. The debt-to-GDP ratio evolves according to: Δ(D/Y) ≈ (r − g)(D/Y) − primary surplus/Y. When r < g, the (r − g) term is negative, which means debt compounds more slowly than the economy grows — even a primary deficit leaves the ratio trending downward. When r > g, every dollar of debt compounds faster than the tax base grows, creating explosive dynamics that require primary surpluses to counteract. The absolute debt level matters only in proportion to this dynamic: a 120% debt ratio is benign with r − g = −1%, dangerous with r − g = +4%. The current deficit similarly says nothing about sustainability without knowing the long-run r − g environment.
This is why standard fiscal rules based on deficit-to-GDP or debt-to-GDP thresholds (like the EU's 3% and 60% rules) are theoretically unsatisfying: they fix on static levels rather than the dynamic forces that actually determine whether a debt path converges or diverges. The r − g comparison gives the correct analytical foundation, even though projecting it 30–50 years into the future involves large uncertainty about future growth rates and interest rates.