Fiscal Policy at the Zero Lower Bound
An economy has potential output Y* = 1,000. Aggregate demand is summarized by IS: Y = 880 + 2G - 4,000r, where G is government spending and r is the real policy rate in decimal form. Currently G = 40 and the central bank has set r = 0.001 because inflation is 0.3%, below the 2% target, and the nominal policy rate is already 0.1%. Output is therefore 956. The finance ministry proposes a one-off infrastructure package of 22 units, financed by issuing debt. Debt/GDP is 90%, the average nominal interest rate on debt is 1.0%, and nominal GDP growth is 2.5%. A critic argues that fiscal expansion is pointless because the central bank will offset it and that debt is already too high. You are asked to evaluate the size of the package, the likely multiplier at the zero lower bound, and the debt-sustainability objection.
1. Calculate the output gap and the government spending increase needed to close it using the given IS relationship. What does this imply about monetary policy?
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At G = 40 and r = 0.001: Y = 880 + 2(40) - 4,000(0.001) = 880 + 80 - 4 = 956.
Potential output is 1,000, so the output gap is 1,000 - 956 = 44, or 4.4% of potential.
The IS coefficient on G is 2, so the required increase is ΔG = 44 / 2 = 22. The proposed package of 22 exactly closes the gap if the multiplier is 2 and nothing else changes.
Monetary policy is constrained. The nominal rate is 0.1% and inflation is 0.3%, so the real rate is about -0.2%. Even if the central bank cut the nominal rate to zero, r would fall only from 0.001 to 0, raising Y by 4,000 × 0.001 = 4 units to 960. That leaves a gap of 40. Conventional monetary easing cannot close the gap, so fiscal policy must do the work.
2. Evaluate the likely size of the fiscal multiplier at the zero lower bound. Why might the actual multiplier be smaller than 2?
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At the zero lower bound the usual monetary offset is absent. A fiscal expansion that raises output and inflation would normally induce the central bank to raise rates, crowding out private demand. Here the nominal rate cannot fall further, so the multiplier is likely larger than in normal times, perhaps 1.5 to 2.5.
But several forces can make the actual multiplier smaller than 2. Ricardian households may save the debt-financed transfer, especially if they expect future taxes. Part of the spending may leak into imports. Supply bottlenecks and labour shortages may raise prices rather than output. If financial markets price higher sovereign risk, interest rates on private and public debt may rise, crowding out investment. Forward guidance that the central bank will tighten once recovery begins can also dampen the effect.
If the multiplier is 1, the 22-unit package adds only 22 to output and the gap remains 22. If it is 3, the package overshoots. Because the multiplier is uncertain, the package should be sized with a review clause rather than assumed to hit 1,000 exactly.
3. Assess the debt-sustainability objection. Is debt-financed spending dangerous here?
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The key debt-dynamics condition is the interest-growth differential. The average nominal interest rate is 1.0% and nominal GDP growth is 2.5%, so r - g = -1.5%. With debt at 90% of GDP, the interest-growth differential reduces the debt ratio by about 0.9 × 1.5% = 1.35% of GDP per year before any primary balance. This is favourable: debt can stabilise even with a modest primary deficit.
A one-off 22-unit package is 2.2% of current GDP. If the multiplier is 2, GDP rises to 1,000. Debt rises from about 860 to about 882, but the debt ratio falls to roughly 88%, because the denominator grows. If the multiplier is only 1, GDP rises to 978 and the debt ratio is about 90.2%, still broadly stable given r < g.
The objection would be stronger if the spending were permanent, if the multiplier were low, or if interest rates rose above growth. A one-off, well-targeted infrastructure package is sustainable under these parameters. The government should pair it with a credible medium-term fiscal framework so that the one-off nature is believed.