Valdoria's Output Gap: Choosing a Policy Mix
Valdoria is a medium-sized open economy. Potential output is $500 billion and actual output is $470 billion. Unemployment is 7.8%, against an estimated natural rate of 5.0%. Headline inflation is 1.2%, below the central bank's 2% target, and has fallen for four quarters. The policy rate is 4.5%. Households spend 75 cents of each extra dollar of disposable income, the average tax rate is 20%, and the marginal propensity to import is 0.15. Government debt is 78% of GDP and this year's budget deficit is 4.2% of GDP. Labour force participation is 61%, and employers report 90,000 unfilled vacancies in skilled trades. The finance ministry proposes an $18 billion increase in infrastructure spending, financed by borrowing. The opposition argues that tax cuts would be faster and that fiscal expansion will push up debt and interest rates. The central bank meets in three weeks.
1. Calculate the output gap in dollars and as a percentage of potential output, and estimate the multiplier. Using the multiplier, estimate the effect of the $18 billion package on real GDP, and comment on the reliability of that estimate.
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Output gap. $470bn − $500bn = −$30bn, or −30/500 = −6% of potential output. The economy is in a deflationary (recessionary) gap. Okun's law suggests the 2.8 percentage point gap between actual unemployment (7.8%) and the natural rate (5.0%) is broadly consistent with this.
Multiplier. k = 1 ÷ (1 − MPC(1 − t) + m) = 1 ÷ (1 − 0.75 × 0.8 + 0.15) = 1 ÷ (1 − 0.6 + 0.15) = 1 ÷ 0.55 ≈ 1.82.
Estimated effect. $18bn × 1.82 ≈ $32.7bn, which would close the $30bn gap and slightly overshoot. Given inflation at 1.2% and unemployment well above the natural rate, a mild overshoot is acceptable and may help prevent hysteresis (lost skills and discouraged workers permanently lowering potential output).
Reliability caveats. The multiplier is a model average, not a forecast. It assumes spare capacity and no crowding out; in practice the effect depends on project timing (recognition, design and construction lags mean little is spent in year one), the import content of spending, the central bank's response, and confidence. The 90,000 skilled vacancies suggest part of the gap is structural mismatch, so extra demand may raise wages for scarce trades rather than output, implying a smaller effective multiplier and a steeper short-run aggregate supply curve. A good answer treats $32.7bn as an upper bound and notes the estimate does not tell us the effect on the unemployment rate, which may fall less than the output gap would suggest.
2. Explain why the proposed fiscal expansion might not close the output gap on its own, and assess whether the central bank should also act.
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Why fiscal policy may fall short. First, composition and timing: infrastructure has long lags, so the impulse may arrive after the gap has closed on its own. Second, import leakage (already in the multiplier) means part of the demand escapes abroad. Third, crowding out: with debt at 78% of GDP and a 4.2% deficit, further borrowing may raise bond yields and interest rates, displacing private investment, though in a recessionary gap crowd-out is usually partial. Fourth, the gap may be partly structural: 90,000 vacancies in skilled trades alongside 7.8% unemployment points to a mismatch, and demand stimulus cannot convert an unemployed hospitality worker into a welder. Fifth, Ricardian and confidence effects: households expecting future tax rises may save part of any stimulus.
The case for monetary action. The real policy rate is 4.5% − 1.2% = 3.3%, which is restrictive when output is 6% below potential and inflation has been falling for four quarters. A cut of 50 basis points would lower real borrowing costs, support investment and consumer durables spending, and - if it narrows the interest differential - put downward pressure on the currency, raising net exports. It also lowers the government's borrowing cost, reducing fiscal crowd-out, so the two instruments reinforce each other.
Limits. Transmission takes six to eighteen months, banks may not pass on the cut if their funding costs or capital positions are weak, and if falling inflation raises the real rate further, policy could be tightening even as the nominal rate falls. With rates at 4.5% there is room to cut, so a liquidity-trap argument is weak here.
Judgement. Monetary easing alone is unlikely to close a 6% gap because investment is more sensitive to expectations than to small rate changes, but it materially improves the fiscal package's chance of working. The best answer recommends coordination rather than choosing one instrument.
3. Recommend a policy mix and evaluate the trade-offs against the government's macroeconomic objectives.
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Recommendation. Combine (i) a smaller, front-loaded fiscal package of roughly $12–15bn concentrated on labour-intensive, import-light projects that can start within two quarters, plus apprenticeship and retraining funding aimed at the 90,000 skilled vacancies; (ii) a 50 basis point policy rate cut; (iii) a credible medium-term fiscal anchor, such as returning the deficit below 3% of GDP once the gap has closed, to reassure bondholders.
Why not the alternatives. The full $18bn with a 1.82 multiplier overshoots the gap at a time when part of the slack is structural, risking wage pressure in skilled trades and inflation above 2% while adding to debt. Tax cuts have a lower multiplier here - roughly 0.6 ÷ 0.55 ≈ 1.09 per dollar - because households save part of the gain, though they are faster to implement; the opposition is right about speed but wrong about effectiveness per dollar.
Trade-offs against objectives.
- Unemployment versus inflation: the size of the stimulus should depend on where the natural rate really is; if it is 6.5% rather than 5.0%, there is less slack and a smaller package is appropriate. There is genuine uncertainty about the non-accelerating inflation rate of unemployment.
- Debt sustainability versus demand: at 78% of GDP, higher borrowing raises interest costs and crowds out future spending; but failing to act risks hysteresis, which lowers potential output and worsens debt dynamics. The risk of doing too little currently exceeds the risk of doing somewhat too much, given inflation at 1.2%.
- Short-run versus long-run: demand measures act in months, supply-side measures in years, but only supply-side policy improves the inflation-unemployment trade-off and raises potential output.
- Distribution and external balance: infrastructure jobs favour certain regions and skills, while a rate cut affects the exchange rate and therefore exporters and importers differently.
Judgement. The mix is justified because fiscal and monetary policy reinforce each other, while the supply-side element addresses the mismatch that pure demand stimulus cannot. State a condition: if the central bank signals it will not cut, the fiscal package should be larger; if inflation expectations fall further, act faster.