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FRM Part II · FRM Exam Part II · Monetary and Fiscal Policy: Safeguarding Stability and Trust

A government has a public debt-to-GDP ratio of 80%. Nominal GDP growth is 5% per year and the average nominal interest rate on its debt is 3%. The primary balance is exactly zero. Holding these constant, what happens to the debt-to-GDP ratio over time?

The debt-to-GDP ratio falls. With a zero primary balance, the ratio moves with the gap between the interest rate and nominal growth. Because growth of 5% exceeds the 3% interest rate, GDP grows faster than debt, so the ratio declines by roughly 1.5 percentage points annually.

  1. AIt rises, because the debt stock grows whenever interest is paid
  2. BIt falls, because nominal growth exceeds the interest rateCorrect
  3. CIt stays constant, because the primary balance is zero
  4. DIt rises, because a zero primary balance means the overall deficit equals GDP growth

Explanation

Debt dynamics: change in ratio ≈ (r - g)/(1+g) × d minus primary balance. Here r - g = -2%, so the ratio changes by about -0.02/1.05 × 80% ≈ -1.5 percentage points per year. The 'constant' option wrongly ignores the interest-growth differential.

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