Fiscal sustainability and public debt — African Macro 101 Module 3

Fiscal sustainability is the question of whether a government can keep spending and borrowing the way it currently is without eventually defaulting, monetizing the debt, or imposing a wealth-destroying adjustment. It comes down to one equation and three numbers.

The debt-dynamics equation

text

  Δ ( D / Y )    ≈    ( r  −  g )  ×  ( D / Y )    −    pb / Y

where:
  D / Y        =  the existing public-debt-to-GDP ratio at the start of the period
                   — the most-watched single indicator of fiscal sustainability
  Δ(D/Y)       =  the change in the debt-to-GDP ratio over one period (a year)
                   — what the equation predicts; positive means debt growing
                     faster than GDP, negative means shrinking
  r            =  the real effective interest rate on outstanding government debt
                   — average yield paid on the debt stock, deflated for inflation
                   — for Kenya in 2024-25, real rates on local-currency debt are
                     roughly 5-7% given nominal yields of 14-16% and inflation of 7-9%
  g            =  the real GDP growth rate of the economy
                   — Kenya's recent average around 5%; sub-Saharan Africa average 3-4%
  r − g        =  the interest-growth differential. Critical: if r > g, debt
                   compounds faster than the economy and you need a primary surplus
                   just to stabilise the ratio. If r < g, debt-to-GDP falls
                   automatically as long as the primary deficit is not too large.
  ( r − g ) × ( D / Y )  =  the 'automatic' debt buildup driven by the
                             differential applied to the existing debt stock
  pb / Y       =  primary balance as a share of GDP
                   — primary balance = government revenues − non-interest expenditures
                   — positive number is a primary surplus, negative is a primary deficit
                   — the lever a finance ministry actually controls in any given year

In words: the change in debt-to-GDP each year equals the interest-growth differential applied to the existing debt stock, minus the primary surplus (or plus the primary deficit). This is the equation everyone in sovereign macro fights about because it is the math that decides whether debt explodes, stabilises, or shrinks. Every IMF Debt Sustainability Analysis, every sovereign credit-rating committee, every finance minister's annual budget speech sits ultimately on top of this one equation.

Why each variable matters in practice

D/Y is the level the bond market and rating agencies anchor on. r is partly outside government control (global rates) and partly inside (the country's risk premium, which reflects its own track record). g is what finance ministries chase via structural reform — every percentage point of higher trend growth eases the math meaningfully. r − g is the headline number that decides whether the country is in the 'easy' regime (debt self-stabilising) or the 'hard' regime (needs primary surpluses to avoid debt explosion). pb/Y is what the finance minister can actually move via the budget, by raising taxes or cutting spending — politically painful but mathematically necessary when r > g.

What the equation tells you

If the real interest rate exceeds real growth, debt-to-GDP rises automatically unless you run a primary surplus large enough to offset it
If real growth exceeds the real interest rate (the 'r < g' world), debt-to-GDP can stabilize or fall even with modest primary deficits
Most developed economies post-2008 have lived in r < g territory; most African economies have lived in r > g — they need primary surpluses to keep debt in check
Currency mismatch makes the picture worse: depreciation raises the local-currency value of foreign-denominated debt overnight, even though no new borrowing has occurred

The 70% threshold

Empirically, debt-to-GDP above ~70% in emerging markets correlates strongly with subsequent debt distress, downgrades, and IMF programs. It's not a hard line — Japan operates at 250% — but for an emerging-market sovereign with currency mismatch, shallow domestic markets, and procyclical capital flows, 70% is the number where market access starts to become conditional.

The primary balance — what matters most

Primary balance = revenues − non-interest expenditures. It's the budget surplus or deficit before debt service. Why focus here? Because debt service is downstream of past borrowing decisions, while the primary balance is the choice you can actually make today. A country running a primary surplus of 2% of GDP is meaningfully different from one running a 5% primary deficit, regardless of the headline budget gap.

Reading the IMF Article IV

Every IMF member country gets an annual surveillance report — the Article IV. It contains the IMF's debt sustainability analysis (DSA), with baseline and stressed scenarios, projected debt-to-GDP paths, and explicit discussion of vulnerabilities. For any African country you care about, the Article IV is the single best source of independent fiscal analysis.

Stressed scenarios

A baseline DSA is fine; a stressed DSA is where the work happens. The standard shocks the IMF runs are: (1) growth shock — minus 1 to 2 percentage points for two years; (2) primary balance shock — adverse 2-3% of GDP for one year; (3) interest rate shock — plus 200-400 bps; (4) exchange rate shock — 30% depreciation. Combinations of these tell you how robust the baseline path actually is.

Common red flags

Beware: official growth projections that are 1-2pp above consensus; primary balance projections that show large adjustments without a credible policy plan; debt sustainability that depends on continued market access at favorable rates. These are how baselines look fine on paper while the real path heads for restructuring.

Exercise

A country has debt-to-GDP of 80%, real interest rate of 6%, real GDP growth of 4%, and primary deficit of 1% of GDP. What is the change in debt-to-GDP this year, and is the trajectory sustainable?