Follow the calculation from growth to debt

The model constructs a fiscal baseline, then changes productivity under climate scenarios. The debt equation connects the real economy and public finances.

Debt dynamics

d(t) = [(1 + r(t)) / (1 + g(t))] × d(t−1) − pb(t)

Here d is debt divided by GDP, r is the nominal interest rate on government debt, g is nominal GDP growth, and pb is the primary surplus divided by GDP. Use decimal rates consistently. A larger primary surplus reduces debt. A higher interest-growth multiplier raises the contribution of inherited debt.

The basic equation omits exchange-rate valuation and stock-flow adjustments. The workbook-shaped baseline also floors debt at zero, while climate scenarios allow negative debt, interpreted as net assets. Once that floor binds, a scenario gap can reflect the asymmetry as well as the climate transmission.

Check the source: IMF User Guide, p. 16; official workbook, Baseline!Y36 and Hot!Y35.

Construct real and nominal GDP

Real GDP = labour productivity × employment
1 + real GDP growth = (1 + productivity growth) × (1 + employment growth)
1 + nominal GDP growth = (1 + real GDP growth) × (1 + GDP-deflator growth)

Labour productivity measures output per employed person. Employment growth after WEO is proxied by working-age population growth, holding the employment-to-working-age-population ratio constant. Faster population growth therefore affects this projection through an assumption about employment. It does not establish that the economy will create those jobs.

Historical productivity levels, the WEO-period residual, and the user’s long-run productivity path play different roles. The productivity controls set an asymmetric convergence path after WEO. Its timing parameter shifts that path. The setting is not a halfway-growth date and the start parameter need not equal the first computed annual value.

Check the source: IMF User Guide, p. 25; official workbook, Baseline!Y7:Y15 and Productivity!B24.

Construct the fiscal baseline

After WEO, nominal revenue grows with nominal GDP. Primary expenditure grows with productivity, prices and total population, with those three factors multiplied together. If the fiscal rule is on, the previous year’s adjustment is then added in currency units. Primary balance equals revenue less primary expenditure, excluding interest.

The distinction between working-age and total population matters: one drives the employment proxy and GDP, while the other enters baseline spending. The debt target activates a fiscal response under the rule’s conditions. It is not a hard cap, a plan for specific spending cuts or evidence that the adjustment is politically feasible. The model has no feedback from that adjustment to GDP.

Financing assumptions determine the weighted average nominal interest rate after WEO. The constant-real and normalized interest-growth-differential approaches use lagged baseline inflation or growth. Climate scenarios retain the baseline interest-rate path.

Check the source: IMF User Guide, p. 29; official workbook, Baseline!Y25:Y29, X42 and Interest Rate!B17:B19.

Trace the climate effect through the budget

The scenario supplies an adjustment to productivity growth.
Employment and prices follow the baseline assumptions, so the productivity adjustment changes real and nominal GDP.
Revenue retains the baseline GDP share. A lower GDP level therefore reduces revenue in currency.
Expenditure rigidity determines how much primary spending adjusts to the GDP change.
The resulting primary balance and GDP denominator alter the debt ratio.

Rigidity 1 keeps spending at its baseline currency level in each year. Rigidity 0 keeps its baseline share of GDP. Intermediate settings divide that adjustment proportionately. The debt gap consequently depends on the fiscal response as well as the climate path.

Check the source: IMF User Guide, p. 19; official workbook, Hot!Y8:Y14, Y24:Y28 and Y35.

Match the model to the question

The built-in scenarios address persistent temperature-related effects through productivity. They do not simulate a particular drought’s output loss, emergency spending, inflation and recovery. They also omit sea-level rise, tipping points and the costs of adaptation. The IMF workbook separately accepts manual discrete fiscal overlays. That workbook facility is not implemented by this Explorer.

The reference climate trajectory follows the historical temperature trend. It is not a world without warming. An adaptation-speed comparison changes the empirical adjustment path under Hot temperatures. It does not cost or evaluate a named investment programme.