Core Debt-Dynamics Equation
The model projects the debt-to-GDP ratio using:
dt =
((1 + it) / (1 + gt))
× dt−1
− pbt
+ st
-
d is the debt-to-GDP ratio.
-
i is the effective nominal interest rate.
-
g is nominal GDP growth.
-
pb is the primary balance, with surplus positive.
-
s is the stock-flow adjustment.
Nominal Growth
When growth is entered using real GDP growth and inflation,
nominal growth is calculated as:
1 + gn =
(1 + gr)
× (1 + π)
Primary-Balance Convention
A primary surplus is entered as a positive value and reduces the
projected debt ratio. A primary deficit is entered as a negative
value and increases the projected debt ratio, all else equal.
Interest payments are excluded from the primary balance because
their effect is already represented through the effective
interest-rate term in the debt-dynamics equation.
Scenario Construction
The baseline path uses the assumptions entered by the user.
The favorable scenario adjusts growth, interest rates, and the
primary balance according to the values entered under Favorable
Scenario Adjustments.
The adverse scenario applies temporary growth, interest-rate,
and primary-balance shocks during the selected shock window.
A one-time debt shock is applied only in the first shock year.
These paths are deterministic sensitivity scenarios. They are not
probability-weighted forecasts and do not estimate the likelihood
of any outcome.
Debt-Stabilizing Primary Balance
The debt-stabilizing primary balance is the balance that keeps the
debt-to-GDP ratio unchanged under the initial growth, interest-rate,
and recurring stock-flow assumptions.
pb* =
((i − g) / (1 + g))
× d
+ s
The reported primary-balance gap compares the entered balance with
this stabilizing requirement. A positive gap indicates that the
entered balance is stronger than the calculated requirement.
Target-Reaching Primary Balance
The target-reaching primary balance is the constant annual primary
balance that would mechanically produce the selected target debt
ratio by the end of the projection.
The model estimates this value numerically while preserving the
selected scenario’s growth, interest-rate, and stock-flow
assumptions.
Interest Burden
Interest expense as a share of GDP is approximated by multiplying
the effective nominal interest rate by the opening debt ratio.
Interest / GDP =
i × dt−1
Interest expense as a share of revenue divides this result by the
government revenue-to-GDP ratio entered by the user.
Foreign-Currency Valuation Effect
In the adverse scenario, the model can approximate the direct
increase in the domestic-currency value of foreign-currency debt
following an exchange-rate depreciation.
Valuation effect =
Opening debt
× foreign-currency share
× depreciation
This is added to the stock-flow adjustment in the first shock year.
It is a simplified accounting approximation and does not model
hedging, currency composition, repayment schedules, or indirect
macroeconomic effects.
Trajectory Signal
The model assigns a descriptive trajectory label according to the
change between starting and final debt:
-
Improving:
debt declines by at least 5 percentage points.
-
Broadly stable:
debt changes by more than −5 but no more than +2 percentage
points.
-
Rising:
debt increases by more than 2 but no more than 10 percentage
points.
-
Rapidly rising:
debt increases by more than 10 percentage points.
This is a mechanical model classification. It is not a sovereign
credit rating, crisis indicator, or official risk assessment.
Limitations
-
The model uses simplified annual assumptions and does not
estimate uncertainty around them.
-
It does not model the complete maturity, currency, holder, or
instrument structure of government debt.
-
It does not directly estimate refinancing risk, market access,
contingent liabilities, feedback effects, or fiscal reaction
functions.
-
Interest costs are approximated using an effective average rate
rather than a detailed debt-service schedule.
-
Favorable and adverse scenarios are user-defined sensitivities,
not probabilistic forecasts.
-
Results depend entirely on the assumptions entered and should be
interpreted alongside institutional and country-specific
evidence.
This model is an educational and analytical tool. It does not
constitute an official fiscal forecast, debt-sustainability
assessment, credit opinion, investment recommendation, or
financial advice.