Frank Schmid · 7 November 2026 · The findings of the paper, by its sections

Fiscal Capacity and Sovereign Debt Crises in the G7

The page sets out, in the paper’s order, the fiscal capacities read from each economy’s record, the baselines and the fiscal limit, the central scenarios for the G7 economies and China, the shares of simulated paths with at least one year on the crisis equilibrium, and the settings that would remove it.

The fiscal records the paper reads end in 2024 or 2025; its scenarios start from the position of 2026 and run from 2027 through 2036.

What this page shows

The model
The paper models the public debt of the seven G7 economies, with China modeled beside them, from 2026 through 2036. A government's borrowing cost includes a sovereign spread over the risk-free rate; the spread depends on how far the debt stands from a fiscal limit, the present value of the largest primary surplus the government can sustain; and the debt depends in turn on the borrowing cost. The price of the debt in a year is a root of that loop.
The crisis equilibrium
Over a range of debt, the crisis zone, the loop has three roots, two of them stable: a benign one and a crisis one at a higher yield, with an unstable one between them that the model never selects. Which of the two the market prices is a matter of coordination among investors, drawn in the model as a random event, the sunspot. Beyond the zone only the crisis root exists. An economy is on the crisis equilibrium in a year in which its debt is priced at the crisis root.
The baseline and the two regimes
The baseline is the path on which investors never coordinate on the crisis root. The paper follows two configurations of U.S. policy, each in force in every year of the horizon. Under regime M the U.S. primary balance follows its projected path, the automatic stabilizers, and a response to the sovereign spread, and the policy rate responds more than one for one to inflation. Under regime F the U.S. primary balance does not respond to the spread or the debt, the policy rate responds less than one for one, and the price level bears the adjustment. The other economies keep the rules of regime M under either, so their paths under the two regimes differ only through the U.S. crisis paths, which reach them through long-term interest rates and trade.
Fiscal capacity
The fiscal capacity is the largest primary surplus (the budget balance before net interest) a government can sustain. The paper reads it from each economy's own record, as the largest average primary surplus over 10 consecutive years the government has run, since 1950, or since the record's first year where it begins later, with receipts from abroad excluded. China's record shows no 10-year average of the primary balance above zero, and its capacity is scaled from its revenue.
A share of paths
The model is run 10,000 times, each run with its parameters and its annual shocks drawn at random within stated ranges. A share of paths is the percentage of those runs in which an event occurs in at least one year of 2027 through 2036. It is a share of the model's simulated paths under the stated assumptions, not a forecast and not a probability estimated from a record.

The central scenarios and the simulated paths, by economy

Each row of the strip is one run of the model for one economy: the baseline, regime M, and regime F. A dark cell is a year on the crisis equilibrium; a mid-gray cell, a year in which a crisis root exists and the economy is not on it; and a pale cell, a year with no crisis root.

Years on the crisis equilibrium

on the crisis equilibriuma crisis root exists; the economy is not on itno crisis root

First year on the crisis equilibrium (years on it), and the share of simulated paths with at least one such year

Debt is net debt: debt held by the public for the United States, and the IMF staff's augmented debt for China.

Fiscal capacity: where it is read, and where a result turns on it

The capacity is read from each economy's long record of its primary balance, as the largest average over 10 consecutive years, receipts from abroad excluded. The chart shows the record for the economy selected, with the 10 years shaded.

The historical fiscal capacities

balance before net interest, percent of GDPthe 10-year windowthe fiscal capacity

The largest capacity at which each economy spends a year on the crisis equilibrium, percent of GDP

One economy's capacity is set to each value of a grid, every other economy's at its historical value, and the model is run whole. A point is the largest capacity tried at which the economy spends at least one year on the crisis equilibrium in that run; above it, it spends none. Where the tick, the historical capacity, lies to the left of a point, the economy has a crisis year in that run.

historical capacitybaselineregime Mregime F
The capacity is set from 2027, the operation of a capacity announced in that year, read as a counterfactual record rather than as a policy the market prices; an entry is the largest capacity that leaves a crisis year, and the requirement of the section “Removing the crisis equilibrium” is the smallest that leaves no crisis equilibrium.

The baseline and the limit

This section sets the model's baselines beside published projections and shows what the crisis root rests on: the fiscal limit discounted at a rate that includes the spread being solved for.

The baseline of the United States beside the Congressional Budget Office's projection, percent of GDP

The model's baseline is not fitted to the published projections; the distance is reported. The model's ratios are over calendar-year GDP and the CBO's over fiscal-year GDP.

the model's baselinethe CBO's projection

Debt held by the public

Net interest

The baselines of the six beside the IMF's projected net debt

The model holds each of the six economies' primary balance at its 2026 value, where the published projection has a path of its own; the primary-balance column is what that difference contributes to the gap.

The crisis root exists because the fiscal limit is discounted at a rate that includes the candidate spread. The table reads the pricing equation (the loop of the overview) of one economy and year four ways. With the limit held at its crisis value, the crisis root is the only one; with the limit held at its benign value, or discounted without the spread, the only root is at zero spread.

First year on the crisis equilibrium (years on it): the limit as the model forms it, and discounted without the candidate spread in every economy and year

The central scenarios, by economy

Each chart follows one quantity for the economy selected, under the baseline and the two regimes. Where the three lines coincide, the regimes do not differ for that economy in that year.

baselineregime Mregime Fyears on the crisis equilibrium, regime M
The overview defines the baseline and regimes M and F; an economy whose pricing equation has the crisis root alone is on the crisis equilibrium in the baseline as well.

Across the simulated paths

A bar is a share of the simulated paths of the simulation selected, not a forecast and not a probability estimated from a record: the percentage of paths on which the economy spends at least one year on the crisis equilibrium, and the percentage on which it arrives there by coordination while a benign root exists.

Share of paths, 2027 through 2036, percent

at least one year on the crisis equilibriumof which by coordination while a benign root exists
Every simulation other than the central one changes one feature of the central simulation and replays the same draws, so two simulations differ by that feature alone.

How much of the variance of an outcome lies between the parameter draws

The line is the median path; the bands hold the middle half and the middle nine tenths of the paths in each year. They describe the spread of the model's paths under its draws.

median25th through 75th percentile5th through 95th percentile

Removing the crisis equilibrium: the resolution map

For each economy the map covers, the table gives the setting of one instrument, announced in the year shown and held, at which the crisis equilibrium no longer exists for that economy. Three instruments are solved one at a time: a fiscal capacity, a ceiling on the sovereign spread, and an increment to trend growth.

The same, as bars, by the year of the announcement

2027202920312033

The combination: the smallest capacity that removes the crisis equilibrium at each spread ceiling announced in 2027 (ceiling in percentage points across; capacity in percent of GDP up)

regime Mregime Fthe historical capacity

The swing against the revenue and expenditure base: percent of GDP, percentage points of GDP, and percent of the WEO April 2026 general government revenue and outlays of 2027

The swing is the distance from the primary balance of 2027 to the historical capacity, and to the capacity required under regime M. Announced and priced, not delivered: the table states what a swing of the size would be against the base, not that it is delivered or how it would be split. The shares are on the general government basis of the WEO, while the model's U.S. balance is the federal one of the CBO.

The assumptions of the model

Each parameter with its value, its basis, and its treatment in the simulated paths: fixed, or drawn on the range shown.

The parameters of Appendix A of the paper.

Sources and limits

The paper

Fiscal Capacity and Sovereign Debt Crises in the G7, 7 November 2026. The paper states the model, its equations, its data, and each result shown here.

Public data sources

    The Assumptions panel gives the source of each parameter in its basis column.

    Limits

    • A share is a share of the simulated paths on which the event occurs in at least one year of 2027 through 2036. It is a share of the simulated paths under the stated assumptions, not a forecast and not a probability estimated from a record.
    • The results hold under the assumptions the Assumptions panel lists. Several of them rest on no record and are drawn on ranges of convenience; each is marked as such there.
    • The settings in the section “Removing the crisis equilibrium” are announced and priced by the market and not delivered on the path on which they remove the crisis equilibrium, and at the central calibration each must be held through the horizon and beyond it; they state what each instrument would have to be, not whether it is attainable. Each is reported at two decimals, rounded in the direction that still removes the crisis equilibrium.
    • The largest capacity at which an economy has a crisis year is found for one economy at a time, the others at their historical capacities, with the capacity set from 2027 and read as a counterfactual record rather than as a policy the market prices.
    • The reading of the fiscal limit without the candidate spread is a device for showing what the crisis root rests on; it is not a scenario of the paper.