Debt service and solvency

United States · observed starting scales, conditional stress paths

From borrowers’ cash flow to an economy-wide debt cycle

Households and firms buy each other’s output, borrow from financial institutions, and pay taxes to government. When many borrowers cut spending together, other people lose income. Debt service then becomes harder even for borrowers who were initially sound.

Country, period and measurement

Interactive macro mechanism · no recession probability

Watch pressure accumulate over time

1. Q0
   US historical scales initialize the experiment.
2. Q1–Q2
   Income falls; taxes, extra transfers, liquid buffers and temporary borrowing absorb part of the loss.
3. Q3–Q4
   Temporary gap lending stops. Some borrowers miss principal or capitalize unpaid interest; spending falls.
4. Q5 onward
   The direct shock ends, but overdue balances, lender write-offs and demand feedback persist.

After 12 quarters, overdue principal is $11.4bn and cumulative write-offs are $102.4bn. Lowest modeled employment share: 93.5%. Additional transfers and lower taxes cost $2144.9bn. These are scenario outputs, not estimates of US defaults or a recession probability.

How this becomes a macroeconomic vulnerability

Why taxes and social protection belong in this picture

Income taxes generally fall when taxable income falls. Unemployment benefits and some means-tested programs can rise as eligibility changes. Social Security retirement, survivor and disability benefits provide a continuing income floor, but they are not all unemployment-triggered payments. Medicare and Medicaid support health services; their spending is not interchangeable with cash available for loan payments. These channels change household resilience and government finances together.

Borrowing can delay a loss without curing it

A new loan can pay an old obligation today. If income cannot support the enlarged debt later, the unpaid amount accumulates, lending conditions tighten, spending falls and lenders eventually recognize losses. In the experiment, missed principal remains owed; it is not added to debt a second time. Unpaid interest is explicitly capitalized. A write-off reduces both the borrower’s liability and the lender’s claim.

Credit is a flow; the debt balance is a stock

Use net new borrowing = new loans − principal repayments. The change in a reported debt stock also includes capitalized interest where applicable, write-offs, revaluations and reclassifications. The pure model identity credit = change in debt holds only when those other changes are absent. Debt/GDP can rise because GDP falls, even when borrowing does not rise.

Why distribution can amplify the same aggregate shock

Two economies can have the same debt and income totals but very different exposures. Debt concentrated among borrowers with low cash buffers and high spending needs can create larger consumption cuts. Wealth concentration, leverage, collateral and access to finance matter separately from an income Gini. The income-share control deliberately redistributes a fixed income total between two invented borrower groups; it is not a fitted estimate of US inequality.

Transfers and ownership answer different questions

Transfers can cushion current spending and defaults even if they barely change long-run wealth concentration. Broader ownership can change future capital income and wealth accumulation. Neither result proves that one policy is always superior: compare the intended outcome, financing, behavioral response and time horizon. Federal Reserve research finds associations between inequality and several financial vulnerabilities; it does not establish that inequality alone causes or dates a crisis.

• CBO: automatic stabilizers and the federal budget
• Federal Reserve: inequality and financial-sector vulnerabilities

Actual ForeGlass Engine output · existing BRACKET-1 study

Explore the shock-response simulation paths

New: estimate output and employment fragility under a declared rate shock →

The paths below come from the existing engine, not the teaching ledger above. Employment, wages, profits, investment and debt evolve together. Compare each temporary annual real-interest-rate shock with its own baseline. All four starting-state variants are available; none is a central estimate or probability.

Different experiment: these paths use the existing study’s 2025Q4 debt constructions and assumed borrowing rates, with an older wage-share mapping. They are separate from the 2019 teaching anchors. The two debt endpoints have unresolved coverage comparability; they are not confidence-band edges. The imposed 2-percentage-point annual real-rate pulse affects all modeled debt for the first year, unlike a maturity-specific refinancing ladder.

Read the whole path: this experiment produces a small initial output shortfall and a later rebound above the paired baseline. Its effects are not a demonstrated persistent GDP loss. Horizontal axes show elapsed model years; records stop at 2.984375 years and the separate final state is at year 3.

To turn this into a current resilience service, add reviewed sector definitions and current inputs, a declared shock, maturity and policy/distribution channels where needed, and historical validation against meaningful outcomes. Accounting consistency alone does not establish predictive skill.

Download paths, assumptions, units and reproducibility hashes (JSON)

Can income support the required payments, and what stands behind the debt?

Debt service is a flow of required payments, including principal and interest. If income falls while payments stay fixed, those payments absorb more of the same-period income. Balance-sheet solvency asks a different question: how do asset values compare with all liabilities? Assets can exceed liabilities while cash is unavailable on the payment date. The market fragility index does not directly measure any of these household or company positions.

1. Income falls or required payments rise.
2. A larger share of income goes to debt service.
3. Less remains for other spending; repayment may require cash buffers, asset sales or new funding.

Synthetic teaching example · not a forecast

When income falls but payments do not

An invented household owes $12,000 in principal and interest over one year. Keep those payments fixed and change annual after-tax income and its loss. There is no mortgage escrow in this example. This illustrates payment-to-income arithmetic, not the published aggregate household DSR.

$60,000 × (1 − 20%) = $48,000 annual income after the shock. $12,000 ÷ $48,000 = 25.0% required-payment burden, compared with 20.0% before the shock. $36,000 remains before food, housing costs outside these payments, and other expenses.

Evidence to watch

Keep each observation’s definition, date and reporting frequency. A daily page refresh does not create new daily balance-sheet data.

What this example leaves out

• This example does not estimate a probability of default or define a safe payment ratio. The amount left is before other living expenses, not savings or a complete budget.
• Aggregate household ratios can hide borrowers with much larger burdens. Corporate EBIT coverage, household payment ratios and public-debt measures have different numerators, denominators and populations.
• The example fixes the payment schedule and omits assets, refinancing, arrears and changes in borrowing costs. A full assessment needs those records and their dates.

These mechanisms can overlap. Adding their example outputs does not produce an overall fragility score or a recession probability.

Further mechanism sources

• Federal Reserve: current household debt service ratio definition and methodology
• Federal Reserve: corporate interest coverage and debt-servicing capacity

Observed US starting values and their dates are attributed above. The smaller example uses authored numbers; all stress paths retain their own stated assumptions.

Explore the other dimensions

Return to the vulnerability overview and current market reading →