Introduction: A Nation of Spend First, Ask Questions Later

If there is any enduring law in fiscal economics, it is this: arithmetic always wins. Political rhetoric, on the other hand, is mercifully short-lived.

In Washington, talk of “fiscal cliffs” and “grand bargains” has become background noise, but the numbers keep moving regardless.

The US has long since abandoned the old-fashioned “tax and spend” tradition. Today, it’s simply spend – and leave the arithmetic to tomorrow’s bondholders.

Yet beneath the slogans, we find the same old constraint: debt compounding does not care for politics.

Each new round of tax cuts or entitlement expansion, if unfunded, is simply more grist for the inexorable mill of interest on interest.

Recently, even markets – for so long content to finance the world’s reserve currency on generous terms – have begun to adjust their expectations.

Auctions that would once have been routine now bring higher yields; rating agencies, even if usually last to the party, are finally marking the homework. None of this should be surprising. When arithmetic is neglected, it always finds a way to make itself felt.

Why an Interactive Model? Transparency Over Oracles

Commentary is easy, but transparent arithmetic is harder to find.

That’s why I have build a model for US debt dynamics – not as a forecast, but as a laboratory for disciplined thinking about fiscal sustainability.

It is not a black box and does not pretend to predict political cycles or market moods. It simply lets you interrogate the future with open assumptions, and see how far you have to go before the numbers push back.

You set the key parameters: real growth, inflation, the size of the primary deficit, and—if you wish—a path for new taxes such as a federal VAT.

The model then mechanically computes the evolution of US federal debt from 2025 to 2055, tracking how compounding works for or against you, depending on the scenario. You are free to be as optimistic or pessimistic as you like; the arithmetic doesn’t care.

The Engine: How the Model Works

At its heart, the model is a stylised version of the classic government debt identity.

The debt-to-GDP ratio next year equals last year’s, increased by the nominal interest rate (itself a function of real rate plus inflation), plus any primary deficit, all divided by nominal growth.

The basic relationship is brutally honest: if the interest rate on debt exceeds the economy’s growth rate, debt rises relative to GDP even with a balanced primary budget. If the government is running persistent primary deficits, as the US is, the process is all the more acute.

Real growth and inflation are your two levers for nominal GDP growth. Higher real growth is, naturally, the least painful way to contain the ratio, as the denominator grows faster. Inflation can “dilute” the debt, but only as long as markets do not fully adjust the nominal interest rate in lockstep. Unfortunately, in the long run, they tend to do just that.

The primary deficit is simply the fiscal gap before interest – spending minus revenues, net of debt service. Keep it permanently negative, and the debt snowballs; improve it, and the path stabilises or reverses.

This is the central variable, and, in practice, also the most politically sensitive.

Endogenous Real Rates: When Markets Update Their Expectations

Unlike many official projections, the model does not assume the real interest rate is fixed. Instead, it lets the real rate drift upwards as debt and deficits mount. The logic is that, as fiscal prospects darken, investors will rationally update their expectations about future taxation, inflation, or even default risk (though the latter is unlikely for the US, as long as it borrows in dollars). This higher risk premium feeds directly into interest costs, which then compounds the debt further.

This mechanism is not a forecast of “crisis”, but a sober recognition that the market will not ignore fiscal fundamentals forever. The real rate thus acts as the model’s automatic stabiliser – or, if left unchecked, as the system’s accelerant.

Policy Levers: Stabilising Debt via Tax or Inflation

The model does more than show you the standard path of doom. It also allows you to experiment with two stylised but revealing “solutions”: inflation and new tax revenue.

If you want to see how much inflation it would take to merely stabilise the debt ratio at its current (already high) level, you can do so.

The answer is, for all practical purposes, always uncomfortable – typically far above the central bank’s target, and sustained over decades.

This is not an attractive way out. The required inflation path only grows more extreme the longer fiscal inaction persists.

Alternatively, the model quantifies the fiscal gap—the improvement in the primary balance needed to put the debt back on a stable path.

In the US context, this could mean a broad-based VAT, which is still political kryptonite in Washington.

For perspective: to raise an extra 6-7% of GDP in revenue (enough to stabilise debt in the most plausible scenarios) would require a VAT rate not far off the European norm.

Scenario Analysis: Baseline, Fiscal Consolidation, and “Beautiful Bill”

To make these abstractions concrete, let’s walk through the three main scenarios pre-loaded in the model:

Baseline: Inertia as Policy

The Baseline scenario is “business as usual”. Real growth is set to a modest 1.8%, inflation is a respectable 2%, and the primary deficit trundles along at around 2% of GDP—roughly what the Congressional Budget Office now expects. The real rate, in this scenario, rises gradually as debt mounts.

The results are as sobering as they are predictable. Debt as a share of GDP climbs steadily, at first almost imperceptibly, but with compounding soon driving it towards 250% of GDP by 2055.

Interest payments alone, by then, absorb a colossal share of federal revenue. Fiscal space, in any real sense, disappears. If one is feeling generous, this path can be called unsustainable. A more accurate description is mathematically impossible to maintain for long.

Fiscal Consolidation: The Road Not (Usually) Taken

In the Fiscal Consolidation scenario, we allow for an outbreak of political discipline. New revenue—perhaps a broad-based VAT, perhaps entitlement reform—closes the primary deficit. The result is a flattening of the debt trajectory, followed by gradual improvement as compounding works in the government’s favour for a change.

The required adjustment, to be clear, is substantial.

Moving from a structural deficit of 5-6% of GDP to primary balance or surplus is no small feat, and there is scant evidence of the political appetite.

Still, the model shows that such a path would restore the government’s freedom of action, sharply reduce the interest bill, and lower the risk of future unpleasant surprises.

“Beautiful Bill”: The Populist’s Shortcut

Finally, there is “Beautiful Bill”—a scenario in which the government enacts large, unfinanced tax cuts and adds further to the spending tab, all in the name of growth or electoral convenience. No plausible increase in real growth materialises. Instead, deficits balloon, and the debt ratio follows suit.

Here, the model is merciless. Debt explodes well beyond the baseline, the real rate rises sharply as investors update their expectations, and the fiscal gap required to restore stability becomes almost insurmountable.

This is not so much a forecast as a warning: sooner or later, something must give—be it expectations for inflation, future taxes, or some combination thereof.

What the Model Leaves Out: The Limits of Arithmetic

For all its mechanistic clarity, the model is a simplification.

It assumes expectations adjust gradually and smoothly to fundamentals, but it cannot capture those “unpleasant monetarist arithmetic” dynamics that Sargent & Wallace warned of.

If policymakers persistently refuse to close the fiscal gap, expectations about future policy can, at some point, shift suddenly and en masse. Such an adjustment—where markets collectively realise that only inflation or new taxes can restore stability—can result in far more abrupt changes in borrowing costs, exchange rates, and the credibility of US institutions than any model of compounding can safely accommodate.

There are no sudden jumps in the model. No endogenous “expectations trap”, no capital flight, no regime shifts or market segmentation.

The special role of the dollar, the global search for safe assets, and international spillover effects—all are abstracted away. As such, the results here are likely to be on the optimistic side. The real world is never as forgiving as a spreadsheet.

Conclusion: The Arithmetic Does Not Negotiate

The point of this model is not to forecast the next bond auction or to warn of impending doom.

It is to lay bare the arithmetic: the simple, mechanical logic of debt, compounding, and expectations. Fiscal inaction will, sooner or later, force its own reckoning—not through market “panic”, but because the numbers themselves cease to add up.

You are invited to play with the assumptions, stress-test your own fiscal views, and see how quickly the US moves from mere discomfort to genuine crisis if nothing changes. The numbers do not negotiate, and the unpleasant arithmetic always gets the last word.

The model has been build using the Large Language Model Claude 4.0. You can test the model here.