US Deficit Regression Trend Lines

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The same regression trend lines as the S&P 500 page, applied to the federal budget from the overspending side. Data: OMB Historical Table 1.1, fiscal years 1901–2025, nominal dollars. Fiscal years ended June 30 through 1976 and September 30 since 1977.

• Cumulative deficit (default): every deficit since 1789 added up, minus surpluses. It's a stock of borrowing that, like the index, compounds over time. It approximates debt held by the public ($27.5T at FY2025).
• Annual deficit: outlays minus receipts each year. It turns negative in surplus years, so only the Linear fit applies.
• Outlays / Receipts: total federal spending and revenue each year.
• Interest (% of GDP) / Interest payments: two measures, chosen with Interest measure:
  • Total deficit × Fed rate (default): the prior fiscal year-end cumulative deficit times that fiscal year's average effective Fed funds rate (FRED FEDFUNDS; the 3-month T-bill rate, TB3MS, before FY1955). It prices the whole stock of borrowing at the policy rate, so it moves with the Fed. FY1935–2025 in dollars, FY1940–2025 as a % of GDP.
  • Actual outlays (FRED): federal interest actually paid (FRED FYOINT and FYOIGDA188S), FY1940–2025. That reflects the rates locked in when each bond was issued, so it lags the Fed. It appears to be gross interest, including interest credited to federal trust funds.

Each line is a least-squares fit from its start year through FY2025. Fit types and growth math are identical to the S&P page.

Latest: FY —

Growth rates — ,

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Annual growth rate (% per year) implied by each selected regression, plotted by its start year. Each start year has two values taken from the same trend line:

• Blue: average over window. The trend line's compound annual growth rate (CAGR) from its start year to FY2025.
• Red: at latest. How steep the trend line is at FY2025, as % per year. This is the pace the trend was growing at in FY2025.

Red above blue means borrowing/spending growth has been speeding up. Red below blue means it has been slowing down.

Exponential fits grow at a constant rate, so they show a single line. A Linear fit adds a fixed dollar amount per year, so its % rate falls as the level rises. Its average (CAGR) is shown only where the fitted line stays above zero.

vs. S&P 500 — is the relationship significant?

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The S&P 500 is sampled at each fiscal year-end (June 30 / Sept 30) and compared with the budget series chosen under Compare S&P 500 with, over the years both exist (FY1940–FY2025 for interest, FY1928–FY2025 otherwise). Interest as a % of GDP is the default because it measures the burden of the debt relative to the economy that has to carry it.

• Trend growth by start year: both series fit with the same model from each start year to FY2025. Matching curves mean the two trends compound at similar rates.
• Levels correlation: any two series that both grow over time correlate strongly. A Durbin-Watson statistic far below 2 means that correlation is likely spurious.
• Cointegration (Engle-Granger): tests whether the two levels share a stable long-run relationship. The statistic must be below about −3.37 for 5% significance (−3.07 for 10%).
• Annual growth correlation: compares year-over-year % changes, which removes the shared upward trend. Testing several lags makes a few p < 0.05 likely by chance (a Bonferroni-adjusted cutoff is shown).
• Trend difference: regresses ln(budget) − ln(S&P) on time with Newey-West standard errors, which allow for autocorrelated residuals. A slope near 0 means both grow at the same trend rate.
• Curvature: the t² coefficient of the log-quadratic fit. Significant means the trend growth rate itself has changed over time.
• Burden level → next 10-year S&P return (ratio series only): does a high interest burden predict weaker stock returns over the following decade? Overlapping 10-year windows are handled with 10-lag Newey-West errors.

Dollar series are nominal, so inflation is a shared driver of their long-run growth. Interest as a % of GDP is a ratio: it has no built-in upward trend, so its growth rate measures whether interest is outgrowing the economy.

Fit: change in Trend lines

Is the interest burden sustainable?

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A standard debt-dynamics projection, starting from FY2025 actuals in this data set:

• Debt (the cumulative deficit as a % of GDP) each year = last year's debt ÷ (1 + GDP growth) + interest + primary deficit.
• Interest = the interest rate × last year's debt ÷ (1 + GDP growth). With Total deficit × Fed rate this is exactly how the historical line is built, and the starting rate is the FY2025 average Fed funds rate. With Actual outlays, the starting rate is FY2025 interest paid ÷ the FY2024 cumulative deficit.
• Primary deficit is the deficit excluding actual interest paid (the same under both measures). It's held at the chosen % of GDP, and receipts stay at their FY2025 share of GDP for the "% of revenue" columns.

The key condition: if the interest rate r exceeds nominal GDP growth g, debt compounds faster than the economy even with a balanced primary budget. If r < g, a modest primary deficit can be stable.

The chart shows only your scenario (the red line), set with the inputs on the left. The defaults are r 4.7%, g 3.5% and a primary deficit of 2.5% of GDP. The preset scenarios (status quo, rates ease/rise, primary balance, faster growth) are compared in View scenario details.

Caveats: actual outlays appear to be gross interest (including trust-fund interest). The Fed-rate measure assumes all debt reprices at the policy rate every year, while real debt reprices over several years. The cumulative deficit understates actual debt (it excludes off-budget borrowing and trust-fund holdings), so the effective rate here is interest ÷ that proxy. Treat the crossing years as orders of magnitude, not dates.