Key Findings

• We project that the outer-bound debt-to-GDP ratio that the U.S. economy can sustain is about 210 percent of GDP. Above this level, there is no feasible future additional tax on broad-based labor income that can finance the interest payments at the returns demanded by financial markets.
• The calendar year by which fiscal policy must change (the required “closure year”) varies significantly with a major future cost driver: healthcare excess cost growth. The required closure year is 2051 (25 years from now) under lower healthcare excess cost growth, 2048 (22 years) under medium excess cost growth, and 2045 (19 years) under higher excess cost growth consistent with historical values. Under the historical growth rate of healthcare costs, there is a 25% chance of hitting the debt maximum in 14 years.
• Closing the imbalance at the required closure year would require a permanent additional tax of about 15 percentage points on all (uncapped) labor income. This new tax would raise more money than the combined contributions paid by employees and employers to the Social Security (OASI and DI) and Medicare Part A programs. This new tax is about three times as large as the corresponding static value, which does not account for the additional dynamic effects that our model captures: higher interest rates, a smaller tax base, and the labor-supply response implied by a Frisch elasticity of 0.54.
• As a sensitivity analysis, we consider a scenario with fewer international capital flows, consistent with sustained tariffs on imports of intermediate production goods that make U.S. domestic investment less competitive. Lower openness pulls the outer bound forward (shortens the runway) by two to four years.
• By design, these are outer-bound calculations and make two key assumptions. First, they assume that capital market values are currently efficiently priced; a sudden devaluation (e.g., AI bubble burst) would increase the economywide debt-to-capital ratio and the concomitant return that must be paid to debt holders. Second, the calculations assume that financial markets continue to believe Congress and the President will eventually restore fiscal sustainability, all the way up to the point where such a belief is no longer mathematically possible. Bond markets unravel sooner when investors believe that the government will not restore fiscal sustainability.

Background

In October 2023, the Penn Wharton Budget Model published the first quantitative estimate of the maximum debt-to-GDP ratio that the United States can sustain before financial markets cease to lend at any feasible tax rate.¹ Since then, the value of capital (ex-Treasuries) held by U.S. households has grown faster than GDP, producing an increase in the capital-to-GDP ratio that is more accommodating to new federal debt. This brief updates that estimate and provides more detailed computations and information.

More precisely, the quantity estimated here is the outer bound of federal debt capacity — sometimes called the solvency limit, or the “upper threshold” — beyond which default of either explicit (Treasury) debt or implicit (pay-as-you-go) debt becomes a near certainty on a real (inflation-adjusted) basis. It is the level at which the government can no longer credibly finance its obligations at any feasible tax rate, which we model as a broad-based labor income tax to mitigate distortions. Default need not wait for this bound to be reached, however. As Appendix A discusses, the classic framework of Cole and Kehoe (2000) shows that at lower, intermediate levels of debt a default can still occur rationally through a self-fulfilling run: if lenders come to expect default and refuse to refinance the debt, the resulting liquidity squeeze validates their expectation, much as a fundamentally solvent bank can still fail in a depositor run. The estimates in this brief characterize the outer bound itself, the latest point at which any feasible adjustment remains possible.

The Model

Estimating the outer bound of federal debt capacity requires substantial model sophistication. It cannot be estimated empirically, because the United States has never operated near that bound. It cannot be estimated with reduced-form models, because the outer bound depends on how households and financial markets price risk under fiscal stress, a non-linear behavior that the model must solve for rather than extrapolate.

More importantly, U.S. fiscal policy contains substantial pay-as-you-go transfers (“implicit debt”) that are more than twice as large as explicit (Treasury) debt while producing the same negative economic (“crowding out” of capital) effects (Gokhale and Smetters, 2025). Without this implicit debt, the maximum amount of explicit debt that could be supported would be substantially larger. Measuring implicit debt requires modeling the microfoundations of inter-generational transfers consistent with an overlapping-generations (OLG) lifecycle model. Furthermore, comprehensive analysis must also capture the relative price of risk versus risk-free assets. Capturing a full array of endogenous capital market prices requires an OLG model with aggregate uncertainty.

We use an internal model (olg-agg-2) that was built over the past five years by PWBM’s faculty director and several of his Ph.D. students from Penn’s Applied Mathematical and Computational Science program. The model solves for economic and financial market equilibrium in stochastic steady states and across the entire time-indexed ergodic distribution in stochastic transition paths (not just mean or median paths). Households (and investors) face idiosyncratic shocks (longevity and individual earnings) as well as aggregate productivity and depreciation shocks (asset returns and general wage level). They choose how much to work and save, and how to allocate savings between safe and risky assets. The government issues debt that competes with private capital in household portfolios, and the relative price of safe and risky claims responds endogenously to the size of the debt.

Aggregate productivity and depreciation shocks generate variation in total tax revenues, interest rates, and growth. The model produces realistic risk-free rates, levered and unlevered equity premiums, and a range of covariances (e.g., correlation of stock returns and consumption and wages) using traditional CRRA (not Epstein-Zin) preferences with a plausible value of risk aversion (equal to 3). In other words, there is no “equity premium puzzle” or “risk-free rate puzzle”. The model’s maximum debt is partly bounded by existing implicit debt, including pay-as-you-go transfers in Social Security; much larger debt thresholds could be achieved without those transfers.

The olg-agg-2 model used herein differs from the standard PWBM model that we use in most of our other analysis. While the state space of olg-agg-2 is about 20,000 times larger than that of our standard model, it still lacks some features that are present in our standard model. These missing features include nonstationary demographics, a distinction between pass-through and corporate businesses, and other fiscal institutional richness. Also, olg-agg-2 contains only a basic growth factor for modeling excess healthcare costs, defined as the growth in healthcare costs above economic growth. In contrast, our standard model includes detailed modeling of healthcare at the level of households, employers and healthcare providers, including endogenous dynamic adverse selection and moral hazard that determines prices as well as price growth in equilibrium.

We believe that olg-agg-2 is the first model to solve stochastic transition paths across the entire ergodic set, rather than focusing on just mean or median paths. Until recently this type of computational problem was viewed as NP-hard (infeasible to solve in realistic polynomial time); recent robust mathematical approximations and computational advances have made this problem more tractable. More detailed documentation will be released within a few months.

Calibration of Future Primary Deficits

PWBM (standard model) and the Congressional Budget Office (CBO) both project future spending, taxes and primary deficits (excess spending above tax revenue not including interest payments) as part of their respective budget work. For purposes of the current estimation presented herein, we calibrate future annual primary deficits so that future projected debt-to-GDP ratios are initially the same as CBO’s each year (Figure 1, the blue-colored “lower excess cost” line), using CBO’s main assumptions, including CBO’s projected real interest rates.

In practice, future primary deficits are sensitive to many factors, but especially the rate at which per capita health spending outpaces overall per capita growth in GDP (“healthcare excess cost growth”). The experts at CBO project that excess cost growth in healthcare eventually falls to zero over time. CBO’s projection is completely reasonable, especially since excess cost growth cannot persist indefinitely. PWBM projections are similar but PWBM typically projects higher excess cost growth rates along with a slower decline towards zero over time. CBO also projects that real interest rates will mostly return to a flat level after year 10, despite a rising debt level. The olg-agg-2 model presented below adds additional dynamics.

Figure 1 shows “reduced-form” debt-to-GDP paths (each using CBO interest rate assumptions) under three scenarios for healthcare excess cost growth. The “lower” scenario tracks the current CBO baseline and is constructed to produce the same debt-to-GDP ratio that CBO projects in its long-term projection model. The “higher” excess cost growth assumption tracks closer to historical experience over the past several decades and, for example, projects that healthcare costs per capita will increase by about $800 more next year than under the low path. The “medium” scenario, somewhat arbitrarily, splits the difference.

The debt-to-GDP ratios in Figure 1 grow more slowly than what we will present below. The reduced-form rules also do not compute interest rates (and other macroeconomic variables) where the supply of debt equals demand. Nor do they account for future tax payments required to finance that debt.

The outer bound of federal debt capacity

We now use the primary deficits calibrated from the last section within our olg-agg-2 model where interest rates (and other macroeconomic variables) are fully consistent with supply and demand across debt and capital markets. Household investors also see the potential state space associated with future values and future tax payments required to service the debt.

Figure 2 shows the median debt-to-GDP path implied by the PWBM dynamic olg-agg-2 model, together with the 25th-to-75th-percentile range across the model’s aggregate uncertainty. Importantly, these are not Monte Carlo simulations, in which a path can take any arbitrary form. A Monte Carlo simulation would be uninformative because it imposes no consistency between market demand, supply, and prices. Instead, for each sequence of shocks, each path we show in Figure 2 is always internally consistent, the equilibrium result of forward-looking markets. That consistency means that final closure must be imposed at some point.

When doing these calculations, we impose an upper bound of 210 percent of GDP on the debt-to-GDP ratio because the economy begins to become unstable along many of the simulated paths once debt exceeds that level. To be sure, larger debt-to-GDP ratios can sometimes be sustained, but not as consistently across different shock-driven paths. For computational efficiency, we also impose closure at year 30, even for those simulations with more favorable outcomes that have not breached the upper bound. For this reason, we focus mainly on median (rather than mean) simulated paths, while also reporting the probabilities of shorter paths out of prudence. Moreover, a stream of favorable shocks that raises tax revenue over time should also raise various costs through the accompanying productivity growth. That happens in our model for some major spending programs, including wage-indexed Social Security benefits. Salaries and payments in some other spending programs in our model, however, generally increase only with inflation, not economic growth.

Overall, the calibration of primary deficits in this exercise (outlined above) might bias a bit toward longer outer bounds rather than shorter ones, although it is still an active area of research. “Rare” shocks are limited to autoregressive terms in total factor productivity that generate realistic business cycles, together with depreciation shocks. But the combination of these negative shocks might still fall short of another 2008 financial crisis. We are actively investigating the extreme tail of negative shocks, since the actual data have very large standard errors.

Notice that by 2045, the reduced-form value for the higher excess cost case in Figure 1 shows a debt-to-GDP level equal to 169% whereas its median value is already at the 210% ceiling in Figure 2. The differences come from higher interest costs and relatively smaller GDP due to debt crowding out some capital formation.

Table 1 summarizes, for each excess cost scenario, the calendar year by which the median debt path reaches its outer-bound ceiling and the permanent additional wage tax rate required to hold the debt at that ceiling. The median path reaches a common ceiling of about 210% of GDP under all three scenarios; the scenarios differ in timing, reaching the ceiling in 2051 under lower excess cost growth, 2048 under medium excess cost growth, and 2045 under higher excess cost growth.

Because the required closure year is defined on the median path, it marks the point at which roughly half of the simulated economies have already reached the ceiling. Figure 3 shows the full distribution of timing: the cumulative probability that the debt-to-GDP ratio has reached its outer-bound ceiling by each year. The probability passes 50 percent in the required closure year by construction, but it continues to climb thereafter. By 2055 the ceiling has been reached with probability 60 percent under lower excess cost growth, 74 percent under medium excess cost growth, and 83 percent under higher excess cost growth.

The tax burden required to close the gap

Table 1 reports the permanent additional wage tax rate required to keep the debt-to-GDP ratio at its ceiling once the fixed-debt tax is fully in force. Two estimates appear for each scenario: a “static” tax estimate that mostly ignores dynamic effects as well as a dynamic estimate that comes from the olg-agg-2 model that includes dynamic effects. These dynamic effects include the impact of relatively larger future interest rates driven by debt, a smaller relative tax base (due to debt crowding out some capital) and labor supply responses. Dynamic tax estimates are about three times larger, equal to around 15 percent of all (uncapped) labor income. The revenue raised from this new tax would exceed the combined contributions paid by employees and employers to the Social Security (OASI and DI) and Medicare Part A programs.

Macroeconomic costs of approaching the outer bound

Figure 4 shows the transition paths for the main macroeconomic aggregates — capital, labor, GDP, consumption, and the wage rate — under each excess-cost scenario, expressed as percent changes from the model’s no-additional-debt benchmark. The capital stock falls substantially as the debt absorbs an increasing share of household portfolios. By 2060 the capital stock is 15.2 percent lower in the lower scenario, 17.5 percent lower in the medium scenario, and 18.8 percent lower in the higher scenario. Labor supply falls more modestly, by 3.7 percent below benchmark in the lower scenario, 4.5 percent in the medium scenario, and 4.7 percent in the higher scenario by 2060.

The wage rate declines roughly in line with the capital-labor ratio: by 2060 it is 4.8 percent below benchmark in the lower scenario, 5.5 percent below in the medium scenario, and 6.0 percent below in the higher scenario. GDP declines by 8.3, 9.7, and 10.4 percent across the three scenarios. Consumption falls by 6.8 percent in the lower scenario and by 7.4 and 7.8 percent in the medium and higher scenarios.

Financial market implications

Figure 5 shows the corresponding paths for the mean real return on capital (R), the risk-free rate (rf), and the equity premium (ep = R − rf), expressed in percent. The risk-free rate rises substantially as the debt approaches its outer bound: from 1.33 percent in 2026 to 2.69 percent by 2060 in the lower scenario, from 1.28 percent to 2.97 percent in the medium scenario, and from 1.31 percent to 3.06 percent in the higher scenario. The risk-free rate rises because the supply of government debt absorbs more of the marginal household saving, and households must be compensated more to hold it.

The mean return on capital rises more modestly, from about 3.7 to 4.4 percent in 2026 to about 4.7 to 5.2 percent by 2060, reflecting the scarcity of capital as the debt crowds out productive investment. Because the risk-free rate rises faster than the mean return on capital, the equity premium narrows slightly, from about 2.72 percent in 2026 to between 2.24 and 2.33 percent by 2060. The compression reflects the role of government debt as an absorber of households’ safe-asset demand.

Interpretation

The outer-bound calculation is not a forecast of what will happen. It is an upper limit on what financial markets can accommodate even under the most favorable assumption: that markets continue to believe Congress and the President will act, up to the point where the arithmetic forecloses any feasible action. The required closure year is the latest calendar year by which fiscal policy must change; any delay beyond that year forces an adjustment that is no longer compatible with a market-clearing equilibrium.

The common outer-bound ceiling of about 210 percent of GDP across healthcare excess cost growth scenarios, together with closure years that fall between 2045 and 2051, indicates that the outer bound is approaching within a horizon that current policy choices can still influence. The size of the required tax adjustment — particularly under the dynamic estimate — is large enough that earlier, smaller adjustments would be substantially less costly in present value.

Sensitivity Analysis: Reduced International Capital Flows

The model in the main text assumes that foreign investors purchase almost 40 percent of new U.S. Treasury debt. As a sensitivity, we reduce that share to 20 percent and recalibrate the primary deficits so that the reduced-form debt-to-GDP path remains consistent with Figure 1. A lower degree of openness of this kind is consistent with a future in which higher tariffs on intermediate production goods reduce capital inflows into the United States. The cost of government borrowing increases, thereby more than offsetting the positive revenue gains from tariffs.² Appendix B reports the full results.

Lower openness pulls the outer bound forward. The required closure year, the year the median debt-to-GDP path reaches the roughly 210 percent ceiling, arrives in 2047 under lower excess cost growth (21 years from now), 2045 under medium excess cost growth (19 years), and 2043 under higher excess cost growth (17 years), each two to four years earlier than in the main 40 percent open case.³ The tail timing risk is starker still: under higher excess cost growth there is already a 25 percent chance of reaching the ceiling by 2039, just 13 years from now. And although we do not present it separately for the sake of brevity, the real risk-free borrowing rate rises by an additional 50 to 55 basis points over the horizon relative to the 40 percent open case, as the larger domestic absorption of debt crowds out more capital.

Appendix A: Self-Fulfilling Debt Crises

The outer bound estimated in this brief is a solvency limit: the debt level beyond which no feasible tax can hold the debt-to-GDP ratio stable. A distinct concern is that a crisis can arrive earlier, before that limit is reached, driven by the expectations of lenders themselves. The canonical framework is Cole and Kehoe (2000), which sorts the level of debt into three zones.

Schematic of the Cole–Kehoe (2000) framework. The horizontal axis is the total debt stock.

When debt is low, the government’s incentive to repay is strong enough that it honors its obligations under any circumstances. Lenders anticipate this, so a run never starts and the equilibrium is unique (the safety zone). When debt is very high, the burden is large enough that default is the government’s optimal choice regardless of what lenders do; the equilibrium is again unique, but the outcome is certain default (the default zone).

Between these lies a crisis zone of intermediate debt with multiple equilibria, where the outcome depends on what lenders expect. The government is solvent but illiquid: it could service the debt if lenders keep rolling it over, but it cannot withstand a sudden refusal to refinance. If lenders stay confident, they roll the debt over and the government repays (the good equilibrium). If sentiment shifts toward default — even with no change in fundamentals — lenders refuse to refinance, the liquidity squeeze makes default unavoidable, and the pessimistic expectation validates itself (the bad equilibrium).

The practical implication is that the danger begins at the lower threshold, the point of vulnerability, rather than at the solvency limit itself. Once debt enters the interval of fragility, a crisis becomes possible on a shift in confidence alone. The required closure years in the main text should therefore be read as upper bounds on the time available for orderly adjustment: that window can close earlier if market sentiment turns.

Appendix B: Sensitivity to Lower Openness (20 Percent)

The main analysis assumes an open economy in which foreign investors absorb about 40 percent of federal debt. This appendix repeats the two central calculations, the median dynamic debt-to-GDP path (Figure 2) and the required closure year and extra wage tax (Table 1), under a less open economy in which foreign investors absorb only 20 percent of the debt, leaving a larger share in domestic portfolios. Because domestic households must hold more of the debt, it crowds out capital more heavily and the outer bound is reached sooner. Naturally, the model is recalibrated, consistent with the discussion in the main text for the assumed baseline openness.

Figure B1 shows the median dynamic debt-to-GDP path with its 25th-to-75th-percentile band, the 20 percent open analogue of Figure 2. The outer-bound ceiling is essentially unchanged at about 210 percent of GDP, but each scenario reaches it earlier than under 40 percent openness: in 2047 under lower excess cost growth, 2045 under medium excess cost growth, and 2043 under higher excess cost growth, compared with 2051, 2048, and 2045 in the main text.

Table B1 reports the required closure year and the permanent additional wage tax rate for the 20 percent open case, the analogue of Table 1. The static (conventional) rate is modestly higher than in the main analysis, at about 5.9, 6.5, and 6.6 percent across the three scenarios. The dynamic rate, which incorporates the model’s endogenous response, is again roughly two and a half to three times larger, at about 16.3, 16.6, and 17.1 percent across the three scenarios, somewhat above the corresponding main-text estimates.

This analysis was produced by Hangjun He, Yebiao Jin, and Kent Smetters.

Other References:

Congressional Budget Office. (2026, February 25). The long-term budget outlook data: 2026 to 2056. https://www.cbo.gov/publication/62044

Cole, Harold L., and Timothy J. Kehoe. 2000. “Self-Fulfilling Debt Crises.” Review of Economic Studies 67 (1): 91–116.

Gokhale, Jagadeesh, and Kent Smetters. 2025. “United States Federal Indebtedness and Fiscal Policy Trade-Offs.” Public Budgeting & Finance 45: 21–56. https://doi.org/10.1111/pbaf.12376

Footnotes

1. “When Does Federal Debt Reach Unsustainable Levels?”, Penn Wharton Budget Model (October 6, 2023) ↩

2. “Debt, Tariffs, and Capital Markets in a Dynamic Setting: An Explainer”, Penn Wharton Budget Model (May 23, 2025) ↩

3. Lower openness also strains the economy’s ability to reach the 210 percent ceiling itself, not just the speed at which it is reached. Because foreign investors absorb less of the debt, domestic households must hold a larger share, which crowds out capital more heavily and raises the return the debt must pay, so the economy approaches the point of instability at a lower level of debt. We nonetheless hold the ceiling fixed at about 210 percent for comparability with the main text; to the extent that the sustainable ceiling is in fact somewhat lower under 20 percent openness, the required closure years reported here would be slightly earlier still. ↩