Key Points
Capital markets are forward-looking and can respond rapidly to the growing debt paths, consistent with multiple equilibriums. Dynamic models that fully integrate microeconomics with macroeconomics capture these effects, whereas reduced-form models do not. While the recent modest rise in interest rates will increase the government’s borrowing costs, the much bigger concern is the potential for “jumping” from one equilibrium to the other.
Tariff analysis also requires using dynamic models. When interpreted as part of a larger set of fiscal policies, recent static analysis points to tariffs as being a very efficient revenue raiser that can grow the economy by paying down debt, or, more than fully finance the House budget reconciliation bill. In contrast, the evidence is more consistent with dynamic models with debt and intermediate capital goods, which produce opposite dynamics, including a higher cost of domestic capital and capital outflows. While generating new revenue, these costs dominate new tariff revenue gains.
Debt, Tariffs and Capital Markets in a Dynamic Setting: An Explainer
Bond markets are showing signs of stress that are pushing up yields. Using a large-scale overlapping generations lifecycle (OLG) model with aggregate risk and idiosyncratic risk, Penn Wharton Budget Model previously computed that the United States federal government could carry a maximum federal debt capacity between 175 and 200 percent relative to GDP. As noted in that analysis, this calculation was made under the “most favorable of assumptions for the United States,” where “investors believe (maybe myopically) that a closure rule will then prevent that ratio from increasing into the future. Once financial markets believe otherwise, financial markets can unravel at smaller debt-GDP ratios.”
But options do exist. We have recently shown how a large-scale set of reforms can fully stabilize the debt-GDP while growing the economy and enhancing the social safety net. These calculations are done within a consistent framework that fully accounts for all interactions, incentives, prices, and transfers. Of course, any specific large-scale reform might be viewed as having a small probability of being enacted. But current law is unsustainable, and so it has zero probability of continuing indefinitely.
Still, the problems with current law are not new. So, why are fixed-income markets growing concerned? It is likely more complicated than first meets the eye.
Budget reconciliation itself does not represent new information to capital markets. In fact, its total estimated costs have consistently declined over the past two months. Media routinely reported new primary deficits of $8 trillion or more immediately after the 2024 presidential election.1 (We estimate that the House bill that just passed will cost about $2.8 trillion over the budget window.) Several of these reports originated from third-party groups with a visible media presence. It is plausible that market participants accounted for the nature of these sources in forming their expectations. Still, the likely net effect of early media was to normalize the actual costs of budget reconciliation, making them more palatable. The probability of passing was always high, with more recent dissenters in the majority being cast by the media as unusual. Overall, if there is any recent “news” for budget reconciliation, it is likely favorable for capital markets relative to beliefs just a few months ago.
Two events, however, are newer:
First, it is now clear that DOGE has failed to materially reduce government spending and deficits. Our real-time federal budget tracker of revenue and spending indicates that spending in 2025 exceeds that in 2024 by amounts that cannot be explained by inflation or one-time payouts to separated government workers. Given the reluctance of the current majority to reduce spending on larger entitlement programs, capital markets might, therefore, be placing less faith in eventual closure.
Second, tariff levels announced on Liberation Day (April 2, 2025) were substantially larger than previously understood. Sharp capital outflows and a falling dollar ensued immediately after the announcement. These dynamics are inconsistent with simple, static trade models with fixed production (“endowments”) that predict that tariffs would produce a stronger dollar that reverses some or all the decline in trade deficits. Instead, the real-world dynamics are more consistent with flexible capital and bond markets that include trade in intermediate production goods, as around 40 percent of all U.S. imports (and about 70% of imports from China) are inputs to production. Besides our own analysis, Baqaee and Malmberg (2025, NBER Working Paper #33702) find very similar results in magnitude (discussed below). The more recent partial recovery in capital markets and stock market prices reflect investors’ beliefs that the subsequent 90-day pause in tariffs will remain in place. Still, future risks remain, and it casts its shadow over debt dynamics, with a fresh announcement today by the Trump Administration of a 50 percent tariff on Europe if more progress is not made in negotiations. As of the date of this publication, we are halfway into the 90-day pause. A reversion to the April 2 level of tariffs could sharply challenge the U.S. bond market.
The classic 1928 Ramsey neoclassical growth model is Ricardian, meaning that federal debt has no impact on the economy, regardless of the government’s borrowing rate and the underlying growth rate. The small open-economy model produces similar results for different reasons.
The Congressional Budget Office’s CBOLT model augments the standard growth model by incorporating additional reduced-form rules between capital and federal debt, where $1 more in deficits caused by increased spending is estimated to produce a $0.40 - $0.50 reduction in capital. CBO estimates that a $1 larger deficit caused by tax cuts will produce a smaller $0.15 to $0.25 reduction in capital due to additional household savings. Similar reduced-form models have been used by other entities, although they tend to use larger crowding-out ratios.2
The use of reduced-form models in some DC policy circles likely stems from their simplicity. Reduced-form models might even provide reasonable back-of-the-envelope calculations of capital crowd-out at moderate, mostly stationary levels of government debt without upward secular trends. But they are less suitable when debt is increasing along the baseline, as under current law. Indeed, CBO does not necessarily view CBOLT or its related internal models as CBO’s primary way of capturing debt dynamics. For short-term estimation, CBO uses a forecasting model. For long-term forecasting, CBO also has access to a dynamic overlapping-generations model, despite receiving much less attention.
CBO was established in 1974 to provide impartial information about budgetary and economic issues, not to perform cost-benefit analysis or to be the nation’s bellwether for future long-term financial crises. CBO, and the Joint Committee on Taxation, has some of the nation’s leading experts on budget analysis. But neither the CBO nor the JCT has a mandate to comprehensively model the long-term financial implications of growing federal debt. If they did, that analysis would likely dominate almost all other aspects of their legislative functions.
The limitations of reduced-form models point to the need for more structural, dynamic modeling in the presence of the increasing secular debt that we face today. First, there are specific technical empirical challenges facing reduced-form models, including their inability to truly isolate secular trends from negative business cycle effects when the demand for safe assets increases at the same time as the supply.3 Moreover, a fixed crowding-out ratio based on smaller historical levels of debt is not an “elasticity” that can be applied at higher levels of debt.
Second, the reduced-form model cannot be used to analyze major real-world policies such as entitlement program reforms. Pay-as-you-go transfers across generations (“implicit debt”) in entitlement programs borrows twice as much from future workers relative to explicit Treasury debt, despite having identical economic and inter-generational distributional impacts per transfer dollar.4 Legislation, like the Social Security 2100 Act, appears to fully eliminate Social Security’s actuarial 75-year shortfall---that is, it appears to eliminate the Social Security trust fund’s reliance on general revenue transfers and debt to meet “scheduled benefits”. But it actually increases implicit debt by more than $1 for every $1 of explicit debt reduced, thereby actually harming future generations rather than improving their finances.
Third, and most relevant for the current brief, reduced-form models fail to capture budget closure in the presence of a secular increase in debt.5 This failure is a major problem and not just a technical matter.
Specifically, the reduced-form models allow debt to accumulate almost indefinitely. To be sure, higher interest rates are modeled to cause faster debt buildup. And more debt is often modeled to slow private capital formation and GDP growth. But debt is ultimately just rolled over without bounds. Future interest payments in these models are allowed to exceed thresholds above which bondholders should not hold any reasonable expectation of full repayment in real (inflation-adjusted) terms. Interest payments are even allowed to grow larger than all future tax revenue. Put simply, there is no closure in these simple models. Or, put differently, there is no real budget reconciliation with the actual bondholders.
Inserting realistic closure into reduced-form models is not possible since there is no household, investor, or firm optimization or interactions. It would be mechanically possible to add some ad-hoc additional “penalty term” to the reduced-form crowding-out rule at higher levels of debt. But deriving such a penalty would require solving a dynamic OLG model in the first place. Moreover, the penalty term would not even be a simple, even nonlinear, function of the debt-GDP ratio, and so even this approach would make little sense economically.
While reduced-form models ignore closure, the empirical evidence is overwhelmingly clear: capital markets do not. Instead, capital markets are forward-looking, and key debt dynamics are not smooth above threshold levels. These facts have motivated significant study in the economics community over the past half century.
The economics literature on sovereign debt builds on the seminal work of Eaton and Gersovitz (1981), where sovereigns repay only when the cost of default exceeds the value of debt to be repaid. However, it has been well documented that sovereign debt routinely exceeds the levels implied by these models.6 Two major literatures subsequently emerged: one following Calvo (1988), known as “slow-moving” crises, and the other following Cole and Kehoe (2000), emphasizing contemporaneous default decisions like Diamond-Dybvig bank runs ("fast-moving" crises). The Cole and Kehoe (2000) model has become fundamental for understanding the evidence of macro dynamics of government debt. Crucially, two (or more7) equilibriums emerge: one where the government repays (that is, maintains closure) and another equilibrium where self-fulfilling investor beliefs produce a price spiral where the government does not repay (no closure), i.e., “bank runs” or “doom loops”.
The smooth (continuous) nonlinear dynamics between debt and interest rates only exist in the equilibrium with closure. A sudden sharp fall in bond prices and a concomitant jump in interest rates occur once markets move from a common belief in closure to a common belief in non-closure. In words, bond markets break, not bend.
These dynamics naturally emerge with the OLG lifecycle framework. The OLG model is the modern workhorse model for examining fiscal policy due to its ability to coherently tie microeconomic decisions with macroeconomic variables with equilibrium prices. The OLG model also cannot be “gamed” by converting explicit debt to implicit. It also produces dynamic welfare analysis that includes lifecycle age effects, the economic impact of policy over lifetimes, and the insurance value derived from government progressive tax and spending programs that effectively pool idiosyncratic wage and health shocks. The top major economics journals expect this type of modeling for simulating new policies.
Contrary to its reputation as being a strict fiscal disciplinarian, the lifecycle OLG model also shows how more debt can sometimes “pay for itself” in some limited spending programs that reduce idiosyncratic risks or reverses adverse selection in private lending markets. And that is true even if the pre-policy economy is already “dynamically efficient” and so a crowd-out in private capital otherwise lowers consumption. For example, we previously showed that some pre-K education programs can effectively pay for themselves even though fully debt financed, if program qualification is “means testing” (qualification phases out at higher levels of household income). The PWBM OLG analysis fully incorporated the new marginal tax rates caused by these income phaseouts along with the general negative impact of new debt on the economy. Still, the gains in future productivity to young children of low-income families eventually aggregated up to the macroeconomy to outweigh the costs of the new marginal tax rates and debt.
More importantly for the current context, the OLG model produces two equilibriums consistent with empirical evidence: one sustainable equilibrium with closure, where debt reduces capital in a continuous but nonlinear way, and another equilibrium without closure where debt leads to Cantor-function like “jumps”, where debt is not repaid in real terms (e.g., hyperinflation) and economic conditions quickly deteriorate. In more plain language, one cannot easily explain the “Liz Truss moment” and “bond vigilantes” without the OLG framework.
The path of interest rates in the sustainable equilibrium is a nonlinear function of two basic factors: the direct crowding out of debt on capital markets plus some probability that other investors will lose confidence in the ability of the government to make payments in real terms, maybe after some shock (economic, international, demographic, political). Put differently, bond markets are unique in that bondholders want enough “competition” from other bondholders, as it signals the future ability of the government to roll over its debt.
Still, a truly sustainable equilibrium in the OLG model ultimately demands closure. At a bare minimum, future tax revenue must be sufficient to cover future government spending plus the “r – g” tax times the stock of existing debt, where r is the government borrowing rate and g is growth rate of the economy, and r > g (“dynamic efficiency”). In words, federal debt can grow over time under transversality (closure) but not faster than the size of the economy.
But current law does not include sufficient future tax revenue to meet future spending and “r – g” taxes. So, current U.S. bond markets, which are not yet dominated by vigilantes, must believe that policymakers will eventually figure this out. As noted at the start of this brief, PWBM has calculated the outer limits of this future date, after which point it is basically impossible mathematically for bond markets to hold a rational belief in full real repayment. Instead, some type of default on pass-you-go transfers, be it explicit or implicit, will be required. We calculate that this “XX” date to be now less than 20 years. But, if forward-looking capital markets stop believing that reasonable closure is politically possible before XX date, financial markets backward induct and unravel immediately, both in theory and practice.
At the PWBM, we currently force closer using a mixture of “non-productive spending cuts” (for the baseline) and a broad-based VAT tax (for a policy that changes debt relative to baseline). These assumptions, along with some other assumptions, tend to reduce debt effects. Still, being forward-looking, capital markets in our model anticipate those spending cuts and taxes in our model, producing nonlinear effects prior to closure. These nonlinear effects, in turn, limit how far out closure can be delayed. Even with these dampening effects, the impact of debt looms larger in our model than in reduced-form models without closure.
To be sure, our closure assumptions are not actual policy. But it is not compelling to abandon closure, as done in reduced-form models, simply because closure policy is not actual policy. Failing to include closure at all makes an even more extreme and counterfactual assumption, namely, that capital markets are not forward-looking enough to expect to be repaid. That is a very implausible and economically dangerous modeling assumption.
Going forward, PWBM is turning its focus more toward analyzing comprehensive reform packages. U.S. fiscal policy requires major reform---at least on the order of the 1986 Tax Reform Act times two---to put it on a sustainable path. XX date is not far away. Incrementalism during the past 40 years has simply produced higher levels of debt as a result of spending increases and tax cuts. As the review above emphasizes, the consequences of fiscal failure are not smooth. If failure happens, it arrives with a bang. Single policy discussions and “small” policy bundles, including the current budget reconciliation process, simply pale in economic importance to analyzing comprehensive packages.
The dynamic OLG model is the most persuasive framework for examining large reform packages because of its ability to accommodate deep household and demographic heterogeneity, both with and across time; for its comprehensive treatment of incentives and prices; for its ability to capture of interactions between major programs including entitlements and non-payroll tax bases; and for its focus on actual flows of resources within and across time that prevents it from being gamed. Simply summing gains and losses across program changes across reduced-form model outputs would produce wildly inaccurate estimates, both for budgetary and economic analysis. In fact, interactions are often the dominate force.
Any comprehensive reform package will necessarily involve the healthcare sector, which accounts for a 20 percent (and still growing) share of GDP. So, the PWBM OLG model also incorporates a detailed healthcare sector, with endogenous premium prices (private sector, ACA, related Medicare parts) determined by market providers operating within legal rules related to risk pooling. The private sector offers tax-preferred health care as part of competitive compensation. Additional public programs (Medicaid, Medicare, and ACA) provide some additional safety net. Household decisions include whether to take-up insurance and pay out-of-pocket expenses with or without insurance. Investments in health improve productivity both individually and, in the aggregate, thereby impacting longevity, total population size, increasing both future tax revenue and the costs of age-based entitlement programs (with Medicare often breaking mostly even but Social Security paying more). The quantity of uninsured households and their characteristics (often lower income and often healthy) naturally emerge endogenously from the model rather than being imposed. That allows us to then capture how policy changes can impact both dynamic adverse selection and moral hazard (excess utilization). Barring such a significant policy change, we project that the uninsured population will almost double in size, as a share of the total population, over the next two decades. But we also project that immigration policy can be constructed to mitigate this problem.
Surprisingly, trade theory receives little attention in graduate economics programs. Even top PhD programs do not require a single class with any required course on this topic. It is not surprising that the reaction by some economists to recent tariffs has relied heavily on standard undergraduate textbook theory of “comparative advantage”, efficient allocation, and international borrowing within an endowment (fixed capital) economy. Undergraduate static models of trade dynamics predict that tariffs will produce a stronger dollar that mitigates reductions in trade deficits and net capital flows. These predictions stand in sharp contrast to recent experience and historical data, where tariffs lead to fewer international capital flows, including bonds.8 More recently, the value of the dollar fell, and capital left the United States, especially before the 90-day pause was announced.
Using static models with a fixed supply of capital, some recent analyses of the April 2 Trump “Liberation Day” tariffs (before the 90-day pause) predicted only modest long-term (steady state) losses---a drop of just 0.5 to 1.0 percent of GDP--- despite the tariffs raising $5 trillion in new revenue over the budget window, consistent with the average American family paying $4,000 to $5,000 per year in the form of higher prices.9 These GDP losses were usually presented in isolation from other fiscal policies.
In the context of broader U.S. fiscal policy, however, these static trade models, in effect, are predicting that tariffs would be one of the most efficient ways of raising tax revenue. As a comparison, PWBM recently presented calculations demonstrating how a broad-based value-added tax produces economic losses that are at least as large as those being generated by recent static trade models analyzing the Trump tariffs, even when the VAT is calibrated to match the same amount of annual revenue, with all monies are rebated lump sum to households. Or, put differently, the small economic losses from tariffs predicted by static trade models could be more than reversed---in fact, by several times---simply by using the new revenue to pay down federal debt (which does not exist in static models). Or, alternatively, the tariff revenue could fully finance the current House budget reconciliation legislation, with money left over. The net effect would then be positive for the economy, and capital markets should react just the opposite as recent events.
Instead, the recent capital market dynamics are consistent with dynamic models of capital with intermediate goods of production and bond markets. Combining a simplified OLG model with trade, Baqaee and Malmberg (2025, NBER Working Paper #33702) write: “capital stock adjustment emerges as a dominant driver of long-run outcomes, more important than the standard mechanisms from static trade models — terms-of-trade effects and misallocation of production across countries.” Their assumed tariff rates are lower than those announced on April 2. Nonetheless, they show that consumption falls by almost 5 times more when capital is endogenous relative to static trade models, very similar to our own relative results.
In a dynamic model, additional tariff revenue is not an economic enhancement to the recent House Budget Reconciliation that generates new debt. The reason is that tariffs, despite raising more revenue than the fiscal cost of budget reconciliation, also reduce capital flows, thereby reducing international demand for U.S. assets, including bonds. That is the reason why capital markets have responded so negatively to tariffs: rather than saving budget reconciliation with new revenue, tariffs make it even harder to finance future debt.
Table 1 presents results where we first consider budget reconciliation using a baseline economy with the relatively low tariff levels in place prior to April 2. We used that baseline in our analysis of House Budget Reconciliation up through May 20 with the anticipation that the tariff pause would be permanent (although we still allow for some minor tariffs before April 2). We first consider House Budget Reconciliation on its own (note: we just posted updated analysis of budget reconciliation that was passed by the House.) Then, we add tariff policy along with new tariff revenue. As shown in Table 1, we consider two subcases, one where budget reconciliation includes its actual temporary provisions (as of May 20) and another illustrative case where those temporary provisions are made permanent. Notice that the House Budget Reconciliation alone has a modest positive impact on the economy despite larger debt. However, adding tariff revenue, which would more than fully pay off that new debt, contracts economic growth, both relative to baseline and, especially, relative to the Budget Reconciliation on its own.
| Foreign debt take-up | Bill with temporary provisions | Illustrative Calculations with Permanence | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2034 | 2039 | 2044 | 2049 | 2054 | 2034 | 2039 | 2044 | 2049 | 2054 | ||
| Gross domestic product | |||||||||||
| Reconciliation Alone | 0.5 | 0.6 | 0.8 | 1.1 | 1.7 | 0.1 | 0.0 | -0.1 | -0.2 | 0.2 | |
| Reconciliation and Tariffs | -0.2 | -0.6 | -1.0 | -1.2 | -1.3 | -0.7 | -1.2 | -1.9 | -2.4 | -2.9 | |
| Capital | |||||||||||
| Reconciliation Alone | 0.6 | 0.9 | 1.4 | 2.0 | 3.0 | -0.3 | -0.3 | -0.4 | -0.4 | 0.0 | |
| Reconciliation and Tariffs | -0.6 | -1.3 | -1.9 | -2.4 | -2.7 | -1.5 | -2.5 | -3.6 | -4.7 | -5.8 | |
| U.S Federal Debt Held by the Public | |||||||||||
| Reconciliation Alone | 7.2 | 8.6 | 9.8 | 11.0 | 12.0 | 11.1 | 15.0 | 18.3 | 21.5 | 24.3 | |
| Reconciliation and Tariffs | -3.2 | -4.0 | -4.2 | -3.9 | -3.4 | -1.0 | 0.1 | 1.6 | 3.4 | 5.3 | |
Note: Baseline as of May 20, 2025. Table shows the effects of budget reconciliation combined with a reduction in foreign demand for U.S. federal debt.
Source: Penn Wharton Budget Model.
This analysis was produced by Felix Reichling and Kent Smetters. Portions of the brief are drawn from a separate paper being prepared by Kent Smetters for a journal. Mariko Paulson prepared the brief for the website.
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https://www.barrons.com/articles/treasury-bond-yields-jump-trump-win-6f2145d4 ↩
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See the nice review by Jack Salmon (2025), “The Impact of Public Debt on Interest Rates” available here: https://www.mercatus.org/research/policy-briefs/impact-public-debt-interest-rates. ↩
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The rise in demand for lower-risk assets in the OLG model with aggregate risk occurs when total factor productivity follows an AR(p > 0) process. ↩
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Auerbach, Alan J., Jagadeesh Gokhale, and Laurence J. Kotlikoff. “Generational Accounts: A Meaningful Alternative to Deficit Accounting.” Tax Policy and the Economy 5 (1991): 55–110. http://www.jstor.org/stable/20061801. ↩
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Closure is sometimes called the no-Ponzi game or transversality condition in the field of macroeconomics. ↩
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Bolton, Gulati and Panizza (2023), “Sovereign Debt Puzzles”. https://cepr.org/voxeu/columns/sovereign-debt-puzzles. ↩
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Technically, the Folk Theorem shows how many equilibriums can emerge, although two are most salient for belief coordination. This literature related to “global games”. ↩
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See (i) https://budgetmodel.wharton.upenn.edu/issues/2019/7/24/the-trade-war-trade-off-short-term-gains-then-long-term-losses and (ii) https://budgetmodel.wharton.upenn.edu/issues/2020/9/21/capital-flows-update ↩
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In practice, the average (mean) price increase is much higher than the median since almost half of total consumption is concentrated in the highest decile of the income distribution. ↩
