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The concept of a debt limit in the U.S. is usually identified with the statutory limit that has been in place for the last century (Congressional Budget Office 2017). The statutory limit has never been an effective constraint on fiscal policy. Initially the purpose of the statutory limit was to facilitate the issuance of debt without a cumbersome approval as part of the annual budget process in Congress. Over the past century the statutory limit has been raised many times. Until recently this was a pro forma exercise in which Congress sanctioned debt issued to fund expenditures already approved in the budget.

In recent years the Republican Party has used approval of the statutory limit as a bargaining chip in budget negotiations. In 2011 failure to approve an increase in the statutory limit resulted in a brief shutdown of the federal government. Since then both parties have avoided disruptions caused by a shutdown of the federal government, and approval of the statutory debt limit is again perceived as a pro forma exercise.

Because the statutory debt limit has not constrained fiscal policy in the long term, the concept of an effective debt limit has made little headway in the U.S. In contrast, in other OECD countries, especially members of the European Union, the concept of a debt limit is an important, and some would argue an overriding, issue in fiscal policy. A recent OECD study concludes that

“In designing a fiscal framework, the starting point is to define the targets and instruments. A debt target can be effective in anchoring expectations about future fiscal policy. The prudent debt target serves as the reference point to define numerical fiscal rules, in particular, for countries with high debt that have to converge to a lower prudent debt ratio. A debt target is better than a debt limit. The experience of the EU framework is that, in the absence of a debt target, debt drifted up towards the 60% of GDP limit or even beyond, leaving no room to absorb the sizeable fiscal shock of the recent crisis without breaching the limit (Fall et al. 2015, pp.30-31).”

In this study we explore the concept of debt limits and debt targets and their relevance to fiscal policy in the U.S. We begin with the theoretical basis for a debt limit, and a brief review of the literature estimating debt limits in OECD countries. This analysis is the basis for setting debt targets to constrain fiscal policy. A debt limit for the U.S. is estimated, and is used as a basis for designing a debt target and fiscal rules to constrain fiscal policy

The Theoretical Basis for a Debt Limit

In the public finance literature the debt limit is defined with reference to public debt sustainability, and is based on theoretical models (Bi and Leeper 2013; Bi 2011; Fournier and Fall 2015). The theoretical models assume a fiscal reaction function to rising debt, as well as a market reaction. Debt sustainability is achieved when the intertemporal budget constraint is satisfied. The approach pioneered by Bohn (1998, 2008) determines if the primary balance (i.e. the balance net of interest payments on the debt) responds positively to increases in the level of debt. Controlling for other determinants of the primary balance, a sufficiently positive response ensures that a no-Ponzi-scheme rule is satisfied, and the debt is repaid in the long run.

Critics pointed out that this approach to fiscal sustainability is flawed because as the level of debt rises, it becomes more difficult to generate a primary balance that is sufficient to ensure sustainability. As debt increases beyond a certain level it becomes more difficult to enact tax increases or spending cuts. At sufficiently high levels of debt the required primary balance would exceed GDP.

An alternative approach to sustainability is to estimate the debt limit. The debt limit is defined as that level of debt when the dynamics become explosive, with the debt to GDP ratio increasing without bound. At that point, the government must either enact extraordinary fiscal policies (i.e. primary adjustments beyond the country’s historical response to rising debt) or default on the debt.

A refinement of this approach to sustainability introduces the element of uncertainty and risk. Economies are subject to shocks that can push the government beyond the debt limit. Shocks may take different forms, such as a military conflict, financial crisis, or recession. A shock does not necessarily mean that the outcome will be explosive growth in debt. For example, military conflicts in the U.S. have historically been accompanied by a sharp increase in expenditures, funded in part from debt. In periods of peace the government would then enact fiscal policies to generate the primary balances required to restore debt to levels consistent with a sustainable fiscal policy. However, over the past half century the U.S. has abandoned this ‘Old Time Fiscal Religion’. The federal government has incurred deficits and accumulated a level of debt now in excess of GDP. This unconstrained growth in debt is projected to continue under current law, and is not sustainable in the long term.

Credit markets must factor in the probability that a government will exceed the debt limit in the lending rates charged. Lending rates will in turn affect the probability that the debt limit will be exceeded, and thus impact the probability of default on the debt. Governments also encounter uncertainty in the form of liquidity/roll over risk. For this reason, governments will generally target debt levels lower than the debt limit. This ‘fiscal space’ between the debt target and the debt limit is important in giving the government flexibility or room to respond to shocks. With sufficient ‘fiscal space’ governments can pursue countercyclical fiscal policies without shifting debt levels above the debt limit and risking default on the debt (see box 2 for a formal model of the debt limit, debt targets, and fiscal space.

Estimating Debt Limits

A number of studies have estimated the debt limit for individual countries based on sustainability. The debt limit is defined as the maximum level of debt beyond which the government cannot roll debt over and loses access to the capital market. The debt limit depends upon a number of factors, including the rate of economic growth, risk free interest rates, level of uncertainty, and the previously observed government reaction function to rising debt (for a survey of the literature on debt default see Aguiar and Amador 2013).

Estimates of the debt limit are used to measure fiscal space (Gosh et al. 2013; Fournier and Fall 2015). Fiscal space is measured as the distance between actual debt level and the estimated debt limit. These estimates of fiscal space take into account that as actual debt approaches the debt limit, a risk premium will reflect the higher probability of default. This approach is backward looking in that it is based on a country’s fiscal track record, and the fiscal reaction function to increasing debt.

Debt limit estimates for OECD countries vary widely (Fall et al. 2015). At one extreme are highly indebted countries which have levels of debt that are not sustainable in the long run (Greece, Iceland, Ireland, Japan, Portugal, Slovenia and Slovak Republic). These countries have pursued fiscal policies that have left actual debt at or near their estimated debt limits. Fiscal policies must change significantly for these countries to pursue a path toward sustainable debt.

In most OECD countries, including the U.S., actual debt is significantly below their estimated debt limit (Fall et al. 2015). However, the estimated debt limit can change rapidly, with a loss of market confidence, in response to a number of factors, including economic growth prospects, rising interest rates, external shocks etc. Estimated debt limits depend crucially on fiscal behavior, and whether a country responds to rising debt by increasing the primary balance. If a country allows the primary balance to deteriorate, this not only increases debt, it reduces the debt limit.

Reinhart and Rogoff (2009) studied default episodes over the period 1970 to 2008. They found that developing and emerging nations defaulted at a relatively low debt-to-GDP ratio, i.e. below 60%. These countries were especially vulnerable to external shocks in the form of commodity price cycles. Default was often linked to sharp capital outflows and currency devaluation. In periods such as the Asian financial crisis at the end of the 1990s, these counties experienced contagion, as default in one country increased uncertainly and default risk in other countries. Sovereign defaults were linked to financial crises, reflecting weak financial markets and vulnerability to sharp capital outflows. Fall et al. (2015) find that since the financial crisis of the 1990s, many of these developing and emerging countries strengthened their financial systems, and with better fiscal performance are now less vulnerable to default.

Estimating the Probability of Default at Different Levels of Debt

An alternative to studies that provide a point estimate of the debt limit, are studies that estimate the probability distribution of default at different levels of debt (Botev et al. 2016). These studies measure long run fiscal sustainability, using general equilibrium modeling to project revenues and spending, and macroeconomic responses to shocks. These models can be used to estimate the long term impact on debt sustainability of factors such as economic growth and interest rates. The models can also take into account long term age related spending pressures, and to assess the impact of reforms to contain the costs of pension and health care benefits.

Botev et al. (2016) use this long run fiscal sustainability approach to estimate debt limit distribution probability functions for OECD countries. Their results differ considerably from the point estimates of debt limits based on the market access approach. Using panel data for 31 OECD countries they find different government behaviors at different debt levels. Governments react weakly by increasing their primary balances when debt increases but remains below 120% of GDP. From about 120% to 170% governments react strongly to debt increases. But beyond that debt level governments may abandon fiscal discipline, a phenomenon referred to as debt fatigue. In effect, at high levels of debt the burden of reducing spending and/or increasing taxes becomes overwhelming. In that case the country is most likely to default on debt.

In their empirical analysis Botev et al (2016) estimate the probability of default at each level of GDP for the 67 countries in their sample. They estimate that for all of these countries, including the U.S., when the debt-to-GDP ratio is at or less than 113% the probability of default is zero. For the U.S. they estimate that when the debt-to-GDP ratio is about 150% the probability of default is .5; and when that ratio exceeds 160% the probability of default is unity.

Is U.S. Debt Sustainable?

To determine whether U.S. debt is sustainable we can compare these estimates of the probability of default at different levels of debt with the actual debt. The most recent estimate of total U.S. debt-to-GDP by the OECD, for 2016, is 128% ( OECD 2016). Thus, the current level of total debt in the U.S. is in the range within which a risk premium must be paid, in excess of the risk free interest rate, reflecting the probability of default. There is also indirect evidence that the U.S. has reached this threshold. During the recent financial crisis a sharp increase in debt resulted in a downgrade of U.S. debt by Standard and Poor’s. Short term interest rates are especially sensitive to changes in the probability of default in the U.S. Uncertainty regarding Congressional approval of the statutory debt limit has boosted short term interest rates above the rates on longer dated maturities.

The magnitude of the debt crisis is clear in the debt levels projected by the CBO in their long term forecasts (Congressional Budget Office 2016b). The CBO measures debt held by the public, a narrower measure than that used by the OECD. The CBO estimates that debt-to-GDP doubled, from 35 percent in 2007 to 70 percent by 2012, and is projected to reach 77 percent in 2017. Under current law the CBO projects that the debt-to-GDP ratio will increase continuously in coming decades to, 89 percent in 2027, 106 percent in 2035, and 150 percent in 2047. The assumption underlying this long term forecast is that the federal government will fail to increase the primary balance in response to this rising debt level over the forecast period. The CBO projects that the rising debt levels will be accompanied by higher interest rates; that will in turn contribute to deficits and debt accumulation. The CBO concludes that these fiscal policies are not sustainable in the long run.

If the CBO long term projections are correct, then there is a high probability that the U.S. will default at some point during this forecast period. As total debt levels approach 150% of GDP we should expect the risk premium to increase sharply. When total debt levels approach 160%, interest rates are likely to spiral out of control, and the U.S. will default on the debt.

It is important to emphasize that the CBO long term forecast assumes that the U.S. will not experience a major recession over the forecast period. If the U.S. does experience a major shock, the question is whether the government has fiscal space to pursue macroeconomic stabilization in response to the shock. What we should expect under current law is that the federal government will respond to a fiscal shock with a Keynesian style fiscal stimulus, as it has in recent decades. In response to the recent financial crisis the government enacted a fiscal stimulus that increased deficits to more than $1 trillion per year. If the government responds to a new financial crisis with such a fiscal stimulus, this would push debt levels into the default range within a matter of years rather than decades. The OECD analysis suggests that the U.S. now has little or no fiscal space.

Uncertainty and U.S. Debt

Critics will argue that the CBO long term forecast are too pessimistic, and that the U.S. is not likely to experience default on the debt within their forecast period. The CBO notes the uncertainty regarding these long term forecasts, and estimates the sensitivity of debt projections to their assumptions. There are a number of headwinds that the U.S. could encounter in coming decades that suggest that their long term projections may in fact be too optimistic.

A key assumption in the CBO projections is the rate of economic growth. In recent years the CBO has revised downward its projections for economic growth, reflecting the retardation in economic growth experienced in rent decades. The OMB under the current administration has projected higher rates of economic growth than that projected by the CBO (Office of Budget and Management 2017). But a survey of economists suggests that the optimistic assumptions regarding economic growth by the OMB are unrealistic.

Retardation in economic growth reflects lower labor force participation rates, rates that remain below the labor force participation rates prior to the financial crisis. In part, this reflects a mismatch between the education and skills of the work force, and the skills now demanded in the private sector. Rates of productivity advance have also fallen and remain below that prior to the financial crisis. And, rates of investment and capital formation are below that which usually accompanies and economic recovery. If these headwinds continue, the rate of economic growth over the forecast period could be lower than that projected by the CBO

A major headwind confronting U.S. fiscal policy is the rising cost of entitlement programs. The CBO forecast reflects the rising cost for Medicare, Medicaid, other health care programs, and to a lesser extent Social Security benefits. The CBO also identifies policy reforms that could significantly reduce the cost of these entitlement programs. But, thus far Congress has had little success in enacting these reforms. Legislation to reform the Affordable Care Act has made little progress in Congress. Legislators have virtually abandoned efforts to reform Social Security. Based on this recent history, the most likely scenario is one in which expenditures for entitlement programs will increase at a faster rate than that projected by the CBO.

The CBO projections assume a modest rise in interest rates over the forecast period. But they note a great deal of uncertainty regarding interest rates assumed in these projections. The CBO uses sensitivity analysis to estimate the impact of an increase in interest rates 1 percent above that assumed in the baseline projections. The higher interest rate significantly increases deficits and debt accumulation. Other studies also forecast higher interest rates than that assumed in the CBO projections.

A major uncertainty regarding the CBO long term forecasts is the potential response of the government to shocks. The CBO long term forecast assumes that the U.S. will not experience a major shock, such as the recent financial crisis. Given the high levels of debt projected over the forecast period, it is not clear that the U.S. has fiscal space to pursue macroeconomic stabilization policy. Without fiscal space to pursue a discretionary fiscal policy the U.S. might be forced to rely only on the automatic stabilizers in response to a shock. This would be a blessing in disguise because it would signal a more prudent fiscal policy that could put the country on the path toward a sustainable debt.

At this point there is little evidence that the U.S. is ready to address the debt crisis with more prudent fiscal policies. The more likely scenario is one in which the government incurs deficits and accumulates debt up to the brink of default. Perhaps at that point the government will avoid the fiscal cliff encountered in other OECD countries that have defaulted on their debt. But it is not in anyone’s interest to reach this fiscal cliff, with all the chaos that would result from default.

Some OECD countries have successfully addressed their debt crisis by enacting new fiscal rules to impose fiscal discipline. These fiscal rules set targets for debt and balancing the budget within a finite time frame. The U.S. could follow this precedent and enact new fiscal rules, and the remainder of this study explores this rules based approach to fiscal policy for the U.S.

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Estimating the U.S. Debt Limit

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