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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 Probability of Default at Different Levels of Debt

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