by Ed Dolan

The candidates regularly portray the federal debt, too, as a dire threat to America’s future. Some samples:

- Marco Rubio: “We have a $19 trillion bipartisan debt and it continues to grow as we borrow money from countries that do not like us to pay for government we cannot afford. . . The time to act is now. The time to turn the page is now. If we — if we don’t act now, we are going to be the first generation in American history that leaves our children worse off than ourselves.”
- Chris Christie: “We have $19 trillion in debt. . . And we’re talking about fantasy football? Can we stop? . . . Are you concerned like I am that the debt and deficits of Washington, D.C. are endangering America’s future?”
- Mike Huckabee: “I do not want to walk my five grandkids through the charred remains of a once great country called America, and say, ‘Here you go, $20 trillion dollars of debt. Good luck making something out of this mess.’ ”
- Rand Paul: “You know, I left my medical practice and ran for office because I was concerned about an $18 trillion debt. We borrow a million dollars a minute. Now, on the floor of the Congress, the Washington establishment from both parties puts forward a bill that will explode the deficit. It allows President Obama to borrow unlimited amounts of money. I will stand firm. I will spend every ounce of energy to stop it. I will begin tomorrow to filibuster it. And I ask everyone in America to call Congress tomorrow and say enough is enough; no more debt.”

An exploding debt certainly sounds scary, but are federal finances that far out of control? Not really. If we look at the numbers, we can see that the debt is far from the dire threat the Republican candidates make it out to be.

**Which numbers.?**

First of all, forget about the $18 trillion, $19 trillion, and $20 trillion numbers the candidates like to talk about. Those refer to the government’s *gross debt*, a large part of which is issued by the Treasury but held by other government agencies, especially the Fed and the Social Security Trust Fund. Those interagency transactions create no burden on the public, because what the Treasury pays out in interest and principal goes right back into another government account. The only thing that matters from an economic point of view is *net debt*, also known as debt held by the public. That came to a little over $13 trillion at the end of 2015. You would think $13 trillion sounds like enough without exaggerating, but, evidently, presidential candidates are pledged never to pass up a chance to overstate their case.

Four key numbers determine the long-term growth of the government’s net debt.

- The
that is, the debt stated as a percentage of GDP. A larger economy can support a larger debt. The important thing is whether the debt grows faster than or slower than the economy as a whole.*debt ratio,* - The
of potential GDP, that is, the growth of the economy’s productive capacity when operating at full employment. The faster the economy as a whole grows, the more debt the government can take on without raising the debt ratio.*growth rate* - The
on the debt. Once it borrows, the government must make promised interest payments. The higher those interest payments, the less is left to fund programs people want—roads, warplanes, or benefits for kids and seniors.*interest rate* - The budget surplus or deficit. More specifically, for tracking long-term trends, we need to look at the
, that is, the surplus or deficit after removing interest payments and short-term cyclical effects like the tendency of tax revenue to rise in a boom and unemployment benefits to rise in a recession.*primary structural balance*

We can use either nominal (current dollar) or real (inflation-adjusted) values for these numbers, provided that we are consistent. In what follows, we will use nominal versions of all variables.

To understand intuitively how these four numbers fit together, consider a simple example: Suppose that nominal GDP is $10 trillion and the federal debt is also $10 trillion, so that the initial debt ratio is 1.0. Suppose further that the interest rate and growth rate are equal, for example, that both have a nominal value of 3 percent. Finally, suppose the government borrows exactly what it needs to pay the interest on the debt, that is, $300 billion, no more and no less. If so, the debt at the end of the year will be $10.3 trillion and GDP will also have grown to $10.3 trillion. The debt ratio will not change. In this case, then, the debt ratio is stable over time when the primary structural balance is zero.

Note that a primary structural balance of zero does not have to mean that the overall budget is in balance. In our example, the overall structural balance, including interest, is in deficit by 3 percent of GDP. If the economy were operating below full employment, the current annual deficit would be even larger than that because outlays would be higher than they would be at full employment and tax revenues would be less. The overall federal budget does not have to be in balance each year to hold the debt ratio stable over time.

If the numbers are different from those in our example—say, the debt ratio is larger or smaller than one, or the interest rate and growth rates are not equal—then the value of the primary structural balance that is needed to hold the debt ratio constant may be greater or less than zero. Specifically, in order to hold the debt ratio steady over time, the primary structural balance must be equal to the initial debt ratio multiplied by the difference between the interest rate and the growth rate. In equation form:

PSB* = DEBT (INT-GRO)

Where PSB* is the steady-state value of the primary structural balance, DEBT is the debt ratio, INT is the interest rate on the debt, and GRO is the growth rate of potential GDP growth, all expressed consistently in either nominal or real terms.

**Where do we stand now?**

Where do we stand now? Under current policies, is the federal debt out of control, stable, or on course to shrink? Here are the estimated numbers for 2015 from the latest Budget and Economic Outlook from the Congressional Budget Office:

- Debt in the hands of the public equals 74 percent of GDP
- Average nominal interest rate on the debt equals 1.7 percent
- The growth rate of nominal potential GDP equals GRO = 4 percent (real potential growth of 2.2 percent plus 1.8 percent inflation)

Applying the formula PSB*=DEBT(INT-GRO), these numbers give us a steady-state value for the primary structural balance of 0.74(0.017-0.04) = –0.017. That means that a primary structural deficit equal to 1.7% of GDP would exactly balance new borrowing with GDP growth, so that the debt would remain stable over time.

The CBO estimates the current budget balance at –2.6% of GDP, the structural balance at –1.9%, and the primary structural balance at –0.6%. Since the current value of the PSB, –0.6%, is greater than the steady state value, –1.7% (–0.006 > –0.017), we conclude that current fiscal policies are sufficient to bring the debt down gradually over time.

**Even better news**

A primary structural balance greater than its steady-state value is itself sufficient to undercut the apocalyptic warnings of the GOP candidates, but in fact, the news is even better than that, at least for the time being. Take a closer look at the steady-state formula, PSB*=DEBT (INT-GRO). If the interest rate is less than potential GDP growth, then the term in parentheses is negative. As a result, any increase in the DEBT ratio *decreases* the value of PSB*. That little mathematical quirk turns out to have important policy implications.

Suppose that some event like a war, a deep recession, or some structural change in the economy were to cause an unexpected increase in the current deficit. The debt ratio would begin to increase, but with an interest rate less than GDP growth, the steady-state value of the PSB would at the same time begin to decrease. As the steady-state PSB caught up with the current PSB, growth of the debt ratio would stabilize at a new upper limit. Nothing catastrophic would happen. (See this slideshowfor a more detailed account, including numerical examples and charts.)

Contrast that with the situation where the interest rate is greater than GDP growth. In that case, the term (INT-GRO) is positive. Anything that even temporarily increased the debt ratio would *increase* the steady-state value of the PSB. Unless policy changes were made to reverse the initial cause of the increase, the gap between the current and steady-state values of the PSB would continue to widen year by year. The debt ratio would then rise without limit at an ever- increasing rate. Such a scenario would truly qualify as an “exploding debt.”

Economists have long recognized that the relationship of the interest rate to the rate of GDP growth is critical for the sustainability of fiscal policy. If the average value of the interest rate over the business cycle is less than the rate of growth of potential GDP, then debt growth is inherently self-limiting. If the interest rate is higher than GDP growth, then explosive growth of the debt is at least a theoretical possibility, unless active fiscal management adjusts the primary structural balance as necessary to hold it below its steady-state value on average over the business cycle.

So which is more likely? INT < GRO or INT > GRO? On theoretical grounds, economists have long thought that interest rates will normally average a bit higher than the rate of GDP growth. However, as the following chart shows, that has not consistently been the case in the United States, at least not over the past half century.

Instead, the relationship of the average nominal interest rate on the federal debt and rate of growth of nominal potential GDP falls into three distinct periods.

- From 1965 to 1981, the nominal interest rate on federal debt averaged 4.4 percentage points below the growth of nominal potential GDP. Economists who see that as abnormal explain it by noting that inflation rose steadily over the period. As inflation pushed nominal GDP growth higher, they say, unrealistically low inflation expectations held nominal interest rates down.
- Then, from 1982 to 2001, nominal interest rates averaged 1.1 percentage points higher than nominal GDP growth. That looks like a return to the “normal” pattern, although underestimation of the rate at which inflation was decelerating probably provides a partial explanation for the gap between the interest rate and the growth rate in this period.
- Finally, since the turn of the century, nominal interest rates have returned to levels close to or below potential GDP growth. From 2002 to 2015, interest rates averaged 0.8 percentage points less than growth rates. In the most recent five years, the gap has increased to -1.2 percentage points.

Many economists still expect interest rates to rise above GDP growth rates once again as the lingering effects of quantitative easing and the Great Recession fade away. Others, however, are beginning to wonder if a negative gap might become the “new normal.” They point to factors such as the drag on the global economy from slowing growth in China; a worldwide glut of saving from both households and corporations; and difficulties that central banks in Japan, the EU, and even the US have had in pushing inflation up to their 2 percent policy targets.

**What lies ahead?**

Economists at the CBO do not expect the debt to explode any time soon. Instead, as the next chart shows, they foresee a slight decrease in the debt ratio over the next three years, from the current 74 percent to about 73 percent, and then a gradual increase to about 78 percent by 2025.

The near-term decrease is consistent with our observation that the current value of the primary structural balance is currently well below its steady-state value. However, CBO forecasts suggest the current PSB will rise to or just above its steady state value by 2025.

Much of the forecast increase in the debt ratio in later years comes from the effects on taxes and revenues of the inexorable aging of the US population. Still, even major demographic changes will not touch off a debt explosion if, as the CBO expects, interest rates on the debt to remain below nominal potential GDP growth for the next decade and beyond. If that is the case, any increase in the debt ratio should be contained well within sustainable limits.

Is a debt ratio of 80 percent, even it is stable, too high in some sense? Economists disagree. By historical standards, the US debt ratio is higher than at any time since World War II. However, because twenty-first century interest rates are lower than those of the past, the total cost of servicing the debt is less than half of what it was in the 1980s and 1990s, when the debt ratio was much smaller. Perhaps the best argument for lowering the debt ratio is not that it is currently too burdensome, but rather, that a lower initial debt ratio would give more room for fiscal maneuver in case of a future emergency such as a war or another severe recession.

In any case, as our numbers show, it would take only moderate adjustments in fiscal policy to put the debt ratio on a downward course. Tax and spending changes totaling less than 1 percent of GDP would be enough. Policy changes that brought US healthcare costs in line with those of other advanced countries that offer top-quality care would be especially welcome. However, conservative proposals for radical cuts in social programs and discretionary spending can only be rationalized on ideological grounds, not by a nonexistent fiscal emergency.

Realistically, the greatest danger to fiscal stability does not come not from the policies of the current administration or the Democratic candidates now vying for office. Instead, it comes from policies advocated by the GOP candidates themselves.

Some of them have floated tax cut plans that could balance only if they accelerated real GDP growth to 4 percent or more. If the tax cuts were enacted but the promised growth did not materialize (and few serious economists think it would), structural deficits would quickly rise. If panicky austerity measures were to follow, growth could easily fall below the moderate 2 percent now forecast. That would further accelerate the rise of the debt ratio. If financial markets such developments as indicators of chronic fiscal irresponsibility, real interest rates could easily rise. As our review of budget math has shown, rising deficits, rising interest rates, and slowing growth would be just the combination needed to raise the possibility of a real debt explosion.

*For a more detailed discussion of debt math, with additional charts and examples, see* *this tutorial* *on debt dynamics and sustainability.*