As Congress and the Trump Administration begin to work on their fiscal program, with the potential for tax cuts and expenditure increases, it's important to think about whether our current deficit is sustainable. Now Japan is fast approaching a point where debt issues will overwhelm their financial system. (My senior capstone read a paper by Hoshi & Ito^{Note} that lays forth that case, arguing that the breakdown point will occur by 2027.) The US is not Japan: we have a growing population, less debt, and smaller deficits. Nevertheless at some point we too will need to put our fiscal house in order.

...we don't need to run a surplus, but the current deficit isn't sustainable...

What follows uses a simple (but standard) arithmetic framework to clarify what matters. As long as debt to GDP is stable, we should be OK, because the demand for financial assets grows with the economy. In general institutional investors such as pension funds hold government bonds for good reasons, and that a particular bond has matured doesn't change that. So they want to buy new bonds to replace the old. In other words, at today's level of debt, the Treasury can "roll over" debt, issuing new bonds to replace old. There's not only no need to repay our debt, financial markets would be hard-pressed to find alternative assets if we did so. Indeed, 20 years ago, under the impact of the Clinton administration's budget surpluses, Federal debt was declining rapidly and there was hand-wringing about how financial markets could function if all the debt was repaid. Some of that public worrying was partisan, used by those who wanted to argue that large tax cuts were OK.

Our economy is also growing. So even if the absolute amount of debt continues to rise, potentially debt to GDP will not. Indeed, that's what happened following WWII. By the end of the war debt surpassed GDP, but fell to just over 20% by 1974. This didn't happen because we ran budget surpluses. Quite the contrary, on average we ran small deficits after 1948. But we did grow, enough to outgrow our debt. But today we're running significant deficits and not growing.

Interest rates matter. In the 1950s and 1960s they were relatively low, so the interest the Treasury paid on our debt didn't offset growth. Today we again have low interest rates, but we also have low growth. So we need to ask whether that changes the situation.

Again, what we want to look at is whether debt is stable relative to GDP. That is, if B is the stock of bonds and Y is GDP, is B/Y growing? On its own – assuming bonds are rolled over – the stock grows with accumulated interest: _{t+1} = B_{t}(1 + i), where B_{t} is the stock of bonds at time t and i is the nominal interest rate. Similarly, GDP grows at Y_{t+1} = Y_{t}(1 + g) where Y is nominal GDP and g is the nominal growth rate. Hence debt to GDP will grow at:

__B(1+i)__

Y(1+g)

To put this to use, we need three pieces of information: what is the level of debt, B/Y; what is the growth rate g;, and what is interest rate i. That will give us an indication of whether debt is sustainable, and if not, what level of surplus is needed to keep it within bounds.

The first is easy: Federal debt is approximately 100% of GDP, that is, debt to GDP ratio is 1.0 – convenient for arithmetic, as multiplying by 1 is easy. We then need to know the ratio (1 + i)/(1 + g). When i and g are single digits in percentage terms, as in the US, that ratio is approximately 1 + i - g. In other words, with our debt ratio of 1, B/Y will shrink as long as (1 + i - g) is less than 1. The critical issue then is the value of (i - g). If i > g then our debt level will rise, unless we run surpluses. If i < g then we can run (small) deficits indefinitely, as happened during 1949-1974, yet not see our debt level rise.

Now while it might seem that we ought to be able to earn better than the growth rate, this is fundamentally an empirical question. Thanks to the Great Inflation of the 1970s and 1980s nominal interest rates and nominal growth varied wildly. But real growth and real interest rates stay within fairly narrow bounds, except at the depths of our recent Great Recession. The graph below sets forth those data. Excluding the peak around 2009 we find that the average level of (i - g) is about -0.6%. If we include the peak, the average is roughly 0. Now as the graph below indicates, real long term bond yields fell over the past 15 years and are now on the order of 0.8%. Investors, rightly or wrongly, have not built strong growth into bond prices. So to date there's no evidence that the Fed's ongoing normalization of interest rates will raise real interest rates relative to growth. If so, we can run deficits of 0.6% of GDP forever.

To reiterate, we don't need to run a surplus. However, we do need to bring the budget close to balance. Unfortunately, our current deficit is about 3% of GDP. Now that's a vast improvement over the -10% of GDP level at the trough of the Great Recession. Employment growth and profit growth led to stronger income tax receipts, while the improved employment situation led to a drop in "safety net" expenditures. That combination lowered the deficit by a full 7% of GDP. Unfortunately we can't expect further gains, as profits are now high and (un)employment low. There is however downside potential. So we ought to count on the deficit averaging out at -3.5% of GDP, not -3.0%.

...that means we need to "enhance revenue" by 4% of GDP, not cut taxes...

That does not factor in the aging of the baby boomers, who haven't fully retired and whose healthcare expenses will continue to rise until offset by rising boomer mortality. Such retirement-related expenses will likely come to at least 1% of GDP. Hence we need a fiscal adjustment on the order of 4.0%-4.5% of GDP. Congress needs to "enhance revenue," not cut taxes.

Note: Hoshi, Takeo, and Takatoshi Ito. 2014. “Defying Gravity: Can Japanese Sovereign Debt Continue to Increase without a Crisis?” * Economic Policy* 29(77): 5–44.