Ever since Thomas Piketty published his book on inequality, Capital in the Twenty-First Century, one of the clichés of economic and debt management seems to be the claim that national debt isn’t a problem if interest rates are less than the GDP growth rate. If a country’s GDP grows faster than the accrual rate of its debt, the thinking goes, the relative cost of servicing the debt will decline over time, so the debt is thought to be easily sustainable.

But that is not what Piketty actually says, and the difference matters a great deal. Furthermore, this is a particularly timely topic as many countries have recently passed high-cost stimulus packages and are shouldering greater debt burdens to cushion the economic fallout of the ongoing coronavirus pandemic.

Piketty, Misunderstood

In fact, Piketty is more concerned about how interest rates and the GDP growth rate affect income inequality. As the Economist puts it:

As a general rule wealth grows faster than economic output, he [Piketty] explains, a concept he captures in the expression r > g (where r is the rate of return to wealth and g is the economic growth rate). Other things being equal, faster economic growth will diminish the importance of wealth in a society, whereas slower growth will increase it.

Nevertheless, a lot of analysts seem to think that this analysis also applies to the sustainability of a country’s debt burden. It is much more dangerous for a country to allow its debt to rise, they argue, if r > g than if r < g. For example, a recent Financial Times article about debt sustainability cites the International Monetary Fund as warning that “global public debt will hit its highest level in recorded history, greater even than the peak after the second world war.” It continues:

This seems to portend disaster and require corrective action. But while higher public debt has costs—most significantly if it closes off the ability to respond to a future crisis—there is little cause for immediate alarm. The “safe”, or sustainable, level of national debt is ambiguous and is likely to have risen because of slumping global interest rates.

The article then goes on to argue that one of the keys to judging the sustainability of a country’s debt burden is the relationship between its borrowing cost and its growth rate:

Calculating a safe level of public debt is hard because sustainability depends on both interest rates and the pace of economic growth. If interest rates are 2 per cent and the economy is growing at 3 per cent, for example, then all a country has to do is sit back and wait. As long as it does not borrow more, then debt will gradually dwindle to nothing compared with the size of the economy. If interest rates rise above economic growth, by contrast, then even small debts can get out of hand.

All of this may seem self-evidently true, and it would be true if other things remained equal. But that simply isn’t the case. In fact, the relationship between interest rates and growth is usually much more complicated. It may very well be true in certain cases that the lower r is relative to g, the more sustainable the country’s debt is. This might be the case for external debt, for example, or for the domestic debt of countries that manage their currencies (like China), or countries that cannot control monetary conditions (like the members of the EU), or countries whose currencies aren’t highly credible.

But for countries with monetary sovereignty and a credible fiat currency, like the United States, this just isn’t the case. The reason it isn’t so is not because of modern monetary theory, but because of a kind of fallacy of composition. Of course it is true that if I have a lot of debt, and if my income is rising relative to the cost of my debt, it becomes easier for me to service the debt over time. And if I am able to service the debt now, there is no reason why I will not be able to so in the future—unless, of course, my rising income convinces me to increase my borrowing at a much faster rate than the increase in my income.

The same is true for a business, but it is not true at the macroeconomic level for national debt. At the macroeconomic level, the relationship between interest rates and GDP reveals much more about income transfers and the distribution of income within an economy than it does about the overall sustainability of that economy’s debt. In this respect, conditions operate quite differently for countries than for individuals or businesses.

Basically, at the macroeconomic level, if interest rates are higher than the economy’s growth rate, savers are getting a disproportionately larger share of national income than if interest rates are lower than the economy’s growth rate. We can actually think of the relationship between the two as a kind of tax. When interest rates are higher, borrowers, producers, and speculators are effectively being taxed to subsidize savers and owners of monetary assets. When interest rates are lower, the roles are reversed, in which case it is the savers and owners of monetary assets who are effectively being taxed to subsidize borrowers, producers, and speculators.

To say that debt is not a problem if interest rates are lower than GDP growth, in other words, is just another way of saying that a country’s debt isn’t a problem if an indebted government is running a budget surplus. A government that manages its debt by imposing financial repression is simply managing its debt by imposing a hidden tax on its residents that is used to pay down debt—a tax on savers and owners of monetary assets, in this case.

Interest Rates Affect Income Distribution

This means that whether or not r < g helps debt sustainability in a given instance depends far more on whether the impact of these tax-like transfers is good or bad for future growth than it does on the arithmetic of debt payments. In the case of the United States, for example, repressing interest rates is a double-edged sword. To the extent it provides debtor relief by taxing savers and owners of monetary assets—mostly the wealthy, in which case it redistributes income downward—it helps boost the incomes of ordinary households and so boosts growth. But by subsidizing speculation in the stock and real estate markets, it also shifts wealth upward. Whether or not it makes debt more sustainable depends on how these differing effects affect future growth.

To put it differently, the g variable (GDP growth) is not independent of the r variable (rate of return on wealth), and it is useless to posit a relationship between the two as if they were. Economists love the ceteris paribus condition to make their equations work, but in system theory, ceteris is never paribus.

The point of this piece isn’t to argue whether or not we are better off if r > g or vice versa. It is only meant to point out that, at the national level, the relationship tells us very little about debt sustainability. It tells us instead about the national distribution of income and whether or not its net effect is positive or negative for growth.

Incidentally, lower interest rates can indeed affect a country’s debt burden directly, but they do so by extending the duration of debt and effectively postponing the real cost of debt servicing. This, however, is a very different impact altogether.

Aside from this blog, I write a monthly newsletter that focuses especially global balances and the Chinese economy. Those who want to receive complimentary subscriptions to the newsletter should write to me at chinfinpettis@yahoo.com, stating affiliation. Twitter: @michaelxpettis