If you are looking for an easy read, you might want to skip this one, since it will involve some math and a lot of mental contortions. But reading a paper by the Bank for International Settlement has shown me that – whether you like it or not – there is a way in which governments can run large budget deficits forever without being punished for it.

To get started, let’s make our lives simpler, and let’s assume that real GDP growth is zero (*g = 0*, with *g* denoting real GDP growth). If a country faces positive real rates of interest *r > 0* then it has a problem. Because even without making any deficits, the country has a rising debt burden with the amount of debt to be paid to investors growing by the interest rate *r* paid to investors every year. That is clearly an unsustainable situation since, at some point, investors will refuse to buy government bonds knowing full well that this is essentially a Ponzi scheme where interest rates are paid to investors by selling more debt to new investors.

So, in general, the real rate of interest on bonds has to be negative in which case, the negative real rate of interest will reduce the debt pile a little bit each year. If *r* is negative, the government can in fact make a deficit each year as long as it is not too big. Assume that economic growth is 0 and the real rate of interest is -2%, then each year, debt/GDP-ratio of the country declines by 2% and the government can run up to 2% deficits without creating a Ponzi scheme.

If so far you have struggled with the notion that I assumed economic growth to be zero, you can now go back and add any kind of economic growth you feel comfortable with and see that the government can run deficits to the size of *g – r* without creating a Ponzi scheme where new debt has to be issued to pay for interest.

This is the whole shtick about financial repression. As long as *r < g* a government can run deficits forever. Of course, *r < g* implies that inequality in a country increases since poorer people typically don’t have investments and only earn the real interest rate *r* on their savings and their wages, while “capitalists” can earn a higher rate of return on their capital. But inequality is not what I am concerned with here.

Instead, let us go back to the *r < g* constraint and assume that a government wants to spend more than its deficit allows. Going back to the case of no growth (*g = 0*) and a real interest rate of *r = -2%*, let’s assume the government wants to run a 4% deficit. Above, we have seen that this deficit increases the debt/GDP-ratio and requires the government to finance interest payments with new debt. Most people would argue that this is not sustainable, but not so fast.

The main insight from the paper mentioned above is that governments can indeed run deficits larger than that forever. There are two ways this can be done.

First, if the government uses debt to invest it in activities that enhance real GDP growth (i.e. it spends it on items with a fiscal multiplier > 1). Infrastructure spending is one such possibility. We know that every Dollar spent on infrastructure creates somewhere between 1.2 and 1.3 Dollars in real GDP growth while every Dollar “spent” on tax cuts only creates additional GDP growth in the range of 0.2 to 0.3 Dollars. Thus, cutting taxes is a gift by the government to its people while infrastructure investments are a way to foster future growth. What that means in our case is that the government can run deficits in excess of the limit we discussed so far, as long as the excess spending is for activities like infrastructure investing that creates additional growth. In that case, growth will rise faster than the deficit and the debt/GDP-ratio will decline over time and we are no longer dealing with a Ponzi scheme.

It is effectively the same thing young growth companies do when they take on more and more debt even though they are loss-making. As long as that debt is invested in future growth and the growth eventually comes through in the form of corporate profits, the company can run large amounts of debt on its balance sheet for an extremely long time. If you don’t believe me, just ask Elon Musk.

But there is a second way how governments can run large deficits forever. Remember that all of us have a choice of investments. We can either hold government bonds or invest our savings in the real economy through stocks, etc. And here is what so many other people forget (and I have ignored in the past as well). We will earn a real return on our invested capital (let’s call that return *m*) and that real return is counted as real GDP growth *g*. So, the higher the real return on capital *m* the more real GDP will grow. But if real GDP grows faster, the gap between *g* and the real rate of interest increases. And as we have seen above, the limit to budget deficits is to run deficits that are lower than *g – r*. But if additional investments create additional economic growth not of *g* but of *m* then what really matters for the government deficit is not *g – r* but *m – r*, the difference between the rate of capital return and the real rate of interest.

And here comes the good news. The real rate of return on capital is much larger than the rate of real GDP growth. And this means that the government can sustain deficits that are much larger than what we think. Assume that the real rate of return on capital is 5% (which is roughly what it was historically in the United States). Assume further that real GDP growth is 0 (to make our lives easy) and that the real rate of interest is -2%. A little bit of thought (I told you at the beginning this post would be hard) will show that the government can run deficits of 5% - (-2%) = 7% every year forever without ever creating a Ponzi scheme and without running out of investors willing to hold their bonds. Now add a more realistic long-term GDP growth rate of 1% or 2% and you can run deficits of 8% or 9% of GDP forever.

To put it into investment terms: As long as your return on invested capital (ROIC) is larger than your cost of debt, you can take on more debt.

And that is essentially what the current US government is doing. It i) wants to invest in infrastructure to create a higher return for its government spending, thus boosting GDP growth and tax revenues, and ii) it engages in financial repression to keep the real interest rate (and thus its cost of debt) low and at the same time incentivise people to shift their savings into capital investments, thus creating higher returns on capital like stocks, which in turn creates higher GDP growth and more tax revenues. The current US government acts like a growth company investing in the future. And if you like investing in growth companies like Amazon or Apple, you should be fine with the deficits of the US government because qualitatively, they are all using the same strategy.

I am not anywhere near a financial guy or a quant, so I will need time to digest this. But on the surface, it seems this is an equation with constraints and the feds are using some form of Lagrange multiplier (financial repression?). This means the critical points for spending, outstanding debt, (g-r) or (m-r) would be subject to some ideal value or limit. Now, if private investments for higher-income households get a bubble effect from this (to keep m higher?) and lower-income households languish with the repressed interest rates r, the same government that is looking to provide jobs (infrastructure, higher GDP) is also increasing the inequality gap. I love irony but not here. If the government makes a patch job of increasing taxes on the higher-income households, wouldn't that diminish the capital base of the "rich" from which return m can be generated and eventually lower the allowable gap m-r and any future spending program?

What is the projected number of "rich" as in not really wealthy but potential equity participants as we are encouraged to sock away 401K and IRAs (because surely by fear of inflation, the retirees will have to invest their retirement accounts as if they are "rich", yet once they get to RMD - required minimum distributions, the tax factor above will come to haunt them.

Meanwhile, some of the "value" stocks are doing buybacks and borrowing heavily to prop up their dividends so they appreciate abreast the growth stocks - i.e. join the stock market party?

Before I wrote this, I thought I needed a pencil to try to follow the math, now I am just looking for a spoon. I think my teeny brain just splattered on the floor.

If the real interest rate is greater than zero (r >0), the purchasing power of the investors would increase (hence their wealth would increase). At the same time, if the GDP growth is zero investors would not find better opportunities elsewhere in the economy (risky investments). So why would investors view new issues as part of Ponzi scheme?

Also, governments could keep printing the money to repay debt and stimulate the economy for growth. Once the desired economic growth is achieved government could start issuing new debt to control unsustainable growth and inflation.