US government debt rises to historic highs – Part 2: The government debt Event Horizon Test


In the second part of this series of contributions we develop a simple “sustainability formula” for the national budget. Based on this identity – the formula does not contain any behavioural assumptions and therefore always applies – we check the plausibility of the interest rate at which the financing of the US government debt could be secured in the medium term.


The government debt Event Horizon Test

The change in government debt in a given year is the result of government expenditure minus government revenue (= primary deficit without interest) and interest paid on the outstanding government debt. Simplified:

government debt t – government debtt-1

= (government expenditure – government revenue) + r * government debtt

where r represents the average interest, rate paid by the State for borrowing.

For financing to be sustainable, public debt must not grow faster than gross domestic product (GDP). In other words, the ratio of government debt to GDP must remain constant (assuming that the initial debt ratio was still “acceptable”).

If the above equation is divided by GDP, the following relationship is obtained after some transformations:

Growth of the ratio “government debt as % of GDP”

= (deficit in % of GDP) + (r – g)* government debt in % of GDPt

Where g represents the growth of GDP. Provided that the ratio of government debt to GDP does not increase, the following applies:

Deficit in % of BIP = (g – r) * government debt in % of GDPt

The higher the GDP growth rate (higher g) and the lower the interest rate (lower r), the higher the government deficit as a % of GDP may be. If r>g, i.e. the interest rate is higher than GDP growth, surpluses must be generated (= negative deficit). These surpluses must then be all the greater the higher the debt as a percentage of GDP.

Investors may be interested in the transformation after interest and the transformation of the equation into an inequality (in simple terms we assume that debt is equal to GDP):

r < g – deficit in % of GDP

For the debt pyramid not to collapse (i.e. to be beyond the Event Horizon), the interest rate on government debt must then be lower than GDP growth minus the deficit-to-GDP ratio. Once beyond the Event Horizon, matter will inevitably be destroyed after a long journey in the black hole, there is no escape. If you are beyond the Debt-Event Horizon, the national debt will eventually become worthless in real terms, there is no escape. But once you have crossed the Event Horizon, you are not yet in the black hole. It can still take a long time to reach the centre of the black hole, depending on the observer’s point of view even by cosmic standards “very long”. Once you have crossed the debt Event Horizon, the national debt is far from being worthless, it can still take a very long time for the state to repay or to have to cancel its debts by means of inflation or debt cutting, but there is no escape anymore, the “point of no return” has been crossed.


US trend growth

Let us first look at real growth in the USA over the last 70 years. This will also give you a graphic impression of the current economic slump due to the COVID-19 pandemic):

Chart 1: Real growth in the USA since 1950

Real growth in the USA since 1950


In order to better estimate the future trend growth rates of US real growth, future population growth must be considered (Chart 3):

Chart 2: US population growth since 1950

US population growth since 1950


(Trend-) Real growth is calculated from (trend-) population growth plus labour productivity growth. Unfortunately, labour productivity growth has also fallen sharply.

Chart 3: US labour productivity growth

US labour productivity growth
Source: The slowdown in US labour productivity growth – stylized facts, Chart A


In the following we assume a labour productivity growth of 2% and a population growth of 0.5%. This leads to an estimate of trend growth of 2.5%.


US government deficit

Now to the government deficit: During the 2019 boom (with the lowest unemployment rate in more than 40 years without COVID-19) the deficit was estimated at around 5.8%. If the structural deficit is greater than 2.5% of GDP, a negative interest rate is necessary to prevent the debt pyramid from collapsing.

Look at the development of the US government deficit in relation to GDP since 1930 to get a sense of how high the structural budget deficit might be:

Chart 4: US government deficit or surplus as % of GDP


US government deficit or surplus as % of GDP


The deficit is estimated at 4.7% of GDP in 2019, 3.9% in 2018 and 3.5% in 2017.

In the following, we assume that the structural deficit needed by the US government to provide enough “election gifts”, sufficiently low taxes and sufficiently high government spending not to be without a chance in the next elections is 3%.

You remember the inequality:

r < g – deficit in % of GDP

This means that the interest rate on government debt must be lower than 2.5% (trend growth) minus 3.5%, which according to Adam Riese is -1.0%. The interest rate must therefore be negative for the public debt to be sustainably financed.


Miracles are needed

Unless a miracle (labour productivity miracle, reproductive miracle or electoral miracle) happens, the interest rate on the national debt must also become clearly negative in the USA. How likely is it that US politicians will either cut government spending significantly (= make fewer election gifts, cut defence spending etc.) or generate significantly more government revenue (= unpopular tax increases)? Ask yourself this question.

I personally do not believe in such miracles. One of the recipes to combat this development would be significant tax increases, as Joe Biden has already propagated in his election campaign. Unfortunately, however, the Democrats are at the same time planning new spending on infrastructure, unemployment benefits, etc., which will neutralise the whole thing again, probably even make it much worse.


For a long time, you may not notice anything, but it may already be too late

If you are beyond the Event Horizon, you will inevitably be sucked into the black hole. There is no escape, no rescue. According to modern physics, you don’t even necessarily notice when exactly you have crossed the Event Horizon, everything seems “normal”. But this can be calculated. In physics exactly, in economics only approximately, by making assumptions.


The third and last part of this series will deal with the investment conclusions and will be published here in 2 weeks. Be curious.


 Part 1 of this series



This post was automatically translated

Thomas Härter
Chief Investment Officer Aquila