Predicting economic collapse
The singularity. It’s a popular term in science fiction that was borrowed from physics. Much like most things in physics, however, the physicists pinched it from the mathematicians.
Briefly, a singularity is a point (or more generally a mathematical object) that is undefined. It’s that part of of the graph that just doesn’t behave. For a trivial example the classic equation y=1/x is undefined at 0 because you can’t divide by 0. As you approach that point, the graph explodes to infinity.
In physics, gravitational singularities are known as black holes. The underlying mathematics describing the physics of gravity produce undefined objects in these regions of space-time.
For the purposes of our discussion, we need to consider a finite-time singularity. These occur in systems where an input is time. The plot below is from a paper that demonstrates finite-time singularities present in price indices during historical hyperinflation events.
I can’t stress enough that these plots are not an exponential. Exponential growth accelerates because it’s rate of change at time t is proportional to it’s value at t. The proportionality, however, is a constant. An exponential doesn’t reach infinity until the time is infinity. Hyperbolic growth is like an exponential on steroids. The proportionality is not a constant, but rather also dependent on the value at t. The second order growth means it is reaching infinity in some finite time.
It’s really important to understand singularities because they appear in sometimes unexpected places. In particular, singularities can emerge in complex systems. Lo and behold, human beings interacting with each other in a network create one hell of a complex system. Where are the singularities lurking and how destabilising could they be?
Hyperbolic growth is like an exponential on steroids.
Breeding like Rabbits
In the 1960’s, an Austrian-American physicist looked at population data over the last two millennia and tried to project growth. Heinz von Foerster and his colleagues published their hyperbolic growth model, the so-called “doomsday equation.” Population growth was predicted to explode to infinity by the 13th of November 2026. That was the wild 60’s, so maybe they had it wrong…
Another more recent analysis confirms that human population growth does not fit an exponential, but rather hyperbolic growth regimes. The time-frame for reaching the singularity is essentially the same as von Foersters prediction.
Despite these predictions, the data also suggest that population growth is slowing. Official projections predict a plateau at around 11 billion with a peak in the growth rate in 1968. To be honest, it’s hard to imagine that we are still in a hyperbolic phase with declining birth rates around the world, but you never know…
Positive Feedback
So why was population growth hyperbolic? One possible reason is the relationship between population size, urbanization, and technological development. As a population grows and becomes more dense, innovation and technology accelerates allowing the population to grow faster and more dense, which further accelerates innovation. There is a second order positive feedback in the system that causes hyperbolic growth.
Show me the money
This begs the question, where else might we see these positive feedback mechanisms? Going back to our hyperinflation example, Sornette et al argued that there is loop between expectations of inflation and price setting. After a certain point it’s a self fulfilling prophecy and you get prices running away to infinity and beyond.
Money is an interesting place to think about positive feedback. What even is money? Money is debt. Around 97% of money in circulation was born when a commercial or reserve bank created a new loan. This debt is also an asset. It can be packaged into financial products and sold. These financial products have value because the debt has interest. Treasuries and bonds package federal debt as ‘safe’ investments with a guaranteed payout at expiry. However, debt-based products aren’t always all that, e.g. the 2008 subprime mortgage crisis.
Using debt as the underlying asset supporting the monetary supply creates an interesting dilemma. Money is destined to return to the bank to pay back the loan… plus interest. At any given point in time, the money needed to pay back the interest on circulating money doesn’t exist yet. This creates a loop where banks are required to increase lending and monetary supply to ensure future interest repayments, which requires banks to further increase lending. This is a fairly high level simplification of the system but is the fundamental growth process in monetary supply.
Credit creation is also a fundamental driver of innovation and economic growth. New businesses and technologies require credit to grow and scale. Innovation requires credit creation, which leads to more innovation which requires more credit creation, which leads to more innovation. There is a pretty gnarly positive feedback here on top of an already high growth credit/debt based monetary system. This has all the hallmarks of a potentially hyperbolic economic and financial system.
If we’re approaching a financial black hole, then I reckon we’re well past the event horizon.
Predictions and Analysis
My assertion is that monetary supply and debt are part of a hyperbolic system. If correct then we would expect the following:
- National debt to have a hyperbolic growth pattern
- The velocity of money (the number of times a unit of currency is used to buy goods or services) to decrease as more of the money that is created is almost immediately used to service the underlying debt obligation rather than circulate through the economy.
- The debt to GDP ratio to continually increase as the monetary supply is servicing the debt rather than fuel economic growth.
- Interest rates to hit at all time record lows as more money creation is needed to fund existing debt obligations and make future debt obligations cheaper.
US federal debt looks hyperbolic
Taking the data from the FRED, we can look at total public debt and do some data exploration. Firstly we can look at the inverse trend for the last 10 years and see if it looks like a negative sloped linear, which is a sign of hyperbolic growth.
There certainly is a fairly linear trend.
We can also look at the data and fit an exponential to a sliding 5 year window. If it were hyperbolic, we would expect the fitted exponent coefficient to get more steep with time. This would suggest that the distribution is super-exponential, perhaps even hyperbolic…
This is in fact what we see.
As for the M2 velocity of money, it is at all time lows.
And the Debt to GDP ratio seriously up-trending.
Finally, interest rates have been at record lows in the 0–0.25% range all around the world for a while. Raising them is almost impossible as it makes the asset class of debt more risky as it becomes more likely the borrowers default. Worse still would be if the GDP itself couldn’t keep up with the interest payments alone.
When does the merry-go-round stop?
If this hyperbolic growth system is true, then the singularity hits around April in 2024. This is even sooner than von Foersters population model!
Of course the situation is a lot more complex and none of the assumptions in this modeling could hold. I personally think that the debt-based monetary system is not sustainable in the long run. Consider, for example, the impossible tight rope that federal reserves around the world are forced to walk right now. Interest rates need to stay low to support debt-based money (and therefore debt-based economic growth) but are also the only tool to battle rising inflationary pressures. What a nightmare.
Needless to say, I’m no expert but just a casual observer with some skin in the game. What I’m casually observing, however, is a complex system with some serious flaws. If we’re approaching a financial black hole, then I reckon we’re well past the event horizon.
