Heavy Industry

Continuing the discussion of debt growth, let’s look at leverage. Here we define leverage at time t to be the debt growth from the starting point to time t, divided by the integral of cash flows accumulated from the starting point to time t. This does not necessarily correspond to bank leverage, as government debt or other credit market instruments may be used to fund profits and support interest payments.

With the same notation, at time t, C(t) corresponds to aggregate cash flow profits at time t.

Assume for the moment that cash hoarding is zero — that all cash is used to acquire financial assets. This means that total profits, or the integral of the cash flow, is provided to banks for lending.

In this case, let

x(t) = ratio of accumulated debt to accumulated cash flows.
z(t) = logarithmic derivative of profits (= cash flow/profits)
r(t) = base-e annual interest rate of debt outstanding

Then our debt flow equation can be re-written to obtain:

In the case of hoarding, suppose only a fraction, k, of cash flows is made available to fund debt growth, and the remainder is hoarded. We assume that k is sufficently constant for the time period so that it drops out of the logarithmic derivates.

In this case, we have:

Now, note that if x is less than 1, positive interest rates and positive profit growth rates will drive the ratio higher. Barring a catastrophic collapse in r(t), x will naturally be pushed to 1.

At x = 1, we have

So x will continue to increase.

When x is greater than 1, then positive profit growth rates begin to slow the growth of leverage, and negative profit growth rates begin to increase the growth of leverage.

Cash flows tend to be very volatile whereas r(t) is stable, barring a sudden massive debt default. The reason for the stability is that r(t) does not measure the offered rate for new debt, but the overall realized rate on the entire debt stock. Therefore, r(t) moves on a time scale in proportion to the duration of debt outstanding and the growth of new debt relative to the existing stock.

z(t) will quickly oscillate with time, but assume that it oscillates around some average value. If the interest rate is set above this average value, then x growth will be unbounded. If the interest rate is set below this average value, then x will oscillate with r(t), however the peak points of oscillation can still be extremely high, dependent on the rate at which profits are collapsing in proportion to the prevailing interest rate.

The Need for Leverage

Ignoring hoarding, which mandates leverage in and of itself, assume that x is 1. In this case, we have

Now if, for some reason, there was an upper bound

then, realized nominal interest rates would need to be 0 to maintain x = 1, or would need to be negative, i.e. as a result of mass defaults. Positive interest rates would only resume after a substantial period of negative profits had driven x sufficiently below 1 to support positive realized interest rates. Note that throughout, we consider only nominal rates.

In other words, an environment in which leverage is bounded at 1 drives the value of financial assets to zero, and chokes of lending, and consequently profits. It is incompatible with money accumulation, and mandates only an exchange economy.

Escape from the Malthusian Trap

For most of the world’s history, incomes per person were stagnant. Technological innovation was stagnant. Beginning with the 19th century, and accelerating thereafter, incomes and productivity began to grow. There are many issues at play in this dynamic, but my contention is that the key driver is the transition to money accumulation, as allowed by the growth of the financial markets and their ability to supply leverage. Without leverage, innovation and profits are punished because there is insufficient purchasing power to support profits — there is a ceiling on the value of financial assets — that is, investment — and this value shrinks to zero as the ceiling is reached. Leverage breaks through this ceiling, and allows people to accumulate not cash flows, which are restricted, but debt, which can grow much larger than cash flows. This supports profits and rewards technological innovation and efficiencies. In fact, it requires these efficiencies as the output growth rate must exceed the interest rate. Therefore leverage both rewards and requires improvements in productivity and technology, and the drive for profits.

However, the price paid for this growth is that the accumulated profits (i.e. financial assets) may become illusory if the interest rate is too high relative to the underlying cash flows. But the interest rate r(t) is much more stable than the profit growth rate, z(t). This is because r is computed over the entire debt stock and debts have long duration. Cash flows, on the other hand, swing wildly from year to year.

Therefore, there are inevitable wide divergences between r(t) and z(t). The leverage evolution equation has a growth rate scaled by the difference between r(t) and z(t). This tends to destabilize x, causing it to explode as profits collapse.

When that happens — i.e. leverage is too high — the financial markets will devalue the existing debt stock, ratchet up the interest rate, and force a de-leveraging.

This is just a restatement that the risk of borrowing short and lending long, is that you are dependent on a constant stream of stable cash flows, which the economy is not able to provide. Therefore standard business cycle variations, if they occur in an environment of high leverage, can lead to a debt collapse, and a sharp downward adjustment of r(t), which is necessary to reduce x to sustainable levels. Such a de-leveraging must entail a loss of confidence, since the surplus nodes accept as payment financial claims which are revealed to be unsupportable by existing cash flows (i.e. by additional excess lending). This strikes at the heart of the accumulation economy. More on this later.