Short cash Half-Life and Shortsighted Social Planning

Here's some research on inflation rates throughout history, for consideration in what kind of economic conditions help societies engage in long-term projects, which I assume are some of the fruits of social health. I'm interested if the basic relationship shows up historically, and also in estimating what actual inflation rates tend to work well.

In summary, I find while a society may grow with cash half-lives from 30yr down to a couple years, that lower rates are destructive: half-lives shorter than a year or two coincide with historical examples of market collapse in the short term, or social collapse if carried on. In contrast, a cash half-life significantly greater than 30-40 years coincides with important periods of flourishing.

I find it more intuitive to work in terms of cash half-life than inflation rate. To convert from a 2% rate, or InflationRate=0.02 (which the US Fed targets but never delivers) to a half-life, means to find how long it takes 2% inflation to erode half the value of a dollar. You can find this by iterating "$1 minus 2% annually" every year until you reach 50¢. You'll find this is 34 years: (1-0.02)^34 = 0.50.... The general formula is:

(1-InflationRate)^HalfLife = 0.5

We can also find the HalfLife directly by taking the inverse, or "How many depreciation periods until half value? That's the inverse operation, so logarithm of the HalfLife gives number of periods, or log_x(0.5) = 34, where _x is "base x", x=0.02. Variable base log isn't available on most calculators, but base conversion is done by dividing by the log of the base. So the final form is:

log(0.5)/log(InflationRate) = HalfLife, e.g. log(0.5)/log(1-0.02) = 34.30....

It seems like it would be nice for humans to be able to plan for the future and store up favors to enable those plans. If you can't store value or favors at all, it seems impossible to plan. The longer you can store value, the longer you can plan. But also, storing value forever doesn't seem practical or ethical. Should we be obliged to honor debts from ancestors long-forgotten?

What is the rate of depreciation of money that achieves a good balance of both goals?

The longest plans I know of that humans have achieved are religious shrines, which take a few centuries to build, and I think achieving that did involve storing and paying gold (please correct!). We have good histories for the European cathedral building period, whose golden 😉 age was from 13-1600s. It seems it ended when there came a great influx of gold from the Spanish extraction from the new world, which happens to be the beginning of documented inflation rates. That's pretty interesting.

The earliest data I find are for the late 1600s onwards[Gold], but I assume the gold supply growth at this point was probably much higher than before. It looks like the half-life of value was ~30-40 years (6 tons in 1681 to 15 tons 1721), but probably very roughly distributed, so that some countries (e.g. Spain) had relatively high rates of accumulation (and hence inflation) while everyone else much much less. That suggests that inflation before this may have been significantly lower, and half-life significantly higher, say 2x or 3x that duration, to maybe 90-160 years. Since then the gold supply last doubled since 1985, so that's about the same growth rate for 3 or 4 centuries.

Maybe we can hypothesize that before the Spanish gold influx, inflation in Europe was low enough that some individuals or institutions could satisfactorily save value for their own lifetimes and sometimes for even longer, and that this was one of the conditions that was instrumental for their cultural flourishing?

So there's one set of facts to think about on the low-inflation end.

On the high inflation end, there are many well-known examples of hyperinflation that have wrecked major economies[Hyper]. Looking at the Venezuelan example, the half-life went from 20 years at the left end of the graph to a little under a month at its peak (I estimate half-life from the 90% value there by dividing by 3, (halving 3 times, 1-(1/2)^3 = ~87.5% value loss). Weimar Germany hit 5 days, Zimbabwe in 2008 and Hungary 1946 less than a day.

So we have a potential middle-ground for practical half-lives of 1 month to 100+ years, with the short end of that looking pretty bad for the society, and the long end looking pretty good, imho.

How do some major currencies compare? Apparently the Swiss Franc is the best store of value in recent times[CHF] "Swiss franc is losing half of its value every 15 years. The longest half-life I have ever recorded." (back to 1985). The Swiss certainly life pretty well.

The $USD originally floated[USD], with positive and negative nominal inflation rates, but was largely was traded with Spanish gold in the early days. So let's put that down at a half-life of 30-40 years.

This changed as we went off the gold standard, beginning with banning gold ownership from 1930s-1970s and then decoupling the banks starting in the 1970s. The Fed advertises an inflation target of 2%[Fed], but the average rate for the past 50 years has been closer to 4%[Later]. You can get half-life from inflation with log(2)/log(1+Inflation%/100), so 2% gives 35 years, 4% -> 17yr, and we're currently at 8 or 9% inflation, which funnily gives 8yr or 9yr half-life for the $USD. I think it's highly likely that relatively stable money was instrumental to America flourishing, and going off the gold standard is not just coincident with the end of this period.

Needless to say, fiat currencies are getting a pretty bad rap through all of this.. not a single one has been able to resist the same eventual fate of paying off debts (not storing up favors) by debasement.

We're having trouble keeping our houses, much less building cathedrals.

I'm not suggesting monetary stability is all we need to flourish, but that it may be a necessary pre-condition.