All Shoes All The Time

Perry Metzger has an amusing post about Piketty and the “Shoe Event Horizon” from The Hitchhiker’s Guide to the Galaxy:

On Frogstar B, for a time shoe production increased faster than the rate of overall economic growth. As a result, with time, shoe production became a larger and larger fraction of the economy, until finally the Shoe Event Horizon was hit, at which point nothing but shoes could be manufactured, and lacking any other goods or services, their civilization collapsed.

Thomas Piketty’s “Capital in the Twenty-First Century” describes a similar tragedy that lies inevitably in our future, the point at which the only economic activity left is investment, all money is held by a tiny minority of wealthy people, and our civilization permanently ends.

Metzger points out that if r>g indefinitely, pretty soon investing will completely dominate the economy.  I can pick some small nits with the analogy:

  • It confuses stocks and flows – Wealth is stocks, GDP (our proxy for “the economy”) measures flows.
  • If I understand Piketty correctly, he would argue that once the situation becomes extreme we’ll have war or revolution

These things aside, this is actually a pretty good critique. Piketty’s forecast that investment returns will always exceed growth is highly vulnerable to the charge that ‘trees don’t grow to the sky’.

In fact, the stock of wealth (including sovereign wealth funds and accumulated leveraged government balance sheets) has become large enough that returns have decreased. Piketty didn’t seem to notice that interest rates are scraping the zero bound even in dodgy European countries.

What has changed in investments over the last few decades is the rate at which we capitalize equity investments. This is closely related to interest rates, and the lower the rate, the higher the capitalized value. I would suggest to Piketty that his ‘r’ will look high when rates are low/multiples are high, and vice versa (what would his analysis say in 1980).

Multiple appreciate can’t go on forever – trees do not grow to the sky. There was a point during the dot-com boom when I saw analysts imply long-term growth rates that exceeded any reasonable discount rate. Mathematically, this results in a value of infinity. There was a correction, as I recall.

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