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Decimal Digest
17 Jan 2014

Can St Petersburg's Paradox explain why QE is failing to produce ever lasting recovery?

Since the beginning of 2009, unconventional monetary policy, characterized by zero interest rates and mindless expansion of asset base of central banks, is influencing the movement in global asset markets. However, at the same time, it is failing to produce a consistent, and believable economic growth. The December job number in the USA is a poignant reminder of lack of success of QE.

Maybe, a mathematical construct called St Petersburg’s paradox can explain the apparent lack of success of the recent monetary policy experiment. Let’s first begin with a discussion on what a St Petersburg’s Paradox is. Imagine a casino that wants you, its patron, to win ALL the time. So, it constructs the following game. You flip a coin. If you get a head, you win $1 and you can go home. If you get a tail in the first flip, you do not get paid anything, but you get a second chance. In the second chance, if you get a head, you will be paid $2 (double the previous round) and you go home, while if you get a tail, you get another chance to play. A head in third round will get you $4 (again double the previous round), while a tail will get you another chance. This can, in theory, go on infinitely, till you get a head, and your payoff will be ; n being the round in which you get the head in your flip.

So, in this game, the player can never lose. How much should you be willing to pay to the casino for letting you play this game? The mathematical answer is equivalent to its payoff. The payoff is calculated as followed.

So, theory says, you should bet your house on this game. However, in reality, will you ever do that? Most people will be willing to pay only small sums to play this very profitable game. Psychologists have long called this, in general, irrational behavior. More importantly, statisticians have recently started terming this kind of series as non-ergodic series. Nonergodic series are like playing a game where outcomes manifest in different parallel universes, while the player is trapped in only one universe, like all of us. Hence the outcomes are not really accessible to the players.

This explains the apparent lack of success of virtually infinite QE. What has happened over the last five or six years is that every time the financial markets show negative trends, central banks put a floor on the markets by doing ever larger QE. In addition, they are still committing very large sums in QE, in spite of the tapering noise. In other words, central banks are behaving like our casino owners in the previous paragraphs. Still, the central banks are not finding comparable success, just like the casino owners in our example.

For history to judge 21st century capitalism less harshly, it is imperative that the global central banks realize the folly of their behavior and amend their actions sooner rather than later.


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