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Gillitrut  Reading from the golden book under bright red stars  1yr ago (link.springer.com)   Edited 1yr ago   1381 thread views

Pay no attention to the Model Behind the Curtain!

link.springer.com

Many widely used models amount to an elaborate means of making up numbers—but once a number has been produced, it tends to be taken seriously and its source (the model) is rarely examined carefully. Many widely used models have little connection to the real-world phenomena they purport to explain. Common steps in modeling to support policy decisions, such as putting disparate things on the same scale, may conflict with reality. Not all costs and benefits can be put on the same scale, not all uncertainties can be expressed as probabilities, and not all model parameters measure what they purport to measure. These ideas are illustrated with examples from seismology, wind-turbine bird deaths, soccer penalty cards, gender bias in academia, and climate policy.

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If the point is merely that you shouldn't blindly take numbers from models at face value, that point is well taken. But, for all his criticism of models, Stark doesn't really give any alternatives. Ultimately, we as people and civilizations have number-related decisions to make and those numbers/decisions have to come from somewhere.

Anyway, more generally, I have a hard time taking someone's abstract arguments seriously, when their concrete arguments are bad. For example, Stark refutes the idea of using expected value, saying

There is evidence that human preference orderings are not based on probability times consequences, i.e., on expected returns or expected losses. For instance, there is a preference for “sure things” over bets. Many people would prefer to receive $1 million for sure than to have a 10% chance of receiving $20 million, even though the expected return of the latter is double

This is correct, but is solved by using an increasing, concave function to convert wealth to utility - an idea that is is extremely old, and is almost always used in actual economic literature. See, for instance, virtually anything written on investment in the last 50 years.

He then says

In a repeated game, basing choices on expectations might make sense, but in a single play, other considerations may dominate

But, again, the traditional academic approach is to maximize log-wealth in iterated games, since this strategy (with probability approaching 100%) out-performs naive linear wealth optimization.

These aren't obscure ideas he's ignoring - they're ideas you'd expect most economics undergraduate to encounter, let alone a professor. Why isn't he mentioning them? Lack of knowledge? Dishonesty? Thinking the counter-arguments are obvious? I don't know, but I do know those paragraphs burn a lot of credibility in my eyes.

Wait, why does log-wealth work, in particular? I’m having a hard time seeing how that stacks up vs. linear. Does it just capture that concave function in the limit?

Err... re-reading my comment, that second part is probably a tad unfair to Stark (though I stand by the first quote being a pure weak-man).

If you're still interested (and don't already know), the relevant search term is "Kelly Criterion". It is mostly limited to betting/investing and the central insight is that

  1. Since returns scale linearly with amount invested, the amount of money you have after a large number of sequential bets will be the product of the returns.

  2. log(products) = sum

  3. Therefore, by the Central Limit Theorem, your log(wealth) will converge to the log-expected return.

So, in the long-run, with near-certainty, optimizing for log-wealth actually optimizes for actual wealth, or any other function of wealth.

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