Two models

Just random thoughts, tangentially related to economics, the sort of thing you think about while you’re dozing off on long flights:

  • The drift of civilization. Robert Anton Wilson, among others, has advanced the theory that the center of human civilization has a tendency to drift “westward and slightly northward” over time (China – Middle East – Europe – America), an idea which is drawn from the historian Brooks Adams and his “Law of Civilisation and Decay”. This theory sounds a bit too batty and deterministic to be worth considering, and its main historic use has been to shore up some pretty windy American exceptionalism, but when you start thinking about how one might go about modelling the drift of human society, it seems pretty trivially true. Consider:

    A society is composed of some number of individuals, who start life at time t in the middle of some randomly selected landmass of the planet Earth. Every morning at dawn, they set off walking in some randomly selected direction, and continue until sunset, when they stop … now take a deep breath, think hard, and try to predict the next step … even in this simple model, there is a tendency for society to drift westward. Why? Because when they are moving westward, they’re moving in the direction of the setting sun, so their solar day is a couple of minutes longer than if they’re walking eastward. It’s the same effect which accounts for time zones. You can complicate the model as much as you like, adding terrain features which are hard to cross, etc, but it strikes me that as long as you’re modeling a planet which spins in the same way as Earth, you’re going to have this drift. Also note that, following similar reasoning, if you assume that the model society walks all day only during the summer, and then stays put when winter arrives, there’s going to be a northward drift in there too (more strictly, a drift toward the poles and away from the equator). You don’t need any of Wilson’s more esoteric theories; just the simple properties of a random walk.

  • Stock market anomalies and wristwatches. These are a set of slightly weird anomalies in the stock market, mainly associated with the month of January and with small firms. Basically, there is a strong and predictable seasonal component to some stock returns, which causes all sorts of problems for efficient markets theory. Again, let’s take a more simple model.

    How do you find out the time if you don’t have a watch? Well, an easy way to accomplish this is to ask the first 100 people you meet what the time is and take the average (note that I am an economist and therefore assume that you can carry out this process without it taking any time itself. It’s called “tatonnement”). Most days of the year, this will give you a really very accurate estimate of the exact time, as the errors in other people’s watches will tend to cancel out … shouldn’t they? Actually, this might not be true; some people systematically set their watches a few minutes fast in order to not be late for things, but few people systematically set their watches a few minutes slow. However, two days of the year, the estimate will most likely be quite significantly out, as some of the people concerned won’t have set their watches forward or back. Hey voila, more or less the simplest possible model of trying to make collective decisions on an objective but hidden variable, and I’ve already got an equivalent to the equity premium puzzle and an equivalent to the January effect. Aren’t collective action mechanisms wonderful?

No subtextual political or postKeynesian message here, by the way; just the economics equivalent of chess problems.


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