Tuesday, December 23, 2014

Exploring a model

As Mary Morgan notes in The World in the Model, one of the things we do with models is explore them, and hope that exploration tells us something about the world outside the model as well.

I appreciate this more and more as I experiment with my agent-based models. Look at the following graph of a run of Adam Smith's fashion model:

There are several very interesting things here:

1) Why does the number of followers wearing blue only once drop below the number of trendsetters wearing blue?

2) And why does that drop happen in the second period of the cycle? If I was going to get some one-off behavior from the model, I'd expect it in the first cycle, not the second.

3) And just why is that first cycle so minor compared to the others?

4) And what is going with the trendsetters in that middle stretch where they don't really seem to cycle along with the followers?

Here is a larger point to take from this: Have you ever wondered why testing business cycle theories is difficult, and economists have not all agreed on a single one? Well, the above graph is produced by a very simple model with only a handful of parameters. Real business cycles obviously have essentially an infinite number of "parameters" feeding into what occurs. So that is why!

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