Wednesday, December 18, 2013

The rationality paradox

Dog-Eat-Dog by Ruth Graham
There are important differences between humans and other animals, and we should account for them when trying to model their respective behaviours. One difference is that humans can understand mathematical models, while there is no known example of this in animals.

In economics, the Lucas critique is a useful piece of advice about modelling human behaviour. It alerts us to the fact that if people are aware of the model we are using to predict their behaviour, they can adjust their behaviour to exploit our naivety. Even if they don’t know the exact model we are using, if we have not accounted for their strategic behaviour, they can still take advantage of us.

One paradox about the Lucas critique goes as follows. Lets take the classic example of a model, called the Philip’s curve, used by central bank managers to set inflation and try to reduce unemployment. This model is subject to exploitation by rational firms who can manipulate their employment patterns given that they know the inflation strategy of the bankers. As a result, the Philip’s curve will fail to make a correct prediction and is thus subject to the Lucas critique.

This is a reasonable observation, but why are the firms assumed to be rational and the central bank managers irrational? Surely, these highly qualified, trained economists would have thought of this possibility and incorporated the reaction of the firms into their model? This is all the more surprising when you consider that firms have many other things to think about than inflation five years in to the future. Apparently, on top of all their immediate concerns about their business model, staffing problems etc. these firms have dedicated their time to finding loopholes in the central bank’s thinking.  Why should the bankers (apart from Lucas, of course) have missed this fact, while the firms are able to work it out?

Any Lucas-inspired model of these bankers behaviour should not allow them to use the Philip’s curve in the first place. The only logical conclusion of this line of reasoning is either that the observations of the economists using Philip’s curves was mistaken or it was some temporary insanity which is replaced by a steady state rationality in the future.  

When we build a mathematical model of human behaviour, the Lucas critique should be taken seriously. Understood properly, it says you should think a few steps ahead when making your model. Does your model make sense? Lucas was pointing out that the Philip’s curve model has a particular type of limitation. We should remember this limitation when we are building models. The Lucas critique is one of many such limitations.

But the paradox tells us that the Lucas critque should not be taken too seriously either. Taken to an extreme, the critique says that the only thing economic models should be used for is studying the outcome of rational interactions. If this were the case, then the paradoxical question is why economics exists at all? The rationality assumption is that people are able to work out the consequences of their actions and therefore we don’t need an economist or anyone else presenting them with a model of what those consequences might be.

This description is typical of paradoxes in mathematics where we want to say something about a model using the model itself to say it. Last month I wrote a blog post about Bertrand Russell spending 20 years doing this to no avail in trying to establish the axioms of mathematics.  It just isn’t possible.

I was prompted to write this after a blog post by Simon Wren-Lewis that Richard Mann tweeted me. Although I find scathing attacks on economics amusing, I find it difficult to believe that economists or anyone else takes the Lucas critique as far as appears to be claimed.  This would be completely irrational. I also doubt whether, as is also claimed, that we can really attribute the economic crisis to models based on rationality.  But it is certainly fun thinking about it.

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