Sunday, April 17, 2011

Economists do it with models

This is for RY.

In a comment left here about a month or so ago – I’ve been swamped with my real job – someone complained about the use of models in economics. I get these complaints all the time. Economics uses too many models, the models in economics are unrealistic, the models in economics are too complicated (this amounts to being too realistic), and so on.

All of these complaints have some merit. The models that students encounter in their first economics courses are painfully simple. It’s hard to get into a meaningful discussion about the ideas behind these stripped down models.

Many of the models used, even at higher levels, are unrealistic. There are entire classes of models (rational expectations, perfect information, etc) that I really, really don’t like. We often make heroic assumptions about people that don’t have a lot to do with real live human beings. I cringe whenever I here a job candidate defend a particular model by saying, “this assumption was made for tractability”. That just means they assumed something to make the math easier to solve.

Finally, many of the models used in economics (particularly at the higher levels) are quite complex. It’s easy to lose track of what’s going on if you’re dealing with a system of 6 or 7, never mind 20 equations. Some of this problem is the way the models are sometimes presented. All the equations can usually be reduced to just one or two, but all are shown with the idea that it’s important to know where they come from. The other source of complexity is the math required to solve the models, but more on that later.

So, on its face the indictment has merit. Now we turn to the defense.

A model is just a simplification of the real world so that we can focus on a small part of what’s going on. The models that first year students see are extremely stripped down versions of more robust models. Why strip them down? To allow students to focus on what many in the discipline feel are the fundamental relationships. Everybody knows that price isn’t the only thing that influences how much of something people want to buy, but it is almost always a factor. We ignore all the other stuff in an effort to make sure we get that part right. More complex relationships are added later, not as quickly as I would like, but you can’t have everything.

The unrealism has very little defense in my mind. Assuming that people are always right, except for some small error term bugs the crap out of me. The only defense to unrealism I can buy into so far is we’re slowly working in the direction of realism. So the models maybe unrealistic now, but they’re more realistic than they were. This is progress, of a sort.

Finally we turn to complexity. I get this at all levels, right from intro to graduate. At the lower levels, I’m sorry to say the blame has to fall on the public education system (this is the more on that later issue). A frightening number of students arrive at university illiterate and even more are innumerate. At the undergrad level the models we’re talking about aren’t that complicated (they’re even linear), but many students lack the background preparation to simple algebra. At the upper levels, most economists (including me) aren’t trained in enough mathematics. We all need more. There are few economists who have the ability to invent the math required to solve a problem and translate the math into something accessible. Hell, there aren’t many in physics either. The advantage of using mathematics is precision and the fact that if you’ve done the math correctly, you can’t have made an error in logic.

So given all of these issues, why use models at all? To further our understanding of real world phenomena! Every discipline uses models. All a model is, at its core, as a way of organizing facts and ideas. A model is anything that describes the interconnectedness of two or more things. All the humanities use models and just the sciences and pretenders to science. Economists do it with models, and so does everybody else. Economics is just a little more explicit about it than others.


New said...

Excellent post. I notice that the great, old economists like Keynes and Smith and Minsky all used logical models to make their arguments. I wonder why logical models have fallen out of favour and math has fallen into favour?

economistatlarge said...

Good point. I can think of 3 reasons
1. Precision/certainty : talk to a mathematician and they spend a lot of time worrying about exactness, the idea is we dont want there to be any doubt about what it is we're talking about and the assumptions made. As I said before, if you do the math right, you can't have made a logical error.
2. Efficiency : as a language math can express complex ideas pretty fast.
3. Neutrality : math allows you to come with answers you don't like more easily than the more verbal methods.