Economic Modeling

When I first started learning about Development Economics (in Public Policy 184, Poverty and Policies in Developing Economies, which I actually eventually dropped in favor of other things) I was struck by a lecture on the Harrod-Domar model because it was very obvious to me that the model was completely insufficient and overly simplistic. I had already read The Elusive Quest for Growth by William Easterly who basically made fun of people for ever believing this model could accurately describe anything (Easterly sums it up as "GDP growth will be proportional to the share of investment spending in GDP."). 

After class I decided to ask the Professor about what the benefit of studying a model like this was since there were clearly hundreds of other factors which played a role. She explained that while this was absolutely true, it was important to try to strip away as many factors as possible and build something that one can easily reason about and see if it still makes useful predictions because it can help one get a better understanding of what is actually going on.

One should be careful to realize that there may be lots of other processes at work but that trying to understand all processes at once was not going to lead to any useful analysis. While the Harrod-Domar model is in fact far too simplistic - it's assumption of constant returns to capital make lots of sense in the short term when there is high unemployment but makes little sense once there is a balance between labor and capital - it did lead to a better understanding of some of the processes at work.

While reading a piece by Paul Krugman on High Development Theory (more on that in a future post) I was struck by this following explanation of how useful simple models can be:

Dave Fultz was a meteorological theorist at the University of Chicago, who asked the following question: what factors are essential to generating the complexity of actual weather? Is it a process that depends on the full complexity of the world -- the interaction of ocean currents and the atmosphere, the locations of mountain ranges, the alternation of the seasons, and so on -- or does the basic pattern of weather, for all its complexity, have simple roots?

He was able to show the essential simplicity of the weather's causes with a "model" that consisted of a dish-pan filled with water, placed on a slowly rotating turntable, with an electric heating element bent around the outside of the pan. Aluminum flakes were suspended in the water, so that a camera perched overhead and rotating with the pan could take pictures of the pattern of flow.

The setup was designed to reproduce two features of the global weather pattern: the temperature differential between the poles and the equator, and the Coriolis force that results from the Earth's spin. Everything else -- all the rich detail of the actual planet -- was suppressed. And yet the dish-pan exhibited an unmistakable resemblance to actual weather patterns: a steady flow near the rim evidently corresponding to the trade winds, constantly shifting eddies reminiscent of temperate-zone storm systems, even a rapidly moving ribbon of water that looked like the recently discovered jet stream.

What did one learn from the dish-pan? It was not telling an entirely true story: the Earth is not flat, air is not water, the real world has oceans and mountain ranges and for that matter two hemispheres. The unrealism of Fultz's model world was dictated by what he was able to or could be bothered to build -- in effect, by the limitations of his modeling technique. Nonetheless, the model did convey a powerful insight into why the weather system behaves the way it does.

Much has been said of late about how Krugman specializes in building highly stylized and extremely simple (and initially much criticized) models that turn out to capture everything that is necessary to prove his point:

You make a set of clearly untrue simplifications to get the system down to something you can handle; those simplifications are dictated partly by guesses about what is important, partly by the modeling techniques available. And the end result, if the model is a good one, is an improved insight into why the vastly more complex real system behaves the way it does.

In many of my later Economics classes I found that most Professors just taught the models without explaining their inherent limitations and it made everything feel fake - instead of using the models to elucidate the underlying processes they were using smoke and mirrors to make simplistic points. Lectures became intricate exercises in trying to figure out where the models broke down and started diverging from reality when the lecture itself never mentioned the fact - a useful exercise for the conscious student but very dangerous for everyone else. In conclusion, models are extremely useful in studying economic proccesses (and many other things) as long as one is aware of the limitations, or in Krugman's words:

The problem is that there is no alternative to models. We all think in simplified models, all the time. The sophisticated thing to do is not to pretend to stop, but to be self-conscious -- to be aware that your models are maps rather than reality.