# We need more complicated mathematical models in economics

I am half way through David Colander and Roland Kupers’s book Complexity and the Art of Public Policy: Solving Society’s Problems from the Bottom Up. Overall, it’s a good book, although the authors are somewhat slow to get to the point and there are plenty of lines that perplex or annoy (Arnold Kling seemed to have a similar reaction).

I’ll review later, but one interesting line in the book is that under a complexity approach, you may need more complicated mathematical models than used in neoclassical economics. This is because the purpose of the models under a complexity approach is different. They write:

A person is walking home late one night and notices an economist searching under a lamppost for his keys. The person stops to help. After searching a while without luck he asks the economist where he lost his keys. The economist points far off into the dark abyss. The person asks, incredulously, “Then why the heck are you searching here?” To which the economist responds—“This is where the light is.”

Critics of economists like this joke because it nicely captures economic theorists’ tendency to be, what critics consider, overly mathematical and technical in their research. Superficially, searching where the light is (letting available analytic technology guide one’s technical research) is clearly a stupid strategy; the obvious place to search is where you lost the keys.

Telling old jokes doesn’t do much, and in this case the joke was a setup for a different punch line. That punch line is that the critic’s lesson taken from the joke is the wrong lesson if the economy is complex. For a complex system, which the social system is, a “searching where the light is” strategy makes good sense. Since the subject matter of social science is highly complex—arguably far more complex than the subject matter of most natural sciences—it is as if the social science policy keys are lost in the equivalent of almost total darkness. The problem is that you have no idea where in the darkness you lost them, so it would be pretty stupid to just go out searching in the dark. The chances of getting totally lost are almost 100 percent. In such a situation, where else but in the light can you reasonably search in a scientific way?

What is stupid, however, is if the scientist thinks he or she is going to find the keys under the lamppost.

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The fact that decisions in complex systems are so uncertain and difficult to make does not mean that one should avoid dealing with them mathematically and scientifically. Quite the contrary; it allows for much more complicated mathematical models since the models are used for a different purpose. Returning to our economist joke in the first chapter, they aim not to precisely describe the real world, but to understand the topography of the landscape under the light. The mathematical models are trying to map different types of topography, which may be helpful when searching for the policy keys, but they do not represent the full search for the keys.

The policy answers can be found only by those searching in the dark, which involves dealing with the full complexity of the system. The fact that one is using the models primarily for guidance, rather than for prescriptions, frees one from forcing the models to have direct policy relevance, which, as we will discuss, is a major reason for the problems with existing economic models. Instead one can use higher-level mathematics that is up to the task. In technical terms, instead of using static equilibrium models that can be analytically solved, one is free to use nonlinear, dynamic models that are beyond analytic solution, but upon which computational tools can shed light. As we will discuss in later chapters, the mathematics of complex evolving systems is really hard and still developing. That is why in the past economists and other social scientists have avoided them. It’s also why their policy advice has not been especially useful when the solution required a comprehensive understanding of our complex evolving socioeconomic system.

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[T]he criticism coming from complexity scientists was different from that of most heterodox economists. The usual heterodox criticism of standard economics was that it was too mathematical. This was not the criticism here. Complexity scientists were arguing that economics was not mathematical enough—not only was it not mathematical enough, it was using the wrong mathematics. They agreed that if it was to be science, it had to be “under analytical control.” But they were arguing that by using the right mathematics, highly complex systems containing high levels of agent interdependence could come under analytic or computational scrutiny. Complexity scientists argued that economists needed to start exploring nonlinear dynamic models, path-dependent models by using the mathematics and tools of complexity science.

They also give a word of caution as to where the science is at:

Every period has its excesses: the current hype about the usefulness of formal models in complexity science holds echoes of the overconfidence in models that one saw from the 1930s onward. The time when models will provide complete answers to social policy questions, if such a time ever will exist, is still far in the future. Complexity models, like all models, are very useful and necessary, but they are not sufficient.