Bryan Caplan argues that economists’ use of math has not passed the cost-benefit test, claiming that our intuition is a much more important tool. Paul Krugman responds by mostly agreeing, but noting that sometimes mathematical models help you think through complicated concepts. I’m not sure Caplan’s follow-up addresses Krugman’s point, and, in my opinion, Krugman is right. The point is that models can help our intuition and economics is better off because of it.

My summary of Krugman’s argument: intuition isn’t always right. He gives as an example his experience in trade theory, specifically his development of economies of scale theories of specialization. He notes that there were economists who did foresee his contribution, but that they had mainly come away with erroneous conclusions. Specifically, they were using the economies of scale argument to advocate protectionism. When Krugman developed a simple model and used it to think through these issues he found that, surprise surprise, these economists’ intuitions were wrong and that economies of scale was not a good argument, on its own, for certain types of protections (e.g. tariffs to protect infant industries).

Another example: Austrian business cycle theory. ABCT has been pretty well developed, mostly through the use of intuition (although, Hayek very much believed in the strength of using a simplified mathematical model). However, there continues to be certain ambiguities that have probably gotten worse over time. Take, for example, the differences between Garrison’s and Hayek’s theories (of where inputs are allocated during the boom). If we had a good model, these differences would be easier to work through. Likewise, Austrians generally have only a very broad idea of what the bust looks like, and a model might help stimulate intuitive insights in this area.

When there are only a handful of variables to think about, intuition without a model can be useful. But, we can think of intuition as having diminishing returns and these returns can be manipulated by increasing the “productivity of intuition” with a model. They help keep our thinking straight, especially when we have to keep track of so many things that it muddles our thinking. I’m not using economic terms only as analogies, either. One of the points made by Daniel Kahneman in Thinking, Fast and Slow is that our brains can only think about so many things. By using a model you can “automate” some thinking (e.g. keeping assumptions and variables straight), allowing your brain to work where it’s most useful: intuitive insights. I’d argue, even, that a use of a model not only helps guarantee greater intuitive accuracy, but helps achieve results faster than would otherwise be the case.

One thing that should be said, and that is on Caplan’s side of the debate, is that you can’t substitute models for intuition. Krugman, on his blog, is not saying that you can. But, some of my experience with his writing says otherwise. One of my favorite textbooks is actually Krugman, Obstfeld, and Militz, International Economics, but one of my complaints is that the intuition is not always very clear. For example, the third chapter covers comparative advantage, but the lesson heavily relies on simple algebra to make the point. (Update: I realize that this isn’t the type of modeling most economists have in mind, but the simplicity of algebra, I think, makes the point stronger.) The algebra tells us that specialization follows where opportunity cost is the lowest, but the intuition is poorly explained. In fact, when I took trade theory as an undergrad — using this textbook —, a surprisingly large amount of my classmates failed the first midterm (covering the first five chapters). It wasn’t that the subject material was hard, it was that for a lot of people the intuition was difficult to get. People didn’t know where to start; but, with the use of intuition, I was able to get through the simple math, because I had an idea of where to go.

No intuition, no party. But, sometimes the party gets difficult without a model, because you’re approaching diminishing returns. The best way of keeping things straight is through a model, by increasing our mental productivity. That a lot of people aren’t trained to use models isn’t an argument against them. The average blog reader is not going to come up with a deep theoretical insight, and, to a large extent, blog readers require economists who have thought about complicated issues long enough to be able to simplify them and communicate them through clear prose. Economists are trained to think through models because they’re the ones who are ultimately doing the hard work, thinking about problems that are difficult to sort out in our brains.

Of course, none of this implies, as Krugman notes, that math isn’t also subject to diminishing returns. The key is finding the right balance: where the benefits meet, or exceed, the costs.