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More on models

George Selgin wrote a post on expressing ideas in words rather than mathematics. Here are my two cents of commentary.

Math is useful when we want to know “how much?” How much is the U.S. economy growing? How much is the value of the dollar changing against a trade-weighted basket of other currencies? How much more revenue would income taxes raise if their rates were doubled?

The math that is useful for answering such questions is often nothing more advanced than what college-bound high school students learn, combined with some accounting identities. Deirde (formerly Donald) McCloskey and Arjo Klamer have made the case that accounting rather than higher mathematics is in fact the master metaphor of economics, because so much of applied economics is about what to count and how to account for it.

At bottom, a model is a device for isolating and examining what we consider to be important features of a situation. A model need not be a forest of equations. A verbal description can be a model. So can a balance sheet. So can a historical case—that’s why we say, for instance, “Bank X’s lending practices were a model of good risk management.”

A verbal model is more appropriate than a mathematical one in cases where generality is more important than extreme precision. A small change in the assumptions need not lead to a big change in the conclusions, as can happen with mathematical models (another favorite theme of Deirdre McCloskey).  Economists continue to rely heavily on verbal models in practice. But rather than following Alfred Marshall’s habit of favoring verbal exposition even for results derived from mathematical inquiry, they express insights that were originally verbal only in mathematics. Readers waste much time mentally translating the math back into words.