Some Thoughts About Economic Exposition In Math And Words

Analysis in economics and other social sciences often uses a combination of words and mathematics. There is an ongoing critique by those who argue that while the math may sometimes be useful, it is too often deployed with insufficient regard for whether it captures the underlying economic reality. In such cases, the argument goes, math is used as a way of pretending that an argument about the real-world economy has been definitely made, or settled, when in reality only an equation of limited application has been solved.

Paul Romer recently offered a pithy commentary on this longstanding dispute on his blog. Romer quotes from an earlier post by Dani Rodrik, who in some lists of advice for economists and non-economists, includes the following:

“Make your model simple enough to isolate specific causes and how they work, but not so simple that it leaves out key interactions among causes. … Unrealistic assumptions are OK; unrealistic critical assumptions are not OK. …  Do not criticize an economist’s model because of its assumptions; ask how the results would change if certain problematic assumptions were more realistic. … Analysis requires simplicity; beware of incoherence that passes itself off as complexity. … Do not let math scare you; economists use math not because they are smart, but because they are not smart enough.”

Romer has in recent years expressed concerns over “mathiness,” in which predetermined conclusions masquerade behind what looks like an “objective” mathematical model.As he wrote in a 2015 paper:

“The style that I am calling mathiness lets academic politics masquerade as science. Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content. … [M]athiness could do permanent damage because it takes costly effort to distinguish mathiness from mathematical theory.”