From wordy essays to mathiness
Justin Fox writes that once upon a time economists made their arguments in long, discursive, often contradictory books. To most modern economists these were the dark ages. In the 1940s Paul Samuelson brought enlightenment, in the form of elegant mathematical treatments of the major concepts in economics. Most of these ideas were inherently mathematical anyway, he argued in the introduction to his “Foundations of Economic Analysis,” first published in 1947, which meant that trying to express them in narrative form involved “mental gymnastics of a peculiarly depraved type.” Samuelson and others of his generation believed that mathematical reasoning would clarify economists’ arguments. Romer claims we’ve reached the point where presenting a model is like doing a card trick. Tim Harford writes that if Romer is right, some economics papers are Orwellian Newspeak dressed up as calculus.
Paul Romer writes that 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. The market for mathematical theory can survive a few lemon articles filled with mathiness. But after readers have been disappointed too often by mathiness that wastes their time, they will stop taking seriously any paper that contains mathematical symbols. Economists have a collective stake in flushing mathiness out into the open. We will make faster scientific progress if we can continue to rely on the clarity and precision that math brings to our shared vocabulary.
The disconnect between language and math
Dietz Vollrath writes that one possible interpretation of mathiness is that it refers to “decorative math”. A paper may have a simple model, but there are all these adornments added (endogenous savings rates, endogenous labor supply decisions, heterogeneous agents, etc..) even though they have absolutely nothing to do with the simple model and change none of the conclusions. This decorative math actually makes the paper harder to understand, because now you have to keep track of all this additional notation. This a frustrating feature of modern economics, but this “decorative math” is not what Romer had in mind. What Romer has in mind is the disconnect of the language from the math.
Paul Romer writes that mathiness is a critique of a style that lets economists draw invalid inferences from the assumptions and structure of a model; a style that authors can use to persuade the reader (and themselves) to adopt conclusions that do not follow by the rules of logic; a style that tolerates wishful thinking instead of precise, clearly articulated reasoning. The mathiness that I point to in the Lucas (2009) paper and in the follow up paper by Lucas and Moll (2014) involves hand-waving and verbal evasion that is the exact opposite of the precision in reasoning and communication exemplified by Debreu/Bourbaki, and I’m for precision and clarity.
Chris House writes that mathematical sloppiness can be perfectly fine if it deals with a feature that is not a focus of the paper. Hand-waving of this sort likely comes at very little cost and may have benefits by eliminating a lengthy discussion of issues only tangentially related to the paper. On the other hand, if the hand-waving occurs when analyzing or discussing central features of the paper then I am much more inclined to ask the researcher to do the analysis right.
Mathiness and reality
Simon Wren-Lewis writes that Paul Romer’s mathiness links to the idea by Paul Pfleiderer about theoretical models becoming “chameleons”. To quote: “A model becomes a chameleon when it is built on assumptions with dubious connections to the real world but nevertheless has conclusions that are uncritically (or not critically enough) applied to understanding our economy.” Dietz Vollrath writes that authors often play along by using very complicated math – “mathiness” – making their idea look more “science-ish”. They let people believe their model shows how the world does work, rather than how it might work.
Joshua Gans writes that for Romer mathiness is becoming more pervasive in economics. This is something worth testing, as anecdotal evidence does not necessarily mean that there is a pervasive problem. Noah Smith writes that in no other subject except mathematics itself will you see so many proofs and theorems. But the way math is used in (macro)economics isn't the same as in the hard sciences. In physics, if you write down an equation, you expect the variables to correspond to real things that you can measure and predict. If you read the macro literature, you see that almost every famous, respected paper is chock full of these sort of equations that don’t match reality. Mathematical statements don't remotely correspond to observable reality, nor do they have any evidence in support of them. It’s not just Lucas and Prescott, it’s the whole scientific culture of the field.
Mathiness and academic politics
Paul Romer criticizes several papers by traditionalists that use mathiness to campaign for price-taking models of growth. For them, price-taking is dogma. Given the sharp limits imposed by the mathematics of their formal framework to explain endogenous growth, it is no surprise that traditionalists were attracted to the extra degrees of freedom that come from letting the words slip free of the math. The natural inference is that their use of mathiness signals a shift from science to academic politics, presumably because they were losing the scientific debate. If so, the paralysis and polarization in the theory of growth is not sign of a problem with science. It is the expected outcome in politics.