A Veritable Epidemic of Mathiness

Paul Romer’s eruption against mathiness has been quite a spectacle.  Here you have an iconic name in modern economic theory throwing a fit in public, naming names (some of them also iconic) and denouncing his adversaries as enemies of scientific and ethical norms.  It’s a bit over the top, a bit overdue and a bit underconsidered.

I want to focus on the underconsidered part.  I was alerted to this aspect of Romer’s original paper by his sideswipes at Joan Robinson and the UK faction of the Cambridge capital controversy.  Now, it happens that I take a middle position on this dispute: I think they were both in some sense wrong.  The British Cantabrigians, along with their Italian comrades, were arguing from a model whose equilibrium assumption (equal rates of profit in all processes) is meaningless, in a mathiness sense, in an intertemporal context.  (If you think Lucas rational expectations is a stretch, Sraffa rational expectations is even crazier.)   But the MITers were also defending an aggregation of physical capital and its equivalence to a sum of financial capital that was also shown to be mathy—see here and here.  Romer’s attack on Robinson was signaling that a double standard was at work.

In fact, economics is a veritable empire of mathiness.  I agree with Romer that the use of algebraic entities that have no meaningful correspondence to real world objects and deliberate obfuscation through the use of words with multiple meanings are sins against science, but that is just the beginning.  Here are two more, one theoretical, the other empirical:

1. Equilibrium with mechanisms.  A large part of economic theory takes the form of equilibrium conditions and the comparative statics thereof.  Even theories that describe events transpiring through time usually take the form of traversals: routes mapped from an initial equilibrium state to its successor.  What usually goes missing are the mechanisms, the processes, in principle observable in the real world, by which actors revise their behavior and produce new collective outcomes.  Without such mechanisms the concept of equilibrium is meaningless: you can’t get there from here.  One symptom of this malady is the inability to distinguish between equilibrium conditions and identities—equal signs and identity signs.  The difference is that causal processes apply to the first but not the second, so if your theoretical world lacks processes altogether you won’t know what that extra little line, ≡ vs =, is all about.

2. Misuse of null hypothesis significance testing.  Suppose you have a theory that A causes B.  You can’t observe this directly (or you haven’t bothered to try), but you can infer that, if this is true, a relationship between two measurable variables, an x and a y, will occur.  So you do a study on x and y, run a significance test and conclude you can reject the null hypothesis that x and y are unrelated.  And, if you are like most empirical economists, you will then announce that you have “tested” your theory about A and B and have found that the evidence is “consistent with” it.  But wait!  There are other theories that would also generate expectations on x and y and they may be inconsistent with yours.  If the x-y business actually lends more support to one of these other theories than to yours, the evidence is saying the opposite of what you claim it says.  The reality is that rejecting a null hypothesis says nothing at all about which of the many possible explanations for the non-null is correct.  A conscientious empiricist would put all the potential theories on the table and consider in a systematic manner how the new evidence alters the relative credence we should give them.  The reason utterly implausible theories live on, decade after decade, in economics is that low-bar implications—implications suggested by many theories of greater or lesser plausibility—survive significance testing and are then proclaimed “consistent with” the particular theory to which the researcher is attached.  This too is a kind of mathiness: lots of fancy econometric technique wrapped around a dishonest and thoroughly unscientific core.

So I have mixed feelings about the Romer meltdown.  I definitely understand where he’s coming from and how frustrating it is to see ideologues deploying math to obfuscate rather than clarify.  But the problem is much wider and deeper than he seems to realize.