I have a rule about assigning blame: When a reader misunderstands, it is the writer’s fault.
My paper and posts about mathiness have prompted some reactions that reflect a misunderstanding of my position. Here I’ll try to clarify what that position is. I’ll put off for later a response to people who understand (thank you!) but disagree.
My position is hard to understand partly because it is unfamiliar. It is natural for a reader to think, “In criticizing mathiness, Romer has voiced a grievance that I/we have felt/articulated for years…” Or on the other side to think, “Romer has picked up that discredited argument that…”
What I’m saying does not line up with familiar critiques about political ideology in economics or the use of math in economics, especially critiques voiced by people from outside the discipline.
I’ll take responsibility for having not stated my position clearly. I’ll restate. I’ll keep trying. In return, all I ask is that before you react, you pause to see if you understand.
You can check your understanding by answering these T/F questions and comparing your answers with mine.
1. T/F: Romer thinks that economists should not try to use the mathematics of Debreu/Bourbaki and should instead use math in the less formal way that physicists and engineers use it.
2. T/F: Romer thinks that abstract mathematical models that could turn out to be of no use in understanding data and evidence are examples of mathiness.
3. T/F: Romer thinks that errors in mathematical arguments are examples of mathiness.
4. T/F: Romer says that the economists he has accused of mathiness are using it to promote a right-wing political agenda designed to influence national politics.
5. T/F: Romer thinks that economists should use less math.
6. T/F: Romer is angry.
You see the pattern. Every one of these statements is false.
RE: #1 and #2: Lucas (2009) presents a model based on the assumption that every bit of knowledge that some person will ever know in the future is already known by some person alive today. This assumption does NOT make the model an example of mathiness. I think that it was reasonable to investigate a model based on this assumption. I’m in favor of investigating new models, even if they differ from the ones I’ve proposed. Different models can yield different insights.
I threw my first model overboard, the one from my thesis and my 1986 paper. It served a purpose, but I concluded that we could do better. Still, I’m glad I had a chance to work through the logic of that first attempt. I think that other people should have the same chance to work through the logic of other models that may or may not yield fruit. How do we know until someone tries? Even the ones that seem to lead to a dead end can send us off on a useful line of inquiry.
So my objection to mathiness is not a critique of the assumptions or structure of the models that others propose. It 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.
Re #3: I say explicitly in my AER P&P paper that an error is not mathiness.
Re #4: I wrote that the economists I criticize for using mathiness are engaged in a campaign of ACADEMIC politics, not one of national politics. Whatever was true in the past, the now fight is over ACADEMIC group identity.
For example, one of the things that the people I criticize are campaigning for is a methodological restriction to models with price-taking. For them, price-taking is dogma. To make the case for this restriction, they are not presenting scientific arguments grounded in logic and evidence.
I do not think that the outcome of this campaign over methodological dogma will have any effect on national politics or actual policy decisions. Nor do I think that the proponents of price-taking are fooling themselves into thinking that the outcome of this campaign will have any affect on national politics or actual policy decisions. They are fighting to preserve a sense of academic group identity grounded in a common defense of this dogmatic position.
I have written that Stigler and Friedman opposed Chamberlin’s theory of monopolistic competition because they did think that letting this deviation from Marshallian price-taking into mainstream economics could influence national politics and actual policy decisions. But that was then. This is now.
I suspect that path dependence explains why economists at the University of Chicago still make hostility to monopolistic competition central to their sense of academic identity, but if so, it is a vestigial holdover from battles about national politics from the 1950s to the 1980s, not part of an ongoing battle over national politics.
When I switched from a growth model based on Marshallian price-taking to one based on monopolistic competition, it was as if I was a Crip who started to wear the red colors of the Bloods. It apparently infuriated other Crips for me to show such casual disrespect for symbols that were so important to their sense of who they are and what they stand for. It didn’t help that around the same time, I left my job at the U of Chicago and moved to CA, without even having a job lined up there. People at the U of Chicago invited me into the inner sanctum–promoted me from assistant professor at U. of Rochester to full professor at the U. of Chicago, taken me to a meeting of the Mont Pelerin Society (which by the way, was boring and depressing.) I’m still not sure which caused the deeper wound–adopting the monopolistic competition of the vilified Chamberlin or showing that my wife’s career counted for more than membership in their group.
Re #5: To the contrary, I believe that economists should use more mathematics because as I said, I’m in favor of clarity and precision. What I’m arguing against is mathiness, which undermines clarity and precision.
Mathematics, used correctly, lends precision to our scientific discourse by linking words tightly to mathematical objects and thereby forcing us to define words clearly and use them consistently. Mathiness does just the opposite. It facilitates slippage between the math and the words.
Re #6: I am not angry. I am worried.
I see a marked deterioration in the progress that economics is making as a scientific discipline. I point to objective evidence that economics is not functioning as a scientific discipline should. The problem seems to be getting worse.
Science is about establishing what is true. Scientists say what they believe. They support their claims with evidence and logic. They evaluate seriously the claims that other scientists make. They admit when they are wrong.
Science is not like an inter-faith congress, where everyone is supposed to listen, in tolerant and respectful silence, to recitations of dogma that maintain sub-group cohesion.
I could be wrong. I’ll listen and admit it if I am persuaded that I am wrong. But until logic and evidence show that some other position is closer to being right, I will say what I think because I care about more about protecting science in general and economics in particular than about avoiding hurt feelings.
There is a part of the tradition of economics at the U. of Chicago that I carry with me, something that apparently goes back to Frank Knight:
I think you are getting at something that is (a) the atmosphere at Chicago and (b) intensified by Knight. That an academic is concerned not with being diplomatic, not with trying to avoid hurting other people’s feelings, but an academic is concerned with saying what’s right. Telling the truth, or trying to get at it. (Milton Friedman, quoted in Craig Freedman’s Chicago Fundamentalism, p. 89.)