Needs More Math Needs More Cowbell

Dietz Vollrath has a new post that continues the discussion about how economists use math. He makes an important point (see #4 below) that I’ve tried to capture in the title and has also spurred a few other thoughts.

DV: Romer’s motivation is irrelevant

I agree with Dietz on this point. The attempts at starting a discussion about whether I am a bad person, and what sound like follow-on attempts at starting a discussion about whether Dietz is a bad person, need to be understood as evidence that the problems in the papers I criticize are real.

Think of this as a sequential game with many players, including me, X, the Chicago troll, and Dietz.

- I move first and say, “There is a problem in this paper by X.”

 If you were X, how would you respond?

(i) If there is no problem in the paper, X should go to the text and show that there is no problem in the paper.

(ii) If there is a problem in the paper, X should try to change the subject by starting a discussion about how I am a bad person.

- X or someone who supports X says to Dietz, “Romer is a bad person.” The Bayesian update is that X or the supporter of X agrees that there is a problem with the paper.

- The anonymous Chicago troll also says, “Romer is a bad person.” More evidence that there is a problem. If we were on path (i), there would be no reason for responding anonymously. The use of anonymous smear tactics is decisive evidence in support of my claim that people on the Chicago side are  behaving like politicians not like scientists.

- Dietz says, “I want to talk about the substantive issues Romer has raised.”

- X or the supporter of X says, “Dietz, this means that you are a bad person.” Quoting from Dietz’s post, “But I’ve had people tell me that I’m being hopelessly naive about this, …”

- The right response from other potential players? “Mr. X and Mr. Troll, why is it that you are so eager to avoid talking about the problems in the papers that Romer criticizes? And why do you want to make your case anonymously? Doesn’t this show that Romer is right that you are behaving like politicians not scientists?”

When I decided to start this discussion, I had convinced myself to a high level of confidence that the charges I was going to make were correct. But I take science seriously and this means that I had to be ready to watch for evidence that I was wrong.

Going in, here was my conditional forecast:

Based on the response so far, my Bayesian update makes me confident that I am right.

Me: Anonymous smear campaigns can work

As an aside, it is an interesting exercise in self-control to refrain from responding to attacks that focus on my motivation and/or emotional state.

Because I am not responding, I may suffer some damage to my reputation. Growing up in a political family, I saw first hand how anonymous smear tactics from the other side can succeed. The canonical example is the campaign to smear John McCain in the 2000 Republican primary in SC.

The key in neutering smears is to discredit them immediately so that journalists are ashamed to repeat them. By letting these smears fester, I’m increasing the likelihood that journalists who want to write about what is going on will buy into the “Romer is a bad person narrative.” After all, it is a much easier story to write than that “economic theory is broken.” It starts in comment threads and rumor sites, then moves to anonymous blogs, flake blogs, somewhat more serious blogs. From there, it can move to an online column, then eventually into news stories. Working up the credibility chain, journalists at each stage can cite each other and material from the level just below and maintain plausible deniability that they have not been poking around in the comment/rumor sewer.

I may be making a strategic mistake in not responding more directly, but my objective is not to maximize my stock of reputational capital. It is fix economic theory.I’m willing to give up some reputational capital if it helps us work toward a fix. Agreeing that there is a problem is the first step toward a fix. For now, the best way to reach agreement that there is a problem is to avoid getting sucked into a distracting discussion about motivation.

I am sorry, however, to see that there are already hints of intimidation about how these tactics can also be used to impugn the integrity of someone like Dietz merely because he is willing to join a civil conversation that is not anonymous.

The tell we should be watching for next are anonymous smears directed at Dietz.

DV: Romer is not opposed to abstraction

Dietz is right that I am not complaining about excessive abstraction. I am actually a big fan of abstraction, but see next …

DV: Decorative math wastes mental cycles

Dietz points to a different problem that I have not thought about enough, one that could get worse if I am successful in making the case that math and abstraction can be important tools in our toolkit. I need to emphasize that “they can SOMETIMES be important tools.”

A good working rule for economists might look like this:

Start from

a) a rebuttable presumption that no mathematical theory is needed, and

b) a nonnegotiable requirement that to be considered, any mathematical theory must be transparent.

In clause a), rebuttable means that economists listen when some author tries to make the case that in a specific context, the extra abstraction and precision that math allows will yield enough additional insight to justify the setup costs.  The burden of proof is on the author who proposes the mathematical theory.

This means that a referee who says that the paper “needs more math” is like the producer who says that the song “needs more cowbell.” (Watch the SNL clip if you haven’t seen it.)

Clause b) is required to enforce clause a) and make sure that the author does not use mathiness to mislead. That is, any mathematical theory should be dismissed out of hand if the author cannot present the math with enough transparency:

a) to let the reader see what value the math really adds, and

b) to let the reader to spot check to see whether the words the author uses accurately convey what the math implies.

Economists should not fall into the trap of accepting an assertion from the author as authority that the words the author uses really say what the math shows, so it does not matter that the math is impenetrable. If the author responds to the charge that the math is unreadable by saying, “read my words,” tell the author, “Ok, don’t write math.”

Me: OK now to have a bias against tool building

The idea that we should economize on the use of math is implicit in the endorsement I gave the Solow model, but Dietz’s post has helped me focus more explicitly on the value of a presumption that forces us to economize on the use of math.

If you are familiar with the typology of research offered by Donald Stokes in his book Pasteur’s Quadrant, I take Dietz’s point about decorative math as additional support for Pasteur-style science; that is, science that is directed at solving specific problems. The point that Stokes makes is that this type of science is actually the best path toward basic scientific insight.

There are a few instances in the development of a discipline in which pure Bohr-style science (which is not motivated by any specific problem) can yield a big return. I’d cite the work that Arrow, Debreu, and McKenzie did on formalizing a general equilibrium as an example of successful Bohr-style science that focused on tool building. This was a case where it made sense to listen when these economists said, “let’s build some new tools without worrying about how they will be used.” In the hands of such economists as Samuelson, Solow, Lucas (in the application of rational expectations in macro), these tools did yield new insights.

But that was then. This is now.

The rule I outline under #4 above builds in a bias against Bohr-style tool building. I think that is fine. Economists should be very skeptical of someone who says they want to work on a new version of the ADM program and build new tools without offering any explanation about how these new tools will be used.

We’ve got tools. Plenty of them. The problem now, especially in macro, is to show that with all these tools, we can build something. Anything! We need to show that we can use the tools to reach a consensus about what is true.

DV: Mathiness is how not to use words and math to write theory

Dietz is right that the problem I’ve labeled mathiness concerns the interaction between the formal language of mathematics and the natural language of words. I agree with the suggestion that it is better to focus the discussion on internal criteria for good theory. As I indicate above, the ultimate  test of good theory is the external test: does it yield new insight into data and other evidence. I think that good theory is more likely to do this than mathiness. But I agree that for now, in the discussion of mathiness, it is better to focus only on the internal logic of theoretical models.

I also agree that there is room for me to be more precise about what mathiness is and why it is bad. The complementary activity is to be more precise about what are the internal characteristics of good theory. This deserves its own post… For now, the take away is:

Economics needs new tools <=> The paper needs more math <=> The song needs more cowbell