More on Mathiness

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I managed to not float away this week in the flood in Houston, so I’m back with everyone’s favorite topic: mathiness. I hit on this last week, and there continues to be an on-going discussion about Paul Romer’s original paper on this.

For me, there are two interesting conversations to have about Romer’s critique. The first is about the actual economics of innovation and growth. Ideas mean increasing returns at some level. Is that at the firm level, or just in the aggregate? Is market power over ideas a more useful way of thinking about innovation, or are there frictions or limits to diffusion of ideas? For now, I’m going to hold off on this conversation, because it deserves a thorough discussion and I have to get that more organized in my head before I write anything down.

The second conversation arising from Romer’s paper is about the use of math and language in economics. This is not specific to growth theory, and I’m going to have another go at this conversation in this post.

One of the issues is that Romer’s original concept of “mathiness” was not entirely clear. Having e-mailed a little with Romer on this, I think he will freely admit that he did not get the concept across as clearly as he’d like. His last post on the subject states this outright, and he tries to clarify his position. You should probably read that first if you really want to get your head around this debate. What follows is me thinking out loud about the concept of mathiness.

Pure snark: Let’s start with this interpretation of mathiness. A common response to Romer’s article was that this is some kind of score-settling or point-scoring exercise by someone who is miffed that others are not using his ideas. Essentially, mathiness just means that the authors didn’t take Romer’s comments seriously.

Even if this were true, I don’t care. I don’t care because the conversation about how we use language and math in economics is still worth having, whatever the original motivation. Do I think Romer is just out to settle personal beef’s? No. But I’ve had people tell me that I’m being hopelessly naive about this, and that I’m working too hard to find a reasonable nugget at the core of this whole ball of BS.

Well, yeah, I am. I’m not in junior high. I’ve got better things to do than worry about whatever drama lurks beneath the surface here, because it is irrelevant to the interesting questions.

Let’s actually get to some meaningful ideas about mathiness and what it means.

Math and science: My original post on the subject offered an interpretation of mathiness as confusing math with science. In short, just because you can prove that a certain conclusion follows mathematically from certain assumptions, that does not mean that this is how the world works. And while I think that this is an issue, especially in communicating economic research to the public, this is not what Romer was talking about.

The papers he cites specifically do not make these kinds of claims. And while it is possible to misinterpret their findings, a reader mistaking math for science is not something that you can lay at the feet of the authors in these cases.

Decorative math: Another possible interpretation of mathiness is that it refers to what I think of as “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.

I have a recent paper with Remi Jedwab and Doug Gollin, on urbanization and industrialization, that has a very simple model in it. No dynamics, no endogenous productivity growth, and we don’t even bother to write down a utility function. All the intuition we need for the empirical work we do is in this dead simple model. And yet, throughout our experience of submitting this paper to different journals, we were told repeatedly that we’d have to come up with a fancier model (heterogeneous preferences or productivity levels for individuals in different regions, endogenous productivity growth, dynamic decision-making, explicit congestion and agglomeration technologies for cities, etc. etc..) if we wanted to publish this paper in a top journal. We were supposed to decorate the model, I guess to show that we could?

I think this a frustrating feature of modern economics, but this “decorative math” is not what Romer had in mind, either.

Extreme abstraction: Perhaps “mathiness” refers to something that is almost the opposite of decorative math, extreme abstraction. Chris House’s post on Romer defines mathiness this way. He uses the example of Mankiw, Romer, and Weil (1992) and their Solow-like model that includes both physical and human capital. House wonders if MRW displays mathiness because they assume technology levels are identical across countries, and grows exogenously, and the savings and education rates are exogenously given, etc.. etc.. But I think House is wrong in saying that MRW is an example of mathiness. Romer isn’t arguing against abstraction, as he makes clear in his latest post. He praises the original Solow model for its clarity, despite incredible levels of abstraction. (As an aside, House is clear that adding all the decorative math back into MRW would make it worse.)

Divorcing words and math: I think this is where Romer is going when he discusses the McGrattan and Prescott (2010) paper. This particular post from Romer probably gives the best explanation, as he digs a little deeper into the MP paper for examples of mathiness.

The point of the MP paper is that by failing to accurately measure intangible capital, the BEA falsely finds that there is a difference between the rate of return earned by foreign subsidiaries of US firms (9.4%) and US subsidiaries of foreign firms (3.2%). Okay, cool. That’s a neat problem to think about. MP claim that about 2/3 of that gap in returns is due to mis-measuring intangible capital.

MP use a model to make this claim, and that model needs a production function with constant returns to scale over intangible capital and physical inputs. And I think that if they had said, “We assume there is a stock of intangible capital, X, and a stock of physical inputs, Z, and there are constant returns to scale with respect to these two inputs into production,” that Romer wouldn’t be as bothered. This is abstract. This is hand-waving. We can argue and disagree about that assumption (why are there declining returns to intangible capital?, for example). But it is a relatively clear statement of what is being abstracted from. The words match the math.

What makes Romer’s head explode is that MP don’t just say this. They have a set-up that involves “technology capital” (M), which is a count of the number of “technologies” that are owned by firms in the economy. I guess a technology is something like a firm, as MP use the example later of a technology being Wal-mart or Home Depot. So technology capital is just the number of firms? But there are locations, which I guess are separate markets, and each technology can be operated in each location. What makes a location distinct from another is not ever defined. Oh, and there is also the production function for each technology at each location, which involves the statement “..where A is parameter determining the level of technology..”, and that is presumably different than the prior term “technology” or the term “technology capital”.

What does all this set-up buy you, by the way? A constant returns to scale function over intangible capital and the stock of physical inputs. In the end, MP’s accounting for the discrepancy in rates of return between types of firms has nothing to do with this location/technology thing. It serves only to confuse the situation.

The “mathiness” of the paper comes from the disconnect of the language from the math. The math does not serve to sharply illuminate a piece of intuition, it sows confusion. One example is the word “technology” being used 3 different ways in 2 pages, for no clear purpose. Another is using the word “location” despite there being absolutely no sense of location in any economic transaction in the paper.

So I’m with Romer on this point: it is completely fair to ask for better writing, even from big names like McGrattan and Prescott. Especially from big names, actually, since they are the ones that are going to be read the most. My guess is that we’re too deferential to big names, and excuse this kind of stuff by assuming that we don’t quite get their really deep insight. But we’ve got to expect better; the burden should be on authors to be clear.

6 thoughts on “More on Mathiness

  1. I still think the “revenger” factor is at play, but you are right that the topic is still worthy of discussion. Also, after having read Romer’s clarification, I take back my linking his point on math to McCloskey’s reflections on math and formalism. Her points are much more interesting. I think your last point is right about what Romer is ultimately getting at. In that case, Paul Pfleiderer, whom he reference, in his “Chameleons: The Misuse of Theoretical Models in Finance and Economics” said it better and with less scientific pretentiousness!

  2. Pingback: Needs More Math Needs More Cowbell | Paul Romer

  3. Interesting and enlightening post to understand what is really meant by “Mathiness”. I think Hans Christian Andersen was the first to write about this phenomena that Mathiness represents. In his famous fairy tale “The emperor’s new clothes” , nobody dares to point out that the emperor wears no cloth, since the society subscribed to the false claim of the weavers that only stupid people cannot see these clothes. To continue the analogy, Romer is the little boy who shouts out: “But he wears no clothes!”

  4. (Please tolerate the long post. Some ideas are not reducible to pithy wit.)

    The Cost Of Eliminating Pseudoscience in Economics:

    If a statement in economics cannot be reduced to a sequence of subjectively testable rational operations, then it cannot be true – it is not existentially possible. If a statement in economics can be reduce to a sequence of subjectively testable rational operations, then whether it is true or not is still open to question.

    The philosophical problem (epistemic truth) of correcting pseudoscience (of which mathiness is a subset) in the field of economics is not something that is going to easily be solved by economists, who tend to be good at neither advanced mathematics, nor the ethics of science, nor at the principle problem of truth.

    And this is a serious problem. Because, of all the disciplines save psychology, economics is the **most subject** to pseudoscience: the failure to eliminate imagination, bias, error and deceit. And we have the greatest incentive to insert imagination, error, bias, and deceit.

    And among all the scientific disciplines, the social sciences have been the most subject to pseudoscience other than perhaps philosophy itself (which in truth is objectively a social science).

    We have not yet developed the warranty that the hard sciences have developed, or that psychologists have developed. And this is in no small part because in economics, the warranty that we must give is much broader, and places a much higher burden on authors, because the scope of our statements is much broader in influence than that of our peers in other fields.

    Due Diligence Necessary For Warranty of Truthfulness:
    1) Have we achieved identity? Is it categorically consistent?
    2) Is it internally consistent? Is it logical? Can we construct a proof(test) of internal consistency?
    3) Is it externally correspondent, and sufficiently parsimonious? Can we construct a proof (test) of external correspondence.
    4) Is it existentially possible? Is it operationally articulated? Can we construct a proof (test) of existential possibility?
    5) Is it fully accounted? Do we account for all costs to all capital in all temporal and inter-temporal dimensions? (Have we avoided selection bias?) Can we construct a proof (test) of full accounting?
    6) Is it morally constrained? Does it violate the incentive to cooperate? (Meaning, are all operations productive, fully informed, warrantied, voluntary transfers, free of negative externality of the same criterion?)

    If you cannot answer these questions or do not understand them you cannot know if you speak the truth, or if you are polluting the commons with fantasy, bias, error, or deception.

    Why is it that the informational commons, and by consequence the political and normative commons, are not – in an age of information – as subject to warranty and liability as pollution (“Abusus”) to physical commons, life, body, and private property?

    Truthfulness – testimony that has been subject to due diligence – is a non trivial cost. And economists are too happy (as it appears all social scientists have been) to produce defective products for personal gains, without the warranty that all other products have been subject to.

    Why is it that free speech is not free truthful speech? After all, the cost of producing truthful scientific testimony under due diligence and warranty is much higher than the cost of producing untruthful pseudoscientific testimony without due diligence or warranty.

    There is a great difference between the terms “empirical” (observable and measurable) and “scientific” of which empirical criticism is but a minor subset of the criterion necessary for the production of warranty of due diligence against fantasy,bias, error, and deceit.

    We have had a century of economists running with intellectual scissors, causing inter-temporal externalities of profound consequence. And the Cosmopolitan (freshwater) rationalist’s justification of priors is only more visible than the mainstream Anglo empirical (Saltwater), justification of priors under the pseudoscience of Rawlsian justificationism – itself a fascinating example of the logically impossible, yet pervasively persuasive.

    So just as all enlightenment adaptations were plagued with errors – anglo, french, german and jewish – both freshwater and saltwater economics are plagued with pseudoscience. The freshwater try to justify objective morality, by argumentative construction (pseudoscience), and the saltwater try to justify immorality by intentionally failing to account for profound normative, institutional, civilizational, and genetic consequences (pseudoscience).

    So it’s one thing for all of us to point the finger of accusation of pseudoscience one place or another. But it is quite another to realize that the minute you draw the lens of truth upon either freshwater or saltwater, you will discover that both are pseudosciences that merely confirm priors.

    This is probably the most important remaining problem in the philosophy of science.

    I set out to debunk the pseudoscience of libertarianism (cosmopolitan libertarianism, not anglo libertarianism) and to refute the postmoderns as masters of pseudoscience. And I did. But I did not set out to reform economics. And in truth, I have less interest in reforming economics and social science than I do in reforming law and politics – the sciences will merely follow incentives.

    But some problems must be solved at certain times in human history, when interests align.

    And Paul Romer lit the kindling, and perhaps this is the time to solve it. If we do it will be the most important reformation of thought since the enlightenment. Because our errors – our priors – are all errors of the enlightenment. And the enlightenment was incomplete.

    We can complete it. But only if truth is more valuable than the utility of pseudoscience.

    Curt Doolittle
    The Propertarian Institute
    Kiev, Ukraine.

  5. If I may relay a suggestion from my friend Curt Doolittle of the Propertarian Institute, we need to raise the bar of truth telling (probably by lowering the bar for policing liars).

    Due Diligence Necessary For the Warranty of Truthfulness:
    1) Have we achieved identity? Is it categorically consistent?
    2) Is it internally consistent? Is it logical? Can we construct a proof(test) of internal consistency?
    3) Is it externally correspondent, and sufficiently parsimonious? Can we construct a proof (test) of external correspondence.
    4) Is it existentially possible? Is it operationally articulated? Can we construct a proof (test) of existential possibility?
    5) Is it fully accounted? Do we account for all costs to all capital in all temporal and inter-temporal dimensions? (Have we avoided selection bias?) Can we construct a proof (test) of full accounting?
    6) Is it morally constrained? Does it violate the incentive to cooperate? (Meaning, are all operations productive, fully informed, warrantied, voluntary transfers, free of negative externality of the same criterion?)

    It seems to me that Mathiness is weak on #1, which analysis on the rest of these standards difficult, but as far I can tell, #3 is what fails outright, and has been a problem in all disciplines (math — Cantorian set theory, physics — Bridgman’s commentary on why physics needed Einsten, and certainly economics). Scholars had so much fun playing in the definitional / rational jungle gyms of their own creation, that they lost site of and connection to the real physical universe.

    #5 also fails, and economists consider #6 not their concern.

    This is an important topic. Thank you for the thoughtful post.


  6. Pingback: Market Power versus Price-taking in Economic Growth | The Growth Economics Blog

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