Home > The Economics Profession > Paul Romer on math masquerading as science

Paul Romer on math masquerading as science

from Lars Syll

I have a new paper in the Papers and Proceedings Volume of the AER that is out in print and on the AER website …

Paul_RomerThe point of the paper is that if we want economics to be a science, we have to recognize that it is not ok for macroeconomists to hole up in separate camps, one that supports its version of the geocentric model of the solar system and another that supports the heliocentric model …

The usual way to protect a scientific discussion from the factionalism of academic politics is to exclude people who opt out of the norms of science. The challenge lies in knowing how to identify them.

From my paper:

“The style that I am calling mathiness lets academic politics masquerade as science. 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 and between statements with theoretical as opposed to empirical content.”

Persistent disagreement is a sign that some of the participants in a discussion are not committed to the norms of science. Mathiness is a symptom of this deeper problem, but one that is particularly damaging because it can generate a broad backlash against the genuine mathematical theory that it mimics. If the participants in a discussion are committed to science, mathematical theory can encourage a unique clarity and precision in both reasoning and communication. It would be a serious setback for our discipline if economists lose their commitment to careful mathematical reasoning …

The goal in starting this discussion is to ensure that economics is a science that makes progress toward truth. A necessary condition for making this kind of progress is a capacity for reaching consensus that is grounded in logic and evidence. Given how deeply entrenched positions seem to have become in macroeconomics, this discussion could be unpleasant. If animosity surfaces, it will be tempting to postpone this discussion. We should resist this temptation.

I know many of the people whose work I’m criticizing. I genuinely like them. It will be costly for many of us if disagreement spills over into animosity. But if it does, we can be confident that the bad feelings will pass and we should stay focused on the long run …

Science is the most important human accomplishment. An investment in science can offer a higher social rate of return than any other a person can make. It would be tragic if economists did not stay current on the periodic maintenance needed to protect our shared norms of science from infection by the norms of politics.

Paul Romer

One of those economists Romer knows and — rightfully — criticizes in his paper is Robert Lucas.

Lucas is as we all know a very “mathy” person, and Romer is not he first to notice that “mathiness” lets academic politics masquerade as science …

quote-too-large-a-proportion-of-recent-mathematical-economics-are-mere-concoctions-as-imprecise-as-the-john-maynard-keynes-243582-3

Added 20:00 GMT: Joshua Gans has a post up on Romer’s article well worth reading, not the least because it highlights the nodal Romer-Lucas difference behind the “mathiness” issue.

In modern endogenous growth theory knowledge (ideas) is presented as the locomotive of growth. But as Allyn Young, Piero Sraffa and others had shown already in the 1920s, knowledge is also something that has to do with increasing returns to scale and therefore not really compatible with neoclassical economics with its emphasis on constant returns to scale.

Increasing returns generated by non-rivalry between ideas is simply not compatible with pure competition and the simplistic invisible hand dogma. That is probably also the reason why so many neoclassical economists — like Robert Lucas — have been so reluctant to embrace the theory wholeheartedly.

Neoclassical economics has tried to save itself by more or less substituting human capital for knowledge/ideas. But knowledge or ideas should not be confused with human capital.

In one way one might say that increasing returns is the darkness of the neoclassical heart. And this is something most mainstream neoclassical economists don’t really want to talk about. They prefer to look the other way and pretend that increasing returns are possible to seamlessly incorporate into the received paradigm. Romer’s view of human capital as a good example of non-“mathiness” not-withstanding, yours truly is of the view that talking about “human capital” — or as Lucas puts it,”knowledge ’embodied’ in individual people in the short run” — rather than knowledge/ideas, is only preferred because it makes this more easily digested.

Added 20:55 GMT: Romer has an even newer post up, further illustrating Lucasian obfuscations.

Added May 17: Brad DeLong has a comment up on Romer’s article, arguing that Lucas et consortes don’t approve of imperfect competition models because they are “intellectually dangerous” since they might open up for government intervention and “interventionist planning.” I agree with Brad, but as I’ve argued above, what these guys fear even more, is taking aboard increasing returns, since that would not only mean that policy preferences would have to change, but actually would bring havoc to one of the very fundaments of mainstream neoclassicism — marginal productivity theory.

  1. originalsandwichman
    May 19, 2015 at 6:03 pm

    I have a blog post on that from two and a half years ago:

    “Endogenous Growth Theory and Ecological Unequal Exchange: linkage, displacement and deflection of ‘diminishing returns'”

    http://ecologicalheadstand.blogspot.ca/2012/10/endogenous-growth-theory-and.html

    Also, new, “Mathiness is Next to Growthiness”

  2. May 20, 2015 at 7:39 am

    Mathiness and the Ur-blunder
    Comment on ‘Paul Romer on math masquerading as science’

    What did the great heterodox economist Georgescu-Roegen say about mathiness?

    “Knight lamented that there are many members of the economic profession who are “mathematicians first and economists afterwards.” The situation since Knights time has become much worse. There are endeavors that now pass for the most desirable kind of economic contributions although they are just plain mathematical exercises, not only without any economic substance but also without mathematical value. Their authors are not something first and something else afterwards; they are neither mathematicians nor economists.” (1979, p. 317)

    The definition of mathiness is that somebody gets both wrong: economics and mathematics. This applies without doubt to growth theory from Solow via Romer to Lucas. What is lacking is economic substance, the models are vacuous.

    What did the great heterodox economist Georgescu-Roegen say about the correct application of mathematics?

    “Lest this position is misinterpreted again by some casual reader, let me repeat that my point is not that arithmetization of science is undesirable. Whenever arithmetization can be worked out, its merits are above all words of praise. My point is that wholesale arithmetization is impossible, that there is valid knowledge even without arithmetization, and that mock arithmetization is dangerous if peddled as genuine.” (1971, p. 15)

    Nobody can argue with the great heterodox economist Georgescu-Roegen: formalization is desirable wherever possible but mathiness is not desirable.

    Orthodoxy, of course, is guilty of mathiness but this is only the minor point. The main point is the vacuousness of fundamental concepts like optimization, utility, equilibrium, production function, capital, perfect competition, demand function, etcetera. All these concepts are nonentities like batman or the Easter bunny.

    As a rule, it is not formalization that has to be criticized, it is the all pervasive green-cheese assumptionism which is the hallmark of Orthodoxy.

    “When very sound and proper mathematics is misused and misapplied to fairyland problems without any basis in the real world, that fact that the mathematics itself is impeccable makes the whole obnoxious game just that more offensive.” (Blatt, 1983, p. 173)

    The Ur-blunder of Orthodoxy is that that the whole theoretical edifice is based on a specific behavioral assumption.

    “There is in economics, or at least among the overwhelming majority of its disciples, broad agreement as to what represents the corpus of their subject. This corpus revolves around the concept of maximizing behaviour, whether it be by the individual, firm or institution.” (Blaug, 1990, p. 209) see also (2014)

    The assumption of profit maximization, for one, necessitates a couple of further assumptions. And here the the trouble starts. The firm or the economy must be formally endowed with a production function. This function must have very specific properties. One of them is decreasing returns. Thus, we start with a behavioral assumption and end with an assertion about the physical reality of production. And here is where the Ur-blunder comes in: Reality cannot be molded to make a behavioral assumption applicable. Production functions are nonentities. And this is why growth theories since Solow are vacuous. All of them.

    Orthodoxy can give up all except constrained optimization. Because constrained optimization is a nonentity Orthodoxy has to be given up.

    Egmont Kakarot-Handtke

    References
    Blatt, J. (1983). How Economists Misuse Mathematics. In A. S. Eichner (Ed.), Why
    Economics is Not Yet a Science, pages 166–186. Armonk, NY: M.E. Sharpe.
    Blaug, M. (1990). Economic Theories, True or False? Aldershot, Brookfield, VT:
    Edward Elgar.
    Georgescu-Roegen, N. (1971). The Entropy Law and the Economic Process. Cambridge,
    MA: Cambridge University Press.
    Georgescu-Roegen, N. (1979). Methods in Economic Science. Journal of Economic
    Issues, 13(2): 317–328. URL http://www.jstor.org/stable/4224809.
    Kakarot-Handtke, E. (2014). Objective Principles of Economics. SSRN Working
    Paper Series, 2418851: 1–19. URL http://papers.ssrn.com/sol3/papers.cfm?
    abstract_id=2418851.

  3. yi wen
    July 18, 2016 at 12:57 am

    increasing returns to scale are everywhere, from division of labor to the concept of comparative advantage in international trade.

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