What Math Does and Does Not Do in Economics

Noah Smith updates us on the Paul Romer’s “mathiness” critique. He translates (without necessarily agreeing with) Romer as saying

If I could tell the freshwater economists just one thing, it would be that the rest of economics is doing things differently. Really. We’re out here being honest with each other, trying to get to the truth together, not politicking for our own pet theories. We’re being scientists. You can too. If you get outside your bubble, you’ll see I’m telling the truth.

Pointer from Mark Thoma. My comments:

1. Just as a point of clarification, in the debate between freshwater and saltwater economists, I am certainly not an advocate for freshwater economists. I am definitely in the “plague on both your houses” camp.

2. For this post, I would like to stipulate that saltwater economists are as detached and objective as they claim to be. Put aside my doubts about that for now.

3. What math can do is rigorously connect assumptions with conclusions. You manipulate the equations to show that the conclusions follow from the assumptions.

4. As Noah has pointed out on other occasions, economics differs from physics in that physicists usually can undertake direct tests of their assumptions, while economists generally cannot.

What point (4) means is that when we prove that assumptions a, b, and c together imply outcome X, and we instead observe outcome Y, we have no way of independently testing which of assumptions a, b, and c is untrue in the real world. Because there are so many plausible assumptions available to economists, this means that real world does not constrain economic models nearly as much as it does in physics.

Assumptions persist in economics as they get copied from paper to paper. That is, because of a combination of convenience and path dependence, not because of empirical verification.

I think that this makes the claims of “science” in economics quite dubious, and in macroeconomics downright fraudulent. Even if you think that there is a group of economists who is unbiased and objective, they are not entitled to don white lab coats.

7 thoughts on “What Math Does and Does Not Do in Economics

  1. Wow. I think I deleted the comment I wad going to make about the arrogance in Romer’s piece a few weeks back. Maybe I shouldn’t have.

  2. While I’m not radical optimistic about what economics can achieve, given the level of precision appropriate to the subject matter, I’d like to make two points:

    1. Just because you can’t test your assumptions the way you can in physics doesn’t mean that those assumptions cannot be scrutinized and challenged, or that we can’t provide some evidence for or against them.

    2. I think Noah’s translation of Romer is not that non-freshwater economists are objective, but that they are *honest* and *earnest*. I don’t know if that’s true or not (I don’t follow the macro debate very closely) but it does seem to me that the ethics of the practitioners are _especially_ important in a field where precision is lower.

    • Point 1 is why I feel much better when I read about price theory arguments than I do about macroeconomics arguments. Price theory arguments often have a small number of very light assumptions, such as that people will buy fewer of something if the price goes up.

      Macrostarts out by defining aggregates that aren’t obviously going to be especially useful for reasoning. Then it seems to do an awful lot of regressions against those aggregates, out of a scientistic perspective that we can find the truth just by testing all our measurable variables for correlations. It all feels very shady to me, even before you get into the track record of the field’s pyredictions. But the field has also failed to make accurate predictions, too.

  3. Arnold brilliantly sums up:

    “Because there are so many plausible assumptions available to economists, this means that real world does not constrain economic models nearly as much as it does in physics.”

    Economic perceptions are fundamentally political in nature, i.e. open to competing perspectives and narratives (of strong assertive ambitions, including vigorous policy demands). This carries over into economic reality, which hence is for epistemic reasons alone political. Of course, there are other forms of political competition (lobbying etc.) that are formative for economic reality.

    What guarantees the persistent insignificance of libertarian views in the greater scheme of things is that they insist on the possibility of autonomous spheres of freedom, whose normative desirability and positive feasibility they tend to derive from certain economic models (that are useful in many regards but limited in that they exclude the political dimension of economic reality). From the promises of these sanitised economic models emerges a general assumption that politics can be effectively replaced by “market-solutions” and an irritable disregard of (the spontaneous order of) politics. Libertarianism degenerates into an ideology (rather than a powerful way of looking at and influencing the real word), a very weak ideology though, predestined to serve as an intellectual pastime, since one of its core creeds suggests political abstention).

    In a reasonably free society, the contours of micro economics will remain visible under heavy political overgrowth. What is needed, however, is to better understand from a libertarian standpoint the inevitable (in large measure even) positive contribution of that overgrowth to feasible freedom.

    The mixed economy is real and not optional. Feasible freedom will always be highly qualified and constrained, precisely because freedom encourages and consists of epistemic and political multiplicity.

    The fundamental libertarian error is to refuse to understand that a free society is a highly politicised society – far more politicised than a society where mass political participation is unthinkable. To embrace freedom is to embrace politics.

    For more see: http://redstateeclectic.typepad.com/redstate_commentary/2015/05/the-political-character-of-the-economic-process.html

    and

    http://redstateeclectic.typepad.com/redstate_commentary/2014/10/just-so-stories-in-economics-and-politics.html

  4. It does imply a, b, and c are collectively false and should no longer be assumed. Then one must offer other theories with other assumptions that do predict Y, and then work on discriminating between these alternatives for which fits best. Messier and more difficult, but not impossible. Many sciences are not experimental, but still science.

  5. All of this seems reasonable. But it applies equally to non-mathematical approaches to economic reasoning, which likewise rely on untestable assumptions.

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