Quarreling with Cato

Last week Salon printed an excerpt from How Not To Be Wrong, in which I tweak Daniel J. Mitchell of the Cato Institute for asking the rhetorical question “Why is America trying to become more like Sweden when Swedes are Trying to be Less Like Sweden?”  I describe the vision of economics implied by the headline as “linear” (or, more generally, “monotone”)  In particular, the headline seems to take the view that smaller government is either a good thing or  a bad thing, independent of context.  If it’s good for Swedes, it’s good for us too.


Mitchell didn’t like what I had to say very much, accusing me of calling him a “buffoon”.  He complains that he doesn’t hold any such simplistic linear view.


And that’s right!  He doesn’t.  Nobody does, if they sit down to think consciously about what their views are.  But when you sit down to write a zingy headline, sometimes you just reach for something that expresses your vague rules of thumb instead of your carefully articulated beliefs.  (And yes, as a fellow blogger, I get that sometimes you stretch your point a little bit when you reach for that headline; take it from the guy who just published a piece about Berkson’s fallacy called “Why Are Handsome Men Such Jerks?”)


The headline makes it sound like there’s something incongruous about Sweden shrinking its government while we grow ours.  But there’s nothing strange about that at all – unless you have in mind something like the linear model that Mitchell correctly disavows.

So what is Mitchell’s actual view about the relation between Swedishness and prosperity?  He says it’s governed by something called the Rahn curve.  According to that curve, or at least Mitchell’s take on it, prosperity peaks when government spending is about 20 percent of GDP, and declines roughly linear thereafter.  As of 2012, there was only one country in the developed world, sorta-free Singapore, whose government spending was that low.  Which means that in the range occupied by countries from the United States to Sweden, from Australia to Korea, the relation between Swedishness and prosperity is more or less exactly the one I drew in the picture Mitchell objects to.  It may well be that the US government should spend less on its citizens.  But contra Mitchell’s headline, Sweden’s best course gives no guidance concerning ours.

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6 thoughts on “Quarreling with Cato

  1. […] Thinking about linear assumptions in healthcare, thanks to Jordan Ellenberg’s blogpost. […]

  2. David Bryant says:

    Hi, Jordan. I bought your book a couple of weeks ago — I’ve read it, I like it (most of it, anyway), and yesterday I donated my copy to the local public library (whose math section is woefully small).

    I found your remarks about Mitchell’s headline annoying. Not because they’re inaccurate, or because I’m sympathetic toward the Cato Institute (I am), but because you committed the same logical error in your “refutation” as you’re accusing him of. Let me explain.

    Any metrical idealization of a socio-economic system must simplify a horrendously complex bundle of laws, customs, prior history, and other natural circumstances by marking out some axes, presumably independent. For instance, one might choose to measure “Swedishness” along these four orthogonal line segments.

    1. Restrictiveness of laws affecting markets and finances (tax laws, business licensing, etc.)
    2. Degree to which laws (1) are enforced.
    3. Restrictiveness of laws affecting private personal behavior (drug laws, regulation of sexual behavior, regulation of “pornography”, etc.)
    4. Degree to which laws (3) are enforced.

    So now Sweden can be idealized as a point in 4-space, and “Swedishness” can be measured as, say, the reciprocal of the distance between your country and Sweden in this 4-space (if that distance is zero, your “Swedishness” is infinite).

    This is just an example — a more accurate model might incorporate dozens if not hundreds of dimensions. (I think we can safely rule out Hilbert spaces. ;^>) Anyway, the curve you drew in two dimensions might be constructed by projecting the entire 4-space onto a plane. But that’s essentially the same thing as projecting your quasi-parabola onto a line segment.

  3. quasihumanist says:

    It might be useful to point out a difference in the way different academic disciplines use arguments to justify facts.

    (Pure) mathematics works in an artificial, completely controlled world, with hypotheses that are 100% certain (by assumption) and has experts with long practice at making sure their arguments are completely logically correct. As a result, mathematicians establish a fact by the infinity norm on the quality of arguments – a fact stands on the basis of the strength of the best argument for the fact.

    In science, and especially in social science, the hypotheses one starts with are prone to large amounts of uncertainty. In this environment it is useless to try to make sure arguments are completely logically correct, and any single argument is going to be somewhat suspect. As a result, facts are established by something more like the 1-norm on the quality of arguments – a fact stands on the basis not of a single very good argument for it, but rather on the basis of many plausible arguments for it, with the plausibility of the arguments adding together (after the plausibility of countervailing arguments are subtracted) to form a preponderance of evidence for a claim.

    From this point of view, what Mitchell is saying makes a lot of sense. It is plausible that the relationship between Sweedishness and prosperity is linear or at least monotone (within the domain of interest), and, absent a specific argument otherwise, monotonicity seems intuitively more likely than non-monotonicity. Hence the argument adds to the evidence for his conclusion. It’s not a perfectly sound argument, and perhaps only moves the balance of the arguments a little bit, but this is a very imperfect social science, not mathematics (or even physics).

  4. Dear quasihumanist,

    I don’t see why the linearity or monotonicity you refer to is particularly plausible or intuitive.
    Sweden is typically regarded as one of the more social democratic among the world’s wealthy countries, while the US is typically regarded as one of the least such. In short, they seem rather close to being two extremes in the contemporary experience of how wealthy, first world democracies are governed. In other words, the interval they encompass is somewhat close to the entire domain of the function under discussion, so if it is going to have any non-monotone behaviour at all, it seems quite possible (to me) that it would demonstrate this behaviour somewhere between the US and Sweden.

    (I’m not sure that I put all that much faith in this whole line of analysis; but if one accepts
    that there is some sort of prosperity function defined on some sort of interval between the
    US and Sweden, then what I wrote above seems more plausible to me than your claim.
    Which is just to say — I’m not sure how much stock to put in “intuition” in this context.)



  5. quasihumanist says:

    Perhaps you are right, but if you cannot grant some kind of at least probabilistic Occam’s Razor – that, absent specific reasons to think the contrary, simpler answers are more likely to be correct than more complicated answers – it is hard to imagine doing any kind of science at all. (I might add that I have no idea what I mean by ‘simpler’ or ‘more likely’!)

    I just see this argument as starting down the slippery slope towards “By mathematical standards, nothing economists say is true,” which is of course a true statement, but a rather pointless one. Given that economists are aware that non-monotone functions exist, and given that the choice by some economists to ignore them in this instance is deliberate, I think we should let economists set their own epistemological standards.

    When Marilyn vos Savant complained that the proof of Fermat’s Last Theorem used imaginary objects with no physical referents, we very rightly said that mathematics has strong reasons for allowing the use of imaginary objects, and she should not be trying to impose foreign epistemological standards on mathematics.

  6. David Bryant says:

    Quasihumanist said: “ ‘By mathematical standards, nothing economists say is true,’ which is of course a true statement, …”

    Have you ever heard of Austrian Economics, QH? It proceeds from a single axiom (Humans act) and derives several important economic laws (the law of decreasing returns, the law of decreasing marginal utility, the law of supply and demand) by purely deductive reasoning. See Human Action by Ludwig von Mises, if you’re interested.

    QH also said: “I think we should let economists set their own epistemological standards.”

    I can’t disagree strongly enough. The great intellectual error of modern, mathematicized “economics” is the assumption that meanings can be interchanged willy-nilly, and that different standards of “truth” exist in different disciplines. I’d point to Karl Popper’s work on falsifiable hypotheses, and the aforementoned Human Action as good source material for understanding epistemology and science.

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