Thursday, May 22, 2014

Why It Matters If You Start From Bad Assumptions

-- Posted by Neil H. Buchanan

To my surprise and disappointment, my post last Thursday on the IRS non-scandal scandal turned out not to be the last thing I would write on that topic.  Perhaps my new Verdict column today will be.  Even if I do end up returning to that subject, however, I will not do so here.

Instead, I will continue my discussion of the orthodox-versus-heterodox debate in economics that erupted again recently, in response to Thomas Piketty's blockbuster book.  My most recent entry on this topic, last Friday, includes links to my previous four posts in this series.  Readers might also want to read (or re-read) Professor Hockett's recent Dorf on Law post in which he questioned the usefulness of the orthodox/heterodox delineation.

In last Friday's post, I concluded that Paul Krugman, the most prominent member of the orthodox left, had unexpectedly come to sound like the conservative icon Milton Friedman, who argued in essence that the assumptions underlying an economic model did not matter, so long as the model successfully predicted the real world.  I concluded that Krugman was, in short, a modernist.

I was surprised to find myself concluding that Krugman was a methodological Friedmanite, because Krugman has otherwise shown himself to care very much about the assumptions in economic models.  He rightly mocks the "new classical" economists from Chicago for making crazy assumptions, and he complains that austerians and sado-monetarists (usually the same people) have abandoned established economic theory in order to make economics a morality play.  In a blog post last week, he wrote: "But is it really too much to demand a model, or at least a carefully spelled-out mechanism?"

Even more to the point, I noted in an after-hours update to my post last Friday: "About a half hour after I published this post, Paul Krugman posted 'Faith-based Freaks' on his blog.  In that post, he explicitly distanced himself from Milton Friedman's extreme positivism.  In the post below, I had criticized Krugman's defense of his own work against the Heterodox Left, likening it to Friedmanian positivism.  Even if I thought that Krugman reads Dorf on Law (which I don't), the timing was too close for his post to have been written in response  to mine.  In any event, I view it as a good thing that Krugman is trying to distinguish his methodology from Friedman's, and I plan to return to this issue soon."

Krugman is certainly right to resist the idea that economic models are mere black boxes, to be assessed only on the basis of their predictive power.  On the other hand, he has defended his own use of extremely unrealistic assumptions, noting that assumptions are by definition "wrong," but that they can still be practical.  (Economists will often analogize to the physical sciences.  For example, they can point to the virtues of assuming, say, that a lever is frictionless.  An unrealistic assumption to be sure, but a harmless one in most contexts.)  As I wrote in the comments section on last Friday's post, in response to some very good comments from readers, it is a struggle to come up with an explanation for Krugman's approach that does not boil down to: "Trust me, I know what I'm doing."

Krugman's rejection of the heterodox left then falls into two categories: (1) Everything useful that they say can be (and has been) brought into good orthodox left models.  (In a sense, this is Professor Hockett's point as well.)  (2) The heterodox guys are obsessed with things that are simply not useful or relevant.  Specifically, they need to get over the Cambridge Controversies, because proving definitively that production functions are incoherent (as the British side did) does not mean that production functions cannot be usefully employed (no pun intended) to improve economic policy.  Frictionless levers are not real either, guys!

To a point, the heterodox guys agree.  Galbraith's review of Piketty's book, as I noted in one of my earlier posts, agrees that one can make Piketty's (actually quite narrow) point about wealth concentration without getting into details about measuring capital correctly, or any of the other points debated in the Cambridge Controversies.  Instead, the heterodox argue that the simplifying assumptions that one makes in one context are harmful in another.  And if those assumptions become a matter of habit, the consequences can potentially be disastrous.

Krugman has argued repeatedly that the economists who supported non-Keynesian policies were simply dishonest.  But maybe some of them got it wrong because they made a mistake.  It is hardly a radical claim to say that one's starting point can increase the likelihood of making mistakes.  And it is not just a matter of making mistakes.  Argumentative power derives from the underlying assumptions as well.  For example, in a comment on one of my earlier posts, Professor Dorf suggested as an example the debate over the minimum wage, where it is possible to start from orthodox foundations and make enough correct analytical moves to "get it right," but by giving ground up front, the likelihood of losing the debate increases.  This obviously carries over to the debate over providing extended unemployment benefits, but with even more powerful macroeconomic consequences.

And this is where the Cambridge Controversies come back into the story.  As I described last week, one of the policy take-aways of that debate is that there is no theoretical connection between interest rates and business investment (and ultimately GDP).  The models that Krugman describes as "harmlessly simplified" generally assume, contra reality, that reducing interest rates increases businesses' desire to own "capital."  If we use the orthodox models, we then are more likely to rely on monetary policy to reduce interest rates; and we are more likely to worry about crowding out of investment from expansionary fiscal policy.

Now, it turns out that the orthodox models can "get it right" in the sense that interest rate cuts can expand the housing sector, which expands the economy, which then feeds back and expands business investment.  So what's the harm?  The harm is that, when one listens to policy discussions among orthodox economists, they talk as if the interest rate cuts directly raise business investment and productivity.  But if the effect is indirect, and if some of the expansionary effect is through the increased production of single-family homes rather than productive capital, then the policy prescription is much more of a mixed bag thatn we generally acknowledge.

Again, this does not mean that one cannot get to the right answer by being careful enough and honest enough.  I admire Krugman's work greatly, in large part because he takes textbook Keynesianism and gets the policy analysis right almost all of the time.  But the suggestion that the concern about the Cambridge Controversies, or other things that the heterodox care about, is somehow an annoying side show is simply not defensible.


Bob Hockett said...

Thanks for this, Neil - terrific as always.

I should perhaps clarify that in wondering what difference there actually is between orthodox and heterodox a couple of weeks back, I was thinking solely in terms of the current Krugman/Palley contretemps. As a more general matter, my distinct impression is that those who self-identify as heterodox have tended over time to be much less prone to conceptual unintelligibility, analytic incoherence, and pragmatic sterility or policy mischief than have been those who self-identify as orthodox. In the long run, then, not only are we all dead, but the truth is all Palley.

With respect to the moment - i.e., the current Krugman/Palley argument - on the other hand, I remain somewhat confused. The debate seems to be being conducted with a view to our recent financial-cum-macroeconomic travails, and in that quite particular connection I am confused as to where the two actually differ basically because both seem to be agreed on the significance of what matters most, theoretically speaking, in understanding financial bubbles, busts, and ensuing deflations - viz. (1) Fisher debt-deflation, (2) the shape of the MPC, and (3) the distinction between Keynes/Knight 'uncertainty' and mere 'risk.' Since both seem agreed on the importance of all three of those, it's not clear to me what they are actually disagreeing about now.

With respect to the old Cambridge capital controversies, I couldn't agree more with you and Palley, and hence couldn't agree less, I take it, with Krugman. For (1) Krugman *does* misstate the result of that debate, as you very helpfully emphasize. And (2) pace Krugman, this actually would seem to matter pragmatically as well as theoretically, since the upshot of that debate's conclusion - viz., that the concept of 'capital' employed by the orthodox is unintelligible - is that even to employ it in a mere model is tantamount to employing the 'concept' of a 'round square' in a model; there is no there there, there is literally nothing to 'model.' Insofar as that is the case, the old 'hey, it's only a model' retort is more dodge than rebuttal.

Thanks again for these wonderfully stimulating posts!


Bob Hockett said...

PS: Another way of putting the last point: Krugman's retort to Palley seems to be that it's fine for a model's premises to be 'unrealistic' when the purpose of the model is to trace analytic consequences from assumptions. I doubt that Palley would disagree with that observation as a general matter. But if Krugman means to say this in respect even of models that employ the US Cambridge notion of 'capital,' then his retort is either incomplete or a non sequitur. For Palley's point in this case is not that the premises are merely unrealistic. It is that they are nonexistent. There just *is* no premise of the 'round square' variety from which to derive any interesting logical consequence, let alone any illuminating such consequence, and Palley's point is that US Cambridge 'capital' is of this vareity. Krugman must accordingly either explicitly question the applicability of the 'round square' analogy or recognize that he hasn't yet answered Palley.

I should note in passing that my own recollection of what was at stake in the old Cambridge capital controversy is too rusty for me to state confidently that its upshot was indeed that US Cambridge 'capital' is 'round square' material. (I'll defer to Neil and Thomas on that.) Pace the old logical positivist saw, I think it is possible for a concept to be intelligible even if we lack practical means of quantifying or otherwise measuring its instances. But I just don't recall whether the UK Cambridgeans established mere non-measurability or full-on unintelligibility. I take it from Neil and Thomas that it was the latter.

Thanks again!

Jimmyd said...

Oh this is silly. Simplifying assumptions in the physical science serve different purposes than simplifying assumptions in economics. The physical sciences draw a distinction between theory (physics) and practice (engineering) that economics does not. So when a physicist talks about a frictionless lever he is talking about something that implicitly has no real world consequence. The primary reasons such simplifications are used is for pedagogical clarity--no sane engineer would build a working system off of it. Indeed, those who do try to build working models with frictionless levers are considered cranks in search of a perpetual motion machine! On the other hand, a simplifying assumption in economics is used in order to constrain variables so that a workable model can be produced.

Notice the difference? In physics variables are constrained with simplifying assumptions to create a non-working model for pedagogical purposes. In economics variables are constrained with simplifying assumptions in order to create a working model for policy purposes. Non-working vs working. Get it?

So anyone who tries to justify a conceptual stance in economics based upon a conceptual stance in physics doesn't buttress their argument, on the contrary, they only show their ignorance of how the physical sciences work conceptually.

Michael C. Dorf said...

Jimmyd points to ONE reason why a physicist might make a simplifying assumption: pedagogical clarity. But there are others.

Consider the question of how to calculate the relative speed of a car moving 40 mph west and a nearby train moving 30 mph east. The EXACT answer is given by special relativity, but because the speeds of the car and the train are so small compared to the speed of light, we can approximate by using Galilean relativity to get the answer of 70 mph, which is ever-so-slightly different from the answer given by the Lorentz formula. We use the not-quite-right Galilean formula because the math is easier and at slow speeds the approximation is very good.

Neoclassical economists sometimes make similar claims about rationality, the supposed exogeneity of preferences, the absence of transaction costs, etc.: That these are good enough approximations (especially in large markets where nearly all actors are price-takers and so their marginal demand doesn't move price), that they need not bother using more accurate assumptions that would make the math nearly impossible.

I don't agree with those claims, but one can see why someone who does might think that the analogy to the physical sciences makes sense.

Paul Scott said...

I'll suggest the creation of the Cosmological Constant is a counter example to Jimmyd's supposition about model simplification or the use of things known to be false in the physical sciences in order to make models that work; those models in turn made excellent predictions and expanded our knowledge of the cosmos, in spite of the fact that even its inventor knew it did not represent anything he understood.

There are other other examples, but that is one with a great history.

Remember, I do not consider economics a science; but that has nothing to do the use of mathematical simplifications.

I'll expand the example, actually, now that I am thinking about it. Jimmyd's comparison between a physicist and an engineer runs in the other direction. Newtonian physics effectively makes simplifications and assumptions that are known to be untrue to more generally applicable models. None-the-less, here on Earth when build large structures (e.g. above atomic sizes) engineers correctly rely on Newtonian equations because the parts of "reality" they are choosing to ignore are not material to their model's usefulness in making the correct predictions.

Krugman (at least so far as Krugman is concerned - and unlike Neil I am inclined to agree) is doing the same thing with IS-LM, liquidity trap models, etc. There may come a time when recognizing capital as power is essential to make accurate predictions and prescribe the optimal policy choices, but that time does not appear to be now.

Bob Hockett said...

Much as he incompletely characterizes the purposes that theoretical physicists entertain in employing simplifying assumptions in their models as noted by Mike, I fear Jimmyd likewise mischaracterizes economists' professed purposes in producing simplified models in their own discipline. Contrary to his claim that 'physical sciences draw a distinction between theory (physics) and practice (engineering) that economics does not,' for example, most economists actually distinguish quite overtly between 'pure' and 'applied' economics. Indeed Cornell, like many if not most other schools, even maintains distinct departments devoted to each.

Great modern theorists of, say, Walrasian General Equilibrium Theory - the likes of Arrow, Debreu, and McKenzie - would no more aim or expect to find 'complete' markets in 'time-indexed commodities' and contingent claims that all clear 'once and for all at a single temporal instant' than would Jimmyd's non-crankish physicist or engineer seek a 'frictionless lever.' One principal point of such models here, as in physics, is to draw out logical consequences to which certain commonly made assumptions might unknowingly commit us.

Another, related, such point is to gain clarity as to just what it is that believers in or seekers of 'free markets' are apparently getting at, this in turn partly in order to enable ourselves to point out precisely why it is that markets as we currently find them typically fall so far short of the ideal implicit in 'free' marketeers' overstatements. Much of the great work of Stiglitz and Grossman in the 1970s and '80s, for example, was thus prompted.

Yet another related purpose in constructing such models is to draw out the logical structure and associated commitments involved in propounding this or that normative economic position - e.g., utilitarian, Rawlsian, or opportunity egalitarian positions. Much of Elisha Pazner's, David Schmeidler's, and John Roemer's still breathtaking work has been prompted by this aim. So has a good bit of Baumol's, Varian's, and Sen's.

None of this, of course, is to say that no economists muddy these waters or confuse the ideal with the real. Indeed a nice rough and ready definition of the 'orthodox' - especially the 'rational expectations' orthodox of the Lucasian persuasion - might just be this: 'those who take pure for applied.' But the point here is simply that economists historically have drawn the same would-be 'pure' and 'applied' distinction as have the physycists whom many of them have envied, and many of the best have been those who have kept it in view as they've worked.

Neil H. Buchanan said...

Thanks to all commenters for a stimulating discussion. A few thoughts:

(1) I learned a lot from the responses by Mike, Paul, and Bob to Jimmyd. I will only add that my reference to how economists are eager to analogize to physics was meant to have a sarcastic tone -- as in, "you know, because economists just LOVE to think of themselves as REAL SCIENTISTS." (Bob's last comment alluded to this, referring to "the physicists whom many [economists] have envied.")

Like Jimmyd, I think that is silly. But I do agree with the other three commenters that, as silly as economists can be, the analogy is anything but crazy, and it can be done well.

(2) I hope that my Friday post (the one that I wrote after this one) made it clearer that, contra Paul's apparent belief, I do not disagree with Krugman that IS/LM and liquidity trap economics are useful. They are, which is why Krugman is right to be amazed that so many members of his profession -- despite their orthodoxy -- have blown it so badly for the past 7 years. This is the easiest test imaginable, and they have the simplified tools that will allow them to pass the test, yet they have chosen to go completely against what "economic science" should be telling them. Like Krugman, I'm shocked and disgusted.

(3) Bob is correct that the conclusion of the Cambridge Controversies was of the "round square" variety. The Brits showed that it is impossible to construct a measuring rod that is independent of what it purports to measure. That is, you cannot construct a measure of aggregate capital that is unaffected by changes in the types and quantities of the different types of capital that might be used to construct the measuring rod.

That, in turn, made it impossible to conclude that "capital intensity" (i.e., the K/L ratio) was related to the rate of profit. No matter what one called "more intensive" or "less intensive" -- that is, no matter how one measured K and L -- it turned out that one could not rule out the possibility that the preferred K/L would switch back and forth as r rises. That's why it was important for Levhari and Samuelson to admit that "The Nonswitching Theorem is False."

I, too, am a bit rusty on the details, but that is my best current recollection.

Thanks again to all for sticking with me through a pretty heavy-duty set of posts, and for helping to improve my thinking.

Evin Terna said...

It is that they are nonexistent. There just *is* no premise of the 'round square' variety from which to derive any interesting logical consequence, let alone any illuminating such consequence, and Palley's point is that US Cambridge 'capital' is of this vareity. Krugman must accordingly either explicitly question the applicability of the 'round square' analogy or recognize that he hasn't yet answered Palley.

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