Harald Uhlig (2012) “Economics and Reality”

Harald Uhlig (2012) “Economics and reality,” Journal of Macroeconomics, 34, 1, March 2012, 29-41,

This paper is about methodology. The first, more abstract sections are the weakest, though one useful item was this:

This “Methodenstreit der Nationalökonomie”, this dispute between Menger and Schmoller finds its echo in the modern debates between the proponents of a theory-led deductive approach and the proponents of an empirically grounded inductive approach, all the way to the extreme positions. There are those which reject empirical or econometric techniques altogether, at the one end. At the other end, there are those who reject structural modeling and argue that only natural experiments are valid sources of information.

My own Games and Information says in the Introduction,

Along with the trend towards primitive assumptions and maximizing behavior has been a
trend toward simplicity. I called this “no-fat modelling” in the First Edition, but the term
“exemplifying theory” from Fisher (1989) is more apt. This has also been called “modelling
by example” or “MIT-style theory.” A more smoothly flowing name, but immodest in its
double meaning, is “exemplary theory.” The heart of the approach is to discover the
simplest assumptions needed to generate an interesting conclusion— the starkest, barest
model that has the desired result.

Uhlig’s paper starts to get really good when it discusses the Phillips Curve. The Phillips Curve is the negative relationship between unemployment and inflation. Phillips noticed it in data from 1948 to 1959, and it kind of made sense, though there was no theory to it. In grad school in 1983, our group of 8 or so TA’s for Robert Pindyck’s MBA Economics class hated teaching it, for that reason and because it fell part after 1970. It is not a worthless theory, though, because with lots of caveats, it works, and when it doesn’t work, that’s interesting too– in fact it earned Robert Lucas a Nobel Prize for explaining that it works only so long as the government doesn’t try to make use of it. So it’s a good example for talking about methodology. Correlation isn’t causation, but in this case it is, sort of, so long as you don’t try to use one thing to cause the other.

It’s actually a bit like doing theory, in the way Lakatos pointed out in Proofs and Refutations. You start with a theorem— “What Quasi-Concavity means is that you can take the function and find a monotonically increasing transformation to apply to it o blow it up to be a strictly concave function.” I had that idea, and at church one day I mentioned it to a friend, Christopher Connell, who is a geometry professor. We decided to make it into a paper. But it’s wrong. In fact, pretty much every theory idea is wrong, in its initial formulation. You try to prove your idea, and by trying to prove it, you learn about it. Often you find a fatal flaw and learn that your theorem is false. Usually, you find that it’s not as simple as you thought, and you have to narrow the theorem, inserting caveats and conditions and defining things more carefully. Sometimes you find it’s actually more interesting than you thought— even if you narrow it in one direction, you find a corollary that is more interesting than the original theorem. Here’s the abstract from the final version:

Christopher Connell and Eric B. Rasmusen, “Concavifying the Quasi-Concave,” Journal of Convex Analysis, 24(4): 1239-1262(December 2017). We show that if and only if a real-valued function f is strictly quasi-concave except possibly for a flat interval at its maximum, and furthermore belongs to an explicitly determined regularity class, does there exist a strictly monotonically increasing function g such that g of f is concave. We prove this sharp characterization of quasi-concavity for functions whose domain is any Euclidean space or even any arbitrary geodesic metric space. See or in the longer working paper draft with more explanation,

The regularity conditions are interesting. One set is that the function to be concavified cannot be too flat or too steep if the function unless the function is monotonic. The most interesting is that the slope cannot vary too rapidly if it isn’t monotonic. That’s something we wouldn’t have thought of except for having to prove it. The reason is this. Suppose you have a nonconcave hill that you are trying to blow up to be a nice quadratic smooth slope— or worn down, the Rockies becoming some gentle English hills. If the hill starts off linearly dloping down on the right, but the slope is wildly varying, always positive but with varying slope on left, then you can’t find a single puffing-up function that will apply to both sides and give you a nice concave slope when you’re done. You need “bounded variation” for the slope. We have a nice example, nice because it makes for such a pretty diagram: