A Quick Point on Models

According to Keynes the purpose of economics is “to provide ourselves with an organised and orderly method of thinking out particular problems”; it is “a way of thinking … in terms of models joined to the art of choosing models which are relevant to the contemporary world.” (Quoted here.)

I want to amplify on that just a bit. The test of a good model is not whether it corresponds to the true underlying structure of the world, but whether it usefully captures some of the regularities in the concrete phenomena we observe. There are lots of different regularities, more or less bounded in time, space and other dimensions, so we are going to need lots of different models, depending on the questions we are asking and the setting we are asking them in. Thus the need for the “art of choosing”.

I don’t think this point is controversial in the abstract. But people often lose sight of it. Obvious case: Piketty and “capital”. A lot of the debate between Piketty and his critics on the left has focused on whether there really is, in some sense, a physical quantity of capital, or not. I don’t think we need to have this argument.

We observe “capital” as a set of money claims, whose aggregate value varies in relation to other observable monetary aggregates (like income) over time and across space. There is a component of that variation that corresponds to the behavior of a physical stock — increasing based on identifiable inflows (investment) and decreasing based on identifiable outflows (depreciation). Insofar as we are interested in that component of the observed variation, we can describe it using models of capital as a physical stock. The remaining components (the “residual” from the point of view of a model of physical K) will require a different set of models or stories. So the question is not, is there such a thing as a physical capital stock? It’s not even, is it in general useful to think about capital as a physical stock? The question is, how much of the particular variation we are interested is accounted for by the component corresponding to the evolution of a physical stock? And the answer will depend on which variation we are interested in.

For example, Piketty could say “It’s true that my model, which treats K as a physical stock, does not explain much of the historical variation in capital-output ratios at decadal frequencies, like the fall and rise over the course of the 20th century. But I believe it does explain very long-frequency variation, and in particular captures important long-run possibilities for the future.” (I think he has in fact said something like this, though I can’t find the quote at the moment.) You don’t have to agree with him — you could dispute that his model is a good fit for even the longest-frequency historical variation, or you could argue that the shorter frequency variation is more interesting (and is what his book often seems to be about). But it would be pointless to criticize him on the grounds that there isn’t “really” such a thing as a physical capital stock, or that there is no consistent way in principle to measure it. That, to me, would show a basic misunderstanding of what models are.

An example of good scientific practice along these lines is biologists’ habit of giving genes names for what happens when gross mutations are induced in them experimentally. Names like eyeless or shaggy or buttonhead: the fly lacks eyes, grows extra hair, or has a head without segments if the gene is removed. It might seem weird to describe genes in terms of what goes wrong when they are removed, as opposed to what they do normally, but I think this practice shows good judgement about what we do and don’t know. In particular, it avoids any claim about what the gene is “for.” There are many many relationships between a given locus in the genome and the phenotype, and no sense in which any of them is more or less important in an absolute sense. Calling it the “eye gene” would obscure that, make it sound like this is the relationship that exists out in the world, when for all we know the variation in eye development in wild populations is driven by variation in entirely other locuses. Calling it eyeless makes it clear that it’s referring to what you observe in a particular experimental context.

EDIT: I hate discussions of methodology. I should not have written this post. (I only did because I liked the gene-naming analogy.)  That said, if you, unlike me, enjoy this sort of thing, Tom Hickey wrote a long and thoughtful response to it. He mentions among others, Tony Lawson, who I would certainly want to read more of if I were going to write about this stuff.

Leaping Lizards

At a party last night, I ran into a biologist who studies lizards. So we got to talking, as you do, about bipedalism. The habit of running on two legs has arisen in several different lineages of lizards, but why did it evolve? Speed, energetic efficiency, heat loss, vision, or that all-purpose explanation sexual selection? or maybe, like us and the birds, they’ve got something better to do with their front limbs?

None of the above, says the biologist. Sure, there are bipedal lizards. But very likely, bipedalism in lizards did not evolve.

Wait, how’s that?

Aerts et al., Bipedalism in Lizards:

The exact advantages of bipedal locomotion in lizards remain debated. Earlier claims that bipedalism would increase maximal running speed or would be energetically advantageous have been questioned. Here, we use ‘whole body’ mechanical modelling to provide an alternative solution to the riddle. The starting point is the intermittent running style combined with the need for a high manoeuvrability characterizing many small lizard species. Manoeuvrability benefits from a caudal [rearward] shift of the centre of mass of the body (body-COM), because forces to change the heading and to align the body to this new heading do not conflict with each other. The caudally situated body-COM, however, might result in a lift of the front part of the body when accelerating … [leading to] observable distances passively covered bipedally as a consequence of the acceleration. In this way, no functional explanation of the phenomenon of lizard bipedalism is required and bipedalism can probably be considered non-adaptive in many cases.

In other words, if you, being a lizard, need to change direction quickly when you’re running, it’s better to have your center of mass situated in the back, near your pelvis. That makes it easier to swing the front of your body around when you turn. But a side effect of having your center of gravity toward your back end is that your front end tends to rise when you accelerate sharply, as, being a lizard, you often do. (You, being a person now, have experienced this if you’ve ridden a bike up a steep hill. Conversely, brake suddenly, the back end of the bike goes up.) Air resistance adds to this effect, as does the fact that one of the ways the center of gravity is moved backwards is an overdevelopment of the rear legs relative to the front ones. The result is that lizards evolved for junk in the trunk end up sometimes running on their rear legs, even if that was not selected for at all.

(The linked article is based on experiments with a mechanical model of a lizard. According to dude at the party, the same conclusions are suggested by observations of lizard bipedalism in nature.)

I’m writing about this partly just because it’s cool (go science!) but also because it’s a nice illustration of an aspect of evolution that’s not widely understood, especially, perhaps, by some of its more aggressive proselytes. Darwinism is certainly correct, on some level: on the level that the appearance of design in an organism in no way implies the existence of a designer. But the statement that complex adaptive traits are the result of natural selection, while true, tells us much less than it seems to at first glance, because it’s seldom obvious what constitutes a “trait”; even more seldom what universe of alternatives it was selected from. In this case, we, proud bipeds, see a lizard running on its hind legs and think, that’s a trait; whereas, dancers and gymnasts perhaps aside, we’re not much conscious of where our center of mass is. But what we see as a trait isn’t necessarily what evolution sees; not everything in Borges’ encyclopedia is selected on. Perhaps the majority of what we see as traits are, as in this case, spandrels.

Needless to say, this is especially true when the organisms are human beings and the alleged trait is something psychological, especially something relating to sex and gender roles. A true evolutionary explanation should provide both concrete evidence (not just a just-so story) for the selective advantage of the supposed trait, and an account of the specific developmental pathways through which it arises; at least it should have one of the two. But in many of the “evolutionary” stories that people get most excited about, both are entirely lacking. Certainly when it comes to higher brain functions, with the exception of vision, the only statement genuinely grounded in evolutionary biology is, “We don’t know.”