What we lose by aggregating

Jun 25, JDN 2457930

One of the central premises of current neoclassical macroeconomics is the representative agent: Rather than trying to keep track of all the thousands of firms, millions of people, and billions of goods and in a national economy, we aggregate everything up into a single worker/consumer and a single firm producing and consuming a single commodity.

This sometimes goes under the baffling misnomer of microfoundations, which would seem to suggest that it carries detailed information about the microeconomic behavior underlying it; in fact what this means is that the large-scale behavior is determined by some sort of (perfectly) rational optimization process as if there were just one person running the entire economy optimally.

First of all, let me say that some degree of aggregation is obviously necessary. Literally keeping track of every single transaction by every single person in an entire economy would require absurd amounts of data and calculation. We might have enough computing power to theoretically try this nowadays, but then again we might not—and in any case such a model would very rapidly lose sight of the forest for the trees.

But it is also clearly possible to aggregate too much, and most economists don’t seem to appreciate this. They cite a couple of famous theorems (like the Gorman Aggregation Theorem) involving perfectly-competitive firms and perfectly-rational identical consumers that offer a thin veneer of justification for aggregating everything into one, and then go on with their work as if this meant everything were fine.

What’s wrong with such an approach?

Well, first of all, a representative agent model can’t talk about inequality at all. It’s not even that a representative agent model says inequality is good, or not a problem; it lacks the capacity to even formulate the concept. Trying to talk about income or wealth inequality in a representative agent model would be like trying to decide whether your left hand is richer than your right hand.

It’s also nearly impossible to talk about poverty in a representative agent model; the best you can do is talk about a country’s overall level of development, and assume (not without reason) that a country with a per-capita GDP of $1,000 probably has a lot more poverty than a country with a per-capita GDP of $50,000. But two countries with the same per-capita GDP can have very different poverty rates—and indeed, the cynic in me wonders if the reason we’re reluctant to use inequality-adjusted measures of development is precisely that many American economists fear where this might put the US in the rankings. The Human Development Index was a step in the right direction because it includes things other than money (and as a result Saudi Arabia looks much worse and Cuba much better), but it still aggregates and averages everything, so as long as your rich people are doing well enough they can compensate for how badly your poor people are doing.

Nor can you talk about oligopoly in a representative agent model, as there is always only one firm, which for some reason chooses to act as if it were facing competition instead of rationally behaving as a monopoly. (This is not quite as nonsensical as it sounds, as the aggregation actually does kind of work if there truly are so many firms that they are all forced down to zero profit by fierce competition—but then again, what market is actually like that?) There is no market share, no market power; all are at the mercy of the One True Price.

You can still talk about externalities, sort of; but in order to do so you have to set up this weird doublethink phenomenon where the representative consumer keeps polluting their backyard and then can’t figure out why their backyard is so darn polluted. (I suppose humans do seem to behave like that sometimes; but wait, I thought you believed people were rational?) I think this probably confuses many an undergrad, in fact; the models we teach them about externalities generally use this baffling assumption that people consider one set of costs when making their decisions and then bear a different set of costs from the outcome. If you can conceptualize the idea that we’re aggregating across people and thinking “as if” there were a representative agent, you can ultimately make sense of this; but I think a lot of students get really confused by it.

Indeed, what can you talk about with a representative agent model? Economic growth and business cycles. That’s… about it. These are not minor issues, of course; indeed, as Robert Lucas famously said:

The consequences for human welfare involved in questions like these [on economic growth] are simply staggering: once one starts to think about them, it is hard to think about anything else.

I certainly do think that studying economic growth and business cycles should be among the top priorities of macroeconomics. But then, I also think that poverty and inequality should be among the top priorities, and they haven’t been—perhaps because the obsession with representative agent models make that basically impossible.

I want to be constructive here; I appreciate that aggregating makes things much easier. So what could we do to include some heterogeneity without too much cost in complexity?

Here’s one: How about we have p firms, making q types of goods, sold to n consumers? If you want you can start by setting all these numbers equal to 2; simply going from 1 to 2 has an enormous effect, as it allows you to at least say something about inequality. Getting them as high as 100 or even 1000 still shouldn’t be a problem for computing the model on an ordinary laptop. (There are “econophysicists” who like to use these sorts of agent-based models, but so far very few economists take them seriously. Partly that is justified by their lack of foundational knowledge in economics—the arrogance of physicists taking on a new field is legendary—but partly it is also interdepartmental turf war, as economists don’t like the idea of physicists treading on their sacred ground.) One thing that really baffles me about this is that economists routinely use computers to solve models that can’t be calculated by hand, but it never seems to occur to them that they could have started at the beginning planning to make the model solvable only by computer, and that would spare them from making the sort of heroic assumptions they are accustomed to making—assumptions that only made sense when they were used to make a model solvable that otherwise wouldn’t be.

You could also assign a probability distribution over incomes; that can get messy quickly, but we actually are fortunate that the constant relative risk aversion utility function and the Pareto distribution over incomes seem to fit the data quite well—as the product of those two things is integrable by hand. As long as you can model how your policy affects this distribution without making that integral impossible (which is surprisingly tricky), you can aggregate over utility instead of over income, which is a lot more reasonable as a measure of welfare.

And really I’m only scratching the surface here. There are a vast array of possible new approaches that would allow us to extend macroeconomic models to cover heterogeneity; the real problem is an apparent lack of will in the community to make such an attempt. Most economists still seem very happy with representative agent models, and reluctant to consider anything else—often arguing, in fact, that anything else would make the model less microfounded when plainly the opposite is the case.

 

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