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.


Who are you? What is this new blog? Why “Infinite Identical Psychopaths”?

My name is Patrick Julius. I am about halfway through a master’s degree in economics, specializing in the new subfield of cognitive economics (closely related to the also quite new fields of cognitive science and behavioral economics). This makes me in one sense heterodox; I disagree adamantly with most things that typical neoclassical economists say. But in another sense, I am actually quite orthodox. All I’m doing is bringing the insights of psychology, sociology, history, and political science—not to mention ethics—to the study of economics. The problem is simply that economists have divorced themselves so far from the rest of social science.

Another way I differ from most critics of mainstream economics (I’m looking at you, Peter Schiff) is that, for lack of a better phrase, I’m good at math. (As Bill Clinton said, “It’s arithmetic!”) I understand things like partial differential equations and subgame perfect equilibria, and therefore I am equipped to criticize them on their own terms. In this blog I will do my best to explain the esoteric mathematical concepts in terms most readers can understand, but it’s not always easy. The important thing to keep in mind is that fancy math can’t make a lie true; no matter how sophisticated its equations, a model that doesn’t fit the real world can’t be correct.

This blog, which I plan to update every Saturday, is about the current state of economics, both as it is and how economists imagine it to be. One of my central points is that these two are quite far apart, which has exacerbated if not caused the majority of economic problems in the world today. (Economists didn’t invent world hunger, but for over a decade now we’ve had the power to end it and haven’t done so. You’d be amazed how cheap it would be; we’re talking about 1% of First World GDP at most.)

The reason I call it “infinite identical psychopaths” is that this is what neoclassical economists appear to believe human beings are, at least if we judge by the models they use. These are the typical assumptions of a neoclassical economic model:

      1. Perfect information: All individuals know everything they need to know about the state of the world and the actions of other individuals.
      2. Rational expectations: Predictions about the future can only be wrong within a normal distribution, and in the long run are on average correct.
      3. Representative agents: All individuals are identical and interchangeable; a single type represents them all.
      4. Perfect competition: There are infinitely many agents in the market, and none of them ever collude with one another.
      5. “Economic rationality”: Individuals act according to a monotonic increasing utility function that is only dependent upon their own present and future consumption of goods.

I put the last one in scare quotes because it is the worst of the bunch. What economists call “rationality” has only a distant relation to actual rationality, either as understood by common usage or by formal philosophical terminology.

Don’t be scared by the terminology; a “utility function” is just a formal model of the things you care about when you make decisions. Things you want have positive utility; things you don’t want have negative utility. Larger numbers reflect stronger feelings: a bar of chocolate has much less positive utility than a decade of happy marriage; a pinched finger has much less negative utility than a year of continual torture. Utility maximization just means that you try to get the things you want and avoid the things you don’t. By talking about expected utility, we make some allowance for an uncertain future—but not much, because we have so-called “rational expectations”.

Since any action taken by an “economically rational” agent maximizes expected utility, it is impossible for such an agent to ever make a mistake in the usual sense. Whatever they do is always the best idea at the time. This is already an extremely strong assumption that doesn’t make a whole lot of sense applied to human beings; who among us can honestly say they’ve never done anything they later regretted?

The worst part, however, is the assumption that an individual’s utility function depends only upon their own consumption. What this means is that the only thing anyone cares about is how much stuff they have; considerations like family, loyalty, justice, honesty, and fairness cannot factor into their decisions. The “monotonic increasing” part means that more stuff is always better; if they already have twelve private jets, they’d still want a thirteenth; and even if children had to starve for it, they’d be just fine with that. They are, in other words, psychopaths. So that’s one word of my title.

I think “identical” is rather self-explanatory; by using representative agent models, neoclassicists effectively assume that there is no variation between human beings whatsoever. They all have the same desires, the same goals, the same capabilities, the same resources. Implicit in this assumption is the notion that there is no such thing as poverty or wealth inequality, not to mention diversity, disability, or even differences in taste. (One wonders why you’d even bother with economics if that were the case.)

As for “infinite”, that comes from the assumptions of perfect information and perfect competition. In order to really have perfect information, one would need a brain with enough storage capacity to contain the state of every particle in the visible universe. Maybe not quite infinite, but pretty darn close. Likewise, in order to have true perfect competition, there must be infinitely many individuals in the economy, all of whom are poised to instantly take any opportunity offered that allows them to make even the tiniest profit.

Now, you might be thinking this is a strawman; surely neoclassicists don’t actually believe that people are infinite identical psychopaths. They just model that way to simplify the mathematics, which is of course necessary because the world is far too vast and interconnected to analyze in its full complexity.

This is certainly true: Suppose it took you one microsecond to consider each possible position on a Go board; how long would it take you to go through them all? More time than we have left before the universe fades into heat death. A Go board has two colors (plus empty) and 361 spaces. Now imagine trying to understand a global economy of 7 billion people by brute-force analysis. Simplifying heuristics are unavoidable.

And some neoclassical economists—for example Paul Krugman and Joseph Stiglitz—generally use these heuristics correctly; they understand the limitations of their models and don’t apply them in cases where they don’t belong. In that sort of case, there’s nothing particularly bad about these simplifying assumptions; they are like when a physicist models the trajectory of a spacecraft by assuming frictionless vacuum. Since outer space actually is close to a frictionless vacuum, this works pretty well; and if you need to make minor corrections (like the Pioneer Anomaly) you can.

However, this explanation already seems weird for the “economically rational” assumption (the psychopath part), because that doesn’t really make things much simpler. Why would we exclude the fact that people care about each other, they like to cooperate, they have feelings of loyalty and trust? And don’t tell me it’s because that’s impossible to quantify; behavioral geneticists already have a simple equation (C < r B) designed precisely to quantify altruism. (C is cost, B is benefit, r is relatedness.) I’d make only one slight modification; instead of r for relatedness, use p for psychological closeness, or as I like to call it, solidarity. For humans, solidarity is usually much higher than relatedness, though the two are correlated. C < p B.

Worse, there are other neoclassical economists—those of the most fanatically “free-market” bent—who really don’t seem to do this. I don’t know if they honestly believe that people are infinite identical psychopaths, but they make policy as if they did.

We have people like Stephen Moore saying that unemployment is “like a paid vacation” because obviously anyone who truly wants a job can immediately find one, or people like N. Gregory Mankiw arguing—in a published paper no less!—that the reason Steve Jobs was a billionaire was that he was actually a million times as productive as the rest of us, and therefore it would be inefficient (and, he implies but does not say outright, immoral) to take the fruits of those labors from him. (Honestly, I think I could concede the point and still argue for redistribution, on the grounds that people do not deserve to starve to death simply because they aren’t productive; but that’s the sort of thing never even considered by most neoclassicists, and anyway it’s a topic for another time.)

These kinds of statements would only make sense if markets were really as efficient and competitive as neoclassical models—that is, if people were infinite identical psychopaths. Allow even a single monopoly or just a few bits of imperfect information, and that whole edifice collapses.

And indeed if you’ve ever been unemployed or known someone who was, you know that our labor markets just ain’t that efficient. If you want to cut unemployment payments, you need a better argument than that. Similarly, it’s obvious to anyone who isn’t wearing the blinders of economic ideology that many large corporations exert monopoly power to increase their profits at our expense (How can you not see that Apple is a monopoly!?).

This sort of reasoning is more like plotting the trajectory of an aircraft on the assumption of frictionless vacuum; you’d be baffled as to where the oxidizer comes from, or how the craft manages to lift itself off the ground when the exhaust vents are pointed sideways instead of downward. And then you’d be telling the aerospace engineers to cut off the wings because they’re useless mass.

Worst of all, if we continue this analogy, the engineers would listen to you—they’d actually be convinced by your differential equations and cut off the wings just as you requested. Then the plane would never fly, and they’d ask if they could put the wings back on—but you’d adamantly insist that it was just coincidence, you just happened to be hit by a random problem at the very same moment as you cut off the wings, and putting them back on will do nothing and only make things worse.

No, seriously; so-called “Real Business Cycle” theory, while thoroughly obfuscated in esoteric mathematics, ultimately boils down to the assertion that financial crises have nothing to do with recessions, which are actually caused by random shocks to the real economy—the actual production of goods and services. The fact that a financial crisis always seems to happen just beforehand is, apparently, sheer coincidence, or at best some kind of forward-thinking response investors make as they see the storm coming. I want to you think for a minute about the idea that the kind of people who make computer programs that accidentally collapse the Dow, who made Bitcoin the first example in history of hyperdeflation, and who bought up Tweeter thinking it was Twitter are forward-thinking predictors of future events in real production.

And yet, it is on this sort of basis that our policy is made.

Can otherwise intelligent people really believe that these insane models are true? I’m not sure.
Sadly I think they may really believe that all people are psychopaths—because they themselves may be psychopaths. Economics students score higher on various psychopathic traits than other students. Part of this is self-selection—psychopaths are more likely to study economics—but the terrifying part is that part of it isn’t—studying economics may actually make you more like a sociopath. As I study for my master’s degree, I actually am somewhat afraid of being corrupted by this; I make sure to periodically disengage from their ideology and interact with normal people with normal human beliefs to recalibrate my moral compass.

Of course, it’s still pretty hard to imagine that anyone could honestly believe that the world economy is in a state of perfect information. But if they can’t really believe this insane assumption, why do they keep using models based on it?

The more charitable possibility is that they don’t appreciate just how sensitive the models are to the assumptions. They may think, for instance, that the General Welfare Theorems still basically apply if you relax the assumption of perfect information; maybe it’s not always Pareto-efficient, but it’s probably most of the time, right? Or at least close? Actually, no. The Myerson-Satterthwaithe Theorem says that once you give up perfect information, the whole theorem collapses; even a small amount of asymmetric information is enough to make it so that a Pareto-efficient outcome is impossible. And as you might expect, the more asymmetric the information is, the further the result deviates from Pareto-efficiency. And since we always have some asymmetric information, it looks like the General Welfare Theorems really aren’t doing much for us. They apply only in a magical fantasy world. (In case you didn’t know, Pareto-efficiency is a state in which it’s impossible to make any person better off without making someone else worse off. The real world is in a not Pareto-efficient state, which means that by smarter policy we could improve some people’s lives without hurting anyone else.)

The more sinister possibility is that they know full well that the models are wrong, they just don’t care. The models are really just excuses for an underlying ideology, the unshakeable belief that rich people are inherently better than poor people and private corporations are inherently better than governments. Hence, it must be bad for the economy to raise the minimum wage and good to cut income taxes, even though the empirical evidence runs exactly the opposite way; it must be good to subsidize big oil companies and bad to subsidize solar power research, even though that makes absolutely no sense.

One should normally be hesitant to attribute to malice what can be explained by stupidity, but the “I trust the models” explanation just doesn’t work for some of the really extreme privatizations that the US has undergone since Reagan.

No neoclassical model says that you should privatize prisons; prisons are a classic example of a public good, which would be underfunded in a competitive market and basically has to be operated or funded by the government.

No neoclassical model would support the idea that the EPA is a terrorist organization (yes, a member of the US Congress said this). In fact, the economic case for environmental regulations is unassailable. (What else are we supposed to do, privatize the air?) The question is not whether to regulate and tax pollution, but how and how much.

No neoclassical model says that you should deregulate finance; in fact, most neoclassical models don’t even include a financial sector (as bizarre and terrifying as that is), and those that do generally assume it is in a state of perfect equilibrium with zero arbitrage. If the financial sector were actually in a state of zero arbitrage, no banks would make a profit at all.

In case you weren’t aware, arbitrage is the practice of making money off of money without actually making any goods or doing any services. Unlike manufacturing (which, oddly enough, almost all neoclassical models are based on—despite the fact that it is now a minority sector in First World GDP), there’s no value added. Under zero arbitrage, the interest rate a bank charges should be almost exactly the same as the interest rate it receives, with just enough gap between to barely cover their operating expenses—which should in turn be minimal, especially in a modern electronic system. If financial markets were at zero arbitrage equilibrium, it would be sensible to speak of a single “real interest rate” in the economy, the one that everyone pays and everyone receives. Of course, those of us who live in the real world know that not only do different people pay radically different rates, most people have multiple outstanding lines of credit, each with a different rate. My savings account is 0.5%, my car loan is 5.5%, and my biggest credit card is 19%. These basically span the entire range of sensible interest rates (frankly 19% may even exceed that; that’s a doubling time of 3.6 years), and I know I’m not the exception but the rule.

So that’s the mess we’re in. Stay tuned; in future weeks I’ll talk about what we can do about it.