too much math makes me sleepy

Relevance

/ jdc / Leave a comment

Making Economics Relevant Again, from David Leonhardt in the New York Times, has been recommended to me by more than one tipster. First of all, the most astonishing thing in the article, to me, is this table that includes an account of the number of economics degrees given every year since 1949: I thought majoring in economics had been on a steady upswing for decades, but apparently a lot fewer people were studying economics in the 90s. The number is just back up to where it was in 1990.

Anyway, the article kicks off:

“It was only a decade ago that economics seemed to be an old and tired discipline. The field no longer had intellectual giants like John Maynard Keynes or Milton Friedman who were shaping public policy by the sheer force of their ideas. Instead, it was devolving into a technical discipline that was even less comprehensible than it was relevant.”

Possible revisionism here, but it’s certainly a tempting argument. It might reflect the sleepy state of economic policy rather than the discipline as a whole, but I take the point. We’re pointed to an old New Yorker article from 1996 which drives the point home in spectacular fashion; forgive the long quotation:

“A few weeks ago, the Nobel Prize in Economics was awarded to William Vickrey, an 82-year-old professor at Columbia, and James Mirrlees, a 60-year-old professor at Cambridge…. the newspapers had some difficulty explaining the prize-winning work, which the Nobel committee referred to as “the economic theory of incentives under asymmetric information.” ..But when reporters tracked down Vickrey, an amiable bear of a man, he refused to play along: instead of expanding on the obscure mathematical theory that gained him world attention, he insisted on talking about his practical ideas for reforming the subways, the electoral system, the budget deficit, and much else besides. A “Times” reporter tried to pin him down, but Vickrey quickly dismissed his prize-winning 1961 paper as “one of my digressions into abstract economics.” And he went on to say, “At best, it’s of minor significance in terms of human welfare.””

What a priceless story. However, it might not just be the abstract math that marginalizes economics: Leonhardt goes on to argue that some economists are disgruntled at what they see as the cause of the “recovery” he perceives in economics. I can’t really argue with this:

“the new research often consists of cute findings — which inevitably get covered in the press — about trivial subjects, like game shows, violent movies or sports gambling.”

It’s like the Christmas stuff I talked about before. It isn’t a true reflection of economics research and it makes economics look ridiculous. To try and figure out what really mattered, Leonhardt decided to survey economists to find out who they thought “was using economics to make the world a better place”. It’s a question begging to reject Vickrey’s digressions into abstract economics. Presumably, to be an economist who actually does some good for the world, your research must be good science and very, very close to a solid and appealing economic policy. And lo:

“there was still a runaway winner…. the Jameel Poverty Action Lab at M.I.T., led by Esther Duflo and Abhijit Banerjee.”

I won’t try to put this any better than the original article:

“They want to overhaul development aid so that more of it is spent on programs that actually make a difference. And they are trying to do so in a way that skirts the long-running ideological debate between aid groups and their critics…. The basic idea behind the lab is to rely on randomized trials — similar to the ones used in medical research — to study antipoverty programs. This helps avoid the classic problem with the evaluation of aid programs: it’s often impossible to separate cause and effect.”

Let’s figure out what’s going on here. The research uses randomized trials to disentangle causality, the ubiquitous problem for figuring out relationships from real-world data; because the method is strong, they can rely less on normative judgment when they make the jump from the science to the policy, thus cutting ideology out. Just like the Obama team I was talking about yesterday, the gap between science and policy is vanishingly small here, but clearly it’s crucial for the success of the whole venture that the science be pure as snow. The science can’t tell you you’re right or wrong to hold the belief that children should be educated – that’s all on your head – but it can perform the true role of positive economics and help you figure out exactly how to improve the quality of education if that’s what you want.

The reason why these development economists are perceived as the most “relevant” is twofold: they have easy to understand, convincing science and they explicitly embrace the normative implications of their science. Their science is as sophisticated as it gets, but they certainly don’t need esoteric math. On that note, the last word goes to that New Yorker article:

“One way to encourage economists to become more worldly might be to abolish the Nobel Prize for economics, which since its introduction, in 1969, has helped foster a professional culture that values technical wizardry above all else. Deprived of the publicity surrounding the annual Stockholm ceremony, economists would actually have to do something useful to get noticed.”

EDIT: Actually I’m not sure that should be the last word. By the merits of, for example, the work Duflo, Banerjee and co. are doing, they would absolutely qualify for a Nobel memorial prize in economic science. The prize does seem to have become at least as much an applied math prize as a “good economic science” prize, which I guess is the problem the New Yorker article is highlighting. The problem isn’t the prize, but the criterion for winning, perhaps.

Too complicated?

/ jdc / Leave a comment

One of the principles of writing economic theory is to create a simplified abstraction of reality. If the theory convincingly isolates an idea, it cannot be too simple; hopefully, the narrower the question, the simpler the theory can be written.

Economists therefore appeal to the “all else equal” assumption a lot. The oft-perceived superiority complex of economists is traceable to our willingness to use the “all else equal” clause to make our questions answerable, theoretically and empirically. If we want to write relevant economic models that investigate the link between A and B, we hold C equal; whether or not C would really be equal or relevant in reality, we can’t isolate the effect we’re interested in if we don’t figure out a way stop it from contaminating the abstraction.

It’s the same principle that underlies the ideal of “controlled experiments” in all science; empirically, if we want to figure out how A and B are related, I need to be careful to avoid finding an effect because a third factor C is involved. For example, there’s an important difference between “people who exercise more have a longer lifespan” and “people who exercise more also eat well, and people who eat well have a longer lifespan”. That’s well understood in statistics and empirics generally; there’s no reason why the same principle is not also needed when we use the theoretical standard of proof rather than the empirical standard of proof.

Why, then, is “economic theory” so amazingly bewildering? With very little exaggeration, we can claim that no great development in the science of economics has used very complicated techniques, even when math was involved, yet even to the technically competent a lot of economics research is very difficult to understand. Of course, if an economist could all find ground-breaking theory that can be represented in two lines, I’m sure she’d write it. Is the reason for the complexity an attempt to make average ideas look better?

Let’s be charitable and assume that’s not the case. I think that once we exclude the “obfuscation motive”, there are two possible reasons why economic theory is technically complex. One might be that the relationships being investigated are broader, that less is held equal, that we’re looking to more nuanced explanations. Another possible reason is, paradoxically, that theory gets more complex as the questions get narrower – the more we assume, the higher the complexity.

Why? Imagine I want to figure out the relationship between a person’s income and the number of hours that person does voluntary work. This is a question that asks about how people allocate a scarce resource, time. I might make an abstraction that says “if all people like both money and helping others, then people with higher incomes will spend more time helping others, while people with lower incomes will spend more time trying to earn extra money.” I might make an abstraction that says “people with more income work more so have less time to volunteer”. What assumptions lead to the first conclusion, and what to the second?

If I wanted to broaden my question, I might start including in my theory labor market conditions, the availability of volunteering opportunities, the peer pressure to volunteer, the social pressure to earn more money to buy a big car, and so on and so forth. That would certainly make my theory more complicated; whether or not it makes it a better theory than the one that kept all that stuff equal and abstracted from it is a matter of preference, but I’m sure it would be more difficult to understand.

The second way to make the theory more “complicated”, at least superficially, might be to keep all the same stuff equal, but to say “imagine the person cares this much about money and this much about volunteering; then someone with this income will volunteer this much”. The abstraction is getting more abstract; we are getting more and more specific about the conditions of our model, and we must use more specific techniques to, in particular, quantify the result.

What do we gain from this quantification, and what do we lose? Perhaps we can look at actual evidence on the link between income and volunteering, and compare it to the quantified prediction, but that only works if all else is equal in our evidence, too. A better justification is that we can get a theoretical idea of how big our effect is. However, as we get more specific we get more abstract; in this example, we’re getting more abstract about preferences, which are themselves unobservable. We’ve gone from “a person cares about money and volunteering” to attaching magnitudes to those cares.

The link between simplicity and usefulness is not just in the realism of the abstraction; it’s also in the procedure itself. Economic theory should be neither too broad or too narrow, but “just right”, whatever that means. Assume too little and we can’t figure out what’s really causing what; assume too much and you rest an entire argument on a special case. What’s the simplest model that explores the relationship I care about, and what’s the simplest model that shows what I want to show about that relationship?

Oh, and a practical suggestion: I’d love it if we all stopped writing ceteris paribus and used “all else equal”. What’s with the Latin?