Too complicated?

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?