Sometimes I think we should license economics writers.
Thomas Nagel is a prominent philosopher (author of the provocative and widely anthologized essay What is it Like to be a Bat?) who’s just reviewed Daniel Kahneman’s new (and excellent) book in The New Republic. (Fun fact: When I stepped off an airplane at Heathrow last week, the first thing I saw was a limousine driver holding a sign that said “Daniel Kahneman”. This, incidentally, was my final issue of The New Republic, due to their criminally evil subscription practices — more on that, perhaps, later this week. ) Here is how Nagel describes what he seems to think is orthodox economic theory:
Most choices, and all economic choices, involve some uncertainty about their outcomes, and rational expectations theory, also called expected utility theory, describes a uniform standard for determining the rationality of choices under uncertainty…
The standard seems self-evident: The value of a 50 percent probability of an outcome is half the value the outcome would have if it actually occurred, and in general the value of any choice under uncertainty is dependent on the values of its possible outcomes, multiplied by their probabilities. Rationality in decision consists in making choices on the basis of `expected value’, which means picking the alternative that maximizes the sum of the products of utility and probability for all the possible outcomes. So a 10 percent chance of $1000 is better than a 50% chance of $150, an 80% chance of $100 plus a 20% chance of $10 is better than a 100 percent of $80 and so forth.
AAAAGGGHHH! Even on the Internet, it’s rare to see quite so much ignorance packed into so few words. Where to begin?
First, “rational expectations theory” and “expected utility theory” are not two names for the same thing; they are two names for entirely different things. Rational expectations is a theory of equilibrium (i.e. the outcomes that you get when decision-makers interact); expected utility is a theory of optimization (i.e. the choices made by an individual decision-maker). When Nagel throws around probabilities of 10, 50 or 80 percent, expected utility theory (like Nagel) takes those probabilties as given; rational expectations theory (which has nothing whatsoever to do with anything Nagel is talking about) tries to explain where those probabilities come from.
But far far far more importantly, Nagel’s account of expected utility theory is not just wrong but ridiculously naive. Who is to say that a 10 percent chance of $1000 is better than a 50 percent chance of $150? You might prefer one and your cousin Jeter might prefer the other. Orthodox economics pronounces neither of you irrational.
What Nagel is computing is not an expected utility, but an expected value. You’d have to be an extraordinarily dull observer of human nature to think that people routinely act to maximize expected value, and an extraordinarily dull student of economics to think that economists would ever make such a silly claim.
Indeed, the entire field of finance consists of studying the ways in which people trade off expected value against various measures of risk. To assert that only expected value matters is to assert that the entire field (along with much of the rest of economics) reduces to a triviality, that “risk management” is a pointless activitiy, and that insurance markets don’t exist.
What economists do believe (or act as if they believe) is that people maximize expected utility, which is a different thing altogether. To assess the value of a 50% chance of $100, we multiply 50% times a number called the utility of $100, and we predict that when confronted with multiple choices, they choose the one that maximizes their expected utility. This is a far better theory than Nagel’s bastardized version, for several reasons. First of all, it’s not an assumption; it’s a conclusion. We start with some very simple axioms about human preferences and deduce that people behave so as to maximize expected utility. Second, there’s a vast body of empirical work that’s largely compatible with this theory’s predictions.
One of the most widespread misconceptions among non-economists is that these “utility” numbers represent some subjective measure of well-being. (Because it fosters this misconception, the word “utility” was probably a poor choice from the get-go, but we’re stuck with it.) All the relevant theorem says is that people act as if they assigned a number to each possible outcome (e.g. $100 is assigned a 2, $1000 is assigned a 3, etc) and then act as if their choices were based on these numbers, multiplied by probabilities a la Nagel (so that a 50% chance of $1000 is assigned a 1.5, making it inferior to a sure $100). The numbers, according to the theory, are different for different people, which is why, confronted with identical circumstances, different people make different choices.
(Has Nagel never noticed that when confronted with identical circumstances, different people make different choices? Has he not noticed that his theory predicts otherwise? Or did he think that somehow this phenomenon had somehow gone unnoticed by the entire economics profession?)
Kahneman’s book is a wonderful survey of the ways in which orthodox economic theory can fail. It’s important and surprising work. But if orthodox economic theory looked anything like Nagel’s caricature, then its failure would be no surprise and hardly worth writing about.