Harrison & Kreps 1978: The power of irrational expectations

In the past few weeks I've had discussions with several different people about why financial markets are different from normal markets. I've come to realize that there is a very deep and fundamental fact about financial markets that almost nobody in the lay public - and a good chunk of people in the finance industry itself - don't understand. And that fact just happens to have implications that also shake the foundations of modern macroeconomics.

So it's time for another addition of Papers You Should Know. Today's paper is "Speculative Behavior in a Stock Market With Heterogeneous Expectations" by J. Michael Harrison and David M. Kreps (Quarterly Journal of Economics, 1978).

Before we talk about Harrison & Kreps, we need to understand why financial markets are so weird. In a nutshell, it's this: In normal markets, people who know exactly what they are trading will often still be willing to trade. In financial markets, people who know exactly what they are trading will almost never be willing to trade. For a quick explanation of why this is true, I turn to Brad DeLong:

In a standard economic transaction, it is no mystery where the value to both sides comes from. When I buy a double espresso from Café Nefeli for $2.25, the coffee is more valuabe to me then $2.25 is...The sources of the gains from trade are obvious. 

But in finance neither side is getting useful commodities. Instead, both sides are trading away claims to a pile of money and getting claims to a different pile of money in return. So how is it that me selling this pile of cash I have to you for that pile of cash that you currently own can be a good idea for both of us? Doesn't one of the piles have to be bigger? And isn't the person who trades the bigger for the smaller pile losing?

Think about that for a second. If I offer to sell you a share of stock for $10, why would you buy it? Well, you might buy it because you want to diversify or otherwise adjust your investment portfolio (to give you, say, more risk or longer maturity). But - let's be frank - chances are you'd buy it because you think that sometime in the future it'll be worth more than $10. Right? So now ask yourself: If I (the seller) also thought it would be worth more than $10 in the future, why the heck would I sell it to you for $10???

The answer is: I wouldn't. If someone offers to sell you a stock for $10 and tells you it's going to go up up up, in general don't buy it. Because if the guy selling you the stock really believed his own rosy prediction, he'd keep the stock for himself. The only time you should buy the stock is when you have good reason to believe that you are smarter or better-informed than the guy who's selling - in other words, if you think he's a sucker. Of course, he's only selling to you because he thinks you're a sucker.

So what we see is that while normal markets consist of people making trades because they have different preferences, financial markets mainly consist of a bunch of people with the same preferences all trying to sucker each other. This fact is called the "No-Trade Theorem," and economists have known about it for a long time. 

So in 1978, J. Michael Harrison and David M. Kreps decided to write down a model of a financial market in which everyone was trying to sucker everyone else. As far as I know, this was the first model of its kind. Even though few people believe that the model describes exactly how the real world works, it has become enormously influential, because it gives an idea of what the world would have to be like in order for us to observe the enormous volumes of financial trading that we actually see happening.

Briefly, the model works like this: Different people have different beliefs about the fundamental value of an asset (i.e., how much money the asset will pay them). One person thinks it'll pay A if the economy is good and B if the economy is bad. The other person thinks it'll pay C if the economy is good and D if the economy is bad. They know that they have different beliefs, they know what other people's beliefs are, and they "agree to disagree." So they are willing to trade; each one thinks the other one is a sucker.

So what price do they trade at? Well, you might think that the most bullish investor (i.e. the person who thinks it's worth the most) would just set the price. But actually, the price ends up being even higher than the most bullish person thinks it's worth! The reason is that the asset has resale value. You can buy it, collect some money from it, and then when the economy changes, you can sell it at a profit to someone who is more bullish than you are. So the price ends up being the sum of the asset's fundamental value and its resale value. Ta-da: Speculation!

Now, like I said, nobody really thinks this is exactly how things work. For one thing, people should learn over time - as the asset pays out money, people should update their beliefs. But Harrison & Kreps is not about describing the world, it's about exploring ideas. And the basic idea they explored has become one of the most powerful in all of financial economics. Since 1978, a number of authors have taken this basic notion of investor overconfidence and tried to either make it more realistic, or find it in the data. A few prime examples include Scheinkman & Xiong (2003), who put the overconfidence idea into a modern asset pricing model, Barber & Odean (2001), who find evidence that individual investors are overconfident and trade too much, and a number of "heterogeneous prior" models that allow people to learn as they go. All of these models owe something to the pioneering work of Harrison & Kreps.

But anyway, all that is preamble. This is actually a post about macroeconomics.

You see, the No-Trade Theorem says that financial markets shouldn't have a lot of trading. But we see a LOT of trading in these markets. And Harrison & Kreps showed that those trades are best explained by irrational expectations.

So what does that say about macro? Since the late 70s, nearly all of the models used by macroeconomists have been "rational expectations" models. "Rational expectations" is the idea that people don't make systematic mistakes when predicting the future. If you think that sounds a bit silly, you're not alone, but I kid you not when I say that rational expectations absolutely dominates modern macro.

But if expectations aren't rational in financial markets, why should they be rational in the economy as a whole? The answer is that they shouldn't. This is why Thomas Sargent, who won the Nobel Prize this year and who helped develop the theory of rational expectations, calls himself a "Harrison-Kreps Keynesian." Keynes, though he is usually associated with the idea of fiscal stimulus, was a professional stock speculator, and perceived clearly the irrationality of the markets in which he participated; Sargent is merely recognizing that financial market irrationality, which was formalized by Harrison and Kreps, is a huge hint that rational expectations is not going to get the job done in macro either. 

Pioneering macroeconomists like Sargent have spent a long time hacking through the wilderness of non-rational-expectations models. It is a daunting task, since there are infinitely many ways in which people could be irrational. Rational expectations lends itself to pure logical deduction - you can kind of just sit there and figure out how people should act. But to figure out how expectations really form, you need to get your hands dirty with things like lab experiments and careful empirical work.

But we really have no choice, if we want to understand the economy as it actually exists. As David Glasner says, "expectations are fundamental"; we can't afford to treat the process of human belief formation as an afterthought. That is the insight of Harrison and Kreps, and macro as a whole needs to take it to heart.

Update: Also see this article from today's NYT on Tom Sargent and Chris Sims (this year's other Nobelist). Both believe that modeling irrationality, as it exists in the real world, is the way to go.

Update 2: I just realized that a better title for this post would have been "Why is this market different from all other markets?" Ah, the "stairway wit"...