Too Much Information

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Here at Economic Forces we like to write about information. One possible reason that information is such a popular topic is that issues related to imperfect information are often the source of confusion. Much of this confusion seems to result from using the wrong counterfactual.

One obvious example relates to a favorite topic of mine: the efficient markets hypothesis. According to Eugene Fama, if financial markets are efficient, then my prediction of what the price of an asset will be tomorrow (conditional on all of the information that I have today) should not be systematically different from the realized price.

There are a couple of ways to interpret this definition. One interpretation of the efficient markets hypothesis is that asset prices incorporate all available information. Another way to interpret this definition is that nobody can systematically beat the market. In some ways, this means the same thing. If we all have the same information, then none of us has an information advantage and there is no reason to believe that any of us can beat the market. Nonetheless, there is a subtle difference here that can lead to some confusion.

Sanford Grossman and Joe Stiglitz have a famous paper in which they argue that it is impossible for financial markets to be informationally efficient. That certainly seems like a death blow to the efficient markets hypothesis. But is it? No, not really.

The argument made by Grossman and Stiglitz is that prices can only reflect all available information if information is costless to obtain. In reality, acquiring information requires time and resources. But if information is costly, then people will only accumulate information up until the point at which the marginal benefit of the information is equal to the marginal cost of the information. Thus, it is impossible for all information to be incorporated into the price because at some point additional information simply isn’t worth the cost.

But does this actually violate the efficient markets hypothesis? No. Not really. There are a variety of ways to understand why. First, the efficient markets hypothesis really just means that no one can systematically beat the market. Even if there is information out there that isn’t incorporated into the price, this doesn’t mean that this information could be used by anyone to systematically beat the market. In fact, since the marginal benefit of information equals marginal cost, this necessarily implies that the marginal increase in one’s rate of return from the additional information isn’t sufficient to justify the cost of acquiring that information.

A second way of thinking about this is to go back to the typical definition of efficiency used in economics. That definition states that a market is efficient if all gains from trade have been exhausted. If the marginal benefit of information is equal to the marginal cost of acquiring it, then there are no gains from trade to be had from this foregone information.

(Of course, I’m not telling you that for the first time.)

Another famous example in which information is a source of confusion is in discussing whether information is always socially useful. Jack Hirshleifer is probably the economist most closely associated with this idea. The basic concept is that some information might have a private benefit, but no social benefit. For example, suppose that there are two parties to a trade. Some types of information might result in the surplus from trade being redistributed from one party to another, but does not expand the gains from trade. If this information is costly to obtain, then using resources to acquire this information is socially wasteful in the sense that it does not increase the total surplus from trade, but merely transfers the surplus from one party to the other. Thus, although the information is privately valuable, it has no social value.

Whether this is correct, however, depends on the proper counterfactual. For example, Yoram Barzel challenged the notion that this sort of outcome was inefficient.

To understand Barzel’s argument, consider the following example. Suppose that there is a farmer who produces a particular quantity of output with absolute certainty and who is a price-taker. This farmer will be able to sell his product at a price that is based on the supply of his competitors. When his competitors experience good weather, supply will be high and prices low. When his competitors experience bad weather, supply will be low and prices will be high. Furthermore, suppose that the farmer sells directly to consumers.

In this context, it is easy to construct examples in which information appears to have a private benefit, but no social value. One could imagine a third party (let’s call him a forecaster) who expends resources trying to detect weather patterns. For simplicity, suppose that, for some cost, our forecaster can perfectly predict the weather. If this is true, the forecaster can use this information to generate a private benefit. When he knows that the weather is bad and prices are high, he can buy a futures contract prior to the bad weather being realized that locks in a low price. Once the bad weather is realized, the price will go up and the forecaster will be able to buy crops for the low price and sell the crops to consumers at a higher price. On the other hand, when he knows that the weather will be good, he can sell a futures contract before the weather is realized. Once everyone finds out that the good weather will bring a good harvest, prices will decline. He can then buy crops at a low price and deliver them to the buyer of his higher-priced futures contract.

In these examples, the forecaster makes a profit, but he does so at the expense of the consumer or the farmer. In fact, it is straightforward to show with simple numerical examples that this sort of scenario reduces the expected price that the farmer receives and increases the price that consumers expect to pay. Yet, the forecaster is not doing anything to increase the surplus from trade. There is a private benefit, but no social benefit.

Barzel questions this logic. This sort of example certainly seems to fit the criteria of private benefits with no social value, but only in comparison to the world without the forecaster. What would the world without the forecaster really look like?

Barzel argues that in a world without transaction costs, the world with the forecaster and the world without the forecaster would ultimately look exactly the same. The reason is that the speculation being done by the forecaster is evident in the prices of the crops. As I said, it is straightforward to show that the expected selling price is lower for farmers and the expected purchase price is higher for consumers in the presence of the forecaster. This, after all, is how the forecaster makes his profit. But if this is the case, then over time the farmer would observe lower sale prices and the consumer would observe higher purchase prices. These changes in the prices would reveal that there was a speculator in the market and that this speculator was a detriment to their surpluses. A much more preferable solution for the farmer and the consumer would be to cut out such a middleman and instead agree to a risk-sharing contract that benefited both parties.

Astute readers of Economics Forces will know what is coming. It is actually hard and often not preferable to “cut out the middleman.” The middleman is often performing a valuable service.

The same is true in this example. If people can observe prices and learn from those observations over time, the forecaster would eventually be pushed out of the market. In fact, the only way that we would ever observe the presence of the forecaster in the long run is if there were some sort of transaction costs involved. Why are transaction costs necessary to the explanation? Well, the only way that the farmer and the consumer would tolerate the existence of the forecaster in this market is if the transaction costs of eliminating the forecaster from the market exceeds the value of the surplus lost to the forecaster. But think about that. If that is true, then the outcome is not socially wasteful, but rather is efficient! Why? Because there are no gains from trade to be had. Sure, the farmer and the consumer could be better off, but the benefit isn’t large enough to justify the costs. There are no gains from trade to be had.

As a result, whether we think of this sort of example of the farmer, the consumer, and the forecaster as efficient or inefficient depends on our choice of the proper benchmark to serve as a counterfactual. If we think the proper benchmark is a frictionless world without transaction costs, then sure, the forecaster seems wasteful. However, this is the nirvana fallacy. This is choosing a benchmark for comparison that is empirically unrealistic. Instead, we should choose a counterfactual that takes transaction costs seriously. But if we do, we don’t get to yell about inefficiencies all the time.

Information and finding the proper counterfactuals are important. That is why we spend so much time at Economic Forces thinking them through.