Markets as Information Gathering Tools.

• Author: Plott, Charles R.

Charles R. Plott [*]

The academic literature, Wall Street commentary, and even daily news reporting reflect a belief that markets can anticipate events. The current movements in the stock market are interpreted as reflecting the likelihood that the Federal Reserve System will change interest rates. Futures markets are interpreted as reflecting the best estimates of things to come. Movements in individual stock prices are thought to anticipate earnings reports or the probability of a merger or buyout. If we want to know about future weather in the South, we should study the orange juice futures. The academic journals are filled with the concept of rational expectations in which current prices are supposed to reflect the sum of all knowledge in the system. Prices, according to this theory, are a statistic that indicates the aggregation of information about underlying states of the economy. Those who are "outsiders" to the information in the system become "insiders" by simply observing the economic activity.

While such beliefs are pervasive, there is a need to pause and ask ourselves what it means for markets to have such capacities. First, it means that markets can find the solution to a complex set of equations that are part of the knowledge of no one. Second, it means that while finding this solution, it can collect information that is dispersed across the economy, aggregate it like a statistician, and publish the findings in the form of the prices.

Why do the commonly held notions imply such complexity? According to received theory, an economy is best described as a large set of nonlinear, simultaneous equations. Equilibrium is just a solution to the set, the "zeros" so to speak. Of course, no one knows what these equations are since the information that forms the equations is typically known only to the individual agents in the economy. Thus, the information about the equations is not in one head, but there is even more information that must be collected. Each individual has private information about the world around him. Expectations based on this private information are sufficient for decisions so long as such expectations are not inconsistent with other information reflected in the behavior of the economy, such as prices. If prices or other variables contain additional information, the behavior of the individual will change, pushing the system to a different form of equilibrium. Equilibration will not occur until all information is comfortably inco rporated in the publicly observable variables. When the additional information property is added, the computation is challenging indeed. Even if the equations were known to individuals, finding a solution (in finite time) might be very challenging to even the most numerically inclined applied mathematician.

On the surface, the idea that markets can perform such aggregation seems to be false. It seems to be beyond human capacities. One is tempted to dismiss the theory immediately, without further thought. However, such dismissal would be premature. The capacities to infer underlying information from the behavior of others is so commonplace that we hardly notice the complex process that is taking place. When searching for a restaurant in an unfamiliar area, people typically look to see where many others are eating. If one stands and looks into a store window, those passing on the sidewalk will frequently pause to look also. When judging the quality of movies, both the number of favorable reviews as well as the reported ticket sales figure into an otherwise uninformed decision. The odds at horse races or the Las Vegas point spreads on ball games are frequently good predictors of winners. In fact, when these variables are used in models, they leave very little for other variables to explain. The odds and point spre ads are not made by a single mind but instead are the product of many interdependent minds competing for an advantage. These examples illustrate the ability of humans to infer subtle information from systemic properties and suggest that such inferences might be commonplace. In fact, it might not be limited to humans, as will be the testimony of any fisherman who uses the movements of birds to locate fish.

The theory goes much further than the casual observations of the examples and makes rather precise, quantitative claims that are in need of investigation. That issue forms the topic of this talk. Can markets perform the tasks as advertised? Can markets find the zeros? If so, how do they do it? Can markets collect and aggregate information? If markets can do these things, what might be the uses? After all, the capacity to harness such powerful tendencies might be something of value. In addition to these topics there is another issue, which is the substance of the talk. How can we answer the above questions? The answer to the substantive issue is the use of laboratory experimental methods.

In posing the topics, a perspective is in order. The question is whether markets can do it at all, as opposed to whether they can always do it. Are such properties within the capacities of humans and organized markets? We want to establish only the possibility, a proof of principle. Whether markets can always do it and/or the full range of capacities to do it is far beyond the scope of what is known.

1. Systems of Equations

   Can Markets Solve Them?

   Two examples will be explored. Consider first a simple case, which turns out to not be simple at all: a laboratory setting in which each individual is given a "redemption value" and a time interval in which that redemption value is valid. The redemption value is of the form [R.sub.i]([x.sub.i], T), where [x.sub.i], is the quantity of some specific commodity purchased, T is a time interval, and [R.sub.i](., .) is the amount that the subject can collect from the experimenter from holdings of an amount [x.sub.i]. Literally, the subject buys units in the market and resells them to the experimenter at prices reflected in the function [R.sub.i]([x.sub.i], T) as long as the subject resells in the time interval T. Thus, the income to the subject from purchases in the quantity x is

   [R.sub.i]([x.sub.i], T) - [cost of purchases of [x.sub.i]], (1)

   where the cost of purchases of [x.sub.i] is the sum of the prices paid for the units that make the total quantity [x.sub.i].

   If prices were fixed at some level P, then the theory of consumer choice asserts that each individual, i, will attempt to solve the equation:

   [partial][R.sub.i]([x.sub.i], T)/[partial][x.sub.i] - P = 0. (2)

   When inverted, Equation 2 yields the equation

   [x.sub.i] = [D.sub.i](P, T). (3)

   Sellers in the market can buy from the experimenter according to a cost function [C.sub.j]([y.sub.j], T), where the individual is j and the number of units purchased from the experimenter during the time interval T is [y.sub.j]. The income from the experiment is

   [Revenue from sales of [y.sub.j]] - [C.sub.j]([y.sub.j], T). (4)

   If prices are fixed at P, then Equation 4 becomes

   [Py.sub.j] - [C.sub.j]([y.sub.j], T) (5)

   and according to theory, the individual solves the equation

   P - [partial][C.sub.j]([y.sub.j], T)/[partial][y.sub.j] = 0, (6)

   producing supply functions of the form

   [y.sub.j] = S(P, T). (7)

   The law of supply and demand represents another equation of the form

   [[Sigma].sub.i] [x.sub.i] - [[Sigma].sub.j] [y.sub.j] = 0. (8)

   Notice the complexity of this model. If there are n people, then Equations 3, 7, and 8 represent n + 1 equations, without considering the complexity introduced by the variable T. The equations are nonlinear, and no one in the system knows them all. Indeed, no one in the system knows more than one of them. Furthermore, the solution is found under most unusual circumstances because typically there is no single price in a market. There are many prices because of the nature of bids, asks, and contracts.

   Can markets solve such a complex system? Figure 1 illustrates the fact that the answer is "yes." In the market represented in the figure, there were 87 people, approximately half of whom were buyers and half sellers. Shown there is the time series from a market created much like the one described above, only the time, T, is more complicated. [1] It is also more complicated because these people could speculate. They could buy and resell for a profit; thus, the nature of the interactions is extremely complex, suggesting that there are many more equations needed to solve the system than the 88 suggested by theory. Yet, as can be seen in the figure, the price-time path converges to the competitive equilibrium, the dotted line. When the competitive equilibrium is shifted, the markets adjust to the new equilibrium. By observing the time series alone, one knows the solution to this complex set of equations even without going through the complex set of computations.

   To those who have observed this phenomena demonstrated many times in experimental markets, the discussion above is not particularly surprising. For those who have not, a natural suspicion is that the ability of markets to perform this complex...