Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Markets

Vernon L. Smith, Gerry L. Suchanek, and Arlington W. Williams. “Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Markets.” Econometrica 51 (1988): 1119-1151.

Paper Outline and Setting

Rational expectation and market efficiency predict that, in equilibrium, stock prices should change only when there is new information that changes investors' dividend expectations. The paper examines this prediction in an experimental spot market setting in which nine to twelve subjects, with a varying level of experience, make trades for a certain number of periods under the common knowledge on the probability distribution of dividends. 

Specific details on the setting of the experiments are as follows;

1. Price quotes progress so as to reduce the bid-ask spread

2. Each trader is given an asset endowment and cash endowment (or working capital)

3. Working capital amount reflects the accumulated capital gains (losses) and dividend earnings

4. Traders can buy assets as long as their working capital is sufficient to cover the purchase price

5. Everyone is informed that the dividend structure (distributed iid) and actual dividend draws are the same for everyone in the market.

Given this experimental setting, rational expectation theory predicts that possible temporary deviation of the price from risk-adjusted dividend value due to divergent individual expectations cannot persist because of uncertainty in arbitrage profit. In the end, it is expected that investor expectations become common and coincide with dividend value, which leads to a market price commensurate with risk-adjusted dividend value. The experimental setting of this paper enables us to control dividend structure and traders' knowledge of it so that we can explore whether common knowledge of a common dividend payout is sufficient to induce common expectations. By investigating the patterns of price evolution, we can analyze how long it takes until investors form common expectation, and whether, or in what form, such convergence process can be characterized.

More formally, the main objectives of this study are as below;

1. Will economic agents trade an asset whose dividend distribution is common knowledge?

2. If so, can we characterize the price adjustment process and interpret it as a pattern consistent with convergence to risk-adjusted dividend value?

3. Will we observe any price bubbles and crashes occurring as part of the adjustment process?

Observed Patterns from Experiments and Interpretation

The authors identify three general patterns that emerge from a series of experiments conducted. 

1. Stable Markets

: In this group of markets, prices appeared to follow dividend value, or were constant or followed approximately parallel with dividend value over most of the horizon.

2. Growing Markets

: This group consists of the experiments that do not belong to the stable markets or bubble-crash markets group.

3. Bubble-Crash Markets

: This group consists of markets that produced price bubbles that collapsed sometime before the final period.

A general summary of the observed trade and price patterns is as below;

1. Exchanges do occur even when identical probabilistic dividends are to be paid. Therefore, different private dividend values on different traders is not a necessary condition for trades to occur. This may indicate that there is sufficient homegrown diversity in agent price expectations and risk attitudes to induce subjective gains from exchange.

2. Fourteen out of twenty-two experiments exhibit price bubbles followed by crashes relative to the intrinsic value.

3. Observed bubbles can be interpreted as a form of temporary myopia from which agents learn that capital gains expectations are only temporarily sustainable. This realization by investors ultimately leads to the formation of common expectations or common "priors."

4. Sometimes, markets are sensitive to (or strongly dominated by) group endogenous expectational factors that are not reliably manipulated by controllable treatment variables such as experience, information, and horizon length.

5. Expectations and price adjustments are both adaptive, but the adaptation over time across experiments with increasing trader experience tends to a risk-adjusted, rational expectation equilibrium.

6. Common knowledge is not sufficient to induce initial common expectations due to agent uncertainty about the behavior of others. With experience and trial-and-error learning, expectations seem to tend to converge and yield an equilibrium consistent with rational expectations.

Overall, the predominating characteristics of the price patterns observed from experiments indicate the tendency for expectations and price adjustments to converge to intrinsic value across experiments with increasing subject experience.