Bubbles in the Lab andDouble oral auction

Rosemarie Nagel ICREA-UPF-BGSE Barcelona, Spain

Visiting NYU

Three Day Mini Course on Experimental Economics Columbia University

Febr. 15-17. 2013

Definition

• “A bubble may be defined loosely as a sharp rise the price of an asset …, with the initial rise generating expectations of further rises and attracting new buyers – generally speculators interested in profits from trading in the asset rather than its use or earning capacity.”

-- Charles Kindleberger, The New Palgrave

Can bubbles persist?

• Keynes (1936) • “It might have been supposed that competition

between expert professionals, possessing judgment and knowledge beyond that of the average private investor, would correct the vagaries of the ignorant individual left to himself.”

• Fama (1965) “If there are many sophisticated traders in the market, they may cause these “bubbles” to burst before they really get under way.”

Why a lab experiment?

• Too many unknowns in the real world• Control of important variables: Here:– Fundamental values (at least known to the experimenter)– Borrowing constraints are the same for all – Time horizon the same for all– Experience level of subjects can be made the same

(repetition of the same market)– Controlled centralized market: here call market– Control of reason to buy/sell. In contrast e.g. in housing

market, need for a house

Creating a bubble experiment• The experiment we ran in class on today closely resembles many previous

experiments run by researchers. A single Call Market is run for a known finite number of rounds. Traders are allowed to buy and sell, raising the possibility of speculation. The asset being sold is typically a risky security that pays a dividend in each round. If individuals are risk neutral, the price should be a constant over time. If individuals are risk adverse, prices should be bounded above by the expected value line.

• Ex ante, most economists would expect to see little trading in a market like this. However, in fact we typically see frenzied trading. Economists also would expect to see prices at or below the expected value. In fact, we often observe large bubbles – persistent pricing of the security above its fundamental value.

• It has been argued that such bubbles are also a feature of real world security markets. It is hoped that if we can understand how bubbles form in the laboratory, we can also understand how they form (and can be prevented) in real world financial markets.

Market institutionCall market

ID Bid QuantityBid

PriceOffer Price

Offer Quantity

Market Price

4 5 5 15 1 109 5 5 0 0 107 3 6 10 3 10

12 2 20 30 5 1013 4 12 21 6 106 2 15 23 2 105 1 0.2 0 0 108 5 10 17 6 103 1 0.39 1.01 1 10

10 3 7 8 2 101 2 3 0 0 102 7 7.1 7.2 6 10

11 2 1 2 1 10

Bid Quantity

Bid Price

Offer Price

Offer Quantity

Market Price

2 20 0 0 102 15 0 0 104 12 0 0 105 10 1.01 1 107 7.1 2 1 103 7 7.2 6 103 6 8 2 105 5 10 3 105 5 15 1 102 3 17 6 102 1 21 6 101 0.39 23 2 101 0.2 30 5 10

First period behavior

What is the theory?

• What should you bid according to theory? • What theory?• Fundamental Value: F• Data Parameters:

– Interest (i) for cash holding: 10%– random dividend (D) for shares: $0.4; prob 0.4 or $1; 0.6=> EV:0.7

– Redemption value of $7 at the end– Everyone holds 6 shares and $50.– Being indifferent between holding shares and money:– F: D/i=0.7/0.10=7 because 0.1P=0.7 (P price to pay for share). – What is the fundamental value in each period if there is only

dividend of 0.7 and no interest and no redemption value?

Here you also see the fundamental value in each period

Data set of another group

Doubling the interest rate and the dividend

What is the reason for bubbles in these experiments

• What was the best strategy in our experiment• What did the person with the worst strategy do• What are the fundamental values in this experiment

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

5

10

15

20

25

30

Shares hold over time

Series1Series2Series3Series4Series5Series6Series7Series8Series9Series10Series11Series12Series13Market price

time

Shar

es

Market price

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

5

10

15

20

25

Shares hold over time

12345Market price

time

Shar

es

Market price

Fundamental traders; (winning) speculators

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

5

10

15

20

25

Shares hold over time

56789101112Market price

time

Shar

es

Market price

Bubbles in the Laboratory?: Non-rational bubbles

• Smith Suchaneck and Williams (SSW, Ecmta 1988) experimental design reliably generates asset price bubbles and crashes in a .nite horizon economy, thus ruling out rational bubble stories.

• T trading periods (typically T = 15) and 9-12 inexperienced subjects.• Each subject is initially endowed with various amount of cash and assets.

Assets are long-lived (T periods). Endowments, are ex-ante identical in expected value -there is no reason for trade!

• In each trading period, agents are free to buy or sell the asset. Trade takes place via a double auction, and bids and asks must obey standard improvement rules.

• For each unit of the asset held at the end of a trading period, the asset owner earns a dividend payment which is a uniform draw from a known distribution and has mean d. It is public knowledge that the fundamental value of an asset at the start of period t is given by:

Dufwenberg et al. AER 2005• 6 subjects play 10 periods of one market game; • the same market game with the same subjects is repeated again twice•In the fourth game 2 or 4 subjects are replaced by inexperienced subjects

Design:

2 or 4 new subjects Replacing old subjects

Lei, Noussair, and Plott – Research Question

• “Two possible explanations for the occurrence of bubbles are the “speculative hypothesis” and the “active participation hypothesis.” In the first, traders are hoping to take advantage of irrational individuals or other speculators to make a large profit through capital gains. In other words, they are market timing. As the end of the market approaches, the bubble inevitably collapses. (This hypothesis does not require the presence of irrational traders to generate a bubble. All that is needed is a failure of common knowledge of rationality. Think about the relationship between this and Nagel’s guessing game that we studied earlier this semester.) The second hypothesis focuses on the methodology. In most bubble experiments, the only activity available to subjects is trading. To the extent that the protocols encourage participation, subjects make unprofitable trades just to be doing something. In other words, bubbles are a subtle type of demand induced effect. Lei et al aim to test these two hypotheses, separately and in conjunction. “

• And they find that bubbles still exist.

Lei et al. (Ecmta 2001)Explore the boredom/experimenter demand hypothesis

• They consider two main treatment variables.• No-Spec treatment: Buyers and Sellers have distinct roles. In

particular, a buyer cannot resell his asset later in a 2-minute trading period at a higher price. This tests the greater-fool hypothesis that speculation is driving the results.

• Two-Market treatment: Two markets operate simultaneously. One is for a one-period asset Y; holders of this asset sell it to buyers in fixed roles. The other market is the standard 15-period asset of the laboratory bubble design; this asset could be traded (bought and sold) by all subjects.

• Main finding, neither treatment completely eliminates bubbles and crashes. Trading volume is much lower in the two-market treatment as compared with the standard one-market case.

Lei et al..s findings NoSpec/Spec illustrated

Lei et al. (Ecmta 2001)

Result

• Substantial bubbles are observed in the no-spec treatment, indicating that speculators are not needed for bubbles to form. The presence of sales that could not possibly be profitable (buying above the maximum possible dividend payoff or selling below the minimum possible dividend payoff) as well as excess volume indicate systematic errors in decision making.

Conclusion • It is possible to create bubbles in the lab even if fundamental values (FV) are

calculable. However, most subjects do not know how to calculate them in the beginning.

• Experience, precise knowledge about FV and common knowledge about it (e.g. all have the same experience level and it is known to all subjects etc.) helps avoid bubbles.

• Experiments make comparative statics (comparing different parameter constellation) very easy

• The beauty contest game is an excellent tool to demonstrate behavior when there is lack of rationality and common knowledge of rationality. The behavior can be structured by the so called level k model which includes heterogeneous types from random behavior, best reply to random (level 1), best reply to level 1…etc. until rational expectation (equilibrium play).

• The stock market is containing aspects of the beauty contest game as first pointed out by Keynes, as one has to form believes about the behavior of the others which translates into price forecasting.

Double oral auction (DOA)one of the beginnings of experimental

economics by Vernon Smith (1962)• V. Smith participated in a class room experiment in

Chamberlin’s graduate class• Buyers and sellers with induced values• Buyers and sellers found privately a match by walking around• Behavior did not converge to equilibrium • Many years later Smith constructed the double oral auction

• Side remark: our intro econ course in UPF teaches the basic concepts of competitive markets (with taxes, externalities, monopoly, minimum labor wages etc) in connection with the DOA in experiments and the theory. The effect is that students much deeper understand the underlying theory and its success and failures..

Double oral auction

• Induced reservation values for buyers and costs for sellers for a fictitious good

• Buyers put oral bits and sellers oral asks which are recorded on the Board, computer screen

• New bids >last posted bid; new asks < last posted ask

• If there is a match, i.e. a posted bid is higher than a posted ask then there is a match between the seller and buyer of this bid and ask: make a trade at a price between bid and ask.

Experimental implementation vs theory

• Incomplete information of demand and supply function by market participants

• No auctioneer• Few buyers and sellers

Research Question

• Smith’s experiments were designed to study the neo-classical theory of competitive markets. This is the simple model of supply and demand curves that every economics student learns in the first few lecture of principles.

• In spite of the importance of the competitive model to economics, there was little direct evidence prior to Smith’s work that the theory actually would work. – Field data is too dynamic to see if equilibrium is being achieved.– Chamberlin’s (1948) earlier work using a decentralized market

mechanism found that generally the prices were too low and the volumes too high as compared to competitive equilibrium predictions.

– Smith’s experiments were designed to give the theory its best chance to work – this reflects a desire to establish if there were any cases were the market would equilibrate as predicted by the theory.

• Smith was interested in studying what configurations of supply and demand were most (or least) likely to lead to equilibrium, and was also interested in the dynamics that led to equilibrium

This and the following slides are taken from the web“smithoverhead”

Initial Hypotheses

• Markets are expected to converge to the competitive equilibrium. – According to the “Walrasian” hypothesis, this convergence should be faster when there

is larger excess demand (or supply). So, for example, convergence should be faster in Test 2 than in Test 3.

– The “excess rent” hypothesis focuses on unrealizable profits at a price – the higher these are, the faster prices should adjust. [Historically, this has not been an important hypothesis.]

– Allowing more experience should speed up convergence, while changing market institutions should slow convergence.

Summary of Sessions

• The sessions focus primarily on the effect of vary the shape of the supply and demand curves. Some attention is also paid to the effect of changing market institutions and making traders more experienced..– Test 1: Basic supply and demand– Tests 2 and 3: Varies steepness of supply and demand curves without changing equilibrium price.

This allows Smith to study the process that leads to equilibrium.– Test 4: Flat supply curve. This leaves no surplus for the sellers. It is interesting to think of this in light

of much later experiments on equity in market games.– Test 5: Studies the effect of an increase in demand. Given that subjects don’t know how demand has

changed, you might expect this to disrupt convergence.– Test 6: Equilibrium gives a very large surplus to the sellers by using a supply curve that goes vertical.

Once again, this is interesting in light of the later experiments on market games.– Test 7: Very steep supply curve relative to the demand curve.– Test 8: Buyers were not allowed to make bids in early periods. This was supposed to simulate retail

markets. The question is whether this prevents convergence to equilibrium.– Test 9 and 10: Each individual is allowed to make two transactions, doubling the amount of

experience received. This is expected to speed convergence.

Results – Convergence to Equilibrium

• The double oral auctions tend to converge strongly towards equilibrium and achieve high levels of efficiency. For example, the results for Test 1 are shown top right. This is true even when either demand or supply shifts over time. See Test 5 results, bottom right.

• This is a very basic result, but is the most important result in the paper. Competitive market equilibrium is a central concept in economic theory, but generally can’t be observed in the field. These results prove that competitive equilibrium can work (but not that it must work).

Results – Uneven Splits of Surplus• Test 4 and Test 7 both feature uneven

(predicted) splits of the total surplus between buyers and sellers.

• These sessions are among the worst in terms of convergence to equilibrium. – Test 4 prices were consistently above

equilibrium, giving some surplus to the sellers.

– Test 7, which isn’t quite as extreme as Test 4, only converges very slowly to equilibrium. Prices are consistently too low (compared to competitive equilibrium) giving some surplus to buyers.

• These results can be viewed as a precursor to the sorts of results on fairness that we have studied extensively.

Excess rent =2

Excess rent =2 Excess rent =5

Excess rent =5

Excess rent =8

Excess rent =8

Copnvergence to equilibrium

Conclusions• While Smith draws many conclusions from the data, the most important

conclusion is the most basic one: “The most striking general characteristic of tests 1 – 3 5 – 7 9, and 10 is the remarkably strong tendency for exchange prices to approach the predicted equilibrium for each of these markets.”

• It must be remembered that Smith designed his experiments to give the theory its best chance. These experiments don’t establish that in general the theory of competitive equilibrium will have much predictive power.

• On a more general level, this paper played an important role in illustrating how controlled laboratory experiments let economists understand phenomena and theories that were hard to observe in the field. In the field, one never knows what the underlying supply and demand curves are, so you can never truly know that the competitive equilibrium has been achieved. In the lab, you can directly observe the emergence of equilibrium.

Further Research on Markets

• Smith’s general results on convergence have been replicated many times. DOA markets are remarkably good at converging to equilibrium under a wide variety of circumstances. This remains true even if supply and demand curves are shifting (although random shifts do worsen convergence).

• Convergence can be quite sensitive to market institutions. Seemingly small changes in the rules for queuing can substantially affect the speed of convergence. Larger changes in the institutions such as using a posted price market can greatly slow convergence, even leading to non-convergence in some cases.

• Market power has mixed effects on convergence to equilibrium. Holt, Langan, and Villamil (1986) find prices that are significantly above equilibrium when sellers have market power, but others have found little effect in DOA markets. More generally, the impact of market power is going to depend on the game being played. When a single individual can easily manipulate market prices or when institutions reduce competition among sellers, departures from equilibrium are more likely. Game theory does a fairly good job of predicting when departures from equilibrium are likely, although it does a poor job of predicting the size of these departures.