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Bubbles in the Lab and
Double 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 institution
Call market
First period behavior
ID
Bid Quantity
4
9
7
12
13
6
5
8
3
10
1
2
11
5
5
3
2
4
2
1
5
1
3
2
7
2
Bid
Price
5
5
6
20
12
15
0.2
10
0.39
7
3
7.1
1
Offer
Price
15
0
10
30
21
23
0
17
1.01
8
0
7.2
2
Offer
Quantity
1
0
3
5
6
2
0
6
1
2
0
6
1
Market
Price
10
10
10
10
10
10
10
10
10
10
10
10
10
Bid
Quantity
Bid
Price
Offer
Price
Offer
Quantity
Market
Price
2
2
4
5
7
3
3
5
5
2
2
1
1
20
15
12
10
7.1
7
6
5
5
3
1
0.39
0.2
0
0
0
1.01
2
7.2
8
10
15
17
21
23
30
0
0
0
1
1
6
2
3
1
6
6
2
5
10
10
10
10
10
10
10
10
10
10
10
10
10
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
30
Shares hold over time
25
Series1
Series2
Market price
20
Series3
Series4
Series5
Shares
Series6
Series7
15
Series8
Series9
Series10
10
Series11
Series12
Series13
Market price
5
0
1
2
3
4
5
6
7
8
9
11
time
10
12
13
14
15
16
17
18
19
20
25
Shares hold over time
Fundamental traders;
(winning) speculators
20
Market price
1
15
Shares
2
3
4
5
10
Market price
5
0
1
2
3
4
5
6
7
8
9
11
time
10
12
13
14
15
16
17
18
19
20
25
Shares hold over time
20
Market price
5
6
15
Shares
7
8
10
11
9
10
12
Market price
5
0
1
2
3
4
5
6
7
8
9
11
time
10
12
13
14
15
16
17
18
19
20
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
Design:
• 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
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. (Ecmta 2001)
Lei et al..s findings NoSpec/Spec illustrated
Result
• Substantial bubbles are observed in the nospec 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.
Copnvergence to equilibrium
Excess rent =2
Excess rent =2
Excess rent =5
Excess rent =5
Excess rent =8
Excess rent =8
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.