Graduate Experimental Economics

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Graduate Experimental Economics

• Lecture 8
• John Hey

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Sequential Markets and Markets with Private
Information

• The conclusion from many experiments is that,
  with the double auction mechanism, markets
  converge fast to the competitive equilibrium.
• Here we see if it is true in more complicated
  contexts.
• Hey J D and Di Cagno D, "Sequential Markets An
  Experimental Investigation of Clower's Dual
  Decision Hypothesis", Experimental Economics, 1,
  63-87, 1998.
• Hey J D and Morone A, "Do Markets Drive out
  Lemmings (or Vice Versa)?", Economica, 71,
  637-659, 2004.
• Note that we concentrate more on the experimental
  procedures than in analysing the results.

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Sequential Markets

• This experiment was to investigate Clowers Dual
  Decision Hypothesis (reference in Hey and Di
  Cagno).
• If agents have to trade sequentially...
• first sell their labour and then buy goods
• ...this sequentiality may prevent convergence to
  the competitive equilibrium...
• may cause unemployment.
• Money buys goods and goods buy money but goods
  do not buy goods.

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Towards a Laboratory Implementation 1

• Two Markets (morning and afternoon)
• Two Types of Agent (Type 1 and Type 2)
• Labourers and Capitalists
• Two Goods (X and Y)
• Labour and Capital
• Type 1 endowed with (s of) Good X
• Type 2 endowed with (t of) Good Y

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Towards a Laboratory Implementation 2

• In the morning the market for Good X opens and
  Type 1 agents can sell the good and Type 2 agents
  can buy it.
• In the afternoon the market for Good Y opens and
  Type 1 agents can buy the good and Type 2 agents
  can sell it.
• In the evening profits are calculated.

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Incentive Mechanism

• Let x and y denote the amounts of goods X and Y
  with which the subject ends the day.
• Then the subject is paid an amount
• Axay1-a
• Note that if a subject does not trade then their
  payment is zero.
• Different A and a values for different types.

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Competitive Equilibrium

• Let p and q denote the (absolute) prices of Goods
  X and Y.
• Type 1s and Type 2s demands are
• Equilibrium requires

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Other Experimental Details

• We need money in the experiment to faciliate
  trade but it has no value in itself.
• All subjects endowed with experimental money at
  the beginning. Got new endowments of the relevant
  good each period but no new money.
• Problem with no trading if fixed end point!
• So number of periods random.

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Mean Earnings
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Mean End holdings Type 1
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Conclusions

• Standard deviation of prices does not converge to
  zero.
• Absolute prices vary from session to session.
• Relative prices do not converge to the
  equilibrium usually somewhat lower, but
  confused by focal point effect.
• Mechanism very noisy.

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Clearing House Mechanism

• Each buyer puts in a (p,q) bid and each seller a
  (p,q) ask. Then the computer draws the implied
  demand and supply schedule and finds the
  equilibrium.

Buyer 1 (4? 4) Buyer 2 (3? 3) Buyer 3 (2?
2) Seller 1 (1? 1) Seller 2 (2? 2) Seller
3 (3? 3)
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Lemmings

• This is an experiment that combines the herding
  literature with the market literature.
• In the herding literature, because people follow
  others, they may all end up doing the wrong
  thing.
• We wanted to see if this was a possible
  explanation of bubbles in markets.

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Bickhchandani Herding Model(reference in Hey and
Morone)

• There are two possible states of the world W and
  B.
• There is a prize for guessing correctly.
• Sequentially subjects get a private signal and
  can observe the guesses of the previous subjects
  and then guess.
• Signals, w and b, which are noisy, for example
  P(Ww)2/3 P(Bw)1/3
  P(Wb)1/3 P(Bb)2/3.

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What the Model Predicts

• Even if the true state of the world is W people
  may all end of guessing B, because of the effect
  of combining private information with public
  decisions.
• We wanted to see if this was a possible
  explanation of bubbles.
• First we need to translate the problem into a
  market context.

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A Market with Private Information

• An asset which pays a dividend D at the end of
  the period. D is 0 or d each with prob ½.
• Agents endowed with units of the asset and money.
• Can trade assets for money using Double Auction
  mechanism.
• Can buy, at cost c, private signals, s, which
  take the value 0 or 1. They are noisy
• P(s1Dd)p P(s0D0)1-p
• P(s1D0)q P(s0D0)1-q

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Payment

• Subjects start each period with M0 in money and
  N0 assets.
• If they buy n signals at a cost of c per signal
  and end the period with M in money and N assets,
  and the dividend is d...
• ...their profit is Nd nc (M-M0)
• Total payment is their total profits over all
  (10) periods of the experiment.

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Theory

• What should happen?
• If information is aggregated correctly then the
  market price of the asset should converge to the
  true value of the dividend.
• But how and why?
• Notice that there is only one obvious symmetric
  equilibrium...
• ...do nothing!

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Experimental Detail

• 15 subjects in a session, endowed with 10 (at
  the start) and 10 units of the asset each period.
• d was either 0p or 10p.
• 4 practice rounds and 10 real rounds.
• Programmed in Z-tree.
• 4 treatments parameters as in table.1 session
  of Treatments 1 and 2 and 2 sessions of
  Treatments 3 and 4.

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Results

• There is a lot of activity.
• There is a lot of noise in the data (perhaps
  because of the trading mechanism).
• Generally, however, the price converged to the
  correct price (the dividend)...
• ...though there were two sessions in which it did
  not, one a genuine herd and the other caused by
  one misled subject.

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Conclusion

• We have slight evidence that herding behaviour
  can lead to a bubble...
• ...where subjects who have not bought signals
  follow others who have.
• The problem is that the data is very noisy
  because of the market mechanism (double auction)
  and we are just about to repeat it with the
  Clearing House mechanism.

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