Experimental Economics 2000

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Experimental Economics 2000

• Lecture 6
• Herding Models

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Why herding of interest

• It seems there are markets in which people follow
  what others are doing, independently of their own
  private information
• Also non-market contexts - consider, for example,
  the two restaurants example of Banerjee
• More generally do markets aggregate information
  correctly?

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Herding models in the literature

• Banerjee, A. (1992), A Simple Model of Herd
  Behavior, Quarterly Journal of Economics, 107,
  797-817.
• Bichchandani, S., Hirshleifer, D. and Welch, I.
  (1992), A Theory of Fads, Fashion and Cultural
  Change as Informational Cascades, Journal of
  Political Economy, 100, 992-1026.

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Banerjee model

• Winning number from uniform on 0,1
• All who guess winning number get prize
• Players move sequentially
• Probability of getting a signal is a
• Probability signal is winning number is b
• With probability (1-b) signal is from 0,1
• Players observe others guesses but not signals

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Banerjees Assumptions

• A if a player has no signal and all have
  previously chosen 0 they must choose 0
• B if a player is indifferent between following
  their signal and following someone elses choice
  they follow signal
• C if a player is indifferent between following
  two or more players they choose the highest
  previous choice

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Crucial lemma (Lemma 1)

• If the first and second players have both chosen
  the same the third player should choose to follow
  them independently of their own signal
• this means that once a herd has started it will
  not be broken
• This lemma holds irrespective of the values of
  the key parameters a and b

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Proof of Crucial Lemma 1

• Suppose players 1 and 2 have chosen i and player
  3 gets signal j, then the probability that i is
  the winning number is
• a3b2(1-b) a2b(1-b)(1-a)/probH
• and the probability that j is the winning number
  is
• a2b(1-b)(1-a)/probH
• where H is the event stated at the top

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Bickhchandani et al paper

• Two urns A and B - one the chosen urn
• In A a proportion p of black balls in B a
  proportion (1-p) of black balls
• Players move sequentially
• Each get private signal - a ball drawn at random
  from the chosen urn
• All players who guess the chosen urn get a prize

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Bickhchandani et al results

• As with Banerjee the key result is that a player
  may optimally follow previous players guesses
  rather than follow their own private signal - in
  which case a herd or a cascade results
• e.g. p 2/3. You get a white ball and think it
  is from Urn B - but if the previous (two) players
  have chosen Urn A..?

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Two experimental studies

• On Banerjee Allsopp, L. and Hey, J.D. (200),
  Two Experiments to Test a Model of Herd
  Behaviour, Experimental Economics, forthcoming.
• On Bikhchandani et al Anderson, L. R. and Holt,
  C.A. (1997), Informational Cascades in the
  Laboratory, American Economic Review, 87,
  847-862.

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Allsopp and Hey

• Two experimental treatments (1) with Assumption
  A (2) without Assumption A
• Note - general theoretical results for treatment
  (2) not available
• What about Assumptions B and C?

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Allsopp and Hey

• 0,1 replaced by 1,2,3,4,5,6,7,8,10
• 7 subjects
• 4 sessions of 10 rounds each
• repetition for learning
• different sessions with different values for the
  key parameters a and b a 1/4 and 3/4
  combined with b 1/4 and 3/4

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Prop. of rounds in which Banerjee strategy played
- T1
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Prop. of rounds in which Banerjee strategy played
- T2
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Allsopp Hey conclusions

• With assumption A, herding less frequent than
  predicted - more individuality
• Volatility within rather than between rounds
• Without assumption A, herding more frequent than
  with assumption A
• large number of broken runs

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Anderson Holt

• p 2/3
• 72 subjects, 5 participation fee - average
  earnings about 20
• session consisted of 15 periods and lasted about
  90 minutes - 2 for correct guess

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Anderson Holt

• Summary of results with symmetric set-up
• Periods with cascade activity
  normal 28
  reverse 13
• Periods where cascades were possible but did not
  form
  normal 10
  reverse 8

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Anderson Holt

• Econometric analysis of errors story - errors
  in calculating the true posteriors
• About half as many wrong as right cascades
• Errors story implies that players tend to follow
  their own signals too much about 1/3 of the
  subjectsrely on simple counts of signals rather
  than Bayes rule

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Conclusions

• Herding models explain some of the data
• There is a tendency for players to follow their
  own private information too much
• This suggests that there will be more volatility
  and fewer herds/cascades (both correct and
  incorrect) than the two theories suggest
• Two difficult to work out the posteriors?