Jekyll

1

• Jekyll Hyde
• Marie-Edith Bissey (Università Piemonte
  Orientale, Italy)
• John Hey (LUISS, Italy and University of York,
  UK)
• Stefania Ottone (Econometica, Università Milano
  Bicocca, Italy)

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Dynamic Inconsistencies

• Non-EU people may be dynamically inconsistent.
• Are such people aware of their dynamic
  inconsistency?
• If not, they presumably behave naively.
• If they are aware, how do they behave?
• Do they behave resolutely or sophisticatedly?

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Aims of the Experiment

• Inducing dynamic inconsistencies in the lab,
  taking into account the fact that dynamically
  inconsistent people are really several different
  selves.
• Check how people behave when facing dynamic
  inconsistencies.

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Jekyll Hyde

• We look at the way an individual makes his
  consumption/saving decision when the rate at
  which he discounts the future is not constant
  over time
• Jekyll and Hyde were two different people inside
  the same body.
• Each was aware of the other but they clearly
  had different preferences.
• As a whole Jekyll Hyde was a dynamically
  inconsistent person.

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The Context

• We analyse the behaviour of Jekyll Hyde (two
  different subjects) within the context of a
  simple life-cycle consumption/savings model.
• Each period Jekyll Hyde receives an income M
  which he/they can consume or save.
• They take it in turns to decide on consumption.
• Accumulated savings earn interest.

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The Model

• They both get utility out of consumption and both
  try to maximise expected discounted lifetime
  utility of consumption.
• They have different discount factors that of
  Hyde (1) lower than that of Jekyll (2).
• Objective (payment) function (where ?i is the
  discount factor of player i)
• u(c1) ?iu(c2) ?i2u(c3)
• where u(c) ?c.

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Naivety?

• Assuming naivety each ignores the other, or
  equivalently - assumes that the other uses the
  same discount factor as himself.
• The optimal solution is

and ? ?1 in odd periods ? ?2 in even periods

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Resoluteness?

• Assuming resoluteness the first player imposes
  the solution (how?)
• The optimal solution is

and ? ?1
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Sophistication?

• Assuming sophistication players take into
  account the behaviour of the other.
• We assume that Jekyll/Hyde
• receives income M each period
• can save at rate of return r.
• We assume that

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The solution (Sophistication)

• We can show that the optimal consumption strategy
  is given by

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Experimental Design (I)

• 2n subjects and n projects.
• In each project there is an odd player - who
  plays in odd periods and has the lower continuing
  probability...
• ...and an even player who plays in even periods
  and has the higher continuing probability.
• The session as a whole has an earthquake which
  occurs with probability e. When the earthquake
  happens the whole session finishes.
• Player i has a continuing probability equal to
  his or her ?i pi - e. If does not continue,
  exits the project.
• When a player exits from a project he or she is
  re-assigned to a new project in which he or she
  has not been before (if there is a space).
• A subject may change project and role several
  times during the experiment...
• ... and may not be in a project.

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Experimental Design (II)

• Each project is endowed with a given stock of
  wealth in tokens.
• Each period the subject chooses how much of his
  accumulated wealth to convert into money - the
  conversion scale pence ?(conversion)
• Payment for each period to both players is the
  converted value.
• Subjects paid the total of all these payments
  over the duration of the session.  

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Experimental Design (Implications)

• No participant will ever find him or herself in
  any particular project more than once. Thus the
  way a participant behaves in any one project
  cannot affect the earnings that he or she gets
  from any other project ?participants should
  consider each project as completely independent
  of any other project that he or she may be in.
• Each period in each project contributes to the
  determination of the final payment.
• Jekylls behavior influences Hydes payoff and
  vice-versa.
• Unconverted tokens left when the experiment
  finishes become worthless.

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Experimental Design (Parameters)

• T1. ?1 0.85 and ?2 0.85
• T2. ?1 0.82 and ?2 0.85
• T3. ?1 0.85 and ?2 0.88
• T4. ?1 0.82 and ?2 0.88
• Note that Treatment 1 is not a case of dynamic
  inconsistency since both players have the same
  stopping probability.
• M 100
• r 1.25
• e 0.02
• 10 pounds show-up fee

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Experimental Procedure

• Overall, 106 subjects. 26 players in T1, 28
  subjects both in the T2 and in T3, 24 in T4
• 2 hours per session
• Average payoff 13 pounds
• Written instructions
• Power Point presentation with sample screens
• Table with conversion scale and calculator on the
  screen
• Control Questions
• Questionnaire

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Odd Participant Odd period
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Even participant Odd period
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Example of control questions

• A) You are in project 2. You are the odd
  participant. Your partner is the even
  participant. At the end of each period, what is
  the chance that you exit the project?
• 10
• 13
• 20
• At the moment, the stock of tokens associated
  with project 2 is 1600. It is your turn and you
  decide to convert 36 tokens.
• How many pence do you earn?
• 6
• 36
• 72
• How many pence does your partner earn?
• 0
• 6
• 36

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The Optimal apcs
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Results (I)

• Result 1. It is generally true that the subject
  with the lower continuing probability has a
  higher apc.
• Actual apcs

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Results (II)

• Result 2. Naïve fits better during the first
  periods while, over time, Sophisticated shows a
  better performance.

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Mean absolute deviations from optimal
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Results (III)

• Result 3. The treatment effects are not in
  accordance with our theory

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Results (IV)

• Players play erratically there is a big
  difference between different subjects.
• Some understand the nature of the problem and try
  and save.
• Others do not understand and consume all or most
  every period.
• Some subjects realise that there is a trade-off
  the more you consume now the higher the present
  utility, the less you consume now the higher the
  utility in the future. They (probably) cannot
  find the correct trade-off, so they consume in
  some periods and save in others.
• Players are influenced by the time effect and
  their previous experience.

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Some examples of actual play

• From treatments 1, 2 and 4.
• The person with the higher stopping probability
  plays in the odd periods.
• The green graph is what they did.
• The black graph is the optimal strategy.
• The solid red line is the naive response of the
  player in the odd periods.
• The solid blue line is the naive response of the
  player in the even periods.
• The dashed red line is the average response of
  the players in the odd periods.
• The dashed blue line is the average response of
  the players in the even periods.
• The numbers at the top indicate the subject.

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Further analysis

• Random effects tobit regression ? time and the
  fact of being in a new project
• Correlation between subjects decisions and
  partners decisions ? 25 players over 106

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Main conclusions

• We need a good analysis of data!

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Further research

• Analyse the behavior of each player in each
  project and try and define a trend for each
  player over time.
• Why is there so much noise in the data?
• Since subjects do not know with whom they are
  playing it may be best to assume an irrational
  partner?

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• Thank you