Limited Rationality

1

• Limited Rationality Strategic Interaction
• The Case of Money Illusion
•  
• Ernst Fehr
• University of Zurich and MIT
•  
• Jean Robert Tyran
• University of St. Gallen

2
Individual Level Anomalies Aggregate Outcomes

• Large body of evidence from individual
  decision-making experiments suggests that a large
  number of people violate standard rationality and
  selfishness assumptions
• Fairness preferences, Preference
  intransitivities, framing effects,
  overconfidence, updating of probabilities,
  hindsight bias, etc.
• When do deviations from rationality and
  selfishness at the individual level matter for
  aggregate outcomes?
• Question was at the heart of Vernon Smiths
  polemic against behavioral economics and
  Kahneman-Tversky-Thaler (JPE 1990).

3

• No general answer yet, but important pieces of
  evidence
• Double auctions with homogeneous, non-risky goods
• Myopic loss aversion (Gneezy, Kapteyn, Potters
  JF)
• Fairness (Fehr, Kirchsteiger Riedl QJE 1993,
  Fehr Falk JPE 1999)
•                  
• We look at money illusion
• Tobin (1972) An economic theorist can, of
  course, commit no greater crime than to assume
  money illusion.
• Economists dismissal of money illusion was not
  based on sound behavioral evidence but on beliefs
  in rationality.
• Individual level questionnaire evidence by
  Shafir, Diamond and Tversky QJE 1997
• Fehr and Tyran (AER 2001) provide behavioral
  evidence that money illusion has asymmetric
  effects on equilibrium adjustment depending on
  whether the shock is positive or negative.
• We started our research project on nominal
  intertia with the prejudice that money illusion
  is irrelevant.

4
What is Money Illusion?

• Leontief Money illusion prevails if supply and
  demand functions are not homogeneous of degree
  zero in all nominal prices.
• Intuition If the real incentive structure (the
  objective situation) remains unchanged the real
  decisions of an illusion-free individual remain
  unchanged, irrespective of the representation of
  the objective situation.
• Example Whether payoff information is available
  in nominal or in real terms does not affect the
  real decisions of an illusion-free individual.
• Money illusion as a framing effect

5
Evidence for Money Illusion 1

• Agell Bennmarker (2002) Representative survey
  of Swedish human resource managers.
• Assume hypothetically, that your enterprise is
  making a small surplus. There is no inflation and
  unemployment is high. There are many job seekers
  applying for a job at your unit. Under these
  circumstances you decide to propose a wage cut of
  5. How do you think that your employees would
  find this proposal?
• Acceptable 5.7
• Not acceptable 94.3
• Assume hypothetically, that your enterprise is
  making a small surplus. Inflation is 10 and
  unemployment is high. There are many job seekers
  applying for a job at your unit. Under these
  circumstances you decide to propose a wage
  increase of only 5. How do you think that your
  employees would find this proposal?
• Acceptable 49.6
• Not acceptable 50.4

6
Evidence for Money Illusion 2

• Fehr Götte (JME, forthcoming) Nominal wage
  rigidity in CH.

7
Fehr Götte - Are nominal wages downwardly
rigid?

• Switzerland has probably one of the most liberal
  labour laws among European countries.
• Unions are relatively weak and minimum wage laws
  absent or due to wage drift largely irrelevant.

8
Experimental Evidence for Money Illusion(Fehr
Tyran 2003)

• Experimental price setting game with groups of 5
  or six subjects.
• In each period subjects have to choose a nominal
  price between 1 and 30.
• Their payoff depends on their own price Pi and on
  the average price of the other subjects in the
  group P-i.
• Their real payoff ?i depends on their nominal
  payoff divided by P-i.
• Three symmetric equilibria a good one, an
  intermediate, a bad one
• At the end of each period information feedback
  about P-i.
• 2 Treatments
• Payoff tables with real payoffs
• Payoff tables with nominal payoffs
• In the absence of money illusion or beliefs about
  others money illusion the same equilibrium
  should be chosen regardless of the treatment
  condition.

9
Multiple Equilibria (Strategic Complementarity)
45-degree line
Bad stable equilibrium Low real payoffs High
nominal payoffs
Unstable equilibrium
Good stable equilibrium High real payoff Low
nominal payoff
10
Nominal Payoff Table
11
Real Payoff Table
12
Average Prices and Price Expectations over Time
13
Money Illusion or Beliefs about others Money
Illusion
14
Limited Rationality and Strategic Interaction

• Can we identify conditions under which money
  illusion has no effect on aggregate outcomes and
  conditions under which money illusion has effects
  on aggregate outcomes?
• Aggregate outcome in our case Extent of nominal
  inertia after a fully anticipated nominal shock
  in an environment with a unique money neutral
  equilibrium.
• When does money illusion retard adjustment
  towards the post-shock equilibrium?
• Strategic substitutes versus strategic
  complements (Haltiwanger Waldmann AER 1985, QJE
  1989, Russel and Thaler AER 1985, Akerlof and
  Yellen AER 1985)
• Paper is a contribution to the literature on the
  role of bounded rationality in strategic
  interactions and on the causes of nominal inertia
  

15
The Role of the Strategic Environment

• Assume agents are heterogeneous with respect to
  rationality.
• Agents with adaptive expectations under adjust
  nominal prices to a monetary shock.
• Strategic complements positive slope of the
  reaction function.
• ? Incentive "to follow the crowd", rational
  players also under adjust. ? Rational players
  multiply the effect of players with limited
  rationality.
•                       
• Strategic substitutes negative slope of the
  reaction function.
• ? Incentive to counteract, rational players also
  over adjust.
• ? Rational players mitigate the effect of
  players with limited rationality.
• Hypothesis A given amount of limited rationality
  has different effects in aggregate with different
  strategic environment.

16
Experimental Design

• n-player pricing game
• Pre- and post-shock phase exogenous,
  anticipated, negative nominal shock.
• Two treatments Strategic Complements (CT) vs.
  Strategic Substitutes (ST)
• Ceteris paribus variation slope of best reply is
  1 or 1
• Same (money-neutral) payoffs in and out of
  equilibrium
• Same incentives to choose best replies
• Same number of dominated strategies
• To isolate effect of strategic environment, avoid
  confound with alternative explanations
• no external frictions (informational,
  contractual, menu cost)
• sharp incentives to choose best replies (Akerlof
  and Yellen QJE 1985)
• collusion (efficient equilibrium)

17

• The real payoff for agent i is given by
• pi pi(Pi, P-i, M)
• Properties of payoff functions
• (i) Homogenous of degree 0 in all variables.
• (ii) Unique best reply for any P-i
• (iii) The best reply is weakly increasing (CT) or
  decreasing (ST) in P-i
• In addition, the functional specification implies
  that Nash-Equilibrium
• (iv) is unique for every M
• (v) is the only Pareto-efficient point in payoff
  space
• (vi) can be found by iterated elimination of
  strictly dominated strategies.

18
Experimental procedures and parameters

• Information about payoffs in matrix form. Nominal
  payoffs had to be deflated. We know from Fehr
  and Tyran (2001, AER) that money illusion
  prevails in this environment.
• n 4, Two types of agents.
• At t 15 Public information new payoff tables.
  These are based on M1 M0 / 2
• Predictions Equilibrium nominal average price
  Pre-shock 25, Post-shock 12.5.
• Exercises, pocket calculator.
• Decision screen Price decision, Expected average
  price.
• Information feedback after every period Actual
  average price, own real payoff.
• 76 subjects. Average earnings 24 approx. Total
  time 80 minutes.

19
Real Payoff Table Complements, post-shock, Type
x
20
Real Payoff Table Substitutes, post-shock, Type
x Average price of other firms
21
Nominal Payoff Table Complements, post-shock,
Type xAverage price of other firms
22
Nominal Payoff Table Substitutes, post-shock,
Type xAverage price of other firms
23
Results

• Is strategic complementarity a cause of nominal
  inertia? Figure 1
• Pronounced, long-lasting inertia in CT,
  overshooting in ST
• Significant deviation of average prices for 8
  periods in CT, for 0 periods in ST
• Distribution of individual pricing decisions
  Figure 2a, 2b
• Equilibrium also requires that individual actions
  are in equilibrium
• In period 16, about ¼ of subjects choose
  equilibrium prices in CT, about ¾ in ST.
• Best replies Figure 3a, 3b
• No difference in best reply-behavior
  (Expectations were truthful)
• BR-behavior cannot explain the difference in
  aggregate inertia across treatments

24
Results - continued

• Expectations Figure 4
• In period 16, average expectations are 8.0 units
  above equilibrium in CT, only 0.9 units in ST ?
  Difference in expectations is key
• Short-run non-neutrality of money Figure 5
• Inertia translates into income losses (look at
  difference, not absolute level)
• Simple Simulations Figure 6
• Illustrate how a given mix of adaptive and
  rational expectations translates into nominal
  inertia.
• Note, if all players are rational there should be
  not treatment differences.
• If all players have fully adaptive expectations
  equilibrium is reached in period 27 in both
  treatments ? HW predicts treatment positive
  difference in adjustment speed only when
  heterogeneity prevails.

25
Results - continued

• Individual Expectations Figure 7a, 7b
• Details of how adaptive expectations are formed
  don't matter in period 16 because of long periods
  of disequilibrium play before the shock.
• For t gt 16, adaptive players' expectations are
  shaped by responses of rational players
• In period 16, about 1/5 of subjects have approx.
  equilibrium expectations in CT, 4/5 in ST
• About 50 of subjects have fully adaptive
  expectations in CT, less than 5 in ST
• About three times as many have correct
  expectations in ST than in CT (42 vs. 15)

26
Figure 1 Nominal Average Prices over Time
Pre shock average price in equilibrium 25
Significant deviations for 8 post shock periods
under complements
No significant deviation for all post shock
periods
Post shock average price in equilibrium 12.5
27
Figure 2a Distribution of Individual Price
Choices in Period 16 (x-types)
Post shock equilibrium
Pre shock equilibrium
28
Figure 2b Distribution of Individual Price
Choices in Period 16 (y-types)
Post shock equilibrium price
Pre shock equilibrium price
29
Individual Adjustment towards Equilibrium
30
Figure 3a Actual Average Prices and Average Best
Reply for given Expectations Complements
Treatment (Periods 16-18)
31
Figure 3b Actual Average Prices and Average Best
Reply for given Expectations Substitutes
Treatment (Periods 16-18)
32
Figure 4 Average Price Expectations over Time
Significant deviations from equilibrium for 8
periods
33
Figure 5 Efficiency Losses during the Post-shock
Phase
34
Figure 6a Simulations of Price Adjustment with
Varying Numbers of Adaptive Players in the
Substitutes Treatment (ST)
35
Figure 6b Simulations of Price Adjustment with
Varying Numbers of Adaptive Players in the
Complements Treatment (CT)
36
Figure 7a Distribution of Individual Price
Expectations in Period 16 (x-types)
Post shock equilibrium expectation
Pre shock equilibrium expectation
37
Figure 7b Distribution of Individual Price
Expectations in Period 16 (y-types)
Post shock equilibrium expectation
Pre shock equilibrium expectation
38
Cognitive Hierarchy TheoryCamerer and Ho (2002)

• A large majority of players play the equilibrium
  and have equilibrium expectations in the ST
  whereas in the CT a majority has adaptive
  expectations and plays close to the pre-shock
  equilibrium.
• Can Cognitive Hierarchy Theory explain this?
• Players have decision rules based on different
  steps of reasoning.
• Step 0 players randomize across all available
  choices.
• Step 1 players take the actions of step 0 players
  into account and play best reply to this
  expectation.
• Step 2 players take the actions of step 0 and
  step 1 players into account and play best reply
  to this expectation.
• Note Step k players do not recognize that there
  are step h ? k players.
• f(k) e-??k/k! is the frequency of step k
  players.
• Model can explain a large number of data across
  different games. ? is generally between 1 and 2.

39
Cognitive hierarchy theory prediction for period
16 with ? 1.5 and the assumption that players
maximize nominal payoffs.

• Median is predicted remarkably well.
• Mean is predicted slightly less well.
• Distribution of actions is predicted less well,
  in particular in the substitutes treatment Step
  1 players have frequency f(1) e-??k/k! e-??
  34 for ? 1.5.
• 33 of the players are predicted to pick a price
  of 1 but this happens only in 7.5 of the cases.
• Therefore, the model predicts a much larger
  variance for ST.

40
Cognitive Hierarchy Prediction

• In the ST the CH-model predicts considerably more
  out of equilibrium actions relative to the actual
  frequency of equilibrium choices.
• Question Is the fraction of players with more
  thinking steps higher in the ST than in the CT?
• The best-fitting ? in the ST equals 2.7 whereas
  the best-fitting ? in the CT is only 0.55

0.5 relevant in the CT 2.5 relevant in the ST
Fraction of step 1 players 30 21
Fraction of step 2 players 7.6 26
Fraction of step 3 players 1.3 22
41
What drives the differences across treatments?

• CH-theory also implies that in the ST players
  appear to be more rational, i.e. they exhibit
  more steps of reasoning.
• Since expectations drive behavior the key
  question is Why do players in the CT have more
  backward looking, sticky, expectations although
• cost of deviations from best reply is identical
  across treatments
• cost of a given expectation error is identical
  across treatments?
• Conjecture adaptive expectations cause a much
  larger expectation error in the ST compared to
  the CT.
• Hence, adaptive expectations cause a much larger
  payoff loss in the ST.
• Error implied by adaptive expectations is more
  salient.

42
What drives the differences across treatments?
43
What drives the differences across treatments?

• If individual i expects that the average
  pre-shock price of the others will also be the
  average post-shock price, i chooses the price
  that corresponds to B in the CT and to B in the
  ST.
• If all individuals are fully adaptive in this
  way, the average price of the others will
  correspond to C in the CT and to C in the ST.
• Thus the expectation error is much higher in the
  ST.
• In the CT rational subjects who anticipate that
  others are adaptive choose a price that is much
  closer to the adaptive subjects price than in
  the ST.
• This is just another way of saying that it is
  much less costly to be adaptive in the CT
  compared to the ST (because to respond optimally
  one has to change behavior less relative to the
  adaptive players).

44
Summary

• Individual level money illusion exists.
• Individual learning does not suffice to rule out
  aggregate effects of money illusion.
• Strategic environment is key for the aggregate
  effects of money illusion.
• Pronounced, long-lasting nominal inertia with
  strategic complements
• Instantaneous adjustment under strategic
  substitutes.
• Strategic environment also strongly affects
  expectation formation Strategic substitutes
  render subjects more forward-looking probably
  because adaptive expectations are more costly
  under ST.
• ? important lesson for macroeconomics.
• Strategic environment is key for the aggregate
  effects of bounded rationality. There are
  conditions under which bounded rationality does
  not matter much for aggregate results.