limited rationality & strategic interaction the case of money illusion ernst fehr
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Limited Rationality & Strategic Interaction The Case of Money Illusion Ernst Fehr University of Zurich and MIT Jean Robert Tyran University of St. Gallen. Individual Level Anomalies & Aggregate Outcomes. - PowerPoint PPT PresentationTRANSCRIPT
Limited Rationality & Strategic Interaction
The Case of Money Illusion
Ernst Fehr
University of Zurich and MIT
Jean Robert Tyran
University of St. Gallen
• 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 Smith’s polemic against behavioral economics and Kahneman-Tversky-Thaler (JPE 1990).
Individual Level Anomalies & Aggregate Outcomes
• 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.
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
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%
Evidence for Money Illusion 2• Fehr & Götte (JME, forthcoming): Nominal wage rigidity in CH.
Fra
ctio
n
Figure 1: Distribution of Nominal Wage ChangesEvidence from Personnel Files
Firm A, 1993 - 1998 (N=35,779)
-.4 -.2 -.1 0 .1 .2 .4
0
.1
.2
.3
Firm B, 1984 - 1998 (N=20,236)
-.4 -.2 -.1 0 .1 .2 .4
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.
Panel (d): The Extent of Nominal Wage Rigidities over Time
Estimates from SIF
0
0.25
0.5
0.75
91 92 93 94 95 96 97
Fraction ofWorkers Affected
Frequency of Cuts
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.
Multiple Equilibria (Strategic Complementarity)
Own Price
A
B
C
Average Price
Bad stable equilibriumLow real payoffs High nominal payoffs
Good stable equilibriumHigh real payoffLow nominal payoff
Unstable equilibrium
45-degree line
Nominal Payoff TableAppendix A
Table A1: Payoff table in the nominal treatments Average price of other firms
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 selling price
1 13 11 11 15 19 15 13 12 11 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
2 24 25 19 25 32 22 16 14 12 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
3 13 48 44 58 73 37 23 16 13 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
4 6 25 84 112 140 84 39 22 15 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
5 3 11 44 58 73 162 88 37 19 12 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
6 2 7 19 25 32 84 168 80 29 12 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
7 2 5 11 15 19 37 88 152 59 14 13 14 15 16 17 18 19 19 20 21 22 23 24 25 26 27 28 29 30 31
8 2 4 8 10 13 22 39 80 108 18 14 15 15 16 17 18 19 20 21 22 23 24 25 25 26 27 28 30 31 32
9 1 3 6 8 10 15 23 37 59 30 17 16 17 17 18 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
10 1 3 5 7 9 12 16 22 29 50 22 19 18 18 19 19 20 21 21 22 23 24 25 26 27 28 29 30 31 32
11 1 3 5 6 8 10 13 16 19 30 39 26 22 21 20 20 21 21 22 23 24 24 25 26 27 28 29 30 31 32
12 1 3 4 6 7 9 11 14 15 18 66 48 31 25 23 22 22 22 23 23 24 25 26 27 27 28 29 30 31 32
13 1 2 4 5 7 8 10 12 13 14 39 84 59 36 29 25 24 24 24 24 25 25 26 27 28 29 30 31 32 33
14 1 2 4 5 6 8 9 11 12 12 22 48 104 70 42 32 28 26 26 26 26 26 27 28 28 29 30 31 32 33
15 1 2 4 5 6 8 9 10 11 12 17 26 59 126 83 48 36 31 29 28 27 27 28 28 29 30 31 32 33 34
16 1 2 4 5 6 7 9 10 11 11 14 19 31 70 150 96 54 40 34 31 30 29 29 29 30 30 31 33 33 34
17 1 2 3 5 6 7 8 9 10 11 13 16 22 36 83 176 111 61 44 36 33 32 31 31 31 31 32 34 34 35
18 1 2 3 5 6 7 8 9 10 11 12 15 18 25 42 96 204 126 68 48 40 36 34 33 32 32 34 35 35 36
19 1 2 3 4 6 7 8 9 10 10 12 14 17 21 29 48 111 234 143 76 53 43 38 36 35 34 35 37 37 37
20 1 2 3 4 6 7 8 9 10 10 12 13 15 18 23 32 54 126 266 160 84 57 46 41 38 36 38 39 39 38
21 1 2 3 4 5 7 8 9 10 10 12 13 15 17 20 25 36 61 143 300 179 92 62 49 43 40 42 43 42 41
22 1 2 3 4 5 7 8 9 10 10 12 13 14 16 19 22 28 40 68 160 336 198 101 67 53 46 48 50 46 44
23 1 2 3 4 5 6 8 9 9 10 11 13 14 16 18 20 24 31 44 76 179 374 219 110 73 57 59 61 54 49
24 1 2 3 4 5 6 7 8 9 10 11 13 14 15 17 19 22 26 34 48 84 198 414 240 120 78 81 84 67 57
25 1 2 3 4 5 6 7 8 9 10 11 12 14 15 17 18 21 24 29 36 53 92 219 456 263 130 135 140 93 71
26 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 22 26 31 40 57 101 240 500 286 297 308 157 99
27 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 19 21 24 28 33 43 62 110 263 546 567 588 348 168
28 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 19 21 23 26 30 36 46 67 120 286 297 308 667 375
29 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 19 20 22 24 27 32 38 49 73 130 135 140 348 720
30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 17 18 20 21 23 26 29 34 41 53 78 81 84 157 375
Real Payoff TableAverage price of other firms
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 selling price
1 13 6 4 4 4 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 24 13 6 6 6 4 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 13 24 15 15 15 6 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
4 6 13 28 28 28 14 6 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
5 3 6 15 15 15 27 13 5 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
6 2 4 6 6 6 14 24 10 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
7 2 3 4 4 4 6 13 19 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
8 2 2 3 3 3 4 6 10 12 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
9 1 2 2 2 2 3 3 5 7 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
10 1 2 2 2 2 2 2 3 3 5 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
11 1 2 2 2 2 2 2 2 2 3 4 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
12 1 2 1 2 1 2 2 2 2 2 6 4 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
13 1 1 1 1 1 1 1 2 1 1 4 7 5 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
14 1 1 1 1 1 1 1 1 1 1 2 4 8 5 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1
15 1 1 1 1 1 1 1 1 1 1 2 2 5 9 6 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1
16 1 1 1 1 1 1 1 1 1 1 1 2 2 5 10 6 3 2 2 2 1 1 1 1 1 1 1 1 1 1
17 1 1 1 1 1 1 1 1 1 1 1 1 2 3 6 11 7 3 2 2 2 1 1 1 1 1 1 1 1 1
18 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 6 12 7 4 2 2 2 1 1 1 1 1 1 1 1
19 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 7 13 8 4 3 2 2 2 1 1 1 1 1 1
20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 7 14 8 4 3 2 2 2 1 1 1 1 1
21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 8 15 9 4 3 2 2 2 2 2 1 1
22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 4 8 16 9 4 3 2 2 2 2 2 1
23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 4 9 17 10 5 3 2 2 2 2 2
24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 4 9 18 10 5 3 3 3 2 2
25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 4 10 19 11 5 5 5 3 2
26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 4 10 20 11 11 11 5 3
27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 5 11 21 21 21 12 6
Average Prices and Price Expectations over Time
123456789
101112131415161718192021222324252627282930
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Prices in the NH
Expectations in the NH
Expectations in the RH
Prices in the RH
Money Illusion or Beliefs about others’ Money Illusion
123456789
101112131415161718192021222324252627282930
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Period
Nominal treatmentwith humanopponents (NH)
Nominal treatmentwith computerizedopponents (NC)
Real treatment withcomputerizedopponents (RC)
Real treatment withhuman opponents(RH)
• 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
Limited Rationality and Strategic Interaction
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.
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)
• The real payoff for agent i is given by:
i = i(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.
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.
Real Payoff Table: Complements, post-shock, Type x
Average price of other firms selling price
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 39 39 20 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 20 20 39 20 9 5 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 9 9 20 39 20 9 5 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
4 5 5 9 20 39 20 9 5 3 3 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
5 3 3 5 9 20 39 20 9 5 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
6 2 3 3 5 9 20 39 20 9 5 3 3 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1
7 2 2 2 3 5 9 20 39 20 9 5 3 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
8 2 2 2 3 3 5 9 20 39 20 9 5 5 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1
9 2 2 2 2 2 3 5 9 20 39 20 9 9 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1
10 1 2 2 2 2 3 3 5 9 20 39 20 20 20 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1
11 1 2 1 2 2 2 2 3 5 9 20 39 39 39 20 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1
12 1 2 1 2 2 2 2 3 3 5 9 20 20 20 39 20 9 5 3 2 2 2 2 1 1 1 1 1 1 1
13 1 2 1 2 1 2 2 2 2 3 5 9 9 9 20 39 20 9 5 3 2 2 2 2 2 2 2 2 2 2
14 1 1 1 1 1 2 2 2 2 3 3 5 5 5 9 20 39 20 9 5 3 2 2 2 2 2 2 2 2 2
15 1 1 1 1 1 1 1 2 2 2 2 3 3 3 5 9 20 39 20 9 5 3 2 2 2 2 2 2 2 2
16 1 1 1 1 1 1 1 2 2 2 2 3 2 2 3 5 9 20 39 20 9 5 3 2 2 2 2 2 2 2
17 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 5 9 20 39 20 9 5 3 3 3 3 3 3 3
18 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 5 9 20 39 20 9 5 5 5 5 5 5 5
19 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 5 9 20 39 20 9 9 9 9 9 9 9
20 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 2 2 3 5 9 20 39 20 20 20 20 20 20 20
21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 5 9 20 39 39 39 39 39 39 39
22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 5 9 20 20 20 20 20 20 20
23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 5 9 9 9 9 9 9 9
24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 5 5 5 5 5 5 5
25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3
26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2
27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Real Payoff Table: Substitutes, post-shock, Type x Average price of other firms
selling price
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 5 9 20 39 39 39 39 39 39 39
2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 2 2 3 5 9 20 39 20 20 20 20 20 20 20
3 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 5 9 20 39 20 9 9 9 9 9 9 9
4 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 5 9 20 39 20 9 5 5 5 5 5 5 5
5 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 5 9 20 39 20 9 5 3 3 3 3 3 3 3
6 1 1 1 1 1 1 1 2 2 2 2 3 2 2 3 5 9 20 39 20 9 5 3 2 2 2 2 2 2 2
7 1 1 1 1 1 1 1 2 2 2 2 3 3 3 5 9 20 39 20 9 5 3 2 2 2 2 2 2 2 2
8 1 1 1 1 1 2 2 2 2 3 3 5 5 5 9 20 39 20 9 5 3 2 2 2 2 2 2 2 2 2
9 1 2 1 2 1 2 2 2 2 3 5 9 9 9 20 39 20 9 5 3 2 2 2 2 2 2 2 2 2 2
10 1 2 1 2 2 2 2 3 3 5 9 20 20 20 39 20 9 5 3 2 2 2 2 1 1 1 1 1 1 1
11 1 2 1 2 2 2 2 3 5 9 20 39 39 39 20 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1
12 1 2 2 2 2 3 3 5 9 20 39 20 20 20 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1
13 2 2 2 2 2 3 5 9 20 39 20 9 9 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1
14 2 2 2 3 3 5 9 20 39 20 9 5 5 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1
15 2 2 2 3 5 9 20 39 20 9 5 3 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
16 2 3 3 5 9 20 39 20 9 5 3 3 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1
17 3 3 5 9 20 39 20 9 5 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
18 5 5 9 20 39 20 9 5 3 3 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
19 9 9 20 39 20 9 5 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
20 20 20 39 20 9 5 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
21 39 39 20 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
22 20 20 9 5 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
23 9 9 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
24 5 5 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
25 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
26 2 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
27 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
28 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
29 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
30 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Nominal Payoff Table: Complements, post-shock, Type x
Average price of other firms selling price
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 39 78 60 34 24 19 17 16 16 16 16 17 18 19 20 20 21 21 22 23 24 25 25 26 27 28 30 31 32 33
2 20 40 117 80 43 29 23 20 18 18 17 18 19 20 21 21 21 22 23 23 24 25 26 27 28 29 30 31 32 33
3 9 17 60 156 100 52 34 26 22 20 19 19 21 22 22 22 22 23 23 24 25 25 26 27 28 29 30 31 32 34
4 5 10 26 80 195 120 60 38 29 25 22 21 23 25 24 23 23 24 24 24 25 26 26 27 28 29 31 32 33 34
5 3 6 14 34 100 234 140 69 43 32 27 24 26 28 26 25 25 25 25 25 26 26 27 28 29 30 31 32 33 34
6 2 5 10 19 43 120 273 160 77 48 36 30 32 34 30 28 27 26 26 26 27 27 27 28 29 30 32 33 34 35
7 2 4 7 13 24 52 140 312 180 86 53 39 42 45 37 32 30 29 28 28 28 28 28 29 30 31 32 33 35 36
8 2 4 6 10 16 29 60 160 351 200 95 58 62 67 49 39 34 32 30 29 29 29 29 29 31 32 33 34 35 37
9 2 3 5 8 12 19 34 69 180 390 220 103 112 120 72 52 42 36 33 32 31 30 30 30 32 33 34 35 37 38
10 1 3 5 7 10 15 23 38 77 200 429 240 260 280 129 77 55 44 39 35 33 32 32 31 33 34 35 37 38 39
11 1 3 4 6 9 12 17 26 43 86 220 468 507 546 300 138 82 58 47 41 37 35 34 33 34 36 37 39 40 41
12 1 3 4 6 8 11 14 20 29 48 95 240 260 280 585 320 146 86 61 49 43 39 36 35 37 38 40 41 42 44
13 1 3 4 6 7 10 12 16 22 32 53 103 112 120 300 624 340 155 91 65 52 45 40 38 40 41 43 44 46 48
14 1 2 4 5 7 9 11 14 18 25 36 58 62 67 129 320 663 360 163 96 68 54 47 42 44 46 48 49 51 53
15 1 2 4 5 7 8 10 13 16 20 27 39 42 45 72 138 340 702 380 172 101 71 57 49 51 53 55 57 59 61
16 1 2 4 5 6 8 10 12 14 18 22 30 32 34 49 77 146 360 741 400 181 106 74 59 62 64 66 69 71 74
17 1 2 4 5 6 8 9 11 13 16 19 24 26 28 37 52 82 155 380 780 420 189 110 78 81 84 87 91 94 97
18 1 2 3 5 6 7 9 10 12 15 17 21 23 25 30 39 55 86 163 400 819 440 198 115 120 125 130 134 139 144
19 1 2 3 5 6 7 9 10 12 14 16 19 21 22 26 32 42 58 91 172 420 858 460 206 215 224 232 241 249 258
20 1 2 3 5 6 7 8 10 11 13 15 18 19 20 24 28 34 44 61 96 181 440 897 480 500 520 540 560 580 600
21 1 2 3 4 6 7 8 10 11 13 14 17 18 19 22 25 30 36 47 65 101 189 460 936 975 1014 1053 1092 1131 1170
22 1 2 3 4 6 7 8 9 11 12 14 16 17 18 21 23 27 32 39 49 68 106 198 480 500 520 540 560 580 600
23 1 2 3 4 6 7 8 9 11 12 13 15 16 18 20 22 25 29 33 41 52 71 110 206 215 224 232 241 249 258
24 1 2 3 4 5 7 8 9 10 12 13 15 16 17 19 21 23 26 30 35 43 54 74 115 120 125 130 134 139 144
25 1 2 3 4 5 7 8 9 10 11 13 14 16 17 18 20 22 25 28 32 37 45 57 78 81 84 87 91 94 97
26 1 2 3 4 5 7 8 9 10 11 13 14 15 16 18 20 21 24 26 29 33 39 47 59 62 64 66 69 71 74
27 1 2 3 4 5 6 8 9 10 11 12 14 15 16 18 19 21 23 25 28 31 35 40 49 51 53 55 57 59 61
28 1 2 3 4 5 6 8 9 10 11 12 14 15 16 17 19 20 22 24 26 29 32 36 42 44 46 48 49 51 53
29 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18 20 21 23 25 28 30 34 38 40 41 43 44 46 48
30 1 2 3 4 5 6 7 9 10 11 12 13 14 15 17 18 20 21 23 24 27 29 32 35 37 38 40 41 42 44
Nominal Payoff Table: Substitutes, post-shock, Type x
Average price of other firms selling price
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1 2 3 4 6 7 8 10 11 13 14 17 18 19 22 25 30 36 47 65 101 189 460 936 975 1014 1053 1092 1131 1170
2 1 2 3 5 6 7 8 10 11 13 15 18 19 20 24 28 34 44 61 96 181 440 897 480 500 520 540 560 580 600
3 1 2 3 5 6 7 9 10 12 14 16 19 21 22 26 32 42 58 91 172 420 858 460 206 215 224 232 241 249 258
4 1 2 3 5 6 7 9 10 12 15 17 21 23 25 30 39 55 86 163 400 819 440 198 115 120 125 130 134 139 144
5 1 2 4 5 6 8 9 11 13 16 19 24 26 28 37 52 82 155 380 780 420 189 110 78 81 84 87 91 94 97
6 1 2 4 5 6 8 10 12 14 18 22 30 32 34 49 77 146 360 741 400 181 106 74 59 62 64 66 69 71 74
7 1 2 4 5 7 8 10 13 16 20 27 39 42 45 72 138 340 702 380 172 101 71 57 49 51 53 55 57 59 61
8 1 2 4 5 7 9 11 14 18 25 36 58 62 67 129 320 663 360 163 96 68 54 47 42 44 46 48 49 51 53
9 1 3 4 6 7 10 12 16 22 32 53 103 112 120 300 624 340 155 91 65 52 45 40 38 40 41 43 44 46 48
10 1 3 4 6 8 11 14 20 29 48 95 240 260 280 585 320 146 86 61 49 43 39 36 35 37 38 40 41 42 44
11 1 3 4 6 9 12 17 26 43 86 220 468 507 546 300 138 82 58 47 41 37 35 34 33 34 36 37 39 40 41
12 1 3 5 7 10 15 23 38 77 200 429 240 260 280 129 77 55 44 39 35 33 32 32 31 33 34 35 37 38 39
13 2 3 5 8 12 19 34 69 180 390 220 103 112 120 72 52 42 36 33 32 31 30 30 30 32 33 34 35 37 38
14 2 4 6 10 16 29 60 160 351 200 95 58 62 67 49 39 34 32 30 29 29 29 29 29 31 32 33 34 35 37
15 2 4 7 13 24 52 140 312 180 86 53 39 42 45 37 32 30 29 28 28 28 28 28 29 30 31 32 33 35 36
16 2 5 10 19 43 120 273 160 77 48 36 30 32 34 30 28 27 26 26 26 27 27 27 28 29 30 32 33 34 35
17 3 6 14 34 100 234 140 69 43 32 27 24 26 28 26 25 25 25 25 25 26 26 27 28 29 30 31 32 33 34
18 5 10 26 80 195 120 60 38 29 25 22 21 23 25 24 23 23 24 24 24 25 26 26 27 28 29 31 32 33 34
19 9 17 60 156 100 52 34 26 22 20 19 19 21 22 22 22 22 23 23 24 25 25 26 27 28 29 30 31 32 34
20 20 40 117 80 43 29 23 20 18 18 17 18 19 20 21 21 21 22 23 23 24 25 26 27 28 29 30 31 32 33
21 39 78 60 34 24 19 17 16 16 16 16 17 18 19 20 20 21 21 22 23 24 25 25 26 27 28 30 31 32 33
22 20 40 26 19 16 15 14 14 14 15 15 16 17 18 19 20 20 21 22 23 23 24 25 26 27 28 29 30 31 33
23 9 17 14 13 12 12 12 13 13 14 14 15 16 18 18 19 20 21 21 22 23 24 25 26 27 28 29 30 31 32
24 5 10 10 10 10 11 11 12 12 13 14 15 16 17 18 19 20 20 21 22 23 24 25 26 27 28 29 30 31 32
25 3 6 7 8 9 10 10 11 12 13 13 14 16 17 18 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
26 2 5 6 7 8 9 10 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 25 27 28 29 30 31 32
27 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 23 24 25 26 27 29 30 31 32
28 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 21 22 23 24 25 26 27 28 29 31 32
29 2 3 4 6 7 8 9 10 11 11 12 13 15 16 17 18 18 19 20 21 22 23 24 25 26 27 28 29 30 31
30 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
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
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.
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 > 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%)
Figure 1: Nominal Average Prices over Time
10
12
14
16
18
20
22
24
26
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Period
Ave
rag
e p
rice
ComplementsSubstitutes
Pre shock average price in equilibrium: 25
Post shock average price in equilibrium: 12.5
Significant deviations for 8 post shock periods under complements
No significant deviation for all post shock periods
Figure 2a: Distribution of Individual Price Choices in Period 16 (x-types)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Prices
Rela
tive f
req
uen
cy
Complements (x)Substitutes (x)
Post shock equilibrium
Pre shock equilibrium
Figure 2b: Distribution of Individual Price Choices in Period 16 (y-types)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Prices
Re
lati
ve
fre
qu
en
cy
Complements (y)Substitutes (y)
Post shock equilibrium price
Pre shock equilibrium price
Individual Adjustment towards Equilibrium
Table 3: Percentages of Nominal Price Choices above, in and below Equilibrium
(Subjects as Units of Observation)
Strategic complements Strategic substitutes
Period Above
equilibrium
in
equilibrium
Below
equilibrium
above
equilibrium
in
equilibrium
below
equilibrium
13 - 15 3 93 5 1 96 3
16 75 23 3 14 67 19
17 75 23 3 19 67 14
18 68 28 5 3 92 6
19 - 21 48 51 1 1 97 2
22 - 24 34 65 1 3 96 1
25 - 27 18 77 6 3 96 1
28 - 30 2 94 4 1 99 0
Figure 3a: Actual Average Prices and Average Best Reply for given
Expectations Complements Treatment (Periods 16-18)
0
5
10
15
20
25
1-3 4-6 7-9 11-14 13-15 16-18 19-21 22-24 25-27 28-30
Expectation of others' average price
average best reply
actual average price
0,11
0,18
0,11
0,18
0,330,09
Figure 3b: Actual Average Prices and Average Best Reply for given
Expectations Substitutes Treatment (Periods 16-18)
0
5
10
15
20
25
1-3 4-6 7-9 10-12 13-15 16-18 19-21 22-24 25-27 28-30
Expectation of others' average price
average best reply
actual average price
0,01
0,03
0,46
0,46 0,01
0,01 0,02
Figure 4: Average Price Expectations over Time
10
12
14
16
18
20
22
24
26
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Period
Ave
rag
e p
rice
exp
ecta
tio
n
Av. Expect CT
Av. Expect. ST
Significant deviations from equilibrium for 8 periods
Figure 5: Efficiency Losses during the Post-shock Phase
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Complements
Substitutes
Figure 6a: Simulations of Price Adjustment with Varying Numbers of
Adaptive Players in the Substitutes Treatment (ST)
1
6
11
16
21
26
31
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1x
2x
2x,1y
2x,2y
actual
Figure 6b: Simulations of Price Adjustment with Varying Numbers
of Adaptive Players in the Complements Treatment (CT)
10
12
14
16
18
20
22
24
26
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1x
2x
2x,1y
2x,2y
actual
2x,2y (t = 16 actual)
Figure 7a: Distribution of Individual Price Expectations in Period 16 (x-types)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Expectation of others' average price
Rela
tive f
req
uen
cy
Complements (x)
Substitutes (x)
Pre shock equilibrium expectation
Post shock equilibrium expectation
Figure 7b: Distribution of Individual Price Expectations in Period 16 (y-types)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Expectation of others' average price
Rela
tive f
req
uen
cy
Complements (y)
Substitutes (y)
Pre shock equilibrium expectation
Post shock equilibrium expectation
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.
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.
Median Mean Standard Deviation
Actual = 1.5 Actual = 1.5 Actual = 1.5 x-comps 21 21 17.65 19.75 4.23 4.73 y-comps 22.5 24 20.55 23.04 6.35 5.97 x-subs 11 11 10.17 9.12 2.93 7.30
Nash Prediction:
x plays 11
y plays 14 y-subs 14 14 12.5 10.16 4.10 7.79
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%
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.
What drives the differences across treatments?
45o-line best reply in CT before shock
A
A'
B
B'
P i
C
C'
best reply in CT after shock
best reply in ST before shock
best reply in ST after shock
P -i
P AP CP C'
P B
P B'
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).
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.