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.

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.

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 P i 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) Bad stable equilibrium Low real payoffs High nominal payoffs Good stable equilibrium High real payoff Low nominal payoff Unstable equilibrium 45-degree line

Nominal Payoff Table

Real Payoff Table

Average Prices and Price Expectations over Time

Money Illusion or Beliefs about others’ Money Illusion

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 (P i, 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 M 1 = M 0 / 2 Predictions: Equilibrium nominal average price: Pre-shock: 25, Post- shock: 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

Real Payoff Table: Substitutes, post-shock, Type x Average price of other firms

Nominal Payoff Table: Complements, post-shock, Type x Average price of other firms

Nominal Payoff Table: Substitutes, post-shock, Type x Average price of other firms

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 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) Post shock equilibrium Pre shock equilibrium

Figure 2b: Distribution of Individual Price Choices in Period 16 (y-types) Post shock equilibrium price Pre shock equilibrium price

Individual Adjustment towards Equilibrium

Figure 3a: Actual Average Prices and Average Best Reply for given Expectations Complements Treatment (Periods 16-18)

Figure 3b: Actual Average Prices and Average Best Reply for given Expectations Substitutes Treatment (Periods 16-18)

Figure 4: Average Price Expectations over Time Significant deviations from equilibrium for 8 periods

Figure 5: Efficiency Losses during the Post-shock Phase

Figure 6a: Simulations of Price Adjustment with Varying Numbers of Adaptive Players in the Substitutes Treatment (ST)

Figure 6b: Simulations of Price Adjustment with Varying Numbers of Adaptive Players in the Complements Treatment (CT)

Figure 7a: Distribution of Individual Price Expectations in Period 16 (x-types) Pre shock equilibrium expectation Post shock equilibrium expectation

Figure 7b: Distribution of Individual Price Expectations in Period 16 (y-types) Pre shock equilibrium expectation Post shock equilibrium expectation

Cognitive Hierarchy Theory Camerer 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.

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?

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.