**A joint initiative of Ludwig-Maximilians University’s**Center for Economic Studies and the Ifo Institute for Economic Research Area Conference on B Be eh ha av vi io ou ur ra al l E Ec co on no om mi ic cs s 28 – 29 October 2011 CESifo Conference Centre, Munich Heterogeneous Agents in Intertemporal Choice: Theory and Experimental Evidence Daniel Schunk CESifo GmbH Poschingerstr. 5 81679 Munich Germany Phone: Fax: E-mail: Web: +49 (0) 89 9224-1410 +49 (0) 89 9224-1409 office@cesifo.de www.cesifo.dePreliminary version – please do not cite or quote without permission of the author. Heterogeneous Agents in Intertemporal Choice: Theory and Experimental Evidence∗ Daniel Schunk∗∗ Johannes Gutenberg-Unviversity Mainz, Germany University of Zurich, Switzerland This version: June 15, 2011 Abstract: A rapidly growing literature in macroeconomics and finance argues that the cross-sectional distribution of heterogeneous agents is decisive for aggregate economic outcomes, yet empirically substantiated information on the nature, origins, and temporal stability of behavioral heterogeneity is unavailable. Applying structural estimation to laboratory panel data from an intertemporal choice task, I obtain a parsimonious representation of behavioral heterogeneity and provide three insights: First, a small set of both rational and rule of thumb types explains 92% of all observed decisions. Second, there is evidence for type stability, i.e. many subjects’ types remain unchanged over several weeks. Third, time pressure affects the type distribution and halves the fraction of rational agents. Hence, this paper provides a structural microfoundation of the assumption of temporally stable heterogeneous agents, and it shows that generic features of the decision environment can fundamentally affect aggregate outcomes by changing the cross-sectional distribution of heterogeneous agents. Keywords: intertemporal choice; behavioral heterogeneity; structural estimation; mi- crofoundations; temporal stability of behavior JEL classification: D01; D83; C91; D12; E10; G10 ∗The author would like to thank George Akerlof, Charles Efferson, Ernst Fehr, Wouter den Haan, Cars Hommes, Daniel Houser, Wolfgang Luhan, Michael Roos, Georg Weizsaecker, and participants of several seminars and conferences for their helpful comments on this paper.

1 Introduction Intertemporal choices are an ubiquitous feature of social and economic life. For example, savings and labor supply decisions, producers’ employment and pricing choices, and stock market trading choices all have an intertemporal dimension. It has long been discov- ered that there is heterogeneity in people’s intertemporal choice behavior (e.g., Simon, 1955) and heterogeneous agent models are now the norm rather than the exception in dynamic macroeconomics and finance (see Heathcote et al., 2009). One important rea- son for assuming heterogeneous agents is that quite many economic agents do not derive their choices rationally from solving the corresponding intertemporal optimization prob- lem, but rather follow rules of thumb (e.g., Akerlof, 2002; Heckman, 2001).1A second important reason for introducing heterogeneity is that it is of fundamental relevance for our understanding of aggregate phenomena (see, e.g., Heathcote, 2005): even though rule of thumb behavior imposes only small losses on individual agents, the existence of only small proportions of rule of thumb types in a population can lead to substantial changes in aggregate (equilibrium) outcomes. More generally, the literature emphasizes that the cross-sectional distribution of different types of agents may be decisive for aggregate out- comes (e.g., Brocks and Hommes, 1997; Haltiwanger and Waldman, 1985, 1989; Hommes, 2006; Chapman and Polkovnichenko, 2009). In particular, the proportion of rational types in a population matters for the aggregate (e.g., Fehr and Tyran, 2005; Kluger and Wyatt, 2004).2This poses a serious problem for economics, because only very little is known, first, about the nature and cross-sectional distribution of heterogeneous types and, second, about whether this distribution depends on generic characteristics of the intertemporal choice environment.3 The objective of this paper is to provide structural and parsimonious evidence on be- havioral heterogeneity in intertemporal choice tasks. distribution of rational types and rule of thumb types. Second, I discuss the stability of types over time and with respect to time pressure, a generic feature of the decision envi- ronment. Since it is hardly possible to obtain clean evidence on the determinants and the stability of the type distribution from aggregate field data, I use a laboratory experiment which involves a simple intertemporal choice task. This ensures observability of individual decisions and full control over unobserved factors such as peoples’ beliefs. Moreover, to First, I discuss the nature and 1These rule of thumb types are often very efficient since in stochastic intertemporal problems there is a wide latitude for deviating from the behavior of a rational agent without incurring significant individual losses (e.g., Powell, 2007). 2Kluger and Wyatt (2004), for example, show that an error-free asset market equilibrium is reached only when the fraction of rational traders exceeds a certain threshold. 3As I have motivated above, the study of agent heterogeneity in intertemporal choice behavior is of particular interest and policy relevance in macroeconomics and finance. However, there is also a very recent literature in experimental and behavioral economics that studies heterogeneity and shows its crucial impact on aggregate outcomes, for example in social dilemma situations (e.g., Bellemare et al., 2008), in risk-taking behavior (e.g., Bruhin et al., 2010), or in network formation (e.g., Goeree et al., 2009).

learn about the distribution of types, I apply a statistical classification procedure that is able to draw structural inference about individual behavior. This classification procedure reveals latent heterogeneity by estimating the proportions of distinct behavioral types in the population and assigning each individual to one behavioral type from an endogenously defined set of types. Of course, the experimental investigation of the foundations of intertemporal choice be- havior requires a decision task that is not only implementable in the laboratory without loss of control, but also representative of intertemporal choice situations in real life and thus relevant for economics and finance. Price search is such a task. First, the simple deci- sion structure of search tasks masks a complicated stochastic intertemporal optimization problem that – comparable to intertemporal choice situations in everyday life – cannot be solved without a computer. At the same time, search tasks occur often in everyday life – e.g., when looking for the best price for a certain product or when searching for a new job. Consequently, search behavior is being studied intensively in many fields, such as labor economics, monetary economics, industrial organization, finance, and mar- keting (see, Rogerson et al., 2005, for an overview). Second, search tasks are attractive for laboratory investigations, because participants in a laboratory experiment understand them immediately. Third, search tasks with full information about the underlying price distribution ensure control even over subjects’ beliefs about this distribution; thus, they have a solution which is both theoretically and empirically identified. And fourth, work in search theory indicates that a better understanding of the nature of agent heterogeneity in search is important in itself; in a labor market context, for example, the distribution of heterogeneity in the population of searchers is related to the degree of labor market frictions and efficiency (see, e.g., Woodbury and Davidson, 2002). Beyond providing gen- eral insights about latent heterogeneity, its temporal stability, and its relationship to the decision environment, this paper provides specific information on agent heterogeneity in search contexts. While the former is of general interest for heterogeneous agent models in macroeconomics and finance, the latter is also of specific relevance for labor economists who study the sources of labor market frictions and unemployment. This paper shows the following main results. First, there is considerable heterogeneity in the population, consisting of a mix of rational types and rule of thumb types. This mix is influenced by a modification of the decision environment: Under time pressure, the proportion of rational types in the same intertemporal choice task reduces significantly. This suggests that heterogeneous agent models for contexts that involve time constraints and time-dependent incentive schemes (see, e.g., Kocher and Sutter, 2004), such as models of stock-market trading behavior, should adopt fundamentally different assumptions about the mix of types than models involving contexts without time pressure. Second, for a large fraction of the sample, assigned behavioral types do not change over a five week test-retest period and the assigned types can be linked to cognitive ability, a dispositional character trait variable which is known to have high temporal stability over the life cycle. These findings not only lend further support to the validity of the 2

structural type classification algorithm applied in this paper, but they also provide a structural microfoundation of the assumption of temporally stable heterogeneous agents. Finally, the paper also offers a methodological contribution: It uses an experimental manipulation of the decision environment (time pressure) to demonstrate that the mere analysis of aggregate behavioral data can lead to fundamentally different conclusions about the underlying individual behavior than the model-based analysis of individual decisions. The study of the foundations of intertemporal choice is thus an important area where two distinct disciplines – macroeconomics and experimental economics – can interact fruitfully. In sum, there is recently emerging empirical evidence on the distribution of different be- havioral types as well as its robustness over time and across different cultures (see, e.g., Bruhin et al., 2010). At the same time, a rapidly growing theoretical literature, in par- ticular in dynamic macroeconomics and finance, uses heterogeneous agent models which critically depend on assumptions about the distribution of the heterogeneous types (see, e.g., Heathcote et al., 2009). Thus, I believe that work on the parsimonious representation of behavioral heterogeneity, on its temporal stability, and on the identification of general environmental conditions – such as time pressure – that affect behavioral heterogeneity is an important task for economic research. It provides empirically well grounded infor- mation for a new but already very broad literature in applied and theoretical economics. The remainder of this paper is structured as follows: Section 2 presents the experimental design and the experimental procedure. Section 3 derives rational decision rules and rules of thumb that characterize the different types of agents in the intertemporal choice task studied in this paper. Section 4 develops the statistical classification algorithm. Section 5 presents and discusses the results, and section 6 concludes. 2 The Experimental Design The experiment consisted of two parts, part A and part B, that were presented in a fixed order. In part A, I observed intertemporal choice behavior in a series of repeated price search tasks. Part B was a questionnaire and a test for cognitive skills. 2.1 Part A: The Intertemporal Choice Task In part A, subjects performed a sequence of search tasks. Each subject’s goal was to purchase a good that she valued at 500 experimental currency units (ECU). This good was sold at 40 different locations and visiting a new location cost 1 ECU. The instruction sheet (see appendix) informed subjects graphically and verbally that the price at each of the 40 locations was drawn independently from a truncated normal distribution with a mean of 500 ECU, a standard deviation of 10 ECU, and truncation at 460 ECU (lowest price) and 540 ECU (highest price). The price distribution was discretized such that only integer prices were realized. 3

After each price draw – i.e., at each location they visited – subjects could stop and choose any price (location) encountered so far, or they could continue their search at the incremental cost of 1 ECU. The outcome of each search task was calculated as the evaluation of the object (=500 ECU) minus the price at the chosen location minus the accrued search cost. In case this outcome was a negative number, it was counted as a zero payoff, i.e. the lowest possible payoff was zero. There are several reasons why I allowed subjects to recall previously rejected offers and why I provided subjects with full knowledge about the price distribution. First, allowing for recall makes the task closer to real-world situations, such as price search in the internet: In these situations, individuals can typically search and compare offers as long as they want; at a certain moment, they decide to stop their search and then choose one of all the offers that they came across during their search. Second, providing subjects with information about the price distribution ensures full control over subjects’ beliefs about the underlying price distribution. This enables the derivation of simple rational decision rules that serve as a benchmark for observed behavior.4 To ensure that subjects were experienced with the task and comfortable with the computer interface, and to minimize the observation of learning behavior, subjects were allowed to perform an unlimited number of practice search tasks before performing a sequence of 20 tasks that determined their payoff for part A of the experiment. After the experiment was completed, one of these 20 rounds was selected randomly to determine the part A payoff. The experiment involved two treatments: Treatment Baseline and treatment Time Pres- sure. To avoid potential confounding effects, each subject was taking part in only one of the two treatments. In both treatments, subjects performed the search task described above. However, while in treatment Baseline, every stop-or-go decision was made with- out time pressure, every stop-or-go decision in treatment Time Pressure had to be made within four seconds. The remaining time per decision was indicated by a red clock on the computer screen, counting down from four to zero for every decision. If no decision was made within the four second interval, the payoff for this search round was counted as zero, which is the lowest payoff a subject could achieve in the search task. To ensure maximum similarity of the computer screens in both treatments, subjects in the Baseline treatment also saw a red clock on their computer screen. However, each subject in the Baseline treatment had 240 seconds for every stop-or-go decision, i.e. the clock was counting down from 240 to zero for every decision. It is important to note that the 240 seconds interval is not binding for any of the subjects; the longest time needed for a stop-or-go decision in the Baseline treatment was only 28 seconds. 4If subjects did not know the price distribution, they would update their priors about the price distribu- tion at each visited location. This can also be incorporated in a theoretical model, but the experimental environment would be less controlled, since subjects’ potentially different priors would be unobserved and this could substantially distort inference about the different agent types. 4

2.2 Part B: The Questionnaire Part B started with a rating question. Subjects had to specify their level of agreement with the following statement on a 7-point Likert-scale: I understood the instructions and it was totally clear to me, how the payoffs are determined. Then, subjects took part in a test for cognitive abilities. I used a short form of Raven’s Advanced Progressive Matrices test, a culture-free test which has been specifically adapted to reliably differentiate among university students (Bors and Stokes, 1998). Finally, subjects were asked for the usual personal information (gender, age, field of studies). 2.3 Administration and Payoffs The experiment was conducted in the laboratory of the Institute for Empirical Research in Economics at the University of Zurich (Switzerland). It was run on computers using software written by the author which is available upon request. The payoff procedures took place after the experiment was over. The instruction sheet (see appendix) presented full information about the search task and it was emphasized that, (i), subjects’ payoff from the search task was at least 0 ECU and, (ii), that for each round in which subjects would violate the time restrictions, they would also receive a payoff of 0 ECU. In addition to the payoff from the search task, subjects received 5 ECU for completing the questionnaire. As standard in experimental research, at the very end of the experiment, experimental currency (ECU) was exchanged into real money: 1 ECU equaled 2 Swiss Francs. The experiment involved 246 subjects in total. All of them were undergraduate students from the University of Zurich or the Technical University of Zurich. 166 undergraduate students took part in study 1 and were randomly assigned to one of the two treatments: 82 subjects were assigned to treatment Baseline and 84 subjects were assigned to treatment Time Pressure. Another 82 subjects took part in study 2, a panel experiment in which I observed them in the Baseline task twice, with five weeks in between. 3 Agent Types in Intertemporal Choice To be able to draw structural inference about the distribution of behavioral types, the intertemporal decision rules underlying each type must first be derived from theory. This section derives and characterizes the decision rules of different types of agents that solve the task considered in this paper, resulting in a large universe of potential candidate types: In principle, my approach allows for 77 different types, i.e. it distinguishes between 77 different candidate decision rules, both rational rules and rules of thumb. The universe of types has been chosen so large because it should be able to capture all potentially observable types of agents. Of course, the classification method will then endogenously determine the relevant subset of types that classifies all observed behavior. More specifically, this section first presents the decision rule of a rational agent type (see subsection 3.1), i.e. an agent who follows the theoretically optimal decision rule. The 5

second part of this section (subsection 3.2) deals with rule of thumb types which can be derived from behavioral theory; this section exploits the fact that price search tasks have been intensively studied in the literature, such that reliable knowledge about relevant rules of thumb exists. 3.1 Rational Agent Types Assume an agent whose goal is to purchase a certain good that she values at 500. In every period, the agent visits a new search location and observes a realization of a random variable X, the price of the good. This random variable has the distribution function F(·). In the task considered in this paper, F(·) is a truncated discrete normal distribution with mean 500 and standard deviation 10. The truncation ensures that 460 and 540 are the lower and upper bound of the price distribution, respectively. Let the cost of visiting a new location be c. Furthermore, let us denote by m the minimal price that the agent has observed so far. In this task, the agent stops searching only if the value from stopping the search is higher than the value from continuing the search process. If the search cost c is 1, as in the task considered here, the agent has no incentive to search for more than 40 periods. The reason is that after 40 periods, she has paid a total accumulated search cost of 40, and the lowest price that she can find is 460. Moreover, the subjects were also instructed that they can visit at most 40 locations. Consequently, the intertemporal choice task is a finite horizon problem which is solved with backward induction. Finally, note that subjects were instructed that their payoff after t periods was 500−m−t·c, and in case this term was negative the resulting payoff was 0. Assume first that the agent is risk neutral, i.e. she behaves as an expected value maxi- mizer. To formalize the agent’s decision problem, define St= {t,m} as the agents’ state vector after period t. After the agent has stopped searching, she buys the item and receives the following total payoff: Π(St) = max{0,500 − m − t · c}. The agent stops searching only if the continuation value of the search is lower than the stopping value. The recursive formulation of the decision problem is therefore: (1) Jt(St) = max{Π(St),E[Jt+1(St+1)|St]}. E(·) represents the mathematical expectations operator, and the expectation is taken with respect to the distribution of St+1|St. The solution of this problem has the reservation price property in every period t. That is, there exists a reservation price P(t) at every t, and the agent stops the search if a certain price draw at t is less than or equal to P(t). The reservation price of a risk neutral agent begins at 490, then starts decaying slowly, reaches 485 in round 14, and then decays at a rate of one per round. (2) As a more general case, consider now an agent with an arbitrary, monotone utility function u(·). The total payoff is: Πu(St) = max{0,u(500 − m − t · c)}. (3) 6

The recursive formulation of the corresponding intertemporal choice problem is: t= max{Πu(St),E[Ju I assume a utility function of the power form which assumes that agents have constant relative risk aversion (CRRA)5: Ju t+1(St+1)|St]}. (4) u(x) = x(α+1) (5) Here, α characterizes an agent’s risk attitude under the CRRA-assumption. If α > 0, the agent is risk seeking; if α < 0, the agent is risk averse. The decision behavior of a rational agent with risk attitude α is thus characterized by the corresponding solution to the optimality equation (4). Figure 1 provides a detailed characterization of the behavior of rational types. The left panel of figure 1 shows the solutions of optimality equation (4) for different degrees of risk attitude α. We see that the solution has the reservation price property at every t, and the reservation price path is monotonically falling in t.6The different rational agent types are denoted by rP1, where P1is the particular reservation price level at t = 1; from the derivations above, it is clear that a risk neutral rational agent is denoted by r490, because her reservation price path starts at 490. Each of the shown types corresponds to a certain α-interval, i.e. it represents an agent with a certain risk attitude. The higher the reservation price at t = 1, the more risk averse is the agent. In total, I consider 15 different types (r484,...,r498), corresponding to 15 different risk attitudes.7For each of the 15 types, the right panel of figure 1 shows the corresponding average payoff as well as the average number of periods an agent continues searching before taking the stopping decision. As expected, the risk neutral rational rule r490 yields the highest possible average payoff (9.55 ECU) of all rational rule types. Moreover, the right panel shows that a risk neutral rational type would search for 8.5 periods on average. 3.2 Rule of Thumb Agent Types As is clear from the derivation in the previous section, the computation of the rational decision rule is a cognitively demanding task. This suggests that some agents’ behav- ior could be better described by rules of thumb (or ‘heuristics’) rather than the rational 5If I assume a CARA-utility function instead, e.g. based on an exponential functional form, the derived optimal decision rules differ slightly for large t. It has to be stressed, however, that all findings in this paper do not change if I use CARA-utility functions. Results are obtainable from the author upon request. 6Note, that the monotonically falling reservation price implies that rational agents should not exercise recall, i.e. they should not recall previously rejected prices. I anticipate here that recall decisions are very rare. Only 2.98 percent of all decisions in the Baseline Treatment and only 2.30 percent of all decisions in the Time Pressure Treatment are recall decisions. 7Allowing for 15 rational agent types – 1 risk neutral type (r490), 6 risk seeking types (rP1with P1∈ {484,...,489}), and 8 risk averse types (rP1with P1∈ {491,...,498}) – is sufficient for describing all behavior observed in the data. No subject behaves outside this range of behavior and all classification results presented later remain unchanged if I increase the number of rational agent types included in the universe of types. 7

Figure 1: Behavior, Payoffs, and Number of Decisions: Rational Types 500 10 35 Types: Average Payoff 495 30 9 r496 Average Number of Decisions r494 r492 490 Reservation Price [ECU] Average Payoff [ECU] 25 8 485 r490 20 r488 r486 480 7 15 r484 475 6 Average Number of Periods before Stopping 10 470 5 5 465 4 0 460 r484 r485 r486 r487 r488 r489 r490 r491 r492 r493 r494 r495 r496 r497 r498 1 4 7 10 13 16 19 Period 22 25 28 31 34 37 40 Type decision rule. Based on this insight, numerous existing studies (e.g., Cox and Oaxaca, 1989; Hey, 1981, 1982, 1987; Houser and Winter, 2004; Kogut, 1990; Moon and Mar- tin, 1990; Schunk and Winter, 2009; Sonnemans, 1998, 2000) have been concerned with investigating which rules of thumb describe observed behavior in search tasks. One key finding emerges from these studies: There is substantial heterogeneity with respect to agent types and a number of simple rules of thumb describe the behavior of quite many of the observed subjects. Thus, in addition to the rational agent types discussed in the section above, I use these rules of thumb to classify agent types. Specifically, I use three classes of simple rules of thumb: (i) constant reservation price heuristics, (ii) satisficer heuristics, and (iii) pattern- based heuristics. Besides characterizing these behavioral rules in detail, this section also shows that most of these rules of thumb are very efficient and lead to only small losses for the individual, compared to the rational rule.8 (i) Constant Reservation Price Types Each type of the constant reservation price class uses an arbitrary reservation price which is constant over all periods. A characterization of the behavior of these types is provided in figure 2. The left panel shows the different constant reservation price heuristics; they are denoted by cR where R denotes the level of the constant reservation price. For example, a subject that stops whenever a price less than or equal to 490 is drawn, is of type c490. Again, I consider 15 different types, c484,...,c498.9For each of the 15 types, the right 8The fact that even large behavioral deviations from rationality lead to only small deviations in payoffs is a generic feature of stochastic intertemporal choice problems. It is a consequence of the envelope theorem and has very recently been studied in many different fields beyond economics (see, e.g., Powell, 2007). It implies that individual agents’ objective functions are flat. Agents are thus deemed near- rational in their achieved profits (Akerlof, 2002), although their behavior might deviate considerably from the rational behavioral rule. Akerlof (2002), for example, writes that “...rules of thumb (...) are not only commonplace but also sensible – neither foolhardy nor implausible: the losses from reliance on such rules are extremely small.” 9No subject behaved outside this range and all classification results remain unchanged if I increase the number of constant reservation price types included in the universe of types. 8

panel of figure 2 shows the corresponding average payoff as well as the average number of periods an agent continues searching before taking the stopping decision. The c489-type has the highest possible average payoff (9.39 ECU) among all constant reservation price types. Notice that the highest possible payoff of a rule of thumb type thus deviates only little from the payoff of a risk neutral rational type who would earn 9.55 ECU, as the last subsection has shown. Figure 2: Behavior, Payoffs, and Number of Decisions: Rule of Thumb Types (Constant Reservation Price Types) 500 10 35 495 30 Average Payoff 9 Average Number of Decisions 490 Reservation Price [ECU] Average Payoff [ECU] 25 8 485 20 Types: 480 7 c496 15 c494 475 6 c492 10 c490 470 Average Number of Periods before Stopping c488 5 5 465 c486 c484 460 4 0 c484 c485 c486 c487 c488 c489 c490 c491 c492 c493 c494 c495 c496 c487 c498 1 4 7 10 13 16 19 22 25 28 31 34 37 40 Period Type (ii) Satisficer Types Subjects using a satisficer heuristic stop searching as soon as their payment exceeds a certain individual satisfaction or aspiration level which the subject minimally wants to achieve, say 7 ECU for example. Thus, in contrast to the constant reservation price types, the satisficer types do not only take the price level into account, but also the accumulated search cost. In the task considered here, this results in a reservation price that falls linearly over time. The behavior of satisficer types is characterized in figure 3. The different satisficer heuristics are denoted by sA, where A denotes the individual satisfaction or aspiration level. For example, a satisficer type using rule s7 would be satisfied with a payoff of 7 ECU. Consequently, this subject stops the search process as soon as the achieved payoff is at least 7 ECU, and her reservation price at t = 1 is 492 ECU (since she would obtain a payoff of 7=500-492-1, if she stops at t = 1 after having seen a price offer of 492). Again, I consider 15 different types.10For each of the 15 types, the right panel of figure 3 shows that the satisficer type with the highest possible average payoff would use rule s6 and would reach an average payoff of 9.14 ECU. (iii) Pattern-Based Types The literature on intertemporal choice behavior has also studied heuristics that do not have a reservation price form, but predict that subjects stop after having seen a certain 10No subject behaved outside this range of behavior and all classification results remain unchanged if I increase the number of satisficer types included in the universe of types. 9

Figure 3: Behavior, Payoffs, and Number of Decisions: Rule of Thumb Types (Satisficer Types) 500 10 35 Types: Average Payoff 495 30 s3 9 Average Number of Decisions s5 490 Reservation Price [ECU] Average Payoff [ECU] 25 s7 8 s9 485 20 s11 480 7 s13 15 s15 475 6 10 470 5 5 465 Average Number of Periods before Stopping 460 4 0 s15 s14 s13 s12 s11 s10 s9 s8 s7 s6 s5 s4 s3 s2 s1 1 4 7 10 13 16 19 Period 22 25 28 31 34 37 40 Type pattern in the observed sequence of prices. So-called “bounce rules”, for example, were suggested by Moon and Martin (1990) following earlier work by Hey (1982). Subject types following the “one-bounce rule” have at least 2 searches and stop if a price quote is larger than the previous quote. The “modified one-bounce rule” is similar to the one-bounce rule, but an agent following this rule stops only if a price quote is larger than the previous quote minus the search cost. Both bounce rules earn much less payoff on average than the other heuristics considered above: The “one-bounce rule” earns 4.74 ECU on average, and the “modified one-bounce rule” yields 4.54 ECU. Finally, findings on decision-making in uncertain environments suggests that people might use rules that are based on winning streaks (see, e.g., Rabin, 2002). Types who follow “winning streak heuristics” stop searching if they receive two (or three) consecutive price draws that are below some fixed threshold level F. The streak-based rule with the highest payoff is the rule with F = 498 and it earns 7.50 ECU, i.e. much less than most rational types, constant reservation price types, or satisficer types. Since pattern-based types achieve a substantially lower payoff than all other types and do not classify behavior very well in search tasks (see, e.g., Schunk and Winter, 2009), a detailed characterization of the pattern-based types, including average payoff and search duration, is presented only in appendix A.1 of this paper.11 4 Classification of Agent Types in the Intertemporal Choice Task This section describes how I classify intertemporal choice behavior on an individual level. The first subsection summarizes the universe of candidate types which has been devel- 11I anticipate here that all results from the paper remain unchanged if I do not consider pattern-based types in the universe of all types; the classification algorithm sorts them out, indicating that they do not describe actual behavior well. However, since – ex ante – all types that are reported in the literature are potential candidate types, I still consider them at this point of the paper. 10

oped in section 3. The second subsection then derives a formal statistical classification procedure that estimates each subjects’ type by assigning each subject to the best-fitting behavioral type from an endogenously defined subset of the universe of candidate types. 4.1 The Universe of Types The universe of types is summarized in table 1is a fixed set of candidate decision rules that are used to classify each subjects’ intertemporal choice behavior. As candidate decision rules I use all the 77 rules that have been derived in section 3. The universe of types is summarized in table 1 and it is composed as follows: I take 15 rules from each of the three decision models (the rational decision model, the constant reservation price model, and the satisficer model). In all three cases, the rule with the highest reservation price path starts at t = 1 with a reservation price of 498 (i.e., the corresponding rules are r498, c498, and s1). Similarly, in all three cases, the rule with the lowest reservation price path starts at t = 1 with a reservation price of 484 (i.e., the corresponding rules are r484, c484, and s15). I further include the 32 pattern-based rules, i.e. the “one-bounce rule”, the “modified one-bounce rule”, and the 30 “winning streak rules”. 4.2 Statistical Classification Procedure The classification algorithm assigns to each experimental subject the type that fits best the observed behavior and it explicitly models decision errors. To avoid overfitting, the algorithm assigns the type from only a subset of the universe of candidate types, and the subset is itself endogenously determined by the algorithm.12 the statistical classification algorithm is, first, the subset of types which best classifies the behavior of all subjects in a certain treatment. Second, the algorithm assigns one (or more) best-fitting decision rules from this subset to each subject, thereby giving each subject a type. Third, it yields an estimate for the amount of decision errors that subjects make. Hence, the result of Formally, the classification procedure works as follows: Assume that each subject i = 1,...,I follows exactly one of the decision rules in the universe of candidate rules and that she uses the same rule in each of the 20 dynamic choice tasks. This assumption seems reasonable in view of the fact that all subjects are experienced with the task when they begin the 20 payoff-relevant tasks, since they were instructed to practice the task without payoff as long as they wanted (see section 2.1). Now, define C as the universe of candidate types (or decision rules). Notice that each type ci∈ C is a unique map from subject i’s information set Sitto her continuation decision 12Of course, each single subject could also be assigned his or her best-fitting type from the complete universe of types. This, however, would be uninformative and not generalizable, and it would not lead to a parsimonious characterization of type heterogeneity. 11

Table 1: The Universe of Agent Types C. Agent types Rational types Description of corresponding decision rule Stop searching in period t as soon as a price lower than or equal to the reservation price P?(t), as specified by the optimal search model (see section 3.1), is found. See figure 1. Stop searching in period t as soon as a price lower than or equal to R is found. See figure 2. Stop searching as soon as the payoff from stopping exceeds a certain threshold or satisfaction/aspiration level A. See figure 3. Have at least 2 searches and stop if a price quote is received larger than the previous quote (minus the search cost). Stop searching as soon as 2 (3) consecutive price draws that are below some fixed threshold level F are received. Number and names of types Corresponding parameters ?? (-1.0, +4.3] Alternatively: P1?{484,…,498} 15 types: r484, r485, …, r498 Constant reservation price types 15 types: c484, c485, …, c498 R ?{484,…, 498} Satisficer types 15 types: s1, s2, …, s15 A ?{1,…, 15} Bounce heuristic types 2 types: b1, b2 Winning streak heuristic types 30 types: w(2)484, w(2)485 …, w(2)498, and w(3)484, w(3)485 …, w(3)498 F?{484,…, 498} 12

dit∈ {0,1} : dci t. Then, define the indicator function: it(Sit) → {0,1}. Let d∗ itdenote the observed decision of subject i in period xci it= dci it(Sit) = 1(d∗ it(Sit)) (6) The indicator variable xci with the prediction of type ciand 0 otherwise.13 it(Sit) takes value 1 if subject i’s continuation decision is consistent Finally, the last decision that a subject makes in every game is the location decision: Since the search problem is one with recall, once she has decided to stop, she selects the location at which the good is bought from all locations visited in the current search round. Assume that each location decision is made with an identical error rate ε and it is made independently of the continuation decision. That is, we assume that a subject who stops with J location alternatives chooses the location that is given by some candidate decision rule with probability (1−ε) and every other possible location with probability ε, independent of J. Let further Tibe the number of decisions that are observed for subject i. We define the following sufficient statistic: Ti X Xci xci i= it(Sit) (7) t=1 Then, the likelihood function for subject i is: iTi) = (1 − ε/2)Xci i(ε/2)Ti−Xci fci,ε(xci i1,...,xci i. (8) This expression is based on the assumption that conditional on making an error, subjects make either decision (continue or stop) with probability 50%. To estimate each subject’s type ci, I use maximum likelihood: X where ˆ c = (ˆ c1,..., ˆ cTi). log(fci,ε(xci i1,...,xci (ˆ c, ˆ ε) = argmax iTi)) (9) {ci∈C,ε} i=1,I To avoid overfitting with respect to the number of types, I follow El Gamal and Grether (1995). They suggest that if there are k decision rules in the set C used to explain all of the subjects’ decisions, then the log-likelihood should be penalized by an amount R(k). 13Note that no difficulty arises if an error leads a subject to continue her search when she should have stopped, since the subject’s state and corresponding continuation decisions remain defined in subsequent periods. It is, therefore, not inconsistent to assume that a subject who violates her decision rule in one period can still act according to this rule during the remaining search periods. 13

In the simple intertemporal choice task considered here, this implies the following penalty factor14: R(k) = k · log(2) − #subjects · log(k) − k · log(#decision rules in C) To determine the subset of k decision rules that best describe observed behavior and to attribute to each subject his or her type, the log-likelihood (9) minus the penalty factor (10) is maximized over the set of all possible k-tuples (k = 1,...,77) that can be formed from our universe of 77 candidate types.15The result of this estimation procedure is the subset of types which best describes the behavior of all subjects in a certain treatment; this subset containsˆk types. The estimation also assigns to each subject one (or more) best-fitting type from this subset, and it yields the estimate ˆ ε for the average probability with which subjects make decision errors. (10) 5 Results In this section, I first present descriptive statistics on intertemporal choice behavior. Then, I turn to the results from the type classification and show that there is evidence for considerable type heterogeneity in the observed population. A comparison of the type distribution between treatments demonstrates that the fraction of rational types decreases under time pressure and reveals why this insight can only be obtained from a structural analysis of individual decision data. Finally, I discuss the temporal stability of the type classification by linking it to a dispositional personality trait and by observing subjects in a panel experiment. Before starting this section, note that there is evidence that all experimental participants fully understood the instructions and the payoff mechanism. This evidence is shown in appendix A.2 of this paper. 5.1 Descriptive Statistics Table 2 reports descriptive statistics for aggregate behavioral data. Subjects had a median payoff of 8.53 ECU in the Baseline Treatment. This is about 11 percent lower than the payoff of a risk neutral rational decision maker, who would earn 9.55 ECU (see section 3.1). In the Time Pressure Treatment, the median payoff is 0.08 ECU (or about 1 percent) 14The variable #subjects equals to the number of subjects in each treatment, and #decision rules in C equals 77, as we have explained in section 4.1. The rationale behind this penalty factor is as follows: Let Ckdenote a set of k decision rules. The penalized likelihood is the Bayesian posterior that arises under the following priors. (i) The probability that the population includes exactly k decision rules is 1/2k. (ii) All possible k-tuples of decision rules are equally likely, i.e. each has probability 1/77k. (iii) All allocations of heuristics to subjects are equally likely, i.e. since we are applying the classification method independently to the data from each treatment, we have probability 1/kntreatwhere ntreatis the number of subjects in treatment treat. El Gamal and Grether (1995) as well as Houser and Winter (2004) provide a detailed explanation for this penalty factor. 15I maximize the likelihood using a grid search algorithm on the grid {c,k,ε} = {ci ∈ C,k ∈ {1,...,77},ε ∈ {0.00,0.01,0.02,...,0.99}}. This ensures that the maximum of the likelihood is truly found. 14

lower than in the Baseline Treatment and amounts to 8.45 ECU. The second row of table 2 shows the average number of periods subjects have searched before stopping. In both treatments, subjects take considerably less decisions than risk neutral rational agent types, who would search for 8.5 periods (see section 3.1). Hence, compared to behavior under the risk neutral optimal stopping rule, most subjects are early stoppers. This is consistent with the results in other work that has studied the average number of decisions in search tasks (e.g., Hey, 1987; Sonnemans, 1998). Importantly, the discussion of the aggregate data lead to the conclusion that there are no significant differences between the treatments (see the Mann-Whitney tests in table 2). Moreover, the hypothesis that the observed experimental data stem from a risk averse representative agent of type r494 cannot be rejected for both treatments (Mann-Whitney test, all p-values > 0.43).16 Table 2: Descriptive Statistics of Aggregate Behavioral Data for Both Treatments Baseline Treatment (n=82; 7361 decisions) Time Pressure Treatment (n=84; 7165 decisions) ?sign. Median Std. Dev. Median Std. Dev. MW-Test (p-value) Avg. Payoff [ECU] 8.53 0.86 8.45 0.92 0.36 Avg. # Periods 4.3 1.33 4.2 1.05 0.43 Notes: (1) ‘MW-Test’ refers to a Mann-Whitney-test. (2) In 13 cases, people earned no payoff in one of their 20 rounds because of violating the 4-second time constraint in the Time Pressure Treatment. If these 13 rounds are excluded from the payoff calculation, differences between treatments remain insignificant. The median is 8.55 ECU in this case. (3) ‘Avg. Payoff’ refers to the average payoff per person for one search round, i.e. we divide the total payoff from all 20 search rounds by 20. Similarly, ‘Avg. # Periods’ refers to the average number of periods. 5.2 Type Classification Results Model-based statistical classification yields a type assignment for each subject. This reveals latent behavioral heterogeneity and is thus crucial for assessing the impact of time pressure on the type distribution. The first main result of this paper concerns the nature of this behavioral heterogeneity and its relationship to time pressure. The fact that this result surprisingly seems to contradict the findings from the descriptive analysis above underlines the value of individual-level choice data and structural estimation approaches for drawing inference on the determinants of behavioral heterogeneity: Result 1: There is considerable behavioral heterogeneity in the population, consisting of a mix of rational and rule of thumb types. Under time pressure, the proportion of rational types reduces significantly. Support for Result 1 comes from figure 4 which summarizes the findings from the type classification. Figure 4 shows that in the Baseline Treatment, heterogeneity is captured 16A risk averse agent of type r494 would have an average payoff of 8.56 ECU and would stop on average after 4.4 decisions (see section 3.1). 15

by eight different behavioral types: there are three rational types (r488, r490, and r495), four rule of thumb types that use a constant reservation price rule (c487, c489, c491, and c493), and one rule of thumb type that uses a satisficer heuristic (s8). In the Time Pressure Treatment, seven types capture behavioral heterogeneity: two rational types (r490 and r494), two rule of thumb types that use a constant reservation price rule (c490 and c491), as well as two satisficer rule of thumb types (s10 and s5).17The bar charts in figure 4 show the fraction of subjects that have been assigned to a specific type. Most importantly, the bar charts reveal that the fraction of rational types is much smaller in the Time Pressure Treatment compared to the Baseline Treatment. 32% of the subjects were classified as rational types in the Baseline Treatment, but only 17% in the Time Pressure Treatment. This difference is significant in a binomial test of proportions (p < 0.01). The bar charts reveal further that 12%–13% of the subjects could not be assigned a unique type, i.e. these subjects were assigned two or three types all of which classified behavior equally well.18Finally, figure 4 shows that between-treatment differences in the amount of decision errors do not explain the observed differences in the cross-sectional distribution of types either, since the estimates for ε are identical in both treatments. Figure 4: Summary of the Results from the Classification of Individual Behavior Baseline Treatment (n=82; 7361 decisions) Time Pressure Treatment (n=84; 7165 decisions) Number of assigned types (k) 8 7 r488, r490, r495, c487, c489, c491, c493, s8 r490, r494, c489, c490, c491, s10, s5 List of assigned types Fraction of decisions with error ( 8% 8% ?/2) Distribution of types rational type 17% 32% c-heuristic type 52% 50% s-heuristic type 19% 6% ambiguous type 13% 12% 0% 20% 40% 60% 0% 20% 40% 60% Fraction of subjects Fraction of subjects Note: An ambiguous type is a subject to whom none of the types could be unambiguously assigned. In the Baseline Treatment, this is the case for 10 subjects, in the Time Pressure Treatment for 11 subjects. 17As a technical remark, I should note that the particular 8-tuple or 7-tuple that maximized the likelihood in both treatments, respectively, was the unique maximum of the likelihood. See section 4.2 for more details on the likelihood estimation procedure. 18However, between-treatment differences in these “ambiguous types” cannot explain the significant reduction in rational types in the Time Pressure Treatment. This can be seen in the appendix (section A.4), which contains a listing of all experimental subjects and shows their type classification in both treatments, such that the type classification results that are summarized in figure 4 can be followed on the level of each individual subject that participated in the experiment. 16

The finding of a fundamental effect of time pressure on behavioral heterogeneity raises a question that is important for our understanding of intertemporal choice behavior: How can there be such a strong difference in the type distribution between both treatments while at the same time there is no difference in descriptive behavioral characteristics, such as payoffs and the average number of decision steps? Result 2 summarizes this important point and gives an answer to this question: Result 2: The analysis of aggregate individual data (e.g. payoffs) can lead to differ- ent conclusions about the underlying behavioral heterogeneity than the structural analysis of individual decisions. This is because stochastic intertemporal choice tasks have the inherent property that individual agents’ objective functions are flat. Figure 5 provides support for Result 2. It combines the payoff charts of the different agent types that were shown in figures 1, 2, and 3 in section 3 (as well as figure A.1 in the appendix). For each of the types, I added to the figure a round circle, the diameter of which indicates the fraction of subjects classified by the particular type. The upper panel of figure 5 shows that 12% of all subjects in the Baseline Treatment are classified as risk neutral rational types (type r490). 5% are classified as risk averse rational types (type r488) and 15% are classified as risk seeking rational types (type r495). The remaining subjects are constant reservation price or satisficer types, i.e. they use simple rules of thumb. Figure 5 reveals that all observed rule of thumb types – even those whose behavior deviates strongly from a rational type – are close to the risk neutral rational type in terms of their average payoff. Moreover, even the “worst” rule in the population – rule r495, which is used by only 5% of the agents – still yields more than 86% of the payoff of a risk neutral rational agent. The lower panel of figure 5 shows that the type distribution is fundamentally different in the Time Pressure Treatment. Here, more subjects use rules of thumb. But the flatness of the payoff functions prevents the shift towards an increased usage of rules of thumb from reducing the average payoffs compared to the Baseline Treatment. 5.3 Validity of the Type Classification A question arising after the first two main results of this paper concerns the validity of the type classification. Does the classification algorithm lead to a reliable classification of individual intertemporal choice behavior? In this section, I provide two pieces of evidence to give an answer to this question. First, I show that the individual type assignment can be linked to independent dispositional measures of the subjects, namely their cognitive ability. Second, I reinvited the subjects five weeks later to do the same intertemporal choice task and find that a large fraction of the subjects have not changed their type. This addresses a fundamental concern in the social sciences, namely the temporal stability of basic behavioral regularities. 17

Figure 5: Distribution of Agent Types and Corresponding Payoffs for Both Treatments Baseline T Treatment r490 12% c487 6% r488 15% c491 10% s 6 6% s8 10 9 8 c489 17% Payoff [ECU] Average P 7 c493 16% r495 5% 6 5 Payoff of randomly choosing type 4 3 2 1 0 rational types c-heuristic types s-heuri istic types pattern-based types Time Pressur re Treatment c489 21% c491 14% r494 10% r490 8% s5 13% s10 s10 6% 10 9 8 c490 10% ECU] Average Payoff [E 7 6 5 Payoff of randomly choosing type 4 3 2 2 1 0 rational types c-heuristic types s-heuri istic types Pattern-based types Note: The percentages add up to a number smaller than 100% assigned unambiguously to a certain type. because the figure shows only the subjects that could be 18

Behavioral Types and Cognitive Ability Cognitive ability is a powerful predictor of economic and social outcomes, and it is one of the personality measures with the highest temporal stability and with the most reliable measurement methods (Borghans et al., 2008). Raven’s Advanced Progressive Matrices (APM) test is a widely accepted measurement method of cognitive ability that has been applied in numerous studies and many different cultures. The twelve-item version of the APM-test that experimental subjects completed in part B of the experiment has been successfully used to differentiate among university students (Bors and Stokes, 1998). When linking APM-test scores to observed intertemporal choice behavior, it is important to have the experimental design of part A in mind. In part A, all subjects had the possibil- ity to practice the intertemporal choice task as long as they wanted. Consequently, every subject could practice the task until he or she was using a decision rule that maximized payoff, given individual preferences. Due to the cognitive complexity of the experimental task, I hypothesized that subjects with higher cognitive abilities would thus be better able to detect the individually rational decision rule. In other words, subjects whose behavior is best classified by a decision rule derived under the assumption of rational behavior were hypothesized to have higher cognitive ability – i.e., higher APM-scores – than subjects whose behavior is best classified by a rule of thumb. The findings confirm this hypothesis and are summarized in the following result: Result 3: Rational types have a significantly higher cognitive ability. Behavioral types can thus be linked to cognitive ability, a dispositional character trait which is known to have a high temporal stability. Support for Result 3 can be found in figure 6. This figure shows that in both treatments, subjects who have been classified as rational types have a significantly higher APM-score. Importantly, this finding does not imply that the usage of heuristics is per se a sign of low cognitive skills or imprudent behavior. There are decision environments – e.g., very complex decision environments about which the decision-maker has no prior experience or decision situations in which learning is not possible – where it could be a reasonable and clever strategy to rely on an efficient and simple behavioral heuristic. However, the design of the experiment studied here explicitly allowed for experiencing and learning the intertemporal choice task as long as desired. Every subject had the opportunity to discern the best and individually rational decision rule at no costs. Thus, only cognitive constraints of the subjects remain as a limiting factor which could prevent a subject from learning a rational rule. The Temporal Stability of Behavioral Types: A Panel Experiment To investigate the stability of the type classification, I conducted another experiment, the design of which was identical with the Baseline treatment of the experiment discussed above. The only difference was that subjects participated in the experiment twice, with a 19

Figure 6: Type Classification and Cognitive Ability. Baseline Treatment (n=82; 7361 decisions) Time Pressure Treatment (n=84; 7165 decisions) 12 12 11 11 10 10 Cognitive ability (APM-score) 9 9 8 8 7 7 6 6 rational type c-heuristic type s-heuristic type ambiguous type rational type c-heuristic type s-heuristic type ambiguous type Note: The graphs show mean values and the error bars denote +/- the standard error of the mean. 5 weeks break in between.1986 subjects showed up at the first session and 82 of those also showed up five weeks later, such that repeated information on both sessions is available for 82 subjects. Before investigating the temporal stability of the types, it is important to examine whether general behavioral characteristics observed in the Baseline Treatment reported above (see table 2) are replicated in the panel experiment. This is the case. The Appendix (table A.2) shows clearly that aggregate descriptive characteristics do not differ from the findings in the Baseline Treatment, thus lending further support to our findings in section 5.1.20 Turning now to the analysis of individual level data from the panel experiment, I first look at the within-subject correlation of individual behavior in the two panel sessions. This is a concept which is referred to as a test-retest correlation in psychology and it serves as a measure for the temporal stability of individual behavior. Figure 7 illustrates the temporal stability of payoffs and of the number of decisions per subject. The Spearman correlation coefficients of r = 0.48 and r = 0.47 are both highly significant (p < 0.01) and they are similar to test-retest stability estimates of important dispositional personality dimensions that are extensively studied in psychology: in a meta-analysis, Roberts and DelVecchio (2000) report stability estimates of 18 to 22 year-old people to be on average about r = 0.50. The findings summarized in figure 7 already provide evidence of considerable stability of individual decisions over time. Rather than temporal stability of individual decisions, however, economic researchers dealing with heterogeneous agent models are interested in the temporal stability of the cross-sectional representation of behavioral heterogeneity that they have chosen. If the individual type classification remained stable over time, the cross- sectional distribution of types and thus the parsimonious representation of behavioral 19Furthermore, the test for cognitive ability was only included in the first of the two panel sessions, i.e. part B was dropped in the second session. 20Concerning the link between cognitive ability and type classification in the panel data, the findings in the subsection above could not be supported. Cognitive ability scores of the rational types were not significantly higher for the rational types than for the other types in the population of the panel experiment. I do not have an explanation for this observation. 20

Figure 7: Test-retest correlation in the panel experiment. Avg. payoffs per subject [in ECU] Avg. # decisions per subject 12 10 r=0.47 r=0.48 8 10 Panel Session 2 (5 weeks later) Panel Session 2 (5 weeks later) 6 8 4 6 2 4 4 6 8 10 12 2 4 6 8 10 Panel Session 1 Panel Session 1 heterogeneity could be assumed to be temporally stable. The findings about temporal stability are summarized in the following result. Result 4: The cross-sectional representation of behavioral heterogeneity remains stable over a five-week test-retest period. In particular, for a large fraction of the sample, the assigned behavioral type remains unchanged over a 5-week test-retest period. Support for Result 4 comes from figure 8, which shows the results from the type classi- fication in panel session 1 and in panel session 2.21The left column of this figure shows the type classification findings based on the data in panel session 1. This column shows that eight types – whose distribution is very similar to the distribution found in the Base- line Treatment shown in figure 422– provide a parsimonious characterization of latent behavioral heterogeneity in session 1. I hypothesized that these eight types which were assigned in session 1 also represent behavioral heterogeneity in session 2 and estimated the type classification for panel session 2 based on these 8 types. The right column of figure 8 shows the findings. The error rate ˆ ε has not changed compared to the findings in session 1 and the fraction of subjects that could not be unambiguously designed increased only slightly. As well, the distribution of types has not changed very much. Figure 8 thus provides evidence that the cross-sectional representation of behavioral heterogeneity remains surprisingly stable over a period of 5 weeks. Further support for Result 4 comes from a detailed analysis of each single subject’s type in both sessions. This analysis is summarized in table 3, which presents the type classification in the first and the second panel session in the form of a transition matrix. The main diagonal of this matrix shows that 40% of the subjects (33 out of the 82 21Again, as a technical remark, I should note that the tuple that maximized the likelihood in panel session 1 and 2, respectively, was the unique maximum of the likelihood. See section 4.2 for more details on the likelihood estimation procedure. 22Note that this also provides further support for the results discussed in section 5.2. 21

Figure 8: Classification of Behavioral Types in the Panel Experiment. Panel Session 1 (n=82; 7449 decisions) Panel Session 2 (5 weeks later) (n=82; 7165 decisions) Number of assigned types (k) 8 8 r488, r492, r496, c487, c489, c491, c493, s8 r488, r492, r496, c487, c489, c491, c493, s8 List of assigned types Fraction of decisions with error ( 9% 9% ?/2) Distribution of types rational type 28% 29% c-heuristic type 49% 55% s-heuristic type 11% e 2% ambiguous type 12% 15% 0% 20% 40% 60% 80% 0% 20% 40% 60% 80% Fraction of subjects Fraction of subjects Note: An ambiguous type is a subject to whom none of the types could be unambiguously assigned. This is the case for 10 subjects in Panel Session 1, and for 12 subjects in Panel Session 2. subjects) were assigned exactly the same type in both sessions. This value is strong evidence for temporal stability of types: if the type assignment were random, only about 13% of all subjects were assigned the same type in both sessions.23Furthermore, this stability estimate of 40% is a lower bound, because it excludes the ambiguous types, for many of whom behavior was quite stable over time. For example, consider a subject who was classified as a c487-type in session 1, and was ambiguously classified as a c487- or a r488-type in session 2. While this subject is counted as temporally instable in the analysis above, her behavior was clearly very similar in both sessions, since a c487-type described behavior best in both sessions. For some reason, e.g. some randomness in choice or a decision error, her behavior in session 2 only turned out to be also consistent with the behavior of a r488-type.24An upper bound on type stability is obtained by counting all subjects such as the example above as stable types and excluding the remaining subjects that could not be unambiguously assigned to a single type. This results in a stability estimate of 61% (42 out of 69 subjects). Table 3 also presents evidence on the stability of the classification into the three basic types of agents: rational types, constant reservation price types (c-heuristic), and satisficer-types (s-heuristic). 46% of the subjects are assigned the same basic type in both sessions, but only 34.5% would be expected if the classification were random. Again, this number is a lower bound on the stability estimate, because it ignores the stability of the ambiguously classified types. For example, a subject who was classified as a c493- or a r491-type in session 1 and as a c487- or a r491-type in session 2 is clearly a c-heuristic type in both 23See the appendix (subsection A.3) for the calculation of this percentage. 24The appendix (subsection A.4) contains a listing of all experimental subjects and their type classifica- tion in both sessions. Hence, the type stability analysis which table 3 synthesizes can be followed on the level of every individual subject. The subject that is discussed in the example above has ID no. 59. 22

sessions, but is not counted in the conservative estimate of 46% reported above.25An upper bound on the stability of the 3 basic types is obtained by counting subjects such as those discussed in the example above as stable types and excluding the subjects that could be unambiguously assigned. This results in a stability estimate of 68%. Table 3: Type classification in the panel experiment. Panel Session 2 (5 weeks later) heuristic c c491 rational s s8 r488 r492 r496 c487 c489 c493 Ambig. r488 2 0 0 2 1 1 1 0 4 rational r492 1 4 0 0 2 0 0 0 1 Panel session 1 r496 0 1 3 0 0 0 0 0 0 c487 1 1 0 0 1 0 0 0 3 heuristic c489 1 0 0 1 12 1 2 0 1 c c491 0 1 0 0 1 5 0 0 1 c493 0 1 1 0 0 0 5 0 0 s s8 2 0 0 0 2 2 0 2 1 Ambig. 2 2 0 2 0 2 0 0 3 6 Conclusions A large body of recent theoretical and applied literature in macroeconomics and finance emphasizes the fundamental importance of a better understanding of behavioral hetero- geneity in intertemporal choice for predicting aggregate outcomes (e.g., Heathcote et al., 2009; Hommes 2006, 2009). At the same time, the study of behavioral heterogeneity in intertemporal choice situations has received very little attention by empirical and exper- imental economists, probably because the complexity of intertemporal decision processes requires non-standard data analysis tools. Moreover, it has been pointed out repeatedly that the empirical literature has failed to adequately address the issue of latent behavioral heterogeneity in a way that structural information on individual behavior becomes avail- able (e.g. Durlauf, 2005). This failure of providing empirically well grounded structural information is problematic for macroeconomics and finance, because structural estima- tion allows for direct feedbacks between empirical findings and theory and has thus proven invaluable in the evolution of economics. In this paper, I used a structural classification procedure that was able to successfully uncover latent heterogeneity in intertemporal choice behavior. I provided a parsimo- nious representation of behavioral heterogeneity in the population which was grounded in well-established economic or psychological theories of intertemporal choice. The overall 25Again, more information is contained in the appendix (subsection A.4). The subject that is discussed in the example above has ID no. 14. 23

contribution of this paper was to show how controlled information on the nature, deter- minants, and temporal stability of behavioral heterogeneity in intertemporal choice can be obtained from data obtained in a simple laboratory experiment. Rather than discov- ering the specific set of decision rules that characterize behavior, the paper attempts to shed general light on the fundamental principles underlying heterogeneity in intertemporal choice behavior. The specific contributions of this paper are threefold: First, I show that there is con- siderable heterogeneity in the population, consisting of a mix of rational types and rule of thumb types. The mix of types is influenced by time pressure; this illustrates how important characteristics of the decision environment can influence aggregate outcomes by way of influencing the distribution of behavioral heterogeneity at the micro-level. For example, an increase in time pressure reduces the fraction of rational types in a popula- tion which, in turn, determines whether an error-free asset market equilibrium is reached (Kluger and Wyatt, 2004). Second, for a large fraction of the sample, assigned behavioral types can be assumed to be stable over a five week test-retest period. These findings pro- vide a structural microfoundation of the assumption of temporally stable heterogeneous agents. Moreover, the finding in itself as well as the underlying estimation methodol- ogy are informative for the calibration of heterogeneous agent models which often use modeling assumptions about agent heterogeneity that are empirically not well grounded (Duffy, 2006; Hommes 2006). Third, as a methodological point, the paper demonstrates why the mere analysis of aggregate behavioral data can lead to fundamentally different conclusions about the underlying individual behavior than the model-based analysis of individual decisions. Still, these are first results, which could depend on the particular design chosen here. Replication studies in different contexts will have to show the extent to which they can be generalized. For example, a future line of research would be to modify the experimental design and verify the generalizability of the findings with respect to, e.g., different price distributions, different degrees of time pressure, and out-of-sample stability of the assigned types. Moreover, the experimental design used in this paper did not involve any sort of interaction between the choices of the individual decision-makers. This ensured a clean empirical identification of agent types by fully excluding the confounding effects of uncontrolled factors such as social preferences and higher-order beliefs about the behaviors of the other individuals. However, an extension to interactive decision contexts would be of particular interest for exploring the link between behavioral heterogeneity on the micro-level and the outcomes of market interactions on an aggregate level. I believe that structural estimation of the type presented here is valuable for the evolution of economics. It allows for feedbacks between empirical findings and theory in micro- and macroeconomics, and – on a methodological note – it shows how experimental economics, macroeconomics and finance can interact fruitfully. I thus see this paper as a first step in a longer research program. 24

References Akerlof, G., Yellen, J., 1985. Can Small Deviations from Rationality Make Significant Differences to Economic Equilibria? American Economic Review, 75, 4, 708-720. Akerlof, G., 2002. Behavioral Macroeconomics and Macroeconomic Behavior. Ameri- can Economic Review, 92, 3, 411-433. Bellemare, C., Kroeger, van Soest, A., 2008. Measuring Inequity Aversion in a Heterogeneous Population using Experimental Decisions and Subjective Probabilities. Econometrica, 76, 4, 815-839. Borghans, L., Duckworth, A. L., Heckman, J. L., ter Weel, B., 2008. The economics and psychology of personality traits. Journal of Human Resources, 43, 4, 972-1059. Bors, D. A., Stokes, T., 1998. Raven’s Advanced progressive matrices: Norms for first-year university students and the development of a short form. Psychological Measurement 58, 3, 382.398. Educational and Brocks, W. A., Hommes, C., 1997. A rational route to randomness. Econometrica, 65, 5, 1059-1095. Bruhin, A., Fehr-Duda, H., Epper, T., 2010. Risk and Rationality: Uncovering Heterogeneity in Probability Distortion. Forthcoming: Econometrica. Chapman, D. A., Polkovnichenko, V., 2009. First-Order Risk Aversion, Hetero- geneity, and Asset Market Outcomes. Journal of Finance, 64, 4, 1863-1887. Cox, J. C., Oaxaca, R. L., 1989. Laboratory experiments with a finite-horizon job search model. Journal of Risk and Uncertainty 2, 301-330. Duffy, J., 2006. Agent-based models and human subject experiments. In: Tesfatsion, L., Judd, K.L. (Eds.), Handbook of Computational Economics, Agent-Based Computational Economics, vol. 2. Elsevier, Amsterdam, 949-1011. El-Gamal, M., Grether, D. M., 1995. Are people Bayesian? Uncovering behavioral strategies. Journal of the American Statistical Association, 90, 432, 11371145. Fehr, E., Tyran, J.-R., 2005. Individual Irrationality and Aggregate Outcomes. Jour- nal of Economic Perspectives, 19, 4, 43-66. Goeree, J. K., Riedl, A., Ule, A., 2009. In search of stars: Network formation among heterogeneous agents. Games and Economic Behavior, 67, 2, 445-466. Haltiwanger, J. C., Waldman, M., 1985. Rational Expectations and the Limits of Rationality: An Analysis of Heterogeneity. American Economic Review, 75, 3, 326-40. Haltiwanger, J. C., Waldman, M., 1989. Limited Rationality and Strategic Com- plements: The Implications for Macroeconomics. Quarterly Journal of Economics, 104, 3, 463-83. Heathcote, J., Storesletten, K., Violante, G. L., 2009. Quantitative Macroeco- nomics with Heterogeneous Households. Annual Review of Economics 1, 319 – 54. 25

Heathcote J., 2005. Fiscal policy with heterogeneous agents and incomplete markets. Review of Economic Studies 72, 1, 161 – 188. Heckman J. J., 2001. Micro data, heterogeneity, and the evaluation of public policy: Nobel lecture. Journal of Political Economy, 109, 4, 673 – 748. Hey, J. D., 1981. Are optimal search rules reasonable? And vice versa? (And does it matter anyway?). Journal of Economic Behavior and Organization 2, 47-70. Hey, J. D., 1982. Search for rules for search. Journal of Economic Behavior and Organization 3, 65-81. Hey, J. D., 1987. Still searching. Journal of Economic Behavior and Organization 8, 137-144. Hommes, C., 2006. Heterogeneous agent models in economics and finance. In: Tesfat- sion, L., Judd, K.L. (Eds.), Handbook of Computational Economics, Agent-Based Com- putational Economics, vol. 2. Elsevier, Amsterdam, pp. 11091186. Houser, D., Winter, J., 2004. How do behavioral assumptions affect structural in- ference? Evidence from a laboratory experiment. Journal of Business and Economic Statistics 22(1), 64-79. Kluger, B. D., Wyatt, S. B., 2004. Are Judgment Errors Reflected in Market Prices and Allocations? Experimental Evidence Based on the Monty Hall Problem. Journal of Finance 59,3, 96997. Kocher, M., and Sutter, M., 2004. Time is money – Time pressure, incentives and the quality of decision-making. Journal of Economic Behavior and Organization, 61, 3, 375-392. Kogut, C. A., 1990. Consumer search behavior and sunk costs. Journal of Economic Behavior and Organization, 14, 381-392. Moon, P., Martin, A., 1990. Better heuristics for economic search: Experimental and simulation evidence. Journal of Behavioral Decision Making 3, 175-193. Powell, W. B., 2007. Stochastic Dynamic Programming. John Wiley and Sons, New Jersey. Rabin, M., 2002. Inference by believers in the law of small numbers. Quarterly Journal of Economics 117, 775-816. Roberts, B. W., DelVecchio, W. F., 2000. The Rank-Order Consistency of Person- ality Traits from Childhood to Old Age: A Quantitative Review of Longitudinal Studies. Psychological Bulletin, 126, 1, 325. Rogerson, R., Shimer, R., Wright, R., 2005. Search-Theoretic Models of the Labor Market: A Survey. Journal of Economic Literature 43, 959-988. Schunk, D., Winter, J., 2009. The Relationship Between Risk Attitudes and Heuris- tics in Search Tasks: A Laboratory Experiment. Journal of Economic Behavior and Organization 71, 347-360. Simon, H., 1955. A Behavioral Model of Rational Choice. Quarterly Journal of Eco- nomics 69, 1, 99-118. 26

Sonnemans, J., 1998. Strategies of search. Journal of Economic Behavior and Orga- nization 35, 309-332. Sonnemans, J., 2000. Journal of Economic Psychology 21, 91-102. Decisions and strategies in a sequential search experiment. Woodbury, S. A., Davidson, C., 2002. Search Theory and Unemployment. Kluwer Academic Publishers. Norwell, MA, USA. 27

Appendix A.1 Details about the Pattern-Based Types Figure A.1 provides a characterization of the pattern-based types. Following the same graphical design as the right panels of figures 1, 2 and 3, figure A.1 shows for each of the 32 pattern-based types their corresponding payoffs as well as the average number of periods before stopping.1Figure A.1 shows clearly that the payoffs of the pattern-based types are much lower than the payoff of the rational types, the constant reservation price types (c-heuristic types) and the satisficer types (s-heuristic types). Note that a behavioral description of the pattern-based types and an explanation of their names (e.g., b1, b2, w(2)484, ...) is given in table 1 in the main text. Figure A.1: Characteristics of the Pattern-Based Rule of Thumb Types 10 40 Average Number of Periods before Stopping Average Number of Decisions 8 Average Payoff [ECU] 30 6 20 4 10 2 Average Payoff 0 0 b1 b2 w(2)484 w(2)485 w(2)486 w(2)487 w(2)488 w(2)489 w(2)490 w(2)491 w(2)492 w(2)493 w(2)494 w(2)495 w(2)496 w(2)497 w(2)498 w(3)484 w(3)485 w(3)486 w(3)487 w(3)488 w(3)489 w(3)490 w(3)491 w(3)492 w(3)493 w(3)494 w(3)495 w(3)496 w(3)497 w(3)498 Type Bounce types Winning streak (2) types Winning streak (3) types A.2 Details about Subjects’ Understanding of the Experimental Protocol and about the Time Pressure Manipulation Question on Subjects’ Understanding of the Experimental Protocol The question presented in part B of the experiment was asked to examine whether subjects understood the experimental protocol. Subjects had to specify their level of agreement with the following statement on a 7-point Likert-scale: I understood the instructions and it was totally clear to me, how the payoffs are determined. In the Baseline Treatment and the Time Pressure Treatment, the mean response to this question was 6.86. The mean did not differ between the two treatments (Mann-Whitney test, p=0.79), the lowest rating given was a 5 in the Baseline Treatment and a 4 in the Time Pressure Treatment. There is no evidence that the subjects reporting the lowest rating in each treatment differ exhibit intertemporal choice behavior which differs from the other subjects in the treatment. For example, the average payoffs time needed for a decision, the average payoff from all 20 rounds, and the average number of decision steps taken all lie between the 5th and the 95th 1Note that the scales of the y-axes in figure A.1 differ from the corresponding scales in figures 1, 2, and 3. 1

percentile of the distribution of all subjects in the particular treatment. Similarly, in the panel experiment, the mean response to this question was 6.82. Here, one subject gave a rating of 2. However, this subject performed well, and all behavioral characteristics (time needed for a decision, average payoff and average number of decision steps) lay well within the 5th and the 95th percentile of the distribution of all subjects. Moreover, discarding this subject from the sample did not change the results in any respect. Overall, the response to this question showed that subjects understood the experiment. Thus, all subjects that participated in the experiment were kept in the sample that is analyzed in this paper. The Time Pressure Manipulation and its Effect on Decision Times Table A.1 gives information on the decision times of the subjects and confirms the ob- servation above that the time pressure manipulation was sufficiently strong to have an effect on decision behavior: While subjects in the Baseline Treatment needed about 1.69 seconds per decision, subjects in the Time Pressure Treatment needed only 1.08 seconds – i.e.g, significantly less. Time pressure affected particularly those individual decisions that required the highest cognitive effort. In other words, the median decision time of 1.69 seconds in the Baseline Treatment masks a huge variability in decision times: The time pressure manipulation did not affect decision time in situations involving very low or very high price offers, i.e. situations in which the decision does not require cognitive efforts since it is straightforward. More than 8 percent of all decisions need more than four seconds time and are affected by exerting a time limit of four seconds in the Time Pressure Treatment. These decisions are mostly those with price offers between about 485 and 495 – i.e. offers in the range of the optimal values where decisions are cognitively most demanding. Table A.1: Decision Times per Period for Both Treatments Baseline Treatment (n=82; 7361 decisions) Time Pressure Treatment (n=84; 7165 decisions) ?sign. Median Std. Dev. Median Std. Dev. MW-Test (p-value) Decision time [in seconds] 1.69 0.66 1.08 0.21 0.00*** Note: ‘MW-Test’ refers to a Mann-Whitney-test. Significance levels: * 10%; ** 5%; *** 1%. A.3 Descriptive Statistics about Behavior in the Panel Experiment Table A.2 presents aggregate descriptive statistics for both sessions of the panel experi- ment. The first row of the table presents average payoffs and shows that average payoffs do not differ between sessions. The second row presents the average number of periods subjects have searched before stopping, and it also shows that there is no significant difference between the two panel sessions. Moreover, the descriptive results reported in 2

table A.2 can be compared to table 2, which reports the same descriptive statistics for the Baseline and the Time Pressure experiment. This comparison reveals that descriptives on behavior in the panel experiment neither differs from descriptives on behavior in the Baseline nor in the Time Pressure experiment. This further underlines the robustness of the results reported in section 5.2. Table A.2: Descriptive Statistics of Aggregate Behavioral Data. Panel Session 1 (n=82; 7449 decisions) Panel Session 2 (5 weeks later) (n=82; 7165 decisions) ?sign. Median Std. Dev. Median Std. Dev. ST-Test (p-value) Avg. Payoff [ECU] 8.45 1.01 8.83 1.06 0.18 Avg. # Periods 4.3 1.41 4.2 1.37 0.73 Notes: (1) ‘ST-Test’ refers to a sign test for the equality of matched pairs. (2) ‘Avg. Payoff’ refers to the average payoff per person for one search round, i.e. we divide the total payoff from all 20 search rounds by 20. Similarly, ‘Avg. # Periods’ refers to the average number of periods. Calculation of expected type stability rates under the assumption of random assignment In Panel Session 1, the following distribution of types was found (see table A.4. for details): r488: 13.4%, r492: 9.8%, r496: 4.8%, rc487: 7.3%, c489: 21.6%, c491: 9.8%, s8: 10.9%, Ambiguous: 13.4%. If type assignment in panel session 2 (5 weeks later) were randomly drawn with replacement from this type distribution, the probability that a r488-type is assigned the same type as in panel session 1 is 13.4% · 13.4% = 1.8%. Continuing this argument for all types, it can be easily calculated that random type assignment would on average lead to 13% correct reassignment in panel session 2. A.4 Detailed Results of the Type Classification See tables A.3 and A.4. 3

Table A.3: Subjects and their assigned type(s) in the Baseline Treatment and the Time Pressure Treatment. ? Assigned Type(s) c490, c489 c490, c489 r490, c490 r490, c490 c489 c491 c490 c489 c491 c490 c491 c491 c489 c491 c489 c490 c491 c489 c490 c489 c489 c489 r490 r490 r494 r490 r494 r494 r494 r490 s10 s10 s10 s5 s5 s5 s5 s5 s5 s5 s5 s5 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 ID Time Pressure Treatment Assigned Type(s) r490, c491, c490 r490, c490, c489 s10, c490, c489 c491, c490 c491, c489 c491, c490 r494, c491 r490, c490 r494, c491 r490, c490 s10, c489 c490 c489 c489 c491 c491 c491 c491 c489 c489 c489 c489 c490 c489 c490 c489 c491 c489 c491 c489 c490 r490 r494 r494 r490 r494 r490 r494 s10 s10 s5 s5 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 ID 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Assigned Type(s) s8, r490, c487 r490, c491 r488, c489 r490, c491 r490, c491 r495, c493 s8, r488 c487 c491 c489 c493 c489 c489 c489 c489 c491 c493 c493 c493 c489 c487 c487 c493 c491 c491 c491 r495 r488 r490 r490 r495 r488 r495 r488 r488 r488 r490 r488 s8 s8 s8 ID 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 Assigned Type(s) Baseline Treatment c489, c487 r488, c489 s8, c487 s8, r488 c489 c493 c493 c489 c493 c487 c489 c489 c491 c489 c493 c493 c491 c493 c489 c489 c493 c491 c493 c487 r490 r495 r488 r488 r490 r490 r488 r488 r490 r488 r488 r490 r490 r490 c489 s8 s8 ID 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 1 2 3 4 5 6 7 8 9 ? 4

Table A.4: Subjects and their assigned type(s) in the Panel Experiment. ? Assigned Type(s) r488, c489, c487 c491, c489 r496, c493 c487, r488 c487, r488 c487, r488 c489, s8 s8, r488 c493 c491 c489 c489 c487 c491 c489 c489 c489 c493 c489 c489 c487 c489 c487 c493 c489 r492 r492 r496 r488 r492 r488 r488 r488 r492 r492 r492 r488 r492 r488 r496 s8 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 ID Assigned Type(s) r492, c491, c493 c491, c489 c487, c491 c491, c489 r492, c493 Panel Session 2 s8, c493 c489 c489 c489 c493 c493 c491 c489 c491 c489 c489 c491 c489 c487 c491 c491 c489 c493 c491 c489 c491 c487 c489 c493 c491 c493 c491 r488 r492 r488 r488 r492 r496 r492 r496 s8 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 ID Assigned Type(s) r492, c493 r492, c493 r496, c493 s8, r488 c493 c487 c491 c489 c491 c487 c489 c487 c491 c489 c487 c487 c493 c489 c489 c491 c489 c493 c489 c489 r496 r492 r496 r488 r492 r492 r488 r492 r492 r488 r488 r488 s8 s8 s8 s8 s8 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 ID Assigned Type(s) r488, c489, c487 r492, c493, c491 c493, c491 r492, c493 r492, c491 r492, c493 s8, c491 Panel Session 1 c493 c489 c489 c493 c493 c489 c489 c491 c487 c491 c489 c491 c489 c489 c489 c489 c489 c491 c493 r492 r488 r492 r488 r488 r488 r496 r488 r492 r496 r488 s8 s8 s8 s8 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 ID 5

A.5 Instructions for the Experiment without Time Pressure [Translated into English] -Welcome- Welcome to the laboratory of the Institute for Empirical Research in Economics at the University of Zurich. You are participating in a scientific study on individual decision behavior. You can earn money by participating in this study. The amount of money you can earn depends on your decisions. This study consists of two parts, part A and part B, which we will describe below. PART A: This is a search game. Imagine yourself in the following situation: you would like to buy a specific product that is available in various locations at different prices. (You can imagine these locations, for example, as different stores or web addresses that you visit sequentially.) The product you are seeking is worth 500 monetary units (ECU) to you. The product you are looking for is available at the various locations you visit at different prices. The price at any one location is determined by a random draw from a normal distribution with a mean value of 500 ECU and a standard deviation of 10 ECU. The normal distribution is truncated, on the right and on the left, i.e. only prices between 460 and 540 ECU are possible, as shown in the graph to the right. The distribution is symmetric, that the probability of receiving a price below 500 ECU is equal to the probability of receiving a price above 500 ECU. Approximately 95% of all prices lie between 480 and 520 ECU. You can visit as many different locations as you want, and as soon as the search is over, you can buy the product at any location you previously visited. You pay search costs of 1 ECU for every new location you visit, however. You have 2 minutes of time at each location you visit to make your decision whether you want to stop or continue shopping. If you cannot make a decision in this time, your search ends, and the result of 0 ECU will be entered for this search round. Wahrscheinlichkeiten der Preise Probability of prices 4,5% 4,0% 3,5% Wahrscheinlichkeit 3,0% Probability 2,5% 2,0% 1,5% 1,0% 0,5% 0,0% 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 Preis in ECU Price in ECU Your payment at the end of the search game is determined as the value of the product (i.e. 500 ECU) less the purchase price you accepted and less the search costs. In those cases where you are unable to make a decision within the given time, the result of 0 ECU will be entered for you. You can practice the search game for as long as you want in order to become familiar with the computer program and the design of the game. The results of the practice rounds will not be paid out. After the practice phase, you will play 20 rounds that will count for your payment. Here are two examples for the search game: Example 1: You search six times, i.e. you visit six different locations sequentially and then decide to purchase the product at location 3, where it cost 480 ECU. Your payment then amounts to: 500 ECU - 480 ECU - 6 ECU = 14 ECU. You thus earn a profit of 14 ECU. - 1 - 6

Example 2: You search 10 times, i.e. at ten different locations. You finally decide to purchase the product for 490 ECU at location 10. Your payment then amounts to: 500 ECU - 490 ECU - 10 ECU = 0 ECU. PART B: In part B, we ask you to complete a questionnaire that will be distributed on paper. How will the payments for the study be determined? PART A: After the study is completed, one of the 20 played rounds will be randomly chosen for payment. (In this case, it does not matter if the round was completed normally or terminated due to expiry of the time limit.) Each participant will then be credited with the result that he or she attained in this randomly determined round. PART B: You will receive 5 ECU for completing the questionnaire. You will receive your definite payment in Swiss francs at the end of the study. You will earn 2 CHF per ECU. If, for example, you earn 9 ECU in part A, and 5 ECU for completing the questionnaire in part B, you will have earned a total of 14 ECU. This then corresponds to 28 CHF. We are interested in your actions in individual decision situations. Please do not speak with other participants during the study. If you have questions or problems with the computer program, please raise your hand. The study supervisor will then assist you. Please remain at your seat until the study supervisor comes to you and gives you your payment, or until he or she calls you. We thank you for your participation. We wish you success! Please complete the following test questions before we begin: You search seven times, i.e. at seven different locations. You finally decide to purchase the product for 491 ECU at location 7. How high is your payment in ECU? ________________________ How high is your payment in CHF? ________________________ - 2 - 7

A.6 Instructions for the Experiment with Time Pressure [Translated into English] -Welcome- Welcome to the laboratory of the Institute for Empirical Research in Economics at the University of Zurich. You are participating in a scientific study on individual decision behavior. You can earn money by participating in this study. The amount of money you can earn depends on your decisions. This study consists of two parts, part A and part B, which we will describe below. PART A: This is a search game. Imagine yourself in the following situation: you would like to buy a specific product that is available in various locations at different prices. (You can imagine these locations, for example, as different stores or web addresses that you visit sequentially.) The product you are seeking is worth 500 monetary units (ECU) to you. The product you are looking for is available at the various locations you visit at different prices. The price at any one location is determined by a random draw from a normal distribution with a mean value of 500 ECU and a standard deviation of 10 ECU. The normal distribution is truncated, on the right and on the left, i.e. only prices between 460 and 540 ECU are possible, as shown in the graph to the right. The distribution is symmetric, that the probability of receiving a price below 500 ECU is equal to the probability of receiving a price above 500 ECU. Approximately 95% of all prices lie between 480 and 520 ECU. You can visit as many different locations as you want, and as soon as the search is over, you can buy the product at any location you previously visited. You pay search costs of 1 ECU for every new location you visit, however. And, you only have four seconds of time at each location you visit to make your decision whether you want to stop or continue shopping. If you cannot make a decision in this time, your search ends, and the result of 0 ECU will be entered for this search round. Wahrscheinlichkeiten der Preise Probability of prices 4,5% 4,0% 3,5% Wahrscheinlichkeit 3,0% Probability 2,5% 2,0% 1,5% 1,0% 0,5% 0,0% 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 Preis in ECU Price in ECU Your payment at the end of the search game is determined as the value of the product (i.e. 500 ECU) less the purchase price you accepted and less the search costs. In those cases where you are unable to make a decision within the given time, the result of 0 ECU will be entered for you. You can practice the search game for as long as you want in order to become familiar with the computer program and the design of the game. The results of the practice rounds will not be paid out. After the practice phase, you will play 20 rounds that will count for your payment. Here are two examples for the search game: Example 1: You search six times, i.e. you visit six different locations sequentially and then decide to purchase the product at location 3, where it cost 480 ECU. Your payment then amounts to: 500 ECU - 480 ECU - 6 ECU = 14 ECU. You thus earn a profit of 14 ECU. - 1 - 8

Example 2: You search 10 times, i.e. at ten different locations. You finally decide to purchase the product for 490 ECU at location 10. Your payment then amounts to: 500 ECU - 490 ECU - 10 ECU = 0 ECU. PART B: In part B, we ask you to complete a questionnaire that will be distributed on paper. How will the payments for the study be determined? PART A: After the study is completed, one of the 20 played rounds will be randomly chosen for payment. (In this case, it does not matter if the round was completed normally or terminated due to expiry of the time limit.) Each participant will then be credited with the result that he or she attained in this randomly determined round. PART B: You will receive 5 ECU for completing the questionnaire. You will receive your definite payment in Swiss francs at the end of the study. You will earn 2 CHF per ECU. If, for example, you earn 9 ECU in part A, and 5 ECU for completing the questionnaire in part B, you will have earned a total of 14 ECU. This then corresponds to 28 CHF. We are interested in your actions in individual decision situations. Please do not speak with other participants during the study. If you have questions or problems with the computer program, please raise your hand. The study supervisor will then assist you. Please remain at your seat until the study supervisor comes to you and gives you your payment, or until he or she calls you. We thank you for your participation. We wish you success! Please complete the following test questions before we begin: You search seven times, i.e. at seven different locations. You finally decide to purchase the product for 491 ECU at location 7. How high is your payment in ECU? ________________________ How high is your payment in CHF? ________________________ - 2 - 9