University of Pittsburgh John Duffy Pittsburgh Experimental Economics Laboratory

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Working Papers Published & Forthcoming

Working Papers

"Adaptive vs. Eductive Learning: Theory and Evidence" (with Te Bao), December 2013.

Adaptive learning and eductive learning are two widely used ways of modeling learning behavior in macroeconomics. Both approaches yield restrictions on model parameters under which agents are able to learn a rational expectation equilibrium (REE) but these restrictions do not always overlap with one another. In this paper we report on an experiment where we exploit such differences in stability conditions under adaptive and eductive learning to investigate which learning approach provides a better description of the learning behavior of human subjects. Our results suggest that adaptive learning is a better predictor of whether a system converges to REE, while the path by which the system converges appears to be a mixture of both adaptive and eductive learning model predictions.

"All-Pay Auctions vs. Lotteries as Provisional Fixed-Prize Fundraising Mechanisms: Theory and Evidence" (with Alexander Matros), July 2013.

We study two provisional fixed-prize mechanisms for funding public goods: an all-pay auction and a lottery. In our setting, the public good is provided only if the participants' contributions are greater than the fixed-prize value; otherwise contributions are refunded. We prove that in this provisional fixed prize setting, lotteries can outperform all-pay auctions in terms of expected public good provision. Specifically, we state conditions under which the provisional fixed prize all-pay auction mechanism generates zero public good provision, while the provisional fixed prize lottery mechanism generates positive public good provision. We test these predictions in a laboratory experiment where we vary the number of participants, the marginal per capita return (mpcr) on the public good, and the mechanism for awarding the prize, either a lottery or an all-pay auction. Consistent with the theory, we find that the mpcr matters for contribution amounts under the lottery mechanism. However, inconsistent with the theory bids are always significantly higher than predicted and there is no significant difference in public good contributions under either mechanism. We suggest how a non-expected utility approach involving probability weighting can help to explain over-bidding in our experiment.

"An Experimental Test of the Lucas Asset Pricing Model" (with Sean Crockett), May 2013.

We implement a dynamic asset pricing experiment in the spirit of Lucas (1978) with storable assets and non-storable cash. In one treatment we impose diminishing marginal returns to cash to incentivize consumption-smoothing across periods, while in a second treatment there is no induced motive for trade. In the former case subjects smooth consumption, and assets trade at a discount relative to the risk-neutral fundamental price. This under-pricing is a departure from the "bubbles" observed in the experimental asset pricing experiments of Smith et al. (1988). In our second treatment with no induced motive for trade, assets trade at a premium relative to expected value and shareholdings are highly concentrated.

"Are Dynamically Inefficient Equilibria Learnable?" (with Wei Xiao), July 2011.

We consider the stability under adaptive learning dynamics of steady state equilibria in the Diamond (1965) overlapping generations growth model with capital and money. Interior steady state equilibria of this model can be either dynamically inefficient or dynamically efficient. We show that a necessary condition for an equilibrium of this model to be stable under adaptive learning is that the equilibrium is dynamically efficient. In other words, adaptive learning can be used as a selection criterion to exclude dynamically inefficient equilibria. We also provide conditions under which a dynamically efficient equilibrium of this model involving the use of both capital and money will be stable under adaptive learning dynamics.

"Group Size and Cooperation Among Strangers" (with Huan Xie), January 2013.

We study how group size affects cooperation in an infinitely repeated n-player Prisoner's Dilemma (PD) game. In each repetition of the game, groups of size nM are randomly and anonymously matched from a fixed population of size M to play the n-player PD stage game. We provide conditions for which the contagious strategy (Kandori, 1992) sustains a social norm of cooperation among all M players. Our main finding is that if agents are sufficiently patient, a social norm of society-wide cooperation becomes easier to sustain under the contagious strategy as nM.

"Language and Coordination: An Experimental Study" (with Ernest K. Lai and Wooyoung Lim), May 2014.

We report on an experiment exploring whether and how players may learn to use a random device to coordinate on a correlated equilibrium that Pareto dominates the Nash equilibria of a two-player Battle of the Sexes game. By contrast with other studies exploring recommendations and correlated equilibria, the mapping from the random device to the action space of the game is not necessarily known by subjects a priori, which serves to highlight the additional coordination problem that is introduced by the use of such a random device. We find that subjects have an easier time coordinating on the efficient correlated equilibrium of the game when there is a common language mapping from the realizations of the random device to the action space of the game. However, we also find that it is possible for subjects to learn to develop a language mapping from realizations of the random device to the action space of the game when that mapping is not common to begin with. We further find that a random device is more useful as a coordination mechanism when subjects are randomly matched. When subjects are in fixed matches, other strategies that ignore the random device and condition instead on the players' joint history, e.g., "alteration" or "turn-taking" can achieve the same efficient outcome that is made possible by introduction of the random device.

"Learning and Structural Change in Macroeconomic Data" (with James Bullard), December 2005.

We include learning in a standard equilibrium business cycle model with explicit growth. We use the model to study how the economy's agents could learn in real time about the important trend-changing events of the postwar era in the U.S., such as the productivity slowdown, increased labor force participation by women, and the "new economy" of the 1990s. We find that a large fraction of the observed variance of output relative to trend can be attributed to structural change in our model. However, we also find that the addition of learning and occasional structural breaks to the standard and widely-used growth model results in a balanced growth puzzle, as our approach cannot completely account for observed trends in U.S. aggregate consumption and investment. Finally, we argue that a model-consistent detrending approach, such as the one we suggest here, is necessary if the goal is to obtain an accurate assessment of an equilibrium business cycle model.

"Lifecycle Consumption Plans, Social Learning and External Habits: Experimental Evidence," (with Enrica Carbone), June 2014.

We report results from a laboratory experiment exploring the extent to which individuals can solve a deterministic, intertemporal lifecycle consumption optimization problem and the effect of revealing social information on past average consumption amounts; as all individuals have identical induced preferences and lifetime incomes, such social information could be useful in solving for the optimal consumption path. Instead, we find that the provision of social information on past average levels of consumption results in a greater deviation of consumption from both the unconditional and the conditionally optimal paths. We find some improvement in consumption planning relative to the conditional optimum when social concerns (external habits) are explicitly incorporated into subject's period utility functions as in external habit formation preference specifications. Our results on the effects of social information on consumption behavior may help to explain the phenomenon of over-consumption and under-saving that has been observed in many developed countries in recent decades as social information on the behavior of others has become more readily available.

"Macroeconomics: A Survey of Laboratory Research," Revised Draft, April 2014.

This chapter surveys laboratory experiments addressing macroeconomic phenomena. The first part focuses on experimental tests of the microfoundations of macroeconomic models discussing laboratory studies of intertemporal consumption/savings decisions, time (in)consistency of preferences and rational expectations. Part two explores coordination problems of interest to macroeconomists and mechanisms for resolving these problems. Part three looks at experiments in specific macroeconomic sectors including monetary economics, labor economics, international economics as well-as large scale, multi-sector models that combine several sectors simultaneously. The final section addresses experimental tests of macroeconomic policy issues.

"Stochastic Asymmetric Blotto Games: Theory and Experimental Evidence" (with Alexander Matros), May 2014.

We study a 2-player Blotto game where the n items have asymmetric values. The winner of each item is determined stochastically using a lottery mechanism. We analyze two payoff objectives: (i) players maximize their total expected payoffs and (ii) players maximize their probability of winning a majority value of all items. We develop new theoretical results for the majority rule case and show how that payoff objective results in qualitatively different equilibrium behavior than the total expected payoff objective. We report results from an experiment where the two payoff objectives are compared and find strong support for our theoretical predictions.

Published & Forthcoming
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"Gift Exchange versus Monetary Exchange: Theory and Evidence" (with Daniela Puzzello), forthcoming in American Economic Review.

We study the Lagos and Wright (2005) model of monetary exchange in the laboratory. With a finite population of sufficiently patient agents, this model has a unique monetary equilibrium and a continuum of non-monetary gift exchange equilibria, some of which Pareto dominate the monetary equilibrium. We find that subjects avoid the gift-exchange equilibria in favor of the monetary equilibrium. We also study versions of the model without money where all equilibria involve non-monetary gift-exchange. We find that welfare is higher in the model with money than without money, suggesting that money plays a role as an efficiency enhancing coordination device.

"Cooperation and Signaling with Uncertain Social Preferences" (with Félix Muñoz-García), forthcoming in Theory and Decision.

This paper investigates behavior in finitely repeated simultaneous and sequential-move prisoner's dilemma games when there is one-sided incomplete information and signaling about players' concerns for fairness, specifically, their preferences regarding "inequity aversion." In this environment, we show that only a pooling equilibrium can be sustained, in which a player type who is unconcerned about fairness initially cooperates in order to disguise himself as a player type who is concerned about fairness. This disguising strategy induces the uninformed player to cooperate in all periods of the repeated game, including the final period, at which point the player type who is unconcerned about fairness takes the opportunity to defect, i.e., he "backstabs" the uninformed player. Despite such last-minute defection, our results show that the introduction of incomplete information can actually result in a Pareto improvement under certain conditions. We connect the predictions of this "backstabbing" equilibrium with the frequently observed decline in cooperative behavior in the final period of finitely-repeated experimental games.

"Real-Time Learning via Parameterized Expectations" (with Michele Berardi), forthcoming in Macroeconomic Dynamics.

We explore real time, adaptive nonlinear learning dynamics in stochastic macroeconomic systems. Rather than linearizing nonlinear Euler equations where expectations play a role around a steady state, we instead approximate the nonlinear expected values using the method of parameterized expectations. Further we suppose that these approximated expectations are updated in real time as new data become available. We argue that this method of real-time parameterized expectations learning provides a plausible alternative to real-time adaptive learning dynamics under linearized versions of the same nonlinear system.

"On the Use of Fines and Lottery Prizes to Increase Voter Turnout" (with Alexander Matros), Economics Bulletin 34 (2014), 966-975.

We consider implementation issues regarding two mechanisms that have been used to increase voter turnout in elections: fines and lotteries. We focus on the amount of the fine or lottery prize needed to achieve full participation. We then propose a combined, self-financing mechanism by which the fines imposed on non-participants are used to finance the prize that is awarded by lottery to one of the individuals choosing to participate in voting. We argue that this combined mechanism has some advantages over the other two mechanisms and merits consideration.

"Compulsory versus Voluntary Voting: An Experimental Study" (with Sourav Bhattacharya and SunTak Kim), Games and Economic Behavior 84 (2014), 111-131.

We report on an experiment comparing compulsory and voluntary voting institutions in a voting game with common preferences. Rational choice theory predicts sharp differences in voter behavior between these two institutions. If voting is compulsory, then voters may find it rational to vote insincerely, i.e., against their private information. If voting is voluntary so that abstention is allowed, then sincere voting in accordance with a voter's private information is always rational while participation may become strategic. We find strong support for these theoretical predictions in our experimental data. Moreover, voters adapt their decisions to the voting institution in place in such a way as to make the group decision accuracy differences between the two voting institutions negligible. The latter finding may serve to rationalize the co-existence of compulsory and voluntary voting institutions in nature.he co-existence of compulsory and voluntary voting institutions in nature.

"Learning, Forecasting and Optimizing: an Experimental Study" (with Te Bao and Cars Hommes), European Economic Review 61 (2013), 186-204.

Rational Expectations (RE) models have two crucial dimensions: (i) agents on average correctly forecast future prices given all available information, and (ii) given expectations, agents solve optimization problems and these solutions in turn determine actual price realizations. Experimental tests of such models typically focus on only one of these two dimensions. In this paper we consider both forecasting and optimization decisions in an experimental cobweb economy. We report results from four experimental treatments: (1) subjects form forecasts only, (2) subjects determine quantity only (solve an optimization problem), (3) they do both and (4) they are paired in teams and one member is assigned the forecasting role while the other is assigned the optimization task. All treatments converge to Rational Expectation Equilibrium (REE), but at different speeds. We observe that performance is the best in treatment 1 and worst in the treatment 3. We further find that most subjects use adaptive rules to forecast prices. Given a price forecast, subjects are less likely to make conditionally optimal production decisions in treatment 3 where the forecast is made by themselves, than in treatment 4 where the forecast is made by the other member of their team, which suggests that "two heads are better than one" in finding REE.

"Social Norms, Information and Trust among Strangers: Theory and Evidence," (with Huan Xie and Yong-Ju Lee) Economic Theory 52 (2013), 669-708.

Can a social norm of trust and reciprocity emerge among strangers? We investigate this question by examining behavior in an experiment where subjects repeatedly play a two-player binary "trust" game. Players are randomly and anonymously paired with one another in each period. The main questions addressed are whether a social norm of trust and reciprocity emerges under the most extreme information restriction (anonymous community-wide enforcement) or whether trust and reciprocity require additional, individual-specific information about a player's past history of play and whether that information must be provided freely or at some cost. In the absence of such reputational information, we find that a social norm of trust and reciprocity is difficult to sustain. The provision of reputational information on past individual decisions significantly increases trust and reciprocity, with longer histories yielding the best outcomes. Importantly, we find that making reputational information available at a small cost may also lead to a significant improvement in trust and reciprocity, despite the fact that most subjects do not choose to purchase this information.

"Equilibrium Selection in Static and Dynamic Entry Games" (with Jack Ochs), Games and Economic Behavior 76 (2012), 97-116. Instructions used in the experiment.

We experimentally examine equilibrium refinements in static and dynamic binary choice games of complete information with strategic complementarities known as "entry" games. Our aim is to assess the predictive power of two different equilibrium selection principles. In static entry games, we test the theory of global games as an equilibrium selection device. This theory posits that players play games of complete information as if they were playing a related global game of incomplete information. In dynamic entry games, individuals decide not only whether to enter but also when to enter. Once entry occurs it is irreversible. The number of people who have already entered is part of the state description, and individuals can condition their decisions on that information. If the state variable does not indicate that entry is dominated, the efficient subgame perfect equilibrium prediction calls for all players to enter. Further, if there is a cost of delay, entry should occur immediately, thereby eliminating the coordination problem. This subgame perfect entry threshold in the dynamic game will generally differ from the global game threshold in static versions of the same entry game. Nevertheless, our experimental findings suggest that observed entry thresholds in both static and dynamic versions of the same entry game are surprisingly similar. The mean entry threshold in the static game lies below the global game equilibrium threshold while the mean entry threshold in the dynamic game lies above the efficient subgame perfect equilibrium threshold. An important implication of this finding is that if one were to observe only the value of the state variable and the number of people who enter by the end of the game one could not determine whether the static or the dynamic game had been played.

"Patience or Fairness? Analyzing Social Preferences in Repeated Games" (with Félix Muñoz-García), Games 3 (2012), 56-77.

This paper investigates how the introduction of social preferences affects players' equilibrium behavior in both the one-shot and the infinitely repeated version of the Prisoner's Dilemma game. We show that fairness concerns operate as a "substitute" for time discounting in the infinitely repeated game, as fairness helps sustain cooperation for lower discount factors. In addition, such cooperation can be supported under larger parameter values if players are informed about each others' social preferences than if they are uninformed. Finally, our results help to identify conditions under which cooperative behavior observed in recent experimental repeated games can be rationalized using time preferences alone (patience) or a combination of time and social preferences (fairness).

"Differences in Risk Aversion Between Young and Older Adults" (with Steven M. Albert), Neuroscience and Neuroeconomics 1 (2012), 3-9.

Research on decision-making strategies among younger and older adults suggests that older adults may be more risk averse than younger people in the case of potential losses. These results mostly come from experimental studies involving gambling paradigms. Since these paradigms involve substantial demands on memory and learning, differences in risk aversion or other features of decision making attributed to age may in fact reflect age-related declines in cognitive abilities. In the current study, older and younger adults completed a simpler, paired lottery choice task used in the experimental economics literature to elicit risk aversion. A similar approach was used to elicit participants' discount rates. The older adult group was more risk averse than the younger (p<0.05) and had a higher discount rate (15.6-21.0 percent versus 10.3-15.5 percent, p<0.01), indicating lower expected utility from future income. Risk aversion and implied discount rates were weakly correlated. It may be valuable to investigate developmental changes in neural correlates of decision making across the lifespan.

"Competitive Behavior in Market Games: Evidence and Theory" (with Alexander Matros and Ted Temzelides), Journal of Economic Theory 146 (2011), 1437-1463.

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1972). Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.

"Investment and Monetary Policy: Learning and Determinacy of Equilibrium" (with Wei Xiao), Journal of Money, Credit and Banking 43 (2011), 959-992.

We explore determinacy and expectational stability (learnability) of rational expectations equilibrium (REE) in "New Keynesian" (NK) models that include capital. Using a consistent calibration across three different models--labor only, firm-specific capital, or an economy-wide rental market for capital, we provide a clear picture of when REE is determinate and learnable and when it is not under a variety of monetary policy rules. Our findings make a case for greater optimism concerning the use of such rules in NK models with capital. While Bullard and Mitra's (2002, 2007) findings for the labor-only NK model do not always extend to models with capital, we show that determinate and learnable REE can be achieved in NK models with capital if there is (i) plausible capital adjustment costs, (ii) some weight given to output in the policy rule and/or iii) a policy of interest rate smoothing.

"Trust in Second Life" Southern Economic Journal 78 (2011), 53-62.

Some issues are raised with regard to conducting economic decision-making experiments in virtual worlds. The issues are illustrated via a visit to an experimental laboratory on Second Life. Some suggestions for addressing these issues are proposed.

"Correlated Equilibria, Good and Bad: An Experimental Study" (with Nick Feltovich), International Economic Review 51 (2010), 701-721.

We report results from an experiment that explores the empirical validity of correlated equilibrium, an important generalization of Nash equilibrium. Specifically, we examine the conditions under which subjects playing the game of Chicken will condition their behavior on private third-party recommendations drawn from publicly announced distributions. We find that when recommendations are given, behavior differs from both a mixed-strategy Nash equilibrium and behavior without recommendations. In particular, subjects typically follow recommendations if and only if (1) those recommendations derive from a correlated equilibrium and (2) that correlated equilibrium is payoff-enhancing relative to the available Nash equilibria.

"Self-Organized Criticality in a Dynamic Game" (with Andreas Blume and Ted Temzelides), Journal of Economic Dynamics and Control 34 (2010), 1380-1391.

We investigate conditions under which self-organized criticality (SOC) arises in a version of a dynamic entry game. In the simplest version of the game, there is a single location -- a pool -- and one agent is exogenously dropped into the pool every period. Payoffs to entrants are positive as long as the number of agents in the pool is below a critical level. If an agent chooses to exit, he cannot re-enter, resulting in a future payoff of zero. Agents in the pool decide simultaneously each period whether to stay in or not. We characterize the symmetric mixed strategy equilibrium of the resulting dynamic game. We then introduce local interactions between agents that occupy neighboring pools and demonstrate that, under our payoff structure, local interaction effects are necessary and sufficient for SOC and for an associated power law to emerge. Thus, we provide an explicit game-theoretic model of the mechanism through which SOC can arise in a social context with forward looking agents.

"Does Competition Affect Giving?" (with Tatiana Kornienko), Journal of Economic Behavior and Organization 74 (2010), 82-103. Experimental instructions.

Charities often devise fund-raising strategies that exploit natural human competitiveness in combination with the desire for public recognition. We explore whether institutions promoting competition can affect altruistic giving - even when possibilities for public acclaim are minimal. In a controlled laboratory experiment based on a sequential "dictator game," we find that subjects tend to give more when placed in a generosity tournament, and tend to give less when placed in an earnings tournament - even if there is no award whatsoever for winning the tournament. Further we find that subjects' experimental behavior correlates with their responses to a post-experiment questionnaire, particularly questions addressing altruistic and rivalrous behavior. Based on this evidence, we argue that behavior in our experiment is driven, in part, by innate competitive motives.

"Decentralized Organizational Learning: An Experimental Investigation" (with Andreas Blume and April Franco), American Economic Review 99 (2009), 1178-1205.

We experimentally study decentralized organizational learning. Our objective is to understand how learning members of an organization cope with the confounding effects of the simultaneous learning of others. Rather than inferring or postulating some heuristic organizational learning behavior, we experimentally test the optimal learning predictions of a stylized, rational agent model of organizational learning due to Blume and Franco (2007). This model provides sharp testable predictions as to how learning members of an organization might cope with the simultaneous learning of others as a function of fundamental variables that characterize an organization, e.g., the firm size and the discounting of future payoffs. While the problem of learning while others are learning is quite difficult, we find support for the comparative static predictions of the unique symmetric equilibrium of the model.

"Cooperative Behavior and the Frequency of Social Interaction" (with Jack Ochs), Games and Economic Behavior 66 (2009), 785-812. Download the dataset.

We report results from an experiment that examines play in an indefinitely repeated, two-player Prisoner's Dilemma game. Each experimental session involves N subjects and a sequence of indefinitely repeated games. The main treatment consists of whether agents are matched in fixed pairings or matched randomly in each indefinitely repeated game. Within the random matching treatment, we elicit player's strategies and beliefs or vary the information that players have about their opponents. Contrary to a theoretical possibility suggested by Kandori (1992), a cooperative norm does not emerge in the treatments where players are matched randomly. On the other hand, in the fixed pairings treatment, the evidence suggests that a cooperative norm does emerge as players gain more experience.

"Experiments with Network Formation" (with Dean Corbae), Games and Economic Behavior 64 (2008), 81-120. There is also a Technical and Data Appendix for this paper. Instructions are here.

We examine how groups of agents form trading networks in the presence of idiosyncratic risk and the possibility of contagion. Specifically, four agents play a two-stage finite repeated game. In the first stage, the network structure is endogenously determined through a noncooperative proposal game. In the second stage, agents play multiple rounds of a coordination game against all of their chosen `neighbors' after the realization of a payoff relevant shock. While parsimonious, our four agent environment is rich enough to capture all of the important interaction structures in the networks literature: bilateral (marriage), local interaction, star, and uniform matching. Consistent with our theory, marriage networks are the most frequent and stable network structures in our experiments. We find that payoff efficiency is around 90 percent of the ex-ante, payoff dominant strategies and the distribution of network structures is significantly different from that which would result from random play.

"Beliefs and Voting Decisions: A Test of the Pivotal Voter Model" (with Margit Tavits), American Journal of Political Science 52 (2008), 603-618. Instructions are here.

We report results from a laboratory experiment testing the basic hypothesis imbedded in various rational voter models that there is a direct correlation between the strength of an individual's belief that his/her vote will be pivotal and the likelihood that individual incurs the cost to vote. This belief is typically unobservable. In one of our experimental treatments we elicit these subjective beliefs using a proper scoring rule that induces truthful revelation of beliefs. This allows us to directly test the pivotal voter model. We find that a higher subjective probability of being pivotal increases the likelihood that an individual votes, but the probability thresholds used by subjects are not as crisp as the theory would predict. There is some evidence that individuals learn over time to adjust their beliefs to be more consistent with the historical frequency of pivotality. However, many subjects keep substantially overestimating their probability of being pivotal.

"Internet Auctions with Artificial Adaptive Agents: A Study on Market Design" (with Utku Ãœnver), Journal of Economic Behavior and Organization 67 (2008), 394-417.

Many internet auction sites implement ascending-bid, second-price auctions. Empirically, last-minute or "late" bidding is frequently observed in "hard-close" but not in "soft-close" versions of these auctions. In this paper, we introduce an independent private-value repeated internet auction model to explain this observed difference in bidding behavior. We use finite automata to model the repeated auction strategies. We report results from simulations involving populations of artificial bidders who update their strategies via a genetic algorithm. We show that our model can deliver late or early bidding behavior, depending on the auction closing rule in accordance with the empirical evidence. Among other findings, we observe that hard-close auctions raise less revenue than soft-close auctions. We also investigate interesting properties of the evolving strategies and arrive at some conclusions regarding both auction designs from a market design point of view.

"Experimental Macroeconomics"

in: S. Durlauf and L. Blume, eds., New Palgrave Dictionary of Economics, 2nd Ed., New York: Palgrave Macmillan, 2008.

"Giving Little By Little: Dynamic Public Good Games" (with Jack Ochs and Lise Vesterlund), Journal of Public Economics 91 (2007), 1708-1730.

Charitable contributions are frequently made over time. Donors are free to contribute whenever they wish and as often as they want, and are frequently updated on the level of contributions by others. A dynamic structure enables donors to condition their contribution on that of others, and, as Schelling (1960) suggested, it may establish trust thereby increasing charitable giving. Marx and Matthews (2000) build on Schelling's insight and show that multiple contribution rounds may secure a provision level that cannot be achieved in the static, one-shot setting, but only if there is a discrete, positive payoff jump upon completion of the project. We examine these two hypotheses experimentally using static and dynamic public good games. We find that contributions are indeed higher in the dynamic than in the static game. However, in contrast to the predictions, the increase in contributions in the dynamic game does not depend critically on the existence of a completion benefit jump or on whether players can condition their decisions on the behavior of other members of their group.

"Instability of Sunspot Equilibria in Real Business Cycle Models Under Adaptive Learning" (with Wei Xiao), Journal of Monetary Economics 54 (2007), 879-903.

We examine the stability of equilibrium in sunspot-driven real business cycle (RBC) models under adaptive learning. We show that a general, reduced form of this class of models can admit rational expectations equilibria that are both indeterminate and stable under adaptive learning. Indeterminacy of equilibrium allows for the possibility that non-fundamental "sunspot" variable realizations can serve as the main driving force of the model, and several researchers have put forward calibrated structural models where sunspot shocks play such a role. We show analytically how the structural restrictions that researchers have imposed on this type of model lead to reduced form systems where equilibrium is indeterminate but always unstable under adaptive learning. Our findings provide a possible resolution of the "stability puzzle" identified by Evans and McGough (2002).

"The Value of Interest Rate Stabilization Policies When Agents are Learning" (with Wei Xiao), forthcoming in the Journal of Money, Credit, and Banking.

We examine the expectational stability (E--stability) of rational expectations equilibrium in the ``New Keynesian'' model where monetary policy is optimally derived and interest rate stabilization is added to the central bank's traditional objectives of inflation and output stabilization. We consider both the case where the central bank lacks a commitment technology and the case of full commitment. We show that for both cases, optimal policy rules yield rational expectations equilibria that are E-stable for a wide range of empirically plausible parameter values. These findings stand in contrast to Evans and Honkapohja's (2003ab, 2006) findings for optimal monetary policy rules in environments where interest rate stabilization is not a central bank objective.

"The Value of Central Bank Transparency When Agents are Learning" (with Michele Berardi), European Journal of Political Economy 23 (2007), 9-29.

We examine the role of central bank transparency when the private sector is modeled as adaptive learners. In our model, transparent policies enable the private sector to adopt correctly specified models of inflation and output while intransparent policies do not. In the former case, the private sector learns the rational expectations equilibrium while in the latter case it learns a restricted perceptions equilibrium. These possibilities arise regardless of whether the central bank operates under commitment or discretion. We provide conditions under which the policy loss from transparency is lower (higher) than under intransparency, allowing us to assess the value of transparency when agents are learning.

"Words, Deeds and Lies: Strategic Behaviour in Games with Multiple Signals" (with Nick Feltovich), Review of Economic Studies 73 (2006), 669-688.

We report the results of an experiment in which subjects play games against changing opponents. In one treatment, "senders" send "receivers" messages indicating intended actions in that round, and receivers observe senders' previous-round actions (when matched with another receiver). In another treatment, the receiver additionally observes the sender's previous-round message to the previous opponent, enabling him to determine whether the sender had lied. We find that allowing multiple signals leads to better outcomes when signals are aligned (all pointing to the same action), but worse outcomes when signals are crossed. Also, senders' signals tend to be truthful, though the degree of truthfulness depends on the game and treatment, and receivers' behavior combines elements of pay-off maximization and reciprocity.

"Dollarization Traps" (with Maxim Nikitin and R. Todd Smith), Journal of Money, Credit, and Banking 38 (2006), 2073-2098.

The paper analyzes dollarization in the sense of asset substitution, where a foreign currency competes with local assets, especially domestic capital, as a store of value, the impact of dollarization on capital accumulation and output, and why economies remain dollarized long after a successful inflation stabilization. We relate this dollarization hysteresis to a financial intermediation failure that happens during high inflation. We show that in dollarized countries, inflation stabilization policies may not have any effect on domestic capital accumulation, thus preventing such policies from stimulating growth, i.e., dollarized economies are vulnerable to "dollarization traps."

"Multiple Regimes in U.S. Monetary Policy? A Nonparametric Approach" (with Jim Engle-Warnick), Journal of Money, Credit, and Banking 38 (2006), 1363-1377.

We use two different nonparametric methods to determine whether there were multiple regimes in U.S. monetary policy over the period 1955--2003. We model monetary policy using two different versions of Taylor's rule for the nominal interest rate target. By contrast with parametric tests for regime changes, the nonparametric methods we use allow the data to determine the dimensions on which to split the sample for purposes of estimating the coefficients of the Taylor rule. We find evidence for a few structural breaks and consistent agreement between our two nonparametric methods on the dating of those breaks.

"Agent-Based Models and Human Subject Experiments," in: L. Tesfatsion and K.L. Judd, eds., Handbook of Computational Economics Vol. 2 Handbooks in Economics Series, (Amsterdam: Elsevier, 2006), 949-1011.

This chapter examines the relationship between agent-based modeling and economic decision-making experiments with paid human subjects. Both approaches exploit controlled "laboratory" conditions as a means of isolating the sources of aggregate phenomena. Research findings from laboratory studies of human subject behavior have inspired studies using artificial agents in "computational laboratories" and vice versa. In certain cases, both methods have been used to examine the same phenomenon. The focus of this chapter is on the use of agent-based models to explain experimental findings. We point out synergies between the two methodologies that have been exploited as well as promising new possibilities.

"Asset Price Bubbles and Crashes with Near-Zero-Intelligence Traders" (with Utku Ãœnver), Economic Theory 27 (2006), 537-563.

We examine whether a simple agent--based model can generate asset price bubbles and crashes of the type observed in a series of laboratory asset market experiments beginning with the work of Smith, Suchanek and Williams (1988). We follow the methodology of Gode and Sunder (1993, 1997) and examine the outcomes that obtain when populations of zero--intelligence (ZI) budget constrained, artificial agents are placed in the various laboratory market environments that have given rise to price bubbles. We have to put more structure on the behavior of the ZI-agents in order to address features of the laboratory asset bubble environment. We show that our model of "near--zero--intelligence" traders, operating in the same double auction environments used in several different laboratory studies, generates asset price bubbles and crashes comparable to those observed in laboratory experiments and can also match other, more subtle features of the experimental data.

"Sunspots in the Laboratory" (with Eric O'N. Fisher), American Economic Review 95 (2005), 510-529. (Paper title links to our 2003 working paper which is a longer, more detailed version of the paper appearing in the AER.)

We show that extrinsic or non-fundamental uncertainty influences markets in a controlled environment. This work provides the first direct evidence of sunspot equilibria. These equilibria require a common understanding of the semantics of the sunspot variable, and they appear to be sensitive to the flow of information. Sunspots always occur in a closed-book call market, but they happen only occasionally in a double auction, where infra-marginal bids and offers are observable.

"Anarchy in the Laboratory (and the Role of the State)" (with Minseong Kim), Journal of Economic Behavior and Organization 56 (2005), 297-329.

A recent literature on the economics of conflict has provided conditions under which an "anarchic" outcome may come to serve as an equilibrium for an economy, as well as conditions under which a "dictator" or "government agent" is empowered to make collective action choices that enable the economy to achieve a Pareto superior equilibrium. This paper reports results from a laboratory experiment designed to test the predictions of this theory. We find that in the absence of any government, groups of subjects choose forecasts and actions that lie within a neighborhood of the predicted anarchic equilibrium, where some players choose to be producers, while others choose to be predators. The introduction of the government agent, charged with maximizing the consumption of producers, enables the subject groups to achieve nearly perfect coordination on a Pareto superior Nash equilibrium, where the fraction of time devoted to defense is high, but predation is eliminated.

"Learning, Information and Sorting in Market Entry Games: Theory and Evidence" (with Ed Hopkins), Games and Economic Behavior 51 (2005), 31-62. (Download instructions.)

Previous data from experiments on market entry games, N-player games where each player faces a choice between entering a market and staying out, appear inconsistent with either mixed or pure Nash equilibria. Here we show that, in this class of game, learning theory predicts sorting, that is, in the long run, agents play a pure strategy equilibrium with some agents permanently in the market, and some permanently out. We conduct experiments with a larger number of repetitions than in previous work in order to test this prediction. We find that when subjects are given minimal information, only after close to 100 periods do subjects begin to approach equilibrium. In contrast, with full information, subjects learn to play a pure strategy equilibrium relatively quickly. However, the information which permits rapid convergence, revelation of the individual play of all opponents, is not predicted to have any effect by existing models of learning.

"Trust Among Strangers" (with Cristina Bicchieri and Gil Tolle), Philosophy of Science 71 (2004), 286-319.

The paper presents a simulation of the dynamics of impersonal trust. It shows how a "trust and reciprocate" norm can emerge and stabilize in populations of conditional cooperators. The norm, or behavioral regularity, is not to be identified with a single strategy. It is instead supported by several conditional strategies that vary in the frequency and intensity of sanctions.

"Capital-Skill Complementarity? Evidence from a Panel of Countries," with Chris Papageorgiou and Fidel Perez-Sebastian, The Review of Economics and Statistics 86 (2004), 327-344.

Since Griliches (1969), researchers have been intrigued by the idea that physical capital and skilled labor are relatively more complementary than physical capital and unskilled labor. In this paper we consider the cross-country evidence for capital-skill complementarity using a time-series, cross-section panel of 73 developed and less developed countries over a 25 year period. We focus on three empirical issues. First, what is the best specification of the aggregate production technology to address the capital-skill complementarity hypothesis. Second, how should we measure skilled labor? Finally, is there any cross-country evidence in support of the capital-skill complementarity hypothesis? Our main finding is that we find some support for the capital-skill complementarity hypothesis in our macro panel dataset.

"Comment on Adaptive Learning and Monetary Policy Design," Journal of Money, Credit, and Banking 35 (2003), 1073-1080.

This is a comment on the paper "Adaptive Learning and Monetary Policy Design" by George W. Evans and Seppo Honkapohja that was prepared for the FRB-Cleveland/JMCB conference, "Recent Developments in Monetary Macroeconomics" hosted by the Federal Reserve Bank of Cleveland in November 2002.

"Intrinsically Worthless Objects as Media of Exchange: Experimental Evidence" with Jack Ochs, International Economic Review 43 (2002), 637-673. (This paper was formerly titled "Fiat Money as a Medium of Exchange: Experimental Evidence")

This paper reports results from an experiment that examines whether an intrinsically worthless, `token' object serves as a medium of exchange in a laboratory implementation of Kiyotaki and Wright's search model of money. The theory admits Nash equilibria in which the token object is or is not used as a medium of exchange. We find that subjects nearly always offer to trade for the token object when such a trade lowers their storage costs. However, subjects frequently refuse to offer to trade the token object for more costly-to-store goods when the theory predicts they should make such trades. View the raw data from this experiment.

"Do Actions Speak Louder than Words? Observation vs. Cheap Talk as Coordination Devices" with Nick Feltovich, Games and Economic Behavior 39 (2002), 1-27.

This paper reports results from an experiment designed to compare cheap talk and observation of past actions. We consider three games and explain why cheap talk or observation is likely to be more effective for achieving good outcomes in each game. We find that both cheap talk and observation make cooperation and coordination more likely and increase payoffs, relative to our control treatment. The relative success of cheap talk versus observation depends on the game, in accordance with our predictions. We also find that players' signals are informative, and that signal receivers condition their actions on the signal they receive.

"Learning and Excess Volatility" with James Bullard, Macroeconomic Dynamics 5 (2001), 272-302.

We introduce adaptive learning behavior into a general equilibrium lifecycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least squares autoregressions on past data. We show that, in contrast to the perfect foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for these learning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time series data for U.S. stock returns and per capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.

"Learning to Speculate: Experiments with Artificial and Real Agents," Journal of Economic Dynamics and Control 25 (2001) 295-319.

This paper employs an artificial agent-based, computational approach to understanding and designing laboratory environments in which to study and test Kiyotaki and Wright's (1989) search model of money. The behavioral rules of the artificial agents are modeled on the basis of prior evidence from human subject experiments. Simulations of the artificial agent-based model are conducted in two new versions of the Kiyotaki-Wright environment and yield some testable predictions. These predictions are examined using data from new human subject experiments. The results are encouraging and suggest that artificial agent-based modeling may be a useful device for both understanding and designing human subject experiments.

"Equilibrium Selection via Adaptation: Using Genetic Programming to Model Learning in a Coordination Game" with Shu-Heng Chen and Chia-Hsuan Yeh, in The Electronic Journal of Evolutionary Modeling and Economic Dynamics, 2002, issue 1, article 1002.

This paper studies adaptive behavior in a simple coordination game that Van Huyck, Cook and Battalio (1994) have investigated in a controlled laboratory setting with human subjects. We consider how populations of artificially intelligent agents play the same game. The computational approach that we adopt provides us with much greater flexibility in the experimental design than is possible with experiments involving human subjects. We use genetic programming techniques developed by Koza (1992, 1994) to model how players might learn over time. These genetic programming techniques have certain advantages over other artificial intelligence techniques that have been applied to economic models, for example, genetic algorithms. We find that the pattern of behavior generated by our population of artificially intelligent players is remarkably similar to that followed by human subjects who played the same game. In particular, we find that a steady state that is theoretically unstable under a myopic best-response learning dynamic turns out to be stable under our genetic-programming-based learning system, in accordance with Van Huyck et al.'s finding using human subjects. We conclude that genetic programming techniques may serve as a plausible and inexpensive selection criterion in environments with multiple equilibria.

"A Cross-Country Empirical Investigation of the Aggregate Production Function Specification" with Chris Papageorgiou, Journal of Economic Growth 5 (March 2000), 87-120. (An earlier version of this paper circulated under the title "The Specification of the Aggregate Production Function: A Cross-Country Empirical Investigation")

Many growth models assume that aggregate output is generated by a Cobb-Douglas production function. In this article we question the empirical relevance of this specification. We use a panel of 82 countries over a 28-year period to estimate a general constant-elasticity-of-substitution (CES) production function specification. We find that for the entire sample of countries we can reject the Cobb-Douglas specification. When we divide our sample of countries up into several subsamples, we find that physical capital and human capital adjusted labor are more substitutable in the richest group of countries and are less substitutable in the poorest group of countries than would be implied by a Cobb-Douglas specification.

"Approximating and Simulating the Stochastic Growth Model: Parameterized Expectations, Neural Networks, and the Genetic Algorithm" with Paul D. McNelis, Journal of Economic Dynamics and Control 25 (September 2001), 1273-1303.

This paper suggests a new approach to solving the one-sector stochastic growth model using the method of parameterized expectations. The approach is to employ a "global" genetic algorithm search for the parameters of the expectation function followed by a "local" gradient-descent optimization method to ensure fine-tuning of the approximated solution. We use this search procedure in combination with either polynomial or neural network specifications for the expectation function. We find that our approach yields highly accurate solutions in the case where an exact analytic solution exists as well as in cases where no closed-form solution exists. Our results further suggest that neural network specifications for the expectation function may be preferred to the more commonly used polynomial specification.

"Using Symbolic Regression to Infer Strategies from Experimental Data" (with J. Engle-Warnick), in S-H. Chen, Ed., Evolutionary Computation in Economics and Finance, New York: Physica-Verlag, 2002, pp. 61-82.

We propose the use of a new technique--symbolic regression--as a method for inferring the strategies that are being played by subjects in economic decision making experiments. We begin by describing symbolic regression and our implementation of this technique using genetic programming. We provide a brief overview of how our algorithm works and how it can be used to uncover simple data generating functions that have the flavor of strategic rules. We then apply symbolic regression using genetic programming to experimental data from the ultimatum game. We discuss and analyze the strategies that we uncover using symbolic regression and we conclude by arguing that symbolic regression techniques should at least complement standard regression analyses of experimental data.

"Does Observation of Others Affect Learning in Strategic Environments?: An Experimental Study" with Nick Feltovich, International Journal of Game Theory 28 (1999), 131-152.

This paper presents experimental results from an analysis of two similar games, the repeated ultimatum bargaining game and the repeated best-shot game. The experiments examine how the amount and content of information given to players affects the evolution of play in the two games. In one experimental treatment, subjects in both games observe not only their own actions and payoffs, but also those of one randomly chosen pair of players in the just-completed round of play. In the other treatment, subjects in both games observe only their own actions and payoffs. We present evidence suggesting that observation of other players' actions and payoffs affects the evolution of play in both games relative to the case of no observation. Moreover, the effect of observation on learning is different in the two games. In the ultimatum game, players who observe the actions and payoffs of others tend to deviate further from the subgame perfect equilibrium strategy over time than players who observe only their own actions and payoffs. In contrast, in the best-shot game, players who observe the actions and payoffs of others tend to play closer to the subgame perfect equilibrium strategy over time than players who observe only their own actions and payoffs. We conclude that providing players with additional information need not hasten the rate at which they learn to play subgame perfect equilibrium strategies. Rather, our findings support the conclusion of Prasnikar and Roth (1992) that the incentives players face off the equilibrium path strongly influence how behavior evolves over time.

"Emergence of Money as a Medium of Exchange: An Experimental Study," with Jack Ochs, American Economic Review 89 (1999), 847--877.

Kiyotaki and Wright (1989) developed a simple dynamic model of an exchange economy in which one or more commodities are used as media of exchange. In this paper, we report findings from an experiment that implements the Kiyotaki-Wright model. We consider whether the equilibrium predictions of the Kiyotaki-Wright model are robust to the dynamics created by out-of-equilibrium play. In particular, we examine whether individuals placed in the Kiyotaki-Wright environment learn over time to adopt the same commodities as media of exchange as the model implies will be used in equilibrium. We find that subjects have a strong tendency to play "fundamental" rather than "speculative strategies even in environments where speculative strategies would lead to higher payoffs. We examine some possible motivations for subjects' trading behavior and we find that subjects are mainly motivated by their own past payoff experience as opposed to being motivated by the marketability concerns that the theory suggests are important.

"Using Genetic Algorithms to Model the Evolution of Heterogeneous Beliefs," with James Bullard, Computational Economics 13 (1999), 41-60.

We study a general equilibrium system where agents have heterogeneous beliefs concerning realizations of possible outcomes. The actual outcomes feed back into beliefs thus creating a complicated nonlinear system. Beliefs are updated via a genetic algorithm learning process which we interpret as representing communication among agents in the economy. We are able to illustrate a simple principle: genetic algorithms can be implemented so that they represent pure learning effects (i.e. beliefs updating based on realizations of endogenous variables in an environment with heterogeneous beliefs). Agents optimally solve their maximization problem at each date given their beliefs at each date. We report the results of a set of computational experiments in which we find that our population of artificial adaptive agents is usually able to coordinate their beliefs so as to achieve the Pareto superior rational expectations equilibrium of the model.

"Monetary Theory in the Laboratory" Federal Reserve Bank of St. Louis Review 80 (September/October 1998), 9-26.

Empirical tests of macroeconomic and monetary theories are typically conducted using non-experimental field data provided by government agencies. Modern theories, however, have increasingly imposed restrictions on individual behavior that are not embodied in any available field data. An alternative method for testing such theories is to conduct controlled laboratory experiments with paid human subjects. This article provides a critical survey of recent papers that have used laboratory methods to test modern monetary-theory predictions. While the survey focuses on the results obtained from these laboratory studies, I also provide some justification for the experimental methodology and discuss experimental design issues.

"Learning and the Stability of Cycles" with James Bullard, Macroeconomic Dynamics 2 (1998), 22-48.

We study a general equilibrium model where the multiplicity of stationary periodic perfect foresight equilibria is pervasive. We investigate the extent to which agents can learn to coordinate on stationary perfect foresight cycles. The example economy, taken from J.M. Grandmont (1985), is a two period, endowment overlapping generations model with fiat money, where consumption in the first and second periods of life are not necessarily gross substitutes. Depending on the value of a preference parameter, the limiting backward (direction of time reversed) perfect foresight dynamics are characterized by steady state, periodic or chaotic trajectories for real money balances. We relax the perfect foresight assumption and examine how a population of artificial, heterogeneous adaptive agents might learn in such an environment. These artificial agents optimize given their forecast of future prices, and they use forecast rules that are consistent with steady state or periodic trajectories for prices. The agents' forecast rules are updated by a genetic algorithm. We find that the population of artificial adaptive agents is able to eventually coordinate on steady state and low-order cycles, but not on the higher-order periodic equilibria that exist under the perfect foresight assumption.

"A Model of Learning and Emulation with Artificial Adaptive Agents," with James Bullard, Journal of Economic Dynamics and Control 22 (1998), 179-207.

We study adaptive learning behavior in a sequence of n-period endowment overlapping generations economies, where n refers to the number of periods in agents' lifetimes. Agents initially have heterogeneous beliefs and seek to form multi-step ahead consumption plans based on forecasts of future prices. Agents learn in every period by forming new consumption plans and by emulating the consumption plans of other agents. Computational experiments with artificial adaptive agents are conducted. In these experiments, the heterogeneous population of artificial agents nearly always learns over time to form consumption plans that are consistent with perfect foresight knowledge of future prices. The model of learning and emulation that we develop is also used to study transition dynamics from one stationary perfect foresight equilibrium to another.

"On the Robustness of Behavior in Experimental 'Beauty Contest' Games," with Rosemarie Nagel, Economic Journal 107 (1997), 1684-1700.

We report and compare results from several different versions of an experimental interactive guessing game first studied by Nagel (1995), which we refer to as the 'beauty contest' game following Keynes (1936). In these games, groups of subjects are repeatedly asked to simultaneously guess a real number in the interval [0,100] that they believe will be closest to 1/2 times either the median, mean, or maximum of all numbers chosen. In all three versions of the beauty contest game, the unique Nash equilibrium is for all subjects to announce zero. We find that convergence to this equilibrium is fastest in the 1/2-median game and slowest in the 1/2-maximum game and we offer an explanation for the findings. We also use our experimental data to test a simple model of adaptive learning behavior.

"The Transition from Stagnation to Growth: An Adaptive Learning Approach" with Jasmina Arifovic and James Bullard, Journal of Economic Growth 2 (1997), 185-209.

This paper develops the first model in which, consistent with the empirical evidence, the transition from stagnation to economic growth is a very long endogenous process. The model has one steady state with a low and stagnant level of income per capita and another steady state with a high level of income per capita. Both of these steady states are locally stable under the perfect foresight assumption. We relax the perfect foresight assumption and introduce learning into this environment. Learning acts as an equilibrium selection criterion and provides an interesting transition dynamic between steady states. We find that for sufficiently low initial values of human capital--values that would tend to characterize pre-industrial countries--the system under learning spends a long period of time (an epoch ) in the neighborhood of the low income steady state before finally transitioning to a neighborhood of the high income steady state. We argue that this kind of transition dynamic provides a good characterization of the economic growth and development patterns that have been observed across countries.

"Corruption Cycles" with Cristina Bicchieri, Political Studies 45 (1997), 477-498.

We provide a model of political corruption as a cyclical phenomenon.

"On Learning and the Nonuniqueness of Equilibrium in an Overlapping Generations Model with Fiat Money," Journal of Economic Theory, 64 (1994), 541-553.

This paper examines disequilibrium adaptive learning behavior in an overlapping generations model with fiat money. Agents are concerned with forming correct forecasts of future inflation. If they use a disequilibrium, adaptive forecast rule, it is shown that they will eventually learn to believe in a nonstationary, nonunique perfect foresight equilibrium. The nonstationary equilibrium isolated by the adaptive learning process can be used to explain the sluggish adjustment of the price level to monetary disturbances as documented in the work of C.A. Sims (1989).

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