Expectations and learning under alternative monetary regimes: an experimental approach

Summary We design and analyze experimental versions of monetary overlapping generations economies under alternative policy regimes. Economies with a constant level of real deficit financed through seignorage, economies in which the level of deficit is adapted in order to follow a monetary policy with a target rate of inflation, and economies with preannounced changes in deficit levels are reported here. We also examine the behavior of an economy with no stationary competitive equilibrium. Our time series are compared to rational expectations equilibrium paths and to adaptive learning dynamics.Financial support for our work from the Graduate School of the University of Minnesota, the National Science Foundation (SES-8912552), Richard M. and Margaret Cyert Family Funds, and the Ministry of Education of Spain is gratefully acknowledged. We wish to thank Javier Diaz-Giménez, Jean Michael Grandmont, Robert Lucas, Albert Marcet, Charles Plott, Edward Prescott, Thomas Sargent, Neil Wallace and Michael Woodford for commenting on our work. We also thank Vijay Rajan for developing the software for the computerized experimental environment, and Jackie Cuccaro and Dhananjay Gode for their research assistance.     

Learning,forecasting and optimizing: An experimental study

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 main 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 the worst in 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 term of the speed of finding the REE.     

Budget processes: Theory and experimental evidence

This paper studies budget processes, both theoretically and experimentally. We compare the outcomes of bottom-up and top-down budget processes. It is often presumed that a top-down budget process leads to a smaller overall budget than a bottom-up budget process. Ferejohn and Krehbiel [Ferejohn, J., Krehbiel, K., 1987. The budget process and the size of the budget, Amer. J. Polit. Sci. 31, 296–320] showed theoretically that this need not be the case. We test experimentally the theoretical predictions of their work. The evidence from these experiments lends strong support to their theory, both at the aggregate and the individual subject level.     

Market crashes,speculation and learning in financial markets

A natural conjecture is that if agents’ beliefs are almost correct then equilibrium prices should be close to rational expectations prices. Sandroni (J Econ Theory 82:1–18, 1998) gives a counterexample in an economy with sunspots and complete markets. We extend Sandroni’s result by showing that the conjecture is generically true for economies with complete markets. We consider a standard General Equilibrium model with large but finite horizon and complete markets. We show that, for almost every such economy, if conditional beliefs eventually become correct along a path of events then equilibrium prices of assets traded along this path converge to rational expectations equilibria in the sup-norm. Moreover, we establish that, generically, there exist along any such path local diffeomorphisms between individual beliefs and equilibrium prices. I would like to thank C. Ewerhart and A. Kirman for their comments, as well as the seminar participants at the University of Minho, the General Equilibrium Workshop 2005 in Zurich, and the 15th Asian General Equilibrium Conference 2007 in Singapore. An anonymous referee also provided very valuable comments.     

Rational expectations and fixed-event forecasts: An application to UK inflation

This paper tests a version of the rational expectations hypothesis using ‘fixed-event’ inflation forecasts for the UK. Fixed-event forecasts consist of a panel of forecasts for a set of outturns of a series at varying horizons prior to each outturn. The forecasts are the prediction of fund managers surveyed by Merrill Lynch. Fixed-event forecasts allow tests for whether expectations are unbiased in a similar fashion to the rest of the literature. But they also permit the conduct of particular tests of forecast efficiency - whether the forecasts make best use of available information - that are not possible with rolling-event data. We find evidence of a positive bias in inflation expectations. Evidence for inefficiency is much less clear cut.First version received: June 2002/ Final version received: November 2003We would like two anonymous referees and an editor for comments that have significantly improved the paper. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of England.     

Exploring the role of gender in common-pool resource extraction: evidence from laboratory and field experiments in fisheries

There is active debate on gender issues in natural resource management. For example, it is proposed that women are more cooperative than men when dealing with natural resources decisions; however, few scientific studies have directly addressed this hypothesis. We provide evidence for a greater cooperative attitude in women compared to men in both college students and coastal fishing communities of Baja California, Mexico, by means of game theory experiments. In both laboratory and field experiments, women changed their behaviour towards lower extraction compared to men, when regulations, sanctions or social scolding were introduced in the games. These results suggest that raising the role of women in decision-making, along with an adequate institutional framework, may lead to a more sustainable use of natural resources.     

Regret in auctions: theory and evidence

The sealed-bid first-price auction of a single object in the case of independent privately-known values is the simplest auction setting and understanding it is important for understanding more complex mechanisms. But bidders bid above the risk-neutral Nash equilibrium theory prediction. The reasons for this “over bidding” remain an unsolved puzzle. Several explanations have been offered, including risk aversion, social comparisons, and learning. We present a new explanation based on regret and a model that explains not only the observed over bidding in sealed-bid first-price auctions, but also behavior in several other settings that is inconsistent with risk aversion. The authors gratefully acknowledge support from the National Science Foundation.     

Simon's and Siegel's responses to the 'mixed strategy anomaly': a missed case in the sensitivity of economics to empirical evidence

In some of their papers published in the 1950s, Herbert Simonand Sidney Siegel responded to the so-called mixed strategyanomaly in ways which deserve more attention. They producednot only (i) immediate defences of the economic theory of theirown time, but also (ii) ideas and solutions that have laterturned out to be significant contributions to the developmentof the economic theory of choice and decision-making and theseparation of experimental economics from experimental psychology.These observations suggest that economics can be more responsiveto empirical anomalies than has been assumed. Furthermore, knowledgeof the desirable responsiveness to anomalies can provide meansof avoiding the non-desirable immunity to anomalies.     

Second chance offers versus sequential auctions: theory and behavior

Second chance offers in online marketplaces involve a seller conducting an auction for a single object and then using information from the auction to offer a losing bidder a take-it-or-leave-it price for another unit. We theoretically and experimentally investigate this practice and compare it to two sequential auctions. We show that the equilibrium bidding strategy in the second chance offer mechanism only exists in mixed strategies, and we observe that this mechanism generates more profit for the auctioneer than two sequential auctions. We also observe virtually no rejections of profitable offers in the ultimatum bargaining stage.      

Equilibrium play and adaptive learning in a three-person centipede game

The two-person centipede game is one of the most celebrated paradoxes of backward induction in complete information extensive form games. An experimental investigation of a three-person centipede game shows that the paradoxical results are strongly affected by the size of the stakes. When the number of players in the game is increased from two to three and the game is played for unusually high stakes with group composition being randomly changed from trial to trial, the paradox is considerably weakened as players approach equilibrium play with multiple iterations of the stage game. When the game is played with low stakes, there is no evidence for equilibrium play or learning across iterations of the stage game. An adaptive learning model that assumes updating of the individual probabilities of choice outperforms alternative static and dynamic models in accounting for the major results observed in the high-stake experiment.     

Fairness versus efficiency: An experimental study of (mutual) gift giving

Fairness is a strong concern as shown by dictator and ultimatum experiments. Efficiency, measured by the sum of individual payoffs, is a potentially competing concern in games, such as the prisoners’ dilemma. In our experiment, the participants can increase efficiency by giving gifts. In the one-sided treatment, this is only possible for one of the two partners. The two-sided treatment allows for mutual gift giving. In both cases, decisions can be conditioned on whether there is or there is not an efficiency gain by gift giving. Our results indicate that efficiency concerns are dominated by fairness concerns that are less stringent in mutual exchanges than in one-sided gift relationships.     

Global convergence of adaptive learning in models of pure exchange

Summary. This paper develops an adaptive learning scheme for a standard version of the OLG model with pure exchange. Perfect forecasting rules which generate perfect foresight orbits are approximated by cubic spline functions. These approximations are successively constructed using historical data only. Trajectories generated by this scheme converge to perfect foresight orbits globally for all initial conditions. This result holds for all parameterizations guaranteeing the existence of a monetary steady state and hence is independent of consumers' savings behavior. It generalizes to all one-dimensional models of the Cobweb type. Received: October 5, 2000; revised version: February 15, 2001     

Stability under learning: The endogenous growth problem

A local dynamic analysis, in the neighborhood of the steady state, is developed for one and two-sector endogenous growth models. The problem differs from the conventionally assumed growth setups because one considers that expectations concerning the next period value of the control variable (consumption) are formed through adaptive learning. In such scenario, the found stability conditions reveal that convergence to the unique steady state point is feasible if a minimum requirement regarding the quality of learning in the long run equilibrium is fulfilled. Therefore, stability of growth under learning is dependent on the efficiency with which expectations are generated.     

Heterogeneous learning

There is by now a large literature characterising conditions under which learning schemes converge to rational expectations equilibria (REEs). It has been claimed that these results depend on the assumption of homogeneous agents and homogeneous learning. This paper analyses the stability of REEs under heterogeneous adaptive learning, for the class of self-referential linear stochastic models. Agents may differ in their initial perceptions about the evolution of the economy, the degrees of inertia in revising their expectations, or the learning rules they use. General conditions are provided for local stability of an REE. In general, it is not possible to show that stability under homogeneous learning implies stability under heterogeneous learning. To illustrate how to apply the results, several examples are provided.     

Convergence for difference equations with vanishing time-dependence, with applications to adaptive learning

Summary. We provide conditions for local stability and instability of an equilibrium point in certain systems of nonautonomous nonstochastic difference equations. In the systems under study the influence of time is present through a positive scalar “gain” parameter which converges in the limit to zero. These systems have recently been used to study the dynamics of adaptive learning in economic models, and we provide two economic illustrations of the formal results. Received: October 7, 1997; revised version: February 8, 1999     

Inferring repeated-game strategies from actions: evidence from trust game experiments

Summary. Combining a strategy model, an inference procedure and a new experimental design, we map sequences of observed actions in repeated games to unobserved strategies that reflect decision-makers’ plans. We demonstrate the method by studying two institutional settings with distinct theoretical predictions. We find that almost all strategies inferred are best responses to one of the inferred strategies of other players, and in one of the settings almost all of the inferred strategies, which include triggers to punish non-cooperators, are consistent with equilibrium strategies. By developing a method to infer unobserved repeated-game strategies from actions, we take a step toward making game theory a more applied tool, bridging a gap between theory and observed behavior.Received: 23 December 2002, Revised: 19 April 2005, JEL Classification Numbers: C72, C80, C90.The authors are indebted for discussions with Ray Battalio, David Cooper, Robin Dubin, John Duffy, Ellen Garbarino, Susan Helper, Margaret Meyer, John Miller, Jim Rebitzer, Mari Rege, Al Roth, and John Van Huyck. The authors also benefited from discussants at economic department seminars at Case Western Reserve, McMaster and McGill University, University of Pittsburgh, SUNY-Stony Brook, and Texas A&M, and participants at the 2002 European Winter Meeting of the Econometric Society. We are grateful for the financial support provided by the Department of Economics at the University of Pittsburgh and Case Western Reserve University.     

Economic planning for market economies : The optimality of planning in an economy with uncertainty and asymmetrical information

The paper is based on a disequilibrium model which is Keynesian in the ‘short run’, ie with given expectations, but which admits of a continuum of equilibria when expectations are rational. Expectations are adaptive (so that they are rational only in the long run) but can be influenced by an indicative plan. The government and the private sector have differing information sets, each knowing some things the other sector does not (spontaneously) know. It is shown that in this world, an optimal plan dominates a self-fulfilling plan, which in turn dominates a no-planning equilibrium.     

A Markov analysis of social learning and adaptation

A number of recent contributions to the literature have modelled social learning and adaptation in an economic context. Understanding the processes driving these models is important in order to explain and predict the behaviour of the economy. In this paper, we analyze the economic applications for a class of adaptive learning models with bounded rational agents. The dynamics of these economies can be thought of as arising from discrete-time Markov chains. In particular, conditions for uniqueness of equilibria, convergence and stability in the economic systems follow from the accessibility and communication structures of these Markov chains. We establish a correspondence between absorbing states of the Markov chains and economic equilibria, whether stable or unstable, and develop theorems giving conditions for absorption and recurrence. Furthermore, we develop practical applications of these theorems using a cobweb model. We use a genetic algorithm, operating under election, as an example of a well known adaptive learning process.