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29
Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model
, 1998
"... This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their `beliefs' in each period in a boundedly rational way, according to a `fitness mea ..."
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Cited by 167 (12 self)
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This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their `beliefs' in each period in a boundedly rational way, according to a `fitness measure' such as past realized profits. Price fluctuations are thus driven by an evolutionary dynamics between different expectation schemes (`rational animal spirits'). Using a mixture of local bifurcation theory and numerical methods, we investigate possible bifurcation routes to complicated asset price dynamics. In particular, we present numerical evidence of strange, chaotic attractors when the intensity of choice to switch prediction strategies is high.
If You’re So Smart, Why Aren’t You Rich? Belief Selection in Complete and Incomplete Markets
, 2001
"... ..."
2003), “Policy Evaluation in Uncertain Economic Environments (with discussion
 Brookings Papers on Economic Activity
"... It will be remembered that the seventy translators of the Septuagint were shut up in seventy separate rooms with the Hebrew text and brought out with them, when they emerged, seventy identical translations. Would the same miracle be vouchsafed if seventy multiple correlators were shut up with the sa ..."
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Cited by 31 (5 self)
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It will be remembered that the seventy translators of the Septuagint were shut up in seventy separate rooms with the Hebrew text and brought out with them, when they emerged, seventy identical translations. Would the same miracle be vouchsafed if seventy multiple correlators were shut up with the same statistical material? And anyhow, I suppose, if each had a different economist perched on his a priori, that would make a difference to the outcome. 1 This paper describes some approaches to macroeconomic policy evaluation in the presence of uncertainty about the structure of the economic environment under study. The perspective we discuss is designed to facilitate policy evaluation for several forms of uncertainty. For example, our approach may be used when an analyst is unsure about the appropriate economic theory that should be assumed to apply, or about the particular functional forms that translate a general theory into a form amenable to statistical analysis. As such, the methods we describe are, we believe, particularly useful in a range of macroeconomic contexts where fundamental disagreements exist as to the determinants of the problem under study. In addition, this approach recognizes that even if economists agree on the
Learning under Ambiguity
 Review of Economic Studies
, 2002
"... This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extremeit models agents who are implausibly ambitious about w ..."
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Cited by 31 (3 self)
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This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extremeit models agents who are implausibly ambitious about what they can learn in complicated environments. The paper then provides a generalization of the Bayesian model that accommodates the intuitive choices in the thought experiments. In particular, the model allows decisionmakers ’ confidence about the environment to change — along with beliefs — as they learn. A portfolio choice application compares the effect of changes in confidence under ambiguity versus changes in estimation risk under Bayesian learning. The former is shown to induce a trend towards more stock market participation and investment even when the latter does not. 1
Anticipated Utility and Rational Expectations as Approximations of Bayesian Decion Making
, 2005
"... We study a Markov decision problem with unknown transition probabilities. We compute the exact Bayesian decision rule and compare it with two approximations. The first is an infinitehistory, rationalexpectations approximation that assumes that the decision maker knows the transition probabilities. ..."
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Cited by 30 (3 self)
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We study a Markov decision problem with unknown transition probabilities. We compute the exact Bayesian decision rule and compare it with two approximations. The first is an infinitehistory, rationalexpectations approximation that assumes that the decision maker knows the transition probabilities. The second is a version of Kreps ’ (1998) anticipatedutility model in which decision makers update using Bayes ’ law but optimize in a way that is myopic with respect to their updating of probabilities. For several consumptionsmoothing examples, the anticipatedutility approximation outperforms the rational expectations approximation. The rational expectations approximation misrepresents the market price of risk in a Bayesian economy. Key words: Rational expectations, Bayes ’ Law, anticipated utility, market price of risk. ∗ For comments and suggestions, we thank Lars Hansen, Narayana Kocherlakota, Frank Schorfheide, three referees, and seminar participants at Stanford and the CFS Summer School
Evolution and intelligent design
 American Economic Review
, 2008
"... This paper discusses two sources of ideas that influence monetary policy makers today. The first is a set of analytical results that impose the rational expectations equilibrium concept and do ‘intelligent design ’ by solving Ramsey and mechanism design problems. The second is the adaptive learning ..."
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Cited by 21 (1 self)
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This paper discusses two sources of ideas that influence monetary policy makers today. The first is a set of analytical results that impose the rational expectations equilibrium concept and do ‘intelligent design ’ by solving Ramsey and mechanism design problems. The second is the adaptive learning process that first taught us how to anchor the price level with a gold standard, then how to replace the gold standard with a fiat currency wanting nominal anchors. Models of outofequilibrium learning say that such an adaptive evolutionary process will converge to a selfconfirming equilibrium (SCE). In an SCE, a government’s probability model is correct about events that occur under the prevailing government policy, but possibly wrong about the consequences of other policies. That causes mistakes absent from a rational expectations equilibrium and expands the role of learning.
Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited
 Econometrica
, 1998
"... A probability distribution governing the evolution of a stochastic process has infinitely many Bayesian representations of the form # = R # # # d####. Among these, a natural representation is one whose components ## # 's# are `learnable' #one can approximate # # by conditioning # on observation of t ..."
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Cited by 18 (1 self)
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A probability distribution governing the evolution of a stochastic process has infinitely many Bayesian representations of the form # = R # # # d####. Among these, a natural representation is one whose components ## # 's# are `learnable' #one can approximate # # by conditioning # on observation of the process# and `sufficient for prediction' ## # 's predictions are not aided by conditioning on observation of the process#. We show the existence and uniqueness of such a representation under a suitable asymptotic mixing condition on the process. This representation can be obtained by conditioning on the tailfield of the process, and any learnable representation that is sufficient for prediction is asymptotically like the tailfield representation. This result is related to the celebrated de Finetti theorem, but with exchangeability
Recurrent Hyperinflations and Learning
, 2001
"... This paper uses a model of boundedly rational learning to account for the observations of recurrent hyperinflations in the last decade. We study a standard monetary model where the fully rational expectations assumption is replaced by a formal de¯nition of quasirational learning. The model under le ..."
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Cited by 14 (0 self)
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This paper uses a model of boundedly rational learning to account for the observations of recurrent hyperinflations in the last decade. We study a standard monetary model where the fully rational expectations assumption is replaced by a formal de¯nition of quasirational learning. The model under learning is able to match remarkably well some crucial stylized facts observed during the recurrent hyperinflations experienced by several countries in the 80's. We argue that, despite being a small departure from rational expectations, quasirational learning does not preclude falsifiability of the model, it does not violate reasonable rationality requirements and it can be used for policy evaluation.
AspirationBased Reinforcement Learning In Repeated Interaction Games: An Overview
, 2001
"... In models of aspirationbased... This paper provides an informal overview of a range of such theories applied to repeated interaction games. We describe different models of aspiration formation: where (1) aspirations are fixed but required to be consistent with longrun average payoffs; (2) aspiratio ..."
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Cited by 12 (1 self)
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In models of aspirationbased... This paper provides an informal overview of a range of such theories applied to repeated interaction games. We describe different models of aspiration formation: where (1) aspirations are fixed but required to be consistent with longrun average payoffs; (2) aspirations evolve based on past personal experience or of previous generations of players; and (3) aspirations are based on the experience of peers. Convergence to nonNash outcomes may result in either of these formulations. Indeed, cooperative behaviour can emerge and survive in the long run, even though it may be a strictly dominated strategy in the stage game, and despite the myopic adaptation of stage game strategies. Differences between reinforcement learning and evolutionary game theory are also discussed.
Monetary policy, expectations and commitment
 The Scandinavian Journal of Economics
, 2006
"... Commitment in monetary policy leads to equilibria that are superior to those from optimal discretionary policies. A number of interest rate reaction functions and instrument rules have been proposed to implement or approximate commitment policy. We assess these optimal reaction functions and instrum ..."
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Cited by 9 (0 self)
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Commitment in monetary policy leads to equilibria that are superior to those from optimal discretionary policies. A number of interest rate reaction functions and instrument rules have been proposed to implement or approximate commitment policy. We assess these optimal reaction functions and instrument rules in terms of whether they lead to an RE equilibrium that is both locally determinate and stable under adaptive learning by private agents. A reaction function that appropriately depends explicitly on private expectations performs particularly well on both counts.