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.     

Expectations and optimal monetary policy: A stability problem revisited

A landmark result in the optimal monetary policy design literature is that fundamental-based interest rate rules invariably lead to rational expectations equilibria (REE) that are not stable under adaptive learning. In this paper, we make a novel information assumption that private agents cannot observe aggregate fundamental shocks, and use simple linear forecasting rules for learning. We find that with fundamental-based rules, there exist limited information equilibria that are stable under learning. Moreover, there are multiple equilibria. Learning can be used as a selection tool to identify a unique equilibrium.     

Unemployment and econometric learning

We apply well-known results of the econometric learning literature to the Mortensen and Pissarides real business cycle model. Agents can always learn the unique rational expectations equilibrium (REE), for all possible well-defined sets of parameter values, by using the minimum-state-variable solution to the model and decreasing gain learning. From this perspective the assumption of rational expectations in the model could be seen as reasonable. But using a parametrisation with UK data, simulations show that the speed of convergence to the REE is slow. This type of learning dampens the cyclical response of unemployment to small structural shocks.     

Asset pricing with adaptive learning

We study the extent to which self-referential adaptive learning can explain stylized asset pricing facts in a general equilibrium framework. In particular, we analyze the effects of recursive least squares and constant gain algorithms in a production economy and a Lucas type endowment economy. We find that (a) recursive least squares learning has almost no effects on asset price behavior, since the algorithm converges relatively fast to rational expectations, (b) constant gain learning may contribute towards explaining the stock price and return volatility as well as the predictability of excess returns in the endowment economy but (c) in the production economy the effects of constant gain learning are mitigated by the persistence induced by capital accumulation. We conclude that in the context of these two commonly used models, standard linear self-referential learning does not resolve the asset pricing puzzles observed in the data.     

Are Rational Expectations Equilibria with Private Information Eductively Stable?

The paper derives conditions for eductive stability of rational expectations equilibria in simple linear economic models with private information. Following Guesnerie (1992; 2002), the concept of eductive stability is used. It is shown that even in a private information setting, rational expectations equilibria might be justified as a result of mental process of reasoning of the agents. The paper considers an equilibrium concept, where the agents are unable to condition their forecasts on the actual market price. It is shown that eductive stability in this case requires that a condition is satisfied that is also relevant in the symmetric information case. This condition is compared to the respective stability condition that must hold if agents are able to use the current market price as an additional source of information. It turns out that the conditions for eductive stability that emerge under both equilibrium concepts differ.revised version received September 11, 2003     

Coordination on saddle-path solutions: the eductive viewpoint—linear multivariate models

We examine local strong rationality (LSR) in multivariate models with both forward-looking expectations and predetermined variables. Given hypothetical common knowledge restrictions that the dynamics will be close to those of a specified minimal state variable solution, we obtain eductive stability conditions for the solution to be LSR. In the saddlepoint stable case the saddle-path solution is LSR provided the model is structurally homogeneous across agents. However, the eductive stability conditions are strictly more demanding when heterogeneity is present, as can be expected in multisectoral models. Heterogeneity is thus a potentially important source of instability even in the saddlepoint stable case.     

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.     

A spectrum of equilibration processes in game theory

In game theory, four dynamic processes converging towards an equilibrium are distinguished and ordered by way of agents' decreasing cognitive capacities. In the eductive process, each player has enough information to simulate perfectly the others' behavior and gets immediately to the equilibrium. In epistemic learning, each player updates his beliefs about others' future strategies, with regard to their sequentially observed actions. In behavioral learning, each player modifies his own strategies according to the observed payoffs obtained from his past actions. In the evolutionary process, each agent has a fixed strategy and reproduces in proportion to the utilities obtained through stochastic interactions. All along the spectrum, longer term dynamics makes up for weaker rationality, and physical relations substitute for mental interactions. Convergence, if any, is towards an always stronger equilibrium notion and selection of an equilibrium state becomes more sensitive to context and history. The processes can be mixed if associated to different periods, agents or mechanisms and deepened if obtained by formal reasoning principles.     

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.     

Learning and international transmission of shocks

This paper studies the implications of adaptive learning in the modelling of inter-country linkages in a two-region MSG G-cubed model built on micro-founded behaviors of firms and households. The nature of the transmission process under rational expectations versus adaptive learning is explored. We investigate the propagation mechanism within and across borders for various shocks and policy changes within the United States: change in inflation target, fiscal policy, productivity shock, and rise in equity risk. Adaptive learning is found to change the short run sign of transmission in most cases but this also depends on the fraction of forward-looking agents in the economy.     

Adaptive learning in extensive form games and sequential equilibrium

Summary. This paper studies adaptive learning in extensive form games and provides conditions for convergence points of adaptive learning to be sequential equilibria. Precisely, we present a set of conditions on learning sequences such that an assessment is a sequential equilibrium if and only if there is a learning sequence fulfilling the conditions, which leads to the assessment. Received: November 5, 1996; revised version: May 28, 1997     

Is central bank conservatism desirable under learning?

In a New Keynesian model, we consider the delegation problem of the government when the central bank optimally sets discretionary monetary policy taking account of private expectations formed through adaptive learning. Learning gives rise to an incentive for the central bank to accommodate less the effect of inflation expectations and cost-push shocks on inflation and induces thus a deviation from rational expectations equilibrium. However, discretionary monetary policy under learning suffers from an excessively low stabilization bias. To improve the social welfare, the government should appoint a liberal central banker, i.e., set a negative optimal inflation penalty that decreases with the value of learning coefficient. The main conclusions are valid under both constant- and decreasing-gain learning.     

Expectational coordination in simple economic contexts

We consider an economic model that features (1) a continuum of agents and (2) an aggregate state of the world over which agents have an infinitesimal influence. We first review the connections between the ??eductive?? viewpoint on expectational stability and standard game-theoretical rationalizability concepts. The ??eductive?? reasoning selects different plausible beliefs that are a priori, and possibly a posteriori, ??diverse??. Such beliefs are associated with the sets of ??Cobweb tatonnement?? outcomes, ??Rationalizable States?? and ??Point-Rationalizable States?? (the latter two being shown to be convex). In the case where our model displays strategic complementarities, unsurprisingly, all our ??eductive?? criteria support similar conclusions, particularly when the equilibrium is unique. With strategic substitutabilities, the success of expectational coordination, in the case where a unique equilibrium does exists, relates with the absence of cycles of order 2 of the ??Cobweb?? mapping: in this case, full expectational coordination would be achieved. However, when cycles of order 2 do exist, our different criteria predict larger sets of outcomes, although all tied with cycles. Under differentiability assumptions, the Poincaré?CHopf method leads to other global stability results. At the local level, the different criteria under scrutiny can be adapted. They lead to the same expectational stability conclusions, only when there are local strategic complementarities or strategic substitutabilities. However, for the local stability analysis, it is demonstrated that the stochastic character of expectations can most often be forgotten.     

Increasing Returns,Learning-By-Doing And Neural Networks ∗

In this paper we draw an analogy between the process of learning-bydoing and the learning process which develops in a neural network context. The bridging tool we refer to is a dynamic production function whose only variable input is labour. By concentrating on the ‘neural network production function’ we show that the learning process can lead to increasing returns. The simulations show that when learning is characterized by an upper limit. returns are increasing for some time, while in the long run they go back to the level where they are constant.     

Social Economics and Evolutionary Learning

The major premise of this paper is that social and individual well-being depends significantly on people's capacity to learn and unlearn in communication with each other. This paper builds on social economic traditions that see communication and conversation as evolutionary generative and adaptive mechanisms through which individual and social learning occurs. Drawing on educational psychology and organizational behavior scholarship, five dynamic processes of conversational learning are introduced with the contention that they can help social economists understand at a micro level more deeply and more concretely how learning happens in the give-and-take of conversation. The paper explores the role of the state, organizations, and communities in fostering individual freedom and dignity, human rights, and economic democracy and concludes that the investment of value in people and their capability for purposeful action as social economic stakeholders can be enhanced through conversation as learning.     

Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games

Most learning models assume players are adaptive (i.e., they respond only to their own previous experience and ignore others' payoff information) and behavior is not sensitive to the way in which players are matched. Empirical evidence suggests otherwise. In this paper, we extend our adaptive experience-weighted attraction (EWA) learning model to capture sophisticated learning and strategic teaching in repeated games. The generalized model assumes there is a mixture of adaptive learners and sophisticated players. An adaptive learner adjusts his behavior the EWA way. A sophisticated player rationally best-responds to her forecasts of all other behaviors. A sophisticated player can be either myopic or farsighted. A farsighted player develops multiple-period rather than single-period forecasts of others' behaviors and chooses to “teach” the other players by choosing a strategy scenario that gives her the highest discounted net present value. We estimate the model using data from p-beauty contests and repeated trust games with incomplete information. The generalized model is better than the adaptive EWA model in describing and predicting behavior. Including teaching also allows an empirical learning-based approach to reputation formation which predicts better than a quantal-response extension of the standard type-based approach. Journal of Economic Literature Classification Numbers: C72, C91.     

“适应性学习”下人民币汇率的货币模型

传统的汇率货币模型建立在理性预期基础上,无法解释现实中的汇率波动。本文放松了理性预期的假定,并引入适应性学习来考察汇改后人民币汇率的货币模型。结果表明:在适应性学习引入之前,货币模型预测能力比不上简单的随机游走模型;而在引入之后,其预测能力大幅改善,很好地模拟了汇率实际波动。因此传统的货币模型并没有完全失效,引入适应性学习后仍然适宜于刻画汇改后人民币汇率的短期走势。     

“学习场”结构与空间中的创新

在分析战后区域发展思想从"增长极"到"创造场"转变的基础上,提出了"学习场"的概念,认为"学习场"以"学习"为核心,以"场域"为基石,以"惯习"为中介,并以新经济地理学的三个重要方向:尺度地理学、关系经济地理学和演化经济地理学为理论基础,以Storper的"技术-组织-地域"三位一体思想为核心,整合"行动者网络"和"创造场"两种概念工具,旨在调和创新地理研究中地理接近、关系(组织)接近和制度接近之间的争论,从而为分析发展中国家乃至发达国家的空间化学习创新提供一个基本范式.     

基于时间维度的组织学习理论——组织从当前现状中学习的模型

基于组织学习时空理论的时间维度,提出组织从当前现状中学习的模型。该模型包括4个方面:"知",以组织面临的现状、机会和挑战为出发点,运用行动学习的方法,通过团队形式的讨论、反思和质疑、实践的循环,从当前现状中获得知识;"行",将学习到的知识运用于实践,改进自身方案和采取适当行动;知与行的转化,包含知与行的循环;从知和行两个维度评估学习的有效性。最后,总结了理论和实践贡献,并指出存在的不足和未来的改进方向。     

基于时间维度的组织学习理论——组织从未来可能的情景中学习的模型

基于组织学习时空理论的时间维度,提出了组织从未来可能的情景中学习的模型。该模型包含四个方面:"知",通过情景构建,从未来可能的情景中获取知识;"行",将从未来可能的情景中学习到的知识运用于实践;"知"到"行"的转化;评估从未来可能的情景中学习的有效性。该模型详细阐述了这四个方面的方法和步骤,并提出了相应的管理措施。最后,总结了理论和实践贡献,并指出了存在的不足和未来的研究方向。