stability of functional rational expectations equilibria abstract in this paper we examine a representative agent forecasting prices in a first order self referential overlapping generations model we first consider intermediate stage learning where agents update the forecasting rule every m periods we show that in theory and simulations the learning rule does not converge to the rational expectations equilibrium ree we next consider two stage learning where agents learn the functional mapping between the current forecast function and the previous forecast function we show that in theory and simulations the two stage learning rule converges to the ree journal of economic literature classifications numbers c62 c63 d83

are investment expectations rational adaptive or regressive i introduction tests of the rational expectations hypothesis reh outside the experimental laboratory typically utilize two types of data quantitative measures of expectations about publicly observed variables such as inflation usually elicited from small samples of professional forecasters and qualitative measures of expectations about privately observed variables such as personal income elicited from large samples of households analyses of both types of data have produced varying levels of support for the reh for example keane and runkle 1990 1998 find evidence in favor of the reh using the first type of data while bonham and cohen 2001 in part overturn their results after accounting for the nature of cross correlations inherent in a group of individuals forecasting the same publicly observed integrated time series next using household survey data das and van soest 1997 1999 and das et al 1999 find evidence against the reh in contrast benitez silva et al 2008 furthered the econometric analysis of such data and presented evidence in favor of the reh in employing publicly available professional forecaster data several concerns related to pooling data revisions and the possibility of signaling on the part of forecasters have been raised 1 further pesaran and weale 2006 review a large and growing literature on survey expectations of households and the attendant econometric and substantive issues in analyzing qualitative response expectations data from such surveys they conclude for myriad reasons that it remains the case that the analysis of individual responses to such surveys and in particular to those who collect only qualitative information is underdeveloped these issues can be addressed in part by data on quantitative expectations about privately observed variables this paper employs data from two new survey sources that provide such information the resulting panel of 775 firms in canada contains quantitative information on expectations about purchases of new machinery and equipment investment as well as realized levels of investment over 7 yr the data are particularly useful because they avoid some of the issues raised for previous studies and their analysis helps to contribute on the firm side to the agenda laid out by manski 2004 who sees a critical need for basic research on expectations formation figure 1 omitted estimation results suggest that investment expectations are not rational if the assumed underlying loss function is assumed to be symmetric that is the usual unbiasedness and efficiency requirements for rational expectations clearly elucidated for instance by lovell 1986 do not hold for the collected data further hypothesis tests on statistical models implied by conventional adaptive expectations do not suggest the prevalence of such behavior in the data however a particular version of such extrapolative expectations namely regressive expectations formation does find support in the data the paper is structured as follows section ii discusses the data on 775 manufacturing plants over 7 yr that was compiled by merging two national surveys in canada in section iii the statistical models and attendant hypothesis tests as implied by various expectations formation assumptions are described followed by their estimation results section v concludes ii the data data were compiled from two confidential proprietary surveys conducted by statistics canada the capital expenditures survey ces and the annual survey of manufactures asm over 7 yr 1986 1992 2 the ces contains data on one step ahead expected expect sub it and realized actualit capital expenditures on machinery and equipment i e investment and the asm on shipments shipment sub sit 3 owing to the lumpy and long term nature of construction expenditures this variable was excluded finally only manufacturing sector records were selected for both surveys

limited rationality and strategic interaction the impact of the strategic environment on nominal inertia much evidence suggests that people are heterogeneous with regard to their abilities to make rational forward looking decisions this raises the question as to when the rational types are decisive for aggregate outcomes and when the boundedly rational types shape aggregate results we examine this question in the context of a long standing and important economic problem the adjustment of nominal prices after an anticipated monetary shock our experiments suggest that two types of bounded rationality money illusion and anchoring are important behavioral forces behind nominal inertia however depending on the strategic environment bounded rationality has vastly different effects on aggregate price adjustment if agents actions are strategic substitutes adjustment to the new equilibrium is extremely quick whereas under strategic complementarity adjustment is both very slow and associated with relatively large real effects this adjustment difference is driven by price expectations which are very flexible and forward looking under substitutability but adaptive and sticky under complementarity moreover subjects expectations are also considerably more rational under substitutability

heterogeneous expectations adaptive learning and evolutionary dynamics this paper presents a linear self referential macroeconomic model with the possibility of multiple equilibria where agents have the choice of using one of two forecasting models one of minimum state variable form and the other of sunspot form to form expectations of current and future prices endogenous predictor selection is modeled as an evolutionary game where individuals choose among the forecasting models based on relative performance some nash solutions are not relevant as they are not stable under evolutionary or adaptive learning finally it is shown that the sunspot equilibrium is fragile against temporary shocks to information costs

experimental evidence on the persistence of output and inflation this article presents experimental evidence from a monetary sticky price economy in which output and inflation depend on expected future inflation rational inflation expectations do not allow for persistent deviations of output and inflation following a monetary shock in the experimental sessions however output and inflation display considerable persistence and regular cyclical patterns

behavioural heterogeneity under evolutionary pressure macroeconomic implications of costly optimisation a model is developed in which a continuum of agents makes interdependent output decisions in a stochastic environment characterised by strategic complementarity two groups are distinguished naive agents follow a costless adaptive expectations rule while sophisticated agents incur an optimisation cost to achieve self fulfilling expectations the paper studies the dynamics generated as the population composition evolves under pressure of differential payoffs sophisticated agents are favoured if optimisation is cheap or the stochastic environment highly variable but naive agents generally persist a higher long run share of sophisticated agents is associated with greater output variability and low output persistence several attempts have been made in the recent macroeconomic literature to explore the implications of allowing for behavioural heterogeneity among economic agents typically the standard postulates of unbounded rationality are held to apply only to a subset of the population while the remainder is assumed to behave in accordance with some alternative specification the nature of which depends on the situation being analysed akerlof and yellen

adaptive versus eductive learning theory and evidence adaptive and eductive learning are two widely used ways of modeling the process by which agents learn a rational expectation equilibrium ree in this paper we report an experiment where we exploit differences in the conditions under which adaptive and eductive learning converge to ree so as to investigate which approach provides the better description of the learning behavior of human subjects our results suggest that the path by which the system converges appears to be a mixture of both adaptive and eductive learning model predictions

bounded rationality and market fluctuations abstract in a model of a competitive market each firm in each period faces a planning problem caused by random changes in circumstances due to bounded rationality a firm is unable to compute costlessly and exactly its optimal output instead the firm approximates optimal output through a decision making process called a deliberation technology this technology involves a rule of thumb a costly deliberation mechanism and a random deliberation error the issue addressed by the model is how bounded rationality affects market fluctuations the first glance intuition is that fluctuations will increase since deliberation error is an added disturbance to the market however the actual effect is much more complicated and might go either way

expectation calculation and macroeconomic dynamics the authors establish a framework wherein agents make expectation revision decisions subject to a specified calculation technology and preferences over forecast errors the technology endows agents with correctly specified economic models but the cost of expectation calculation using these models leads to gradual and incomplete adjustment to long run rational expectation equilibrium the rational expectations hypothesis emerges as a special case of the equilibrium paths obtained in the authors framework in a natural rate model of monetary policy calculation technology gives rise to long run nonneutrality and hysteresis effects and incomplete adjustment of forecast rules causes output fluctuations to be amplified copyright 1992 by american economic association

replicator dynamics in a cobweb model with rationally heterogeneous expectations abstract this paper extends the adaptively rational equilibrium dynamics of brock and hommes brock w a hommes c h 1997 a rational route to randomness econometrica 65 1059 1160 by introducing a generalized version of the replicator dynamic the replicator equilibrium dynamics red couples the price dynamics of a cobweb model with predictor selection governed by an evolutionary replicator dynamic we show that the red supports the conclusion of sethi and franke sethi r franke r 1995 behavioural heterogeneity under evolutionary pressure macroeconomic implications of costly optimisation the economic journal 105 583 600 that costly rational beliefs persist though unlike them these results obtain in the deterministic case numerical evidence shows that complex dynamics exist as in brock and hommes even though no weight is placed on strictly dominated predictors in an red steady state

intrinsic heterogeneity in expectation formation we introduce the concept of misspecification equilibrium to dynamic macroeconomics agents choose between a list of misspecified econometric models and base their selection on relative forecast performance a misspecification equilibrium is a stochastic process in which agents forecast optimally given their choices with forecast model parameters and predictor proportions endogenously determined under appropriate conditions the misspecification equilibrium will exhibit intrinsic heterogeneity in which all predictors are used at all times even in the neoclassical limit in which only the most successful predictors are used this equilibrium is attainable under least squares learning and dynamic predictor selection based on average profits

optimal policy business cycles the effectiveness of economic policies depends on the nature of expectations under adaptive expectations the philipps curve allows a governement to surprise agents under rational expectations there is less room for economic policies we assume that only an endogenously determined proportion of agents form rational expectations and show that this leads the government to optimal policies which result in a policy cycle with real effects c 1998 elsevier science b v all rights reserved

a near rational model of the business cycle with wage and price inertia this paper presents a model in which insignificantly suboptimal behavior causes aggregate demand shocks to have significant real effects the individual loss to agents with inertial price wage behavior is second order in terms of the parameter describing the shock while the effect on real economic variables is first order thus significant changes in business activity can be generated by anticipated money supply changes provided that some agents are willing to engage in nonmaximizing behavior which results in small losses

living in an imaginary world that looks real abstract in the paper we show using standard approaches general equilibrium modeling and the assumption of complete rationality that the macroeconomic environment is endogenous and is indeterminate specifically it is argued without resorting to sunspot type arguments that microeconomic fundamentals do not suffice to characterize the economy at the macro level in particular we show how perceptions of rational agents of the workings of the economy a shape the environment b affect the environment sufficiently to ensure that rational economic agents find the observed environment consistent with their beliefs even though it is not as a by product we illustrate that endogenous macro uncertainty can arise as an outcome if rational economic agents whose expectations are anchored on endogenous variables expect them to arise finally we show that systematic errors can persist indefinitely under rationality

a model of learning and emulation with artificial adaptive agents we study adaptive learning in a sequence of overlapping generations economies in which agents live for n periods agents initially have heterogeneous beliefs and form multi step ahead forecasts using a forecast rule chosen from a vast set of candidate rules agents learn in every period by creating new forecast rules and by emulating the forecast rules of other agents computational experiments show that systems so defined can yield three qualitatively different types of long run outcomes 1 coordination on a low inflation stationary perfect foresight equilibrium 2 persistent currency collapse and 3 coordination failure within the allotted time frame

are low interest rates deflationary a paradox of perfect foresight analysis we argue that an influential neo fisherian analysis of the effects of low interest rates depends on using perfect foresight equilibrium analysis under circumstances where it is not plausible for people to hold expectations of that kind we propose an explicit cognitive process by which agents may form their expectations of future endogenous variables perfect foresight is justified by our analysis as a reasonable approximation in some cases but in the case of a commitment to maintain a low nominal interest rate for a long time our reflective equilibrium implies neither neo fisherian conclusions nor implausibly strong predicted effects of forward guidance

imperfect credibility and the zero lower bound as the nominal interest rate cannot fall below zero a central bank with imperfect credibility faces a significant challenge to stabilize the economy in a new keynesian model during a large recession we characterize the optimal monetary policy at the zero lower bound for the nominal interest rate if credibility is imperfect confronting monetary policy communication of the u s federal reserve and the swedish riksbank with such a framework the credibility of both institutions is shown to have been low in the aftermath of the 2008 economic crisis

monopolistic competition and the effects of aggregate demand how important is monopolistic competition to an understanding of the effects of aggregate demand on output we ask the question at three levels can monopolistic competition by itself explain why aggregate demand movements affect output can it together with other imperfections generate effects of aggregate demand in a way that perfect competition cannot if so can it give an accurate account of the response of the economy to aggregate demand movements the answers are no yes and yes

anticipated fiscal policy and adaptive learning abstract the impact of anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations is considered agents are assumed to combine limited structural knowledge with a standard adaptive learning rule these issues are analyzed using two well known set ups an endowment economy and the ramsey model in our scenario there are important deviations from both rational expectations and purely adaptive learning the approach could be applied to other frameworks

learning benevolent leadership in a heterogenous agents economy abstract this paper studies the potential commitment value of cheap talk announcements in an agent based dynamic extension of the kydland prescott model in every period the policy maker makes a non binding inflation announcement before setting the actual inflation rate it updates its decisions using individual evolutionary learning the private agents can choose between two different forecasting strategies they can either set their forecast equal to the announcement or use an adaptive learning scheme to potentially forecast the true inflation they switch between these two strategies as a function of information about the associated payoffs they obtain through word of mouth choosing always the currently most favorable one while all agents using the first strategy make the same forecast those using the second strategy may generate different individual forecasts in spite of the complexity of the environment the boundedly rational policy maker learns to sustain a situation with a positive but fluctuating fraction of believers this outcome is pareto superior to the outcome predicted by standard theory interestingly enough the actions taken by the policy maker undergo marked qualitative changes as a function of the prevailing heterogeneity among and learning characteristics of the private agents

an analysis of the cobweb model with boundedly rational heterogeneous producers abstract this paper considers the traditional cobweb model with heterogenous risk averse producers whose supply functions involve their estimates of the conditional mean and variance of the future price the producers seek to learn these quantities by applying geometric decay processes gdp to past prices the heterogeneity manifests itself in the lag lengths and memory parameters applied to past prices as well as in risk aversion coefficients we find that each dimension of heterogeneity changes enriches the cobweb dynamics with respect to the case of homogeneous producers

ex ante efficiency of bankruptcy procedures abstract this paper suggests a framework to analyze the efficiency properties of bankruptcy procedures distinguishing between ex ante and ex post efficiency ex post efficiency consists in maximizing the ex post value of the insolvent firm whereas ex ante efficiency consists in maximizing the proceeds to creditors from the reorganization of the firm and providing incentives for the creditors to monitor the firm we show that the definition of creditors ownership rights over the company and the protection of the creditors seniority are crucial to asses the ex ante efficiency of a bankruptcy procedure

expectational diversity in monetary economies abstract we investigate an overlapping generations monetary economy in which expectations depend upon backward looking predictors of the future price level we use discrete choice theory to model how agents select a predictor based on its past forecast error letting the number of available predictors tend to infinity we obtain the large type limit of the system taking the large type limit dramatically reduces the number of free parameters while maintaining the expectational diversity which we argue is necessary for constructing plausible learning based models the model s dynamics are strongly influenced by the intensity of choice which measures how sensitive an agent s predictor choice is to differences in forecast errors across predictors when the intensity of choice is low the monetary steady state is stable as the intensity of choice increases and if certain parametric restrictions are met the system undergoes a hopf bifurcation in which case we document the existence of highly irregular equilibrium price paths

on information and market dynamics the case of the u s beef market abstract the paper investigates the nature of dynamic prices and expectations in a competitive market the approach is applied to the u s beef market which exhibits cyclical patterns and significant biological lags in the production process beef price equations are estimated under different expectation regimes the empirical results indicate the presence of heterogeneous price expectations with a significant number of market participants neglecting information about the existence of a beef cycle

bounded rationality and strategic complementarity in a macroeconomic model policy effects persistence and multipliers motivated by recent developments in the bounded rationality and strategic complementarity literatures we examine an intentionally simple and stylized aggregative economic model when the assumptions of fully rational expectations and no strategic interactions are relaxed we show that small deviations from rational expectations taken alone lead only to small deviations from classical policy ineffectiveness but that the situation can change dramatically when strategic complementarity is introduced strategic complementarity magnifies the effects of even small departures from rational expectations producing equilibria with policy effectiveness output persistence and multiplier effects

bayesian learning growth and pollution abstract environmental problems such as climate change have great uncertainties current expectations are that uncertainties about climate change will be resolved quickly we examine this hypothesis theoretically and computationally we consider bayesian learning about the relationship between greenhouse gas levels and global mean temperature changes a key uncertainty learning is non trivial because of a stochastic shock to the realized temperature we find theoretically the expected learning time which is related to the variance of the shock and the emissions policy implying a tradeoff between the benefits of controlling emissions and information we imbed the learning model into an optimal growth model with a climate sector and solve the resulting dynamic program we find computationally that learning takes on average over 90 yr far longer than currently believed

persistent and transitory shocks learning and investment dynamics this paper introduces a new approach to understanding investment the distinctive feature of our approach is that shocks to the economic fundamentals have both persistent and transitory components and that firms must disentangle the persistent from the transitory shocks the model generates interesting dynamics simulations of the model show that the response of investment to changes in the interest rate can vary widely over time that the current response of investment depends on the sequence of past shocks that investment will respond less when the firm is confident about its beliefs and more when a change in economic fundamentals challenges the firm s beliefs and that investment booms and crashes may occur without any change in the true state of the economy simulations of the model also show that it captures many stylized facts of investment dynamics documented in previous empirical studies

small menu costs and large business cycles a macroeconomic model of monopoly i introduction the conflict between modern neoclassical and traditional keynesian theories of the business cycle centers upon the pricing mechanism in neoclassical models prices are fully flexible they represent the continuous optimization of economic agents and the continuous intersection of supply and demand in keynesian models prices are often assumed to be sticky they do not necessarily equilibrate all markets at all times one of the reasons for the resurgence of the equilibrium approach to macroeconomics has been the absence of a theoretical underpinning for this keynesian price stickiness this note shows that sticky prices can be both privately efficient and socially inefficient the business cycle results from the suboptimal adjustment of prices in response to a demand shock to the extent that policy can stabilize aggregate demand it can mitigate the social loss due to this suboptimal adjustment in some keynesian models prices are simply exogenously fixed 2 in others agents must set their prices in advance of the transaction date the act of altering a posted price is certainly costly these costs include such items as printing new catalogs and informing salesmen of the new price yet these menu costs are small and therefore generally perceived as providing only a weak foundation for these fixed price models however this inference is flawed small menu costs can cause large welfare losses the claim that price adjustment costs are small does not rebut the claim that they are central to understanding economic fluctuations

modelling cognitively bounded rationality an evaluative taxonomy abstract since its origins in the 1950s the notion of bounded rationality has been incorporated into economic theory using an array of methodological approaches this paper presents a taxonomy by which these approaches can be categorized and understood evaluating each approach against a range of important criteria at a time when the foundations of economic theory are being re examined this paper should be viewed as a first step towards an assessment of the appropriate role that this more realistic view of cognition should take in different areas of economic theory and also of the desirable characteristics of models that incorporate it

expectational stability and the multiple equilibria problem in linear rational expectations models linear models involving expectations of future endogenous variables generally have multiple rational expectations equilibria this paper investigates the stability of solutions in the disequilibrium sense of whether given a small deviation of expectations functions from some rational expectations equilibrium the system returns to that solution under a natural revision rule weak and strong local stability are distinguished stability conditions are calculated for a simple general linear model and applied to two macroeconomic examples in some cases there is a unique stable equilibrium in other cases a continuum of equilibria forms a weakly but not strongly stable class

local convergence properties of a cobweb model with rationally heterogeneous expectations abstract this paper gives local stability conditions for convergence of the price dynamics in a cobweb model with rationally heterogeneous expectations generalizing the example of brock and hommes 1997 when agents choose between rational naive and adaptive beliefs the steady state may be locally asymptotically stable if the adaptive predictor places enough weight on past prices and is costless if adaptive expectations are sufficiently more costly than naive expectations the steady state will be an unstable saddle point our results imply that adding a choice can stabilize a system which is unstable under the brock and hommes model these results illustrate how the critical parameter that governs stability is dependent on the array of available predictors

costly predation and the distribution of competence an evolutionary game model shows how an equilibrium distribution of competence may evolve when members of a population prey on one another but when predatory competence is costly to acquire under one interpretation the competence distribution is an endogenously determined distribution of bounded rationality an example shows how tricksters and suckers might coexist in the long run the analysis leads to a curious result about a mixed equilibrium for a symmetric zero sum game an increase in the costs of one or more competence levels has exactly zero effect on the fraction of the population at those levels