learning to believe in sunspots a number of authors have shown that competitive economies may possess sunspot equilibria that is rational expectations equilibria in which purely extrinsic uncertainty affects equilibrium prices and allocations 2 such results demonstrate that it does not require a lack of faith in the rationality of market participants to believe that competitive markets may be subject to purely speculative fluctuations driven solely by expectations 3 the mere existence of sunspot equilibria as solutions to a system of marketclearing conditions however might not be judged sufficient to indicate that competitive markets with rational participants could ever be subject to speculative instability the sunspot equilibria represent states of affairs in which agents act differently in the case of different realizations of the sunspot variable and it is rational for each agent to do so but it might be thought unlikely that the beliefs of all the participants in the market could ever come to be coordinated so as to bring about an equilibrium of that kind it is rational to believe that sunspots convey information about future states of affairs once the economy is in a sunspot equilibrium but why would rational agents ever begin to believe in such a thing so as to create the conditions under which the belief is rational in order to address such a question one must go beyond the mere statement of the conditions for equilibrium and discussion of what states of affairs satisfy them one must specify an explicit dynamic process according to which the beliefs of agents adjust when out of equilibrium any exercise of this kind is necessarily unsatisfactory as there is no univocal meaning for the postulate of rational behavior outside of an equilibrium it may well be the case that

habit persistence money and overlapping generations abstract this paper provides a comprehensive characterization of the stationary and non stationary monetary equilibria in a two period pure exchange overlapping generations model with multiplicative habit persistence preferences somewhat surprisingly the upshot is that multiplicative habit persistence preferences do not affect the qualitative properties of the dynamical system in these models in addition the qualitative properties of models with subtractive and multiplicative habits are largely similar any possibility of cyclical fluctuations beyond periodicity two is also ruled out

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

a simple model of growth cycles with technology choice abstract in this study we develop a simple computable overlapping generations model that exhibits endogenous fluctuations the key assumption is that a firm can choose from multiple technologies of production since the model reduces to a piecewise linear map on the unit interval it allows us to conduct an in depth analysis of its dynamic properties particularly this piecewise linearization reveals the ability of the model to exhibit periodic attracting cycles of an arbitrarily large period as well as non periodic attractors furthermore it is demonstrated that the occurrence of periodic patterns is completely characterized by the rotation number or the devil s staircase

public health spending old age productivity and economic growth chaotic cycles under perfect foresight abstract this paper analyses the dynamics of a double cobb douglas economy with overlapping generations and public health investments that affect the supply of efficient labour of the old aged it is shown that the positive steady state of the economy is unique moreover we provide necessary and sufficient conditions for the emergence of endogenous deterministic complex cycles when individuals are perfectly foresighted interestingly i the equilibrium dynamics shows rather complicated phenomena such as a multiplicity of bubblings depending on the size of the public health system and ii the higher the degree of thriftiness the likelier an economy is exposed to endogenous fluctuations because the need to save when young to support consumption when old is reduced

a characterization of erratic dynamics in the overlapping generations model abstract in this paper we characterize and give examples o wide classes of utility functions which generate erratic dynamics in the standard deterministic overlapping generations model erratic dynamics refers to feasible trajectories which are bounded but which do not converge to stationary points or periodic orbits we show that such trajectories are pareto efficient we introduce credit into the model and show how a constant credit expansion rate can result in erratic trajectories in prices and the real value of credit finally we briefly discuss certain technical aspects of the mathematics used and the statistical nature of the dynamics that can arise from deterministic dynamical systems

beliefs equilibria in an overlapping generations model we consider a standard two generations version of the overlapping generations model agents predict inflation rates on the basis of a perceived law of motion which is estimated by running a linear regression on past inflation rates we introduce the notion of beliefs equilibrium at such an equilibrium i the perceived law of motion is such that it fits the time series of inflation rates best and ii this time series of actual inflation rates is generated when agents use that perceived law of motion we show that beliefs might converge although inflation rates keep on fluctuating these fluctuations are consistent with the limit belief

equivariant general equilibrium theory abstract the main purpose of this paper is to investigate the properties of a version of the general equilibrium model where symmetry considerations are explicitely taken into account this version called the equivariant model is shown to be a natural framework to study sunspot equilibria the problem of sunspot equilibria can then be viewed as one of symmetry breaking existence of asymmetric or sunspot equilibria is addressed through the dual approach of price income equilibrium analysis that splits the problem of breaking symmetries into two separate easier problems

asset price fluctuations without aggregate shocks we analyze the pricing of a productive asset in a class of dynamic exchange economies with heterogeneous infinitely lived agents and self enforcing intertemporal trades individual incomes fluctuate and are correlated preferences dividends and aggregate income are fixed almost all economies in this class have a unique stationary markovian equilibrium with fluctuations in asset prices as the set of unrationed households changes over time and states excess demand functions shift asset returns fluctuate and some households are shut out of asset markets examples suggest that the amplitude of these movements is negatively correlated with the productivity of the asset and with the penalty for default

endogenous vs exogenously driven fluctuations in vintage capital models in this paper we present a particular case of the creative destruction model of caballero and hammour quart j econ 111 1996 805 851 in which both exogenous and endogenous fluctuation sources are present we show that job creation follows a delayed differential equation with periodic coefficients the delay is equal to the optimal age of capital goods the period of the coefficients is equal to the period of an exogenous profitability cycle we mathematically show that job creation is asymptotically periodic with the same period as the profitability cycle furthermore using an explicit numerical method we find that replacement echoes generally dominate the short run dynamics finally we find that the combination of the two fluctuations sources favors the appearance of asymmetries in job creation and job destruction patterns

stability of cycles and expectations the actual dynamics of an economy depends on how agents forecast the future at every date as a function of their information on the past while possibly learning the structure of their environment we show in the case of a one dimensional state variable that under mild conditions on expectations functions a given cycle with perfect foresight that is stable in the actual dynamics is stable in a fictitious backward perfect foresight dynamics we exhibit a restricted class of expectations functions for which the converse is true

strategic complementarity in business formation aggregate fluctuations and sunspot equilibria the extent to which changes in beliefs can be important factors in initiating economic fluctuations has been a prominent area of investigation for macroeconomists the notion that beliefs about the future influence current decisions is a property of almost all dynamic economic systems the more challenging task is identifying economic environments in which changes in beliefs alone influence current choices in such a way that the variations in beliefs are self fulfilling because the resulting fluctuations arise in the absence of variations in fundamental variables such as preferences and technology they are often termed sunspot equilibria apart from suggesting that instability of expectations may be a distinct source of cyclical volatility sunspot equilibria may also explain why apparently small disturbances in fundamentals lead to large change in macroeconomic aggregates in this study we demonstrate the possibility of sunspot equilibria in an overlappinggenerations economy characterized by a plausible form of strategic complementarity as more agents enter as producers in any particular sector of the economy they create an incentive for agents to enter as producers into other sectors as well 2 the basis for this

exponentially fading memory learning in forward looking economic models abstract in this paper we analyze forward looking economic models under bounded rationality we consider a learning mechanism characterized by exponentially fading memory with a learning step not vanishing in the limit the dynamics of the model under bounded rationality can be parametrized with respect to the memory of the learning mechanism we show that memory plays a stabilizing role in a local sense it induces local convergence towards a stationary rational expectations equilibrium and in some cases it does not allow for nonperfect foresight attractors obtained through local bifurcations we discuss this learning mechanism in pure exchange overlapping generations models we also analyze models with predetermined state variables in this setting the effect of memory on the learning dynamics is controversial

optimal policy in og models in the present paper general stationary overlapping generations economies with many commodities in every period and many different consumers in every generation are considered a government maximizes an utilitarian social welfare function that is the sum of weighted averages of utilities for generations through fiscal policy i e monetary transfers and taxes both situations with and without time discounting are considered it is shown that if the discount factor is sufficiently close to one then the optimal policy stabilizes the economy i e the equilibrium path has the turnpike property moreover the fiscal policy is shown to be time consistent

the household fallacy we refer to the idea that government must tighten its belt as a necessary policy response to higher indebtedness as the household fallacy we provide a reason to be skeptical of this claim that holds even if the economy always operates at full employment and all markets clear our argument rests on the fact that in an overlapping generations olg model changes in government debt cause changes in the real interest rate that redistribute the burden of repayment across generations we do not rely on the assumption that the equilibrium is dynamically inefficient and our argument holds in a version of the olg model where the real interest rate is always positive

firms and tariff regime change explaining the demand for protection although it is commonly argued that there is a connection between tariff levels and business conditions this hypothesis has not been subjected to systematic empirical analysis or given any theoretical basis the author presents two complementary theories of the movement of tariff levels in response to changing business conditions both explain tariff changes in terms of the changing political demands of business firms and both rely on the business cycle to drive these changing demands one theory is a conventional argument about changing opportunities for entry and exit the other treats firms as satisficers the theories yield similar predictions preliminary empirical analysis while consistent with both does not differentiate between them

introduction to market psychology and nonlinear endogenous business cycles abstract the purpose of this symposium is to present geometric methods that are useful to study multiple equilibria and endogenous fluctuations in simple two dimensional macroeconomic models with a single predetermined variable characterizing the support of a sunspot equilibrium by its invariance properties in the underlying deterministic dynamics generates a complete description of stochastic endogenous fluctuations near a stationary state and along local bifurcations graphical methods to perform sensitivity analysis of local indeterminacy and bifurcations with respect to variations of uncertain economic parameters are also presented these methods are applied to specific macroeconomic models with constant returns to scale with external increasing returns and with imperfect competition journal of economic literatureclassification numbers e32 c62

the emergence of chaos from classical economic growth this paper shows how fluctuations of an erratic and unstable nature can emerge from the classical deterministic economic growth process implications of the analysis would appear to be at least two first pronounced changes in the way an economy behaves need not cause us to reject our understanding of how it works second we need not seek in exogenous forces an explanation as to why behavioral patterns change and why it may be so difficult to anticipate future events from the profile of past experience

equilibrium models displaying endogenous fluctuations and chaos abstract this paper surveys current developments in dynamic general equilibrium theory concerned with conditions under which endogenous fluctuations are possible existing contributions are divided into two classes the larger one consists of models with a unique perfect foresight equilibrium while the second includes models where equilibrium is indeterminate and the set of equilibria involving endogenous fluctuations includes sunspots equilibria while the two classes of models involve oscillations of different natures and with different policy implications we show that both are consistent with optimizing behavior and competitive equilibrium

recursive factor of production interrelations and endogenous cycling a multivariate linear rational expectations equilibrium version of the lucas prescott investment model is developed to study the behavior of factors of productions with recursive interrelations the connection between these interrelations and endogenous cycling is established in a testable way maximum likelihood estimates using annual postwar aggregate u s manufacturing data provide strong evidence of capital labor interrelations that induce a labor overshooting type of endogenous cycling this raises questions for the methodology of current real business cycle models which rule out the possibility of such interrelations copyright 1991 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

irregular growth cycles this paper uses the familiar neoclassical theory of capital accumulation to show how complex behavior can emerge from quite simple economic structures indeed when sufficient nonlinearities and a production lag are present the interaction alone of the propensity to save and the productivity of capital can lead to growth cycles that exhibit a wandering sawtooth pattern not unlike those observed in reality these fluctuations need not converge to a cycle of any regular periodicity so they are not quasi periodic because such chaotic trajectories are unstable errors of estimation in parameters or initial conditions however tiny will accumulate rapidly into substantial errors of forecast moreover periods of erratic cycling can be interspersed with periods of more or less stable growth evidently the future behavior of a model solution cannot be anticipated from its patterns in the past a situation that seems to mimic experience apparent structural change and unpredictability is explained in the present theory by a deterministic single equation model random shocks play no role so the reader can visualize just what it is we are are talking about a noteworthy simulation is presented in figure 1 for gnp in a growth model that is described below in section iii a period of relatively rapid growth is followed by a period of cycles then remarkably for a considerable time about twenty periods apparently steady state growth occurs wandering cycles however emerge another brief period close to the steady state appears again toward the end of the series i establish conditions of savings and productivity that lead to results of this kind this analysis makes use of the mathematical theory of chaos which in the form exploited here originated in the work of edward lorenz a formal definition of chaos and sufficient conditions for chaotic trajectories were provided in a seminal paper by t y li and james yorke a survey of these related contributions is found in yorke and evelyn yorke this theory was introduced into economics by jess benhabib and myself 1981 where we showed that sequences of rational choices can be erratic when preferences depend on experience in a certain way by michael stutzer who provides a detailed analysis of trygve haavelmo s growth model by benhabib and myself 1980 in an application of the overlapping generations model and in my forthcoming study of the classical growth model

stabilizing competitive business cycles abstract we study how stylized monetary proportional money transfers fiscal lump sum money transfers and public expenditure policies may eliminate endogenous deterministic cycles and stationary markov sunspot equilibria in a simple version of the overlapping generations model we also present new constructive methods for analyzing stationary markov sunspot equilibria in such a framework

liquidity profit rate cycles in a capitalist economy abstract a monetary economy consisting of independent capitalist firms in which workers spend wages instantly and labor is not scarce is studied the firms create demand for each other s output through their capital outlays and create the backing for money through borrowing when all firms are identical in behavior and initial conditions and the rate of growth of money is constant the economy may be unstable around the equilibrium steady state growth path due to strong accelerator effects and follow a limit cycle trajectory

viewpoint a microfoundation of monetary economics in this lecture i explain what the microfoundations of money are about and why they are necessary for monetary economics then i review recent developments of a particular microfoundation of money commonly known as the search theory of money finally i outline some unresolved issues dans cette presentation l auteur explique ce que sont les microfondations de la monnaie et pourquoi elles sont necessaires a l economie monetaire ensuite il passe en revue certains developpements recents d une microfondation particuliere de la monnaie connue sous le nom de theorie de la recherche de la monnaie enfin l auteur fait le tour d un ensemble de problemes qui restent sans solution pour le moment

endowments stability and fluctuations in og models abstract in the present paper we consider a stationary overlapping generations model with many commodities and many different consumers and investigate how the distribution of endowments influences the dynamical properties of the model such as stability of steady states and existence of cycles our main results are 1 1 preferences place no restrictions on stability properties of steady states 2 2 cycles exist for all aggregate savings real or nominal and 3 3 equilibria of economies with equilibria close to a no trade equilibrium with constant prices are either steady states or equilibria which converge to a steady state in backward time and another steady state in forward time these results are obtained generically in utility functions and do not depend on whether the utility functions are of the discounted form or not

observational equivalence of the overlapping generations and the cash in advance economies abstract this paper demonstrates that any equilibrium in an overlapping generations economy a la grandmont 1985 can be supported as an equilibrium in a cash in advance economy a la lucas and stokey 1987 and vice versa thus business cycles could occur at real life frequencies

on endogenous competitive business cycles the belief that the long run equilibrium of a competitive monetary economy that does not experience any exogeneous shocks whether originating from the external environment or from policy should be modelled as a state that is stationary or perhaps growing at a constant rate seems to be deeply rooted in the mind of some economists

housing appreciation mortgage interest rates and homeowner mobility abstract this paper presents a model of the optimal timing of tradeup which considers consumption and investment motives of homeownership households determine the optimal timing of trading up so as to maximize their intertemporal utility of both housing and nonhousing consumption first we consider current homeowners who already own a house and expect that they trade up to a more valuable house at some point in the future housing appreciation tends to induce an earlier optimal timing of trading up moreover housing appreciation makes current homeowners better off in terms of welfare however current homeowners suffer from a rise in mortgage interest rates second we consider first time home buyers who have decided to buy a house and expect to trade up to a more valuable house in the future their initial housing consumption is determined by an initial downpayment constraint in this case the effect of housing appreciation on the optimal timing of trading up is ambiguous and unlike current homeowners first time home buyers suffer from housing appreciation moreover as current homeowners first time home buyers suffer from a rise in mortgage interest rates most of the theoretical analytic results are ambiguous accordingly we perform numerical simulations based on the theoretical model in order to determine the most likely comparative effects for a stylized set of parameters as is apparent the model captures the recent observations on homewner mobility and suggests that macroeconomic variables such as housing appreciation and mortgage interest rates effect the optimal timing of trading up and homeowner s welfare nevertheless the model in this paper has several shortcomings which should be the subject of future research first transaction costs are ignored if transaction costs are incorporated the lock in effect from a rise in mortgage interest rates is well explained however the general analysis above is not altered in any essential way second multiple moves are not considered in this model therefore we concentrate on the timing of one tradeup as opposed to the timing and frequency of trading up in a different vein it would be interesting to test empirically the importance of the effects of macroeconomic variables on trading up by using microdata

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

rational choice and erratic behaviour in this paper we show that rational choice in a stationary environment can lead to erratic behaviour when preferences depend on experience we mean by erratic behaviour choice sequences that do not converge to a long run stationary value or to any periodic pattern early investigations of the effects of experience on choice goes back to pareto see also benhabib 1979 some keynesian theories of the consumption function incorporate the effects of experience and habit formation on current levels of consumption duesenberry 1949 modigliani 1949 and brown 1952 a general model of experience dependent choice was described in day 1970 and investigated in day and kennedy 1971 while the specific issue of the existence of stable representable long run consumer demand when tastes vary endogenously has been treated by gorman 1967 pollak 1970 1976 weizsaicker 1971 mccarthy 1974 and hammond 1976 pollak gave conditions for the representability of long run choice when the equations of preference dependence are linear and utility additive hammond in a generalization of these findings provides conditions for stable representable long run choice when preferences are acyclic a condition which in essence assures convergence to a long run choice

on rational dynamic strategies in infinite horizon models where agents discount the future abstract in this paper we show that the equilibrium dynamics arising in three models of rational choice over an infinite horizon are described by choice functions belonging to huge classes of maps including chaotic ones the results are obtained by studying the relationship between the primal functions of the models and the corresponding choice functions the three models are the economic growth model with discounting a duopoly game with alternate moves a duopoly with simultaneous moves

incomplete markets and volatility abstract this paper shows that the precautionary motive combined with asset incompleteness is a major source of volatility and indeterminacy in financial markets price fluctuations originate from agents efforts to insure themselves through time by borrowing and lending instead of shifting income across states of nature by trading risky assets a high interest rate at a future date reduces the potential for future consumption smoothing via borrowing which leads to a strong precautionary motive and a low interest rate in the current period the negative feedback between future and current rates generates fluctuations this logic is developed in spec a cara normal exchange economy with many periods and endogenous interest rates when there is an intermediate level of market incompleteness and sufficient investor impatience fluctuations in the real interest rate can be large even though the aggregate endowment is constant spec has a unique equilibrium under a finite horizon on the other hand with a finite number of infinitely lived agents there exists a robust continuum of equilibria that are neither bubbles nor sunspots journal of economic literature classification numbers c61 d52 d58 g11 g12

on the preservation of deterministic cycles when some agents perceive them to be random fluctuations some recent equilibrium models give rise to complex but deterministic fluctuations we modify the hypothesis of universal perfect foresight by injecting into the economy a nonnegligible fraction of less informed agents who optimize their expected utility with respect to the statistical distribution of prices in the deterministic dynamics for the standard overlapping generations model with money the samuelson case it is proved that if the fraction of consumers with limited knowledge is sufficiently high then all equilibrium cycles of period k 2 disappear the global properties of the case of 2 cycles are studied in detail a brief analysis of the classical case is also given

equilibrium and optimality some imprints of david gale abstract the paper is a review of some of the themes to which david gale made lasting contributions it touches upon a number of the fundamental issues in the walrasian equilibrium theory existence uniqueness and stability the overlapping generations model non optimality and indeterminacy of competitive equilibria the von neumann equilibrium as a turnpike and in the theory of decentralized intertemporal allocation through competitive prices efficiency and golden rules duality and existence of optimal programs

unemployment migration and growth economic development is typically accompanied by migration from rural to urban employment this migration is often associated with significant urban underemployment both factors are important in the development process we consider a neoclassical growth model with rural urban migration and urban underemployment which arises from an adverse selection problem in labor markets we demonstrate that rural urban migration and underemployment can be a source of development traps and can give rise to a large set of periodic equilibria display long periods of uninterrupted growth punctuated by brief but severe recessions

mode locking and international business cycle transmission abstract we investigate international business cycle synchronization business cycles in many countries have a tendency to synchronize with one another in what appears to be a world business cycle yet researchers find that trade and capital linkages are not strong enough for one country to drive business cycles in another country how is this world business cycle formed this study suggests that the world business cycle results from a mode locking phenomenon a nonlinear process by which weak coupling between oscillating systems tends to synchronize oscillations in the systems simulations and econometric analyses are performed to attempt to verify this hypothesis

existence and stability of rational expectation equilibria in a simple overlapping generation model abstract we consider a simple overlapping generation model with outside money and one consumption good for a big class of preference relations it is shown that globally no self fulfilling expectation exists except the trivial one if the information set contains only past and present prices even locally positive results can be obtained for homothetic preferences only to get asymptotic stability this class must be restricted again the elasticity of substitution must be very small the implications of this are very negative a learning process can never reach rationality

endogenous imperfectly competitive business cycles abstract we investigate how imperfect competition affects the occurrence and the properties of endogenous rational expectations business cycles in an overlapping generations model with constant returns to scale in production the model has explicit product and labor markets all characterized by monopolistic competition an implicit assumption of barriers to entry justifies that the number of firms is fixed even when positive profits occur it turns out that both market power of firms on the product markets and market power of unions on the labor markets make the occurrence of cycles more likely in particular imperfect competition on the product markets and the positive profits associated with it may have the effect that there is a cycle even if the labor supply curve is increasing in the real wage rate for competitive cycles is required not only a decreasing labor supply curve but a wage elasticity below 1 2 at stationary equilibrium market power on the labor markets may have the effect that imperfectly competitive cycles are in accordance with certain empirical regularities some well known some reported in the paper concerning fluctuations in output and involuntary unemployment since involuntary unemployment does not occur under perfect competition such regularities are incompatible with competitive cycles

chaotic dynamics in a cash in advance economy abstract this paper introduces sufficient conditions for the existence of deterministic cycles and chaos in cash in advance models building on the earlier work of woodford 1994 chaotic equilibria are shown to be particularly likely in the cash in advance model because of a unique characteristic of such models a discontinuous derivative in the difference equation map at the satiation level of real balances the existence of a kink means that chaotic equilibria may exist without implausibly large curvatures in the utility function since a chaotic time series that makes use of the kink would sometimes exhibit zero nominal interest rates the paper also gives an example of chaos in which nominal interest rates remain strictly positive

the emergence of equilibrium cycles in a monetary economy with a separable utility function abstract this paper analyzes the dynamic properties of the monetary economy when money held during the period induces some utility it is shown that the price level and real money balances may have chaotic dynamic paths even if the utility function is separable in real money balances and consumption a crucial point is that a constraint on the utility of money yields the wealth effect that inflation will reduce the real value of assets hence as in the overlapping generations model the conflict between substitution and wealth effects may cause globally stable periodic orbits as well as the complicated dynamics

a family production overlapping generations economy abstract this paper provides a theoretical analysis of an overlapping generations economy in which production decisions and input output allocations are all carried out at the family level i consider a single class of output allocation schemes and various degrees of knowledge about the production technology under complete knowledge i show that a family organizational structure in which everyone receives his marginal contribution to output invests less in physical capital than under a perfectly competitive equilibrium environment under incomplete knowledge i analyze and compare how beliefs about the input output relationship affect the physical capital accumulation dynamics and the long run standards of living

externalities internalization and fluctuations in this paper the authors introduce consumption externalities as developed by k arrow in overlapping generations economies they show how the internalization of externalities through exchanges at markets for externalities may give rise to new phenomena such as altered stability properties and fluctuations even though it restores optimality copyright 1997 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

two period cycles in a three period overlapping generations model abstract we study the properties of two period monetary cycles in simple pure exchange overlapping generations economies in which the households live for three periods we demonstrate that these economies can support cycles under a much broader and arguably more plausible range of assumptions than the analogous two period economies we show that economies that fail the well known grandmont econometrica 53 1985 995 condition can have cycles and that economies that satisfy the condition can fail to have cycles in addition we show that economies can have monetary cycles when they do not have conventional monetary steady states and when aggregate demand for assets is not decreasing in the real return rate at a gross real rate of unity

statistical dynamics and economics abstract it is shown in this paper how complex economic dynamics can be characterized using the statistical or distributional theory of dynamical systems the basic concepts of the latter are summarized then applications to supply and demand adjustments in competitive markets aggregate business fluctuations and economic growth in the very long run are briefly reviewed

stabilization policy can lead to chaos stabilization policy can lead to chaos nonlinearities in economies as elsewhere can generate chaotic equilibria the presence of pareto inferior chaotic equilibria might seem reason enough to use stabilization policy to select preferable equilibria however i show that a stabilization policy with feedback can itself lead to chaotic dynamics thus the existence of nonlinearities in the economy does not by itself justify monetary or fiscal policies aimed at reducing economic instability current evidence cannot distinguish whether monetary policy stabilizes a nonlinear economy creates nonlinear dynamics in the economy or both i introduction in recent years the claim has been made that nonlinearities and self fulfilling expectations in the private economy generate economic instability that can and should be offset by government policies this instability shows up as a positive variance in the steady state of an economy that otherwise would have a steady state with zero variance and higher utility for households on the basis of such models grandmont and malgrange 1986 9 conclude that we should expect a free market economy to perform rather badly under laissez faire in addition there is a possible role for deterministic stabilization policies that would if understood and believed eliminate forecasting mistakes and the corresponding efficiency losses and would guarantee the ultimate disappearance of endogenous fluctuations the purpose of this note is to provide a simple example of stabilization policy leading to chaotic time series behavior this example is an elaboration of friedman s 1953 classic argument that with uncertain knowledge about the economy stabilization policy can increase the variance of the goal variable nonlinearities can make as much a case against stabilization policy as for it the example is ad hoc in some respects but it is based on common ingredients of many models ii a simple example interesting aspects of an economy can be summarized by the quantity equation 1 mv y assume that real income y is constant which implies that changes in nominal income are proportional to changes in the price level in one respect using the quantity equation means that the example below does not have the same force as a tight general equilibrium model of the economy without the underlying detail equation 1 is ad hoc in another respect the example below has more force an equation such as 1 commonly characterizes the general equilibrium models in which money has a significant effect on the economy hence one interpretation is that the example has some generality assume that the monetary authority targets nominal income and knows 1 that the quantity theory characterizes the long run equilibrium of the economy and 2 the level of velocity that is consistent with zero inflation v in these circumstances there is one obvious equilibrium consistent with the goal the money stock is constant and the public expects a constant money supply and zero inflation in this equilibrium nominal income can be stabilized at the target level of nominal income y the monetary authority just need set the money supply to m v 1y if the monetary authority is uncertain about the public s response to its actions one strategy is to adopt a cautious stabilization policy to support the economy s approach to the long run deterministic equilibrium one commonly proposed set of feedback rules is the proportional policies introduced by phillips 1954 in the levels such a rule for the money supply is 2 m m alpha y y sub 1 where y sub 1 is last period s nominal income and alpha is the adjustment parameter assume that private agents believe that the monetary authority eventually will accomplish its goal of setting y equal to y

carl s nonlinear cobweb abstract this essay surveys some of my work on expectations learning and bounded rationality within the classical cobweb model following early inspiring ideas from carl chiarella in particular i focus on the role of nonlinear dynamics learning and heterogeneity within the cobweb framework and how price fluctuations in the cobweb theory fit with observations of individual and aggregate behaviour from laboratory experiments with human subjects

population and the environment a parable of firewood and other tales the author analyzes the relationship between population and the environment with a focus on the role which environmental degradation and natural resources depletion may play in producing the population pressure which lies behind such degradation and depletion especially in developing countries the principal conclusion of this analysis is that the possibilities for a stable equilibrium between human population and its environment are quite limited i show that parental altruism toward their children can only make matters worse if socially unchecked by leading to an increase of the birthrate in every environmental state in comparison with that which would occur in its absence excerpt

asset markets and equilibrium processes the failure of the asset market to be complete causes serial dependence in output and prices which is suboptimal we consider an economy with white noise shocks when the asset market is complete an optimal competitive allocation inherits this strong stationarity when the asset market is only sequentially complete prices and output necessarily display serial dependence at equilibrium the further incompleteness of a monetary economy explains co movements in real and nominal variables

expectations in stability and in viability in realistic overlapping cohorts models abstract in this paper we shall consider the multi cohort generalization of overlapping generations models namely overlapping cohorts olc models each time period consumers of different ages form expectations on future interest rates and conditionally maximize utility arising from their remaining consumption paths under the condition of zero bequest for every time period a coordinator determines the new interest rate to ensure that the total consumption is equal to the total endowment of the society the message of the paper is the following 1 in olc the dynamics generated by rational expectations is frequently not only unstable but unviable 2 in olc the dynamics generated by naive expectations is practically asymptotically stable and viable around the lower steady state

habit persistence in overlapping generations economies under pure exchange abstract this paper analyzes the implications of habit persistence preferences for savings and equilibrium dynamics in the context of an overlapping generations model under pure exchange we show that habit persistence can convert an economy which otherwise has no role for government currency into an economy where there does exist a role for such currency further the increased saving induced by habit persistence implies that governments are able to float higher levels of deficits in such economies relative to economies without habit persistence the paper also shows that relative to standard preferences habit persistence preferences cause the savings function to become decreasing in the rate of interest at lower values for relative risk aversion this is of particular interest since the paper demonstrates that this result is closely related to the relative success of models with habit persistence in explaining the equity premium puzzle journal of economic literatureclassification numbers e21 e32

some evidence concerning macroeconomic chaos abstract an empirical assessment of a linear stochastic perspective for canadian macroeconomic time series is presented the methods used are based on the mathematics of chaos present evidence suggests that low order deterministic chaos does not provide a satisfactory characterization of the data the absence of significant nonlinear structure for the investment and unemployment series is of particular note in light of past findings with american data the degree to which the use of a time trend can impose a pseudo structure on the data is illustrated

ergodic fluctuations in deterministic economic models abstract nonperiodic business fluctuations are shown to exist with positive measure generically and to behave like stationary stochastic processes in the standard dynamic macro model the implication is that so called chaotic fluctuations are probable for random initial conditions in a large class of recursive economies

a volatility bound for endogenous business cycles the case of even period lives with additive utility in a monetary economy abstract this paper provides a simple method for placing a bound on the extent of variation of endogenous business cycles in a monetary economy with additive utility the results apply when individuals have even period lives in general the bound shrinks as individuals discount the future less

correlated equilibria and sunspots we examine when sunspots uncertainty that has no influence on endowments preferences or technology can affect equilibrium in a simple two period two commodity two class economy we find that such an effect is possibly only if the signals random variables that different agents observe are imperfectly correlated neither perfectly correlated nor independent and at least one commodity is a giffen good for two special cases we characterize the set of equilibria due to sunspots we conclude by showing the intimate connection between the sunspot equilibria of our finite horizon model and those of the overlapping generations literature

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

institutions and short run macroeconomic performance abstract this paper reviews the growing interest in institutions it argues that the explanation for this interest is a fresh awareness of how institutions affect economic performance this connection arises because many economic interaction take the form of one or other of three classic games prisoners dilemma coordination and chicken and the outcome in these games and hence performance of the economy is influenced by the institutional context of these interactions the paper provides a detailed illustration of this argument with a survey of the literature which relates unemployment performances to the institutions of wage setting in oecd countries