nonlinearities in economic dynamics two reasons that led to the dominance of the linear stochastic difference equations approach the first one was the fact that the nonlinear systems seemed incapable of reproducing the statistical aspects of actual economic time series at best such models were able to produce periodic motion1 and an examination of the spectra of economic time series showed the absence of the spikes that characterise periodic data the emphasis on the equilibrium approach to aggregate economic behaviour cf lucas i 986 would make things even more difficult the plethora of stability results for models of infinitely lived agents with perfect foresight turnpike theorems suggested that even the regular fluctuations that had been derived in the literature on endogenous business cycles were incompatible with a theory that had solid microeconomic foundations further this indicated that while nonlinearities could be present the explanations of the fluctuations had to rest solely on the presence of exogenous shocks that working through the equilibrating mechanism would create the observed randomness if such shocks were absent the system would tend to a stationary state the second reason was the empirical success of the models based on linear stochastic difference equations low order autoregressive processes captured some of the features of aggregate time series in turn these processes can in principle result from an economy with complete markets where production is subject to exogenous shocks though the task of confronting these equilibrium models with actual data has not yielded uncontroversial results see the discussion and references in section i there was no obvious gain in the

on the indeterminacy of capital accumulation paths abstract in neoclassical optimal growth models the stability of the accumulation paths depends on the discount parameter we prove that for discount factors small enough the policy function which describes an optimal path can be of any type the result is achieved using the notion of concavity we adopt a constructive approach given any twice differentiable map we show how to construct an optimal growth problem which produces that map as the optimal policy function a consequence is that chaos can appear in these models we also provide bounds on the values of the discount parameter for which indeterminacy is possible

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

inflation and reputation in many macroeconomic models with rational expectations optimal policy is time inconsistent and therefore announced policy may not be credible this paper models the government s credibility explicitly using kreps and wilson s analysis time consistent optimal government policy emerges as a sequential equilibrium in a repeated game this policy is at least as good as the inconsistent optimal policy and dominates the consistent policy when reputational effects are ignored thus the analysis resolves the problem of specifying a credible optimal policy in such models the results show why attempts to disinflate may lead to recession even with perfectly flexible prices this abstract was borrowed from another version of this item

adverse selection in the overlapping generations model the case of pure exchange abstract we examine the general equilibrium consequences of credit rationing that results from an adverse selection problem relative to a full information benchmark economy static incentive problems result in reductions in the rate of return at inside money equilibria and hence can cause dynamic inefficiency these problems also create a role for outside money and may convert otherwise classical into samuelsonian economies however even the presence of money does not support steady state equilibria with constrained optimality properties policies that do support constrained optima are outlined as are the consequences of credit rationing for the financing of government deficits journal of economic literature classification numbers e13 e40 e44 e50 g14

occupation induced status social norms and economic growth abstract we analyse a monetary growth model where entrepreneurs borrow funds to invest in projects that produce capital goods in addition to their varying pecuniary returns different projects also vary with respect to the status they confer to the entrepreneurs who operate them we show that i social status increases the growth rate but this effect is mitigated by a social norm that inversely links overall levels of employment in the high return project with the status conferred to it ii the combined effect of social status and inflation is a source of transitional dynamics in an environment where such dynamics would not emerge if considerations of occupational prestige were absent iii when the social norm affects social status the economy s dynamics may be manifested in the form of endogenous volatility iv the presence and characteristics of social status can generate a negative correlation between volatility and growth

interest on reserves and sunspot equilibria friedman s proposal reconsidered friedman s 1960 proposal to pay interest on required reserves is considered in a setting that eliminates the indeterminacy of steady state equilibrium discussed by sargent and wallace 1985 in an overlapping generations model where the real rate of interest is technologically determined the payment of interest on reserves results in a determinate pareto optimal steady state equilibrium however interest payments on reserves reduce the steady state welfare of all young agents and for many economies result in the existence of stationary sunspot equilibria this is the case even if such equilibria cannot exist when reserves do not earn interest

can there be short period deterministic cycles when people are long lived this paper considers whether short period deterministic cycles can exist in a class of stationary overlapping generations models with long but finite lived agents it shows that if agents discount the future positively then as life spans get large nonmonetary cycles will disappear further neither constant monetary steady states nor stationary monetary cycles can exist it also shows that if agents discount the future negatively then there are robust examples in which constant monetary steady states as well as stationary monetary cycles with undiminished amplitude can occur no matter how long agents live

stationary sunspot equilibria in a finance constrained economy abstract stationary sunspot equilibria are shown to exist in a production economy with infinite lived agents when it is not possible to borrow against future wage income equilibrium fluctuations exhibit persistence over time scales of the same order of magnitude as observed business cycles an active fiscal policy that stabilizes aggregate money expenditures can prevent such fluctuations

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

memory and discounting theory and evidence abstract heterogeneous memory capacity is largely neglected in the economics literature although it may have profound economic implications adopting the concept of memory utility proposed by gilboa postlewaite and samuelson 2016 we explore the relationship between memory capacity and individual discounting behavior by building a simple two period model and comparing its predictions with experimental data both theoretical and experimental evidence confirm that memory capacity and discount rates are positively correlated

on competitive cycles in productive economies abstract in a model of overlapping generations with production money and an endogenous labor supply general conditions are given for the existence of two different types of cyclical equilibria the conditions are given in terms of the elasticities of demand for savings and for capital with respect to the interest rate and of the capital consumption ratio at the golden rule steady state examples using ces technologies are also studied

a characterization of ramsey equilibrium abstract consider a perfect foresight equilibrium model with a single capital good a borrowing constraint and many infinitely lived households with fixed but different discount factors the steady state capital stock is held by the most patient household quart j econ 95 1980 375 382 econ j 38 1928 543 559 an example shows the total capital can exhibit an equilibrium cycle in contrast to the stability property of the one household case in the example only the most patient household saves and his income deceases in capital we give a condition implying income is increasing in capital and use it to show any equilibrium converges to the steady state

rational expectations and policy credibility following a change in regime we examine the dynamic path of an economy after a change in regime when neither the policy to be followed nor the reactions of the public are known the model is an application of kreps and wilson s reputation model to barro and gordon s macroeconomic policy game equilibrium is defined to be the dynamically consistent solution to a game between the government and the private sector it involves mixed strategies and bayesian learning by both sides until the uncertainty about government and public behaviour is resolved the absence of complete credibility of government policy and intransigence of private sector wage demands increase the output loss of disinflation the analysis also sheds light on the strategic nature of economic policymaking and the role of information in macroeconomics

competitive business cycles in an overlapping generations economy with productive investment abstract this paper examines the emergence of long run competitive periodic equilibria in a two period overlapping generations model with capital accumulation the existence of periodic equilibria is a consequence of the existence of an aggregate bubble money and of a non linear behaviour of aggregate savings the technique used is to show that the problem can be reduced to the study of a dynamical map from an interval into itself although it is originally two dimensional this will allow us to study the occurrence of cycles from a global point of view

dynamic complexity in duopoly games abstract we discuss the occurrence of periodic and chaotic phenomena in infinite horizon duopoly games where firms maximize their discounted sum of profits and use markov perfect equilibrium strategies in the alternating case their corresponding actions are then constrained orbits of a map similar to a cournot t tonnement we show that any behavior is possible for small discount factors and that one obtains the cournot t tonnement as the discount factor goes to zero in the simultaneous case we show by mean of an example that many cournot t tonnements can be viewed as markov perfect equilibria of an infinite horizon game and that one obtains the nash equilibrium of the static game as the discount parameter goes to zero we are thus led to study in detail the dynamical properties of a cournot t tonnement

policy functions for capital accumulation paths abstract it has recently been shown that in neoclassical optimal growth models the set of policy function contains all twice differentiable functions the question has been raised as to whether this restriction to twice differentiable functions is essential in this paper we show that all c 1 functions with derivative satisfying a lipschitz condition can serve as policy functions and we also show by examples that differentiability is not a required property of a policy function

nonlinearity and chaos in economic models implications for policy decisions this survey paper discusses the policy implications that can be expected from the recent research on nonlinearity and chaos in economic models expected policy implications are interpreted as a driving force behind the recent proliferation of research in this area in general it appears that no new justification for policy intervention is developed in models of endogenous fluctuations although this conclusion depends in part on the definition of equilibrium when justified however policy tends to be very effective in these models copyright 1993 by royal economic society

revisiting asset pricing under habit formation in an overlapping generations economy abstract by incorporating habit formation into an overlapping generations economy we show that the middle aged consumers savings decision has a substantial impact on the equity premium the higher incentive for savings for the middle aged resulting from the habit formation preference causes an even higher demand for bonds and a lower demand for equity which eventually generates a lower risk free rate and a higher required return for holding equity than does the framework of non habit forming models calibration results verify that the habit formation setting together with an olg framework is capable of yielding lower bond returns and higher equity returns than the standard crra utility models and the borrowing constraint imposed on the young aged consumers amplifies the positive effect of habit formation on the equity premium the findings imply that habit formation preferences within the overlapping generations framework under the borrowing constrained economy can provide a more improved explanation of the equity premium puzzle

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

a contribution to the theory of business cycles an economy consisting of identical perfectly competitive firms with real liquidity costs and a one period production lag has a locally unstable stationary equilibrium with complex eigenvalues for a wide range of parameters monetary policy aimed at stabilizing real balances can support nonstationary equilibrium paths that converge to a limit cycle which has keynesian features the first welfare theorem does not hold because the price level appears in the production function through liquidity costs so that production has a positive externality

estate taxes consumption externalities and altruism we study how the introduction of consumption externalities affects the efficiency of the dynamic equilibrium in an economy displaying dynastic altruism when the bequest motive is inoperative consumption externalities affect the intertemporal margin between young and old consumption and thus modify the intertemporal path of consumption and capital the optimal tax policy that solves this intertemporal inefficiency consists of a tax on capital income and a pay as yougo social security system the later solves the overaccumulation of capital due to the inoperativeness of the bequest motive and the former solves the inefficient allocation of consumption due to consumption externalities when the bequest motive is operative consumption externalities only cause an intratemporal inefficiency that affects the allocation of consumption between the generations living in the same period but do not affect the optimality of the capital stock level this suboptimal allocation of consumption implies in turn that the path of bequest is also suboptimal the optimal tax policy in this case consists of an estate tax and a capital income tax the estate tax corrects the intratemporal inefficiency but generates an intertemporal inefficiency which is corrected by means of an appropriate capital income tax

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

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

the absent minded driver abstract the example of the absent minded driver was introduced by piccione and rubinstein in the context of games and decision problems with imperfect recall they claim that a paradox or inconsistency arises when the decision reached at the planning stage is compared with that at the action stage though the example is provocative and worth having their analysis is questionable a careful analysis reveals that while the considerations at the planning and action stages do differ there is no paradox or inconsistency journal of economic literatureclassification numbers d81 c72

learning by doing organizational forgetting and industry dynamics learning by doing and organizational forgetting have been shown to be important in a variety of industrial settings this paper provides a general model of dynamic competition that accounts for these economic fundamentals and shows how they shape industry structure and dynamics previously obtained results regarding the dominance properties of flrms pricing behavior no longer hold in this more general setting we show that forgetting does not simply negate learning rather learning and forgetting are distinct economic forces in particular a model with learning and forgetting can give rise to aggressive pricing behavior market dominance and multiple equilibria whereas a model with learning alone cannot

perfectly competitive models of endogenous business fluctuations the endogenous hypothesis is not new at a pre analytic level it is based on the simple intuition that market mechanisms are inherently dynamically unstable at least around their stationary positions in this note i want to stress the theoretical point that there is nothing in the working of a perfectly competitive market system that prevents it from displaying persistent and endogenous fluctuations and that moreover such fluctuations may have their origins in market fundamentals such as factor intensities factor substitutability degree of impatience and so forth nevertheless macroeconomic models of endogenous fluctuations still have to prove that apart from being very beautiful they can also be useful to understand the so called heal world hit sunt leones this article is not intended to be a survey of all that has been written in this area in the last decade i have no title whatsoever to talk about empirical studies chera sayers contribution in this same volume addresses that guestion scheinkman 1990 is a readily available survey of nonlinear statistical methods that are relevant to this debate as for the theory incompetence recommends that i avoid touching on sunspot equilibria olg models and more generally expectations driven cycles they are instead discussed in jean michel grandmont s article finally marketing awareness implies recommending boldrin and woodford 1990 as a reasonably complete survey of what the endogenous cycle research program has recently produced at a theoretical level

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

cooperation in games with forgetfulness companies and managers are apt to forget information yet classic game theory analysis assumes that all players have perfect recall this paper expands the literature by examining how introducing forgetfulness into a multiplayer game theoretic framework can help or hinder cooperative behavior we find that forgetfulness impacts the ability of firms to cooperate in countervailing directions on one hand forgetfulness can diminish the ability to punish deviators making cooperation more difficult on the other hand under some conditions forgetfulness can make meting out severe punishments even below stage minimax punishments credible and decrease the ability for players to effectively deviate facilitating cooperation even in circumstances where cooperation cannot be sustained under perfect recall we apply our model to a number of strategic games that commonly appear in the literature this paper was accepted by preyas desai marketing

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

the politics of ambiguity politicians face a trade off between the policies that maximize their chances of reelection and their most preferred policies or the policies most preferred by the constituency which they represent this paper analyzes this trade off in a dynamic electoral model in which the voters are not fully informed about the preferences of the incumbent first we show that the incumbent follows a policy which is intermediate between the other party s ideal policy and his own ideal policy second we show that often the incumbent has an incentive to choose procedures which make it difficult for voters to pinpoint his preferences with absolute precision thus politicians may prefer to be ambiguous

endogenous real exchange rate fluctuations in an optimizing open economy model abstract this paper constructs a simple intertemporal model of a small open economy inhabited by forward looking agents in which endogenous fluctuations in the real exchange rate can arise in equilibrium i e fluctuations that are not linked to movements in economic fundamentals the key condition for the main results is the assumption that the marshall lerner condition does not hold i e that the country s exports and imports are inelastic to its real exchange rate it is shown that given that the marshall lerner condition fails there exist periodic equilibria and or stationary sunspot equilibria in the neighborhood of the stationary state

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

solving consumption models with multiplicative habits this paper provides derivations necessary for solving an optimal consumption problem with multiplicative habits and a crra outer utility function either for a microeconomic problem with both labor income risk and rate of return risk or for a macroeconomic representative agent model

double sided moral hazard and the nature of share contracts contractual arrangements involving revenue profit sharing are often based on fairly simple often linear rules in addition in many contexts these contracts are not finely adjusted to the particular circumstances of individual agents or markets nor do they vary over time to the extent current theories based on optimal contracting suggest they should we develop a simple model of such revenue or profit sharing arrangements based on double sided moral hazard and show that this model can account for many of these stylized facts more specifically the model shows that linear contracts can be optimal and that benefits from customizing terms can in some cases be quite limited if not zero

competitive equilibrium cycles recently there has been a surge of interest in endogenous business cycles that arise in competitive laissez faire economies in the context of standard overlapping generations economies conditions for the existence of equilibrium cycles have been given by grandmont 1983 and by benhabib and day 1982 models of the economy with extrinsic uncertainty or sunspots that have been developed by shell 1977 and by cass and shell 1983 see also balasko 1983 can also lead to equilibrium cycles

growing through cycles the neoclassical growth model focuses on factor accumulation as an engine of growth while the neo schumpetarian growth model stresses innovation this paper argues that these two views of growth may capture different phases of a single growth experience in the model presented below the balanced growth path is unstable and the economy achieves sustainable growth through cycles under an empirically plausible condition perpetually moving back and forth between two phases one phase is characterized by higher output growth higher investment no innovation and a competitive market structure the other phase is characterized by lower output growth lower investment high innovation and a more monopolistic market structure both investment and innovation are essential in sustaining growth indefinitely and yet they move in an asynchronized way only one of them appears to play a dominant role in each phase the economy grows faster along the cycles than along the unstable balanced growth path

rejuveniles and growth abstract rejuveniles are people who cultivate tastes and mind sets traditionally associated with those younger than themselves noxon c 2006 rejuvenile crown publishers in this paper we study a standard ak growth model of overlapping generations populated by rejuveniles for our purposes rejuveniles are old agents who derive utility from keeping up their consumption with that of the current young we find that such cross generational keeping up is capable of generating interesting equilibrium growth dynamics including growth cycles no such growth dynamics is possible either in the baseline model one where no such generational consumption externality exists or for almost any other form of keeping up steady state growth in a world with rejuveniles may be higher than that obtained in the baseline model

self fulfilling optimism in a trade friction model of the business cycle models of economic activity with frictions in coordinating trading have been shown to be capable of generating multiple steady states peter diamond 1982 is the pioneering work see my 1987a paper for a general discussion less work has been done on out of steady state dynamics in such models which would enable us to examine what sort of fluctuations these models may generate the absence of dynamics leaves open the question of which steady state the economy will reach as well as whether the comovements of key variables resemble what is observed over the cycle in my earlier paper 1987b i presented a model combining search and aggregate demand approaches to unemployment to show how spillovers between product and labor markets could yield multiple equilibria here a highly simplified dynamic model based on this work is presented in which self fulfilling sales expectations determine to which steady state the economy converges these expectations are summarized by the asset values of firms which are producing output relative to those that are not two types of dynamic paths leading to stationary solutions can arise the first is a saddle path in addition for certain parameter values stable limit cycles emerge interestingly over this cycle asset values of firms which one could interpret as stock market values lead economic activity i model setup

the overlapping generations model with habit formation a comment abstract bunzel 2006 habit persistence money and overlapping generations journal of economic dynamics and control 30 2425 2445 studies an overlapping generations model with habit formation this comment argues that the interior paths analyzed in propositions 4 and 5 from that paper are not global maxima specifically if the coefficient of relative risk aversion is less than one a corner solution is optimal this correction however does not change bunzel s conclusion ruling out the possibility of higher order fluctuations

don t fool yourself to believe you won t fool yourself again abstract a possible solution to the absent minded driver problem is that the decision maker optimizes taking into account the utility he will actually have in the future and not the utility level he should have

limited memory categorization and competition this paper investigates the effects of a limited consumer memory on the price competition between firms it studies a specific aspect of memory namely the categorization of available price information that the consumers may need to recall for decision making this paper analyzes competition between firms in a market with uninformed consumers who do not compare prices informed consumers who compare prices but with limited memory and informed consumers who have perfect memory consumers aware of their memory limitations choose how to encode the prices into categories whereas firms take the limitations of consumers into account in choosing their pricing strategies two distinct types of categorization processes are investigated 1 a symmetric one in which consumers compare only the labels of price categories from the competing firms and 2 an asymmetric one in which consumers compare the recalled price of one firm with the actual price of the other we find that the equilibrium partition for the consumers calls for finer categorization toward the bottom of the price distribution thus consumers have a motivation to invest in greater memory resources in encoding lower prices to induce firms to charge more favorable prices the interaction between the categorization strategies of the consumers and the price competition between the firms is such that small initial improvements in recall move the market outcomes quickly toward the case of perfect recall even with few memory categories the expected price consumers pay and their surplus is close to the case of perfect recall there is thus a suggestion in this model that market competition adjusts to the memory limitations of consumers

the dynamics of optimal wealth distributions with recursive utility abstract in an economy with two agents having recursive preferences an optimal wealth distribution is shown to be stable if and only if a perturbation results in the adversely affected agent becoming more patient than the positively affected one this implies a weaker stability condition than traditionally used in the literature

equilibrium cycles in an overlapping generations economy with production abstract perfect foresight equilibrium trajectories of an overlapping generations model with production may include stable or unstable invariant closed curves these orbits are detected using the hopf bifurcation theorem where the parameter of bifurcation is purely technological the paper also proves that there is a stabilization policy that completely eliminates the cycle finally using a c e s production function it is shown that the range of values of the elasticity of substitution between capital and labor for which cycles may exist is bounded above

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

deficits and cycles abstract this paper shows that periodic equilibria may arise in a simple overlapping generations model with capital if the government follows a policy of fixing the value of the deficit rather than fixing the value of government debt then the difference equation that describes competitive equilibria may posses complex roots in the neighborhood of the golden rule stationary state one may show that if there exist parametric families of economies for which these roots change stability then locally there exists an invariant closed curve the paper provides two simple examples that generate such equilibria and it solves these examples numerically

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

reputation in a model of monetary policy with incomplete information abstract previous models of rules versus discretion are extended to include uncertainty about the policymaker s type when people observe low inflation they raise the possibility that the policymaker is committed to low inflation type 1 this enhancement of reputation gives the uncommitted policymaker type 2 an incentive to masquerade as the committed type in the equilibrium the policymaker of type 1 delivers surprisingly low inflation with corresponding costs to the economy over an extended interval the type 2 person mimics this outcome for awhile but shifts eventually to high inflation this high inflation is surprising initially but subsequently becomes anticipated

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

on the optimality of cyclical employment policies a two state variable continuous time control model of optimal employment of a profit maximizing firm with convex labour adjustment costs is considered the model is analyzed numerically it is shown that a cyclical hiring and firing policy is optimal

rational expectations business cycles in search equilibrium we examine the rational expectations equilibrium paths of the model of search and barter in diamond s aggregate demand management in search equilibrium for some initial positions there are two equilibrium paths converging to different steady states with the high activity path pareto dominating the low activity path with some parameters there is also a continuum of equilibrium paths converging to another steady state moreover there can be cycles that are equilibrium paths even though the environment is stationary

equilibrium beliefs in linear rational expectations models abstract non unique equilibria are widely found in dynamic models with money increasing returns and imperfect competition this paper provides a convenient method for representing the entire set of equilibria in a large class of models similar to those studied by blanchard and kahn the method utilizes restrictions imposed on comovements implied by the structures of such models it is an aid in theoretical analysis and can be instrumental in the development of econometric tests of indeterminacy and sunspots important restrictions on admissible non fundamental uncertainty and on model forecasts are also highlighted

learning forgetting and sales sellers of almost any product or service rarely keep their prices constant through time and frequently offer price discounts or sales this paper investigates an explanation of sales as a way for uninformed consumers to be willing to experience the product and learn about its fit and where informed consumers may forget about or change their preferences we investigate the role of the rate of consumer forgetting on the timing between sales and of the rate of consumer learning and menu costs on the length of a sale the rate of consumer forgetting can be linked to the length of purchase cycle and the level of consumer involvement we show that the discount frequency and the discount depth are increasing in the rate of consumer forgetting and that the discount frequency is increasing in the learning rate the duration of a sale is increasing in the rate of consumer forgetting and the rate of consumer learning

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

add on pricing by asymmetric firms this paper uses an analytical model to examine the consequences of add on pricing when firms are both horizontally and vertically differentiated and there is a segment of boundedly rational consumers who are unaware of the add on fees at the time of initial purchase we find that consumers who know the add on fees can be penalized and increasingly so by the existence of boundedly rational consumers our consideration of quality asymmetries on base goods and add ons plus the inclusion of boundedly rational consumers leads to several novel findings regarding firm profits when quality asymmetry is on base goods only and with boundedly rational consumers add on pricing can diminish profit for a qualitatively superior firm and increase profit for an inferior firm i e a lose win result compared to when add on pricing is prohibited or infeasible when quality asymmetries exist on both base goods and add ons and without boundedly rational consumers the opposite win lose result prevails when quality asymmetries exist on both base goods and add ons and with boundedly rational consumers the result can be win win win lose or lose win depending on the magnitude of quality differentiation on add ons this paper was accepted by j miguel villas boas marketing

a memory based model of bounded rationality in order to investigate the impact of limited memory on human behavior i develop a model of memory grounded in psychological and biological research i assume that people take their memories as accurate and use them to make inferences the resulting model predicts both over and underreaction but provides enough structure to predict when each effect dominates i then use this framework to study the consumption decision the results match empirical work on consumption predictability as well as differences in the marginal propensity to consume from different income streams most importantly because it ties the extent of bias to a measurable aspect of the stochastic process being forecasted the model makes testable empirical predictions

consumption habits in an overlapping generations model abstract this paper introduces consumption habits in the blanchard 1985 overlapping generations model it shows that steady state capital and consumption are higher if individuals have habits than otherwise moreover inward habits lead to higher steady state capital and consumption compared to outward habits

the dynamics of efficient intertemporal allocations with many agents recursive preferences and production abstract the local dynamics of efficient allocations are studied for heterogeneous agent economies with production where preferences are recursive but not time separable in the case of a one sector neoclassical technology it is shown that optimal trajectories locally converge to a unique steady state provided that every agent s utility satisfies normality and increasing marginal impatience conditions in the two sector case with the above restrictions on preferences it is shown that oscillations can result only if the consumption goods sector is sufficiently capital intensive

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

aspirations habit formation and bequest motive we analyze how the presence of endogenous preferences affects the altruistic bequest motive from parents to children we will show that the existence of habits raises the threshold value of the intergenerational discount factor above which altruistic bequests are positive while aspiration formation could push this value down therefore the dynamic inefficiency of the economy with no altruism is not sufficient to prevent the bequest motive from being operative under aspiration formation we also discuss the implications of public debt when the bequest motive is inoperative and preferences exhibit habit and aspiration formation

electing monetary policymakers according to inflation performance abstract in this paper a dynamic model of monetary policymaking in an environment of uncertainty about a policymaker s actions is presented in a world where policymakers preferences are not known and the outcomes of policymakers actions are observed only with noise how do voters choose among different policymakers and how do voters learn about policymakers preferences the model presented solves for the actions of voters in such a noisy environment

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

business cycle asymmetry a deeper look this paper distinguishes two types of asymmetry in business cycles deepness and steepness deepness is defined as the characteristic that troughs are further below trend than peaks are above most previous research has focused exclusively on steepness which refers to cycles in which contractions are steeper than expansions a test for deepness is proposed and applied to u s post war quarterly unemployment real gnp and industrial production evidence of deepness is found for unemployment and industrial production while the evidence for real gnp is weaker previous evidence of steepness in unemployment is confirmed

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

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

the impact of prior decisions on subsequent valuations in a costly contemplation model this paper develops and tests a model of how recall of information from past decisions affects subsequent related decisions a boundedly rational individual has to determine her willingness to pay for a good that she previously considered purchasing at a given price or provide valuations for a set of goods that she previously ranked in order of preference the individual is ex ante uncertain about her utility from consumption of the goods and can exert costly cognitive effort to reduce this uncertainty we show that incorporating information from a prior decision has three primary effects a valuations are expected to exhibit higher variance in particular the spread of valuations between the most and least preferred alternatives increases b decision makers will in expectation exert more effort during the valuation phase and c the relative impact of prior decisions on valuation spread increases the more each attribute contributes to overall utility the model predictions are then tested in a series of controlled lab experiments