stability in a discrete time model of the walrasian tatonnement abstract almost all of the extensive literature on the stability of the walrasian t tonnement models the process in continuous rather than discrete time since the motivation for the use of continuous time is primarily mathematical not economic and since stability for a continuous time model does not imply the stability of its discrete time analogue it is of interest to investigate the stability of the walrasian t tonnement modeled in discrete time the question is of particular importance since much of the recent literature on topics such as expectations disequilibrium trading and temporary equilibrium utilizes discrete time this paper demonstrates that for a certain class of models conditions known to be sufficient for stability in continuous time are also sufficient in a discrete time formulation of the price adjustment mechanism excess demand functions having the properties of gross substitution dominant diagonals and the morishima system of complementary commodities are analyzed

a wage price regime switching model abstract the model we discuss in this paper combines an employment function which is based on a kaldor type consumption function and a simple production function with a wage price subsystem whose parameters switch when a critical level of employment is reached depending on the way in which exogenous variables are specified and on parameter values the model is capable of generating a wide variety of behavior in both real and nominal wages and prices

side effects of nonlinear profit taxes in an evolutionary market entry model abrupt changes coexisting attractors and hysteresis problems in order to demonstrate that nonlinear tax systems may have surprising and potentially undesirable side effects we develop an evolutionary market entry model in which firms decide on the basis of past profit opportunities whether or not to enter a competitive market our main focus is on the case of a proportional tax on positive profits such a piecewise linear tax scheme induces a kink in the firms profit functions and may lead to abrupt changes in a market s dynamics coexisting attractors and hysteresis problems since these phenomena can also be observed in more general models a proper understanding of their basic mechanism may be helpful to explain the intricate behavior of many economic systems

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

complex economic dynamics obvious in history generic in theory elusive in data summary the capacity of nonlinear dynamic models to mimic qualitative features of economic data is illustrated with an adaptive version of the neoclassical growth theory implications for econometric methodology are discussed emphasizing structural estimation and qualitative inference

international trade and the possible occurrence of chaos abstract the paper demonstrates that international trade among fluctuating economies may involve the occurrence of a strange attractor and hence of chaos once autonomous economies display cyclical behavior international trade activities can be considered as a perturbation of the motion of the autonomous economies possible implying chaos via a theorem by newhouse ruelle and takens 1979

caution implies profit abstract the paper illustrates by simple cobweb models that under certain circumstances fluctuations in perpetual disequilibrium may not only be viable but also preferable to a competitive equilibrium from the long run perspective

chaotic price behavior in a non linear cobweb model abstract the cobweb model for the evolution of prices is considered with backward bending supply curves and multi valued demand curves these deterministic non linear dynamical systems are shown to exhibit a broad spectrum of complex time behavior including stable periodic cycles of arbitrary order and chaos

chaotic dynamics in economic time series abstract there has recently been considerable interest in chaotic dynamics in a variety of disciplines this paper introduces and then surveys some of the associated literature and techniques applications to economic theory are discussed but the primary focus is on empirical applicability in addition to surveying the literature we also provide an example of the use of these techniques in economics we conclude by highlighting the importance of the techniques for empirical work as well as considering their context in econometric methodology

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

chaos significance mechanism and economic applications imagine a bargaining model say involving diplomats negotiating tariff levels or a disarmament treaty in which each party has been instructed by higher headquarters to respond to each new offer by her opposite number with a counteroffer that is to be calculated from a simple reaction function provided in advance both negotiating parties are prohibited from revealing their own reaction functions to the other if the perfectly deterministic sequence of offers and counteroffers that must emerge from these simple rules were to begin to oscillate wildly and apparently at random the negotiations could easily break down as each party not understanding the source of the problem came to suspect the other side of duplicity and sabotage yet all that may be involved as we will see is the phenomenon referred to as chaos a case that is emphatically not pathological but in which a dynamic mechanism that is very simple and deterministic yields a time path so complicated that it will pass most standard tests of randomness chaos has become a subject of great interest to specialists and nonspecialists alike besides economics it has entered the literature of geometry physics ecology and meteorology it has been written about at length in the new york times magazine and scientific american as well as technical publications this article seeks to describe what it is how it works and what it means for economics

the role of capital depreciation in multi sectoral models abstract this study investigates the role of capital depreciation in economic fluctuations that may appear in multi sectoral models of optimal growth in the standard literature on non linear optimal dynamics it has been assumed that capital depreciates completely within a period this study in contrast deals with the case in which capital depreciates slowly more precisely only by a certain percentage we adopt the standard two sector model with cobb douglas production functions and characterize the dynamics around the stationary state we derive explicit conditions on parameter values under which cyclical optimal paths appear these conditions reveal the complexity that slow depreciation adds to multi sectoral optimal dynamics the economic interpretation of slow depreciation in multi sectoral models is also discussed

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

poverty equilibrium an introductory systemic analysis abstract this paper represents an attempt to clarify the field of the studies concerning the poor stagnant economy using systemic analysis the original theories are reformulated in such a way as to highlight their similarities and dynamic structure the works of ragnar nurkse gunnar myrdal john k galbraith and harvey leibenstein are presented as components of a general theory of stagnation at low incomes the paper ends with an attempt to formulate a modern version of the theory using the chaotic dynamics approach to depict the situation the main purpose of this paper is to formulate the concept or in other words to clarify mathematically the hypothesis in order to test it the building of the empirical tests and of economic models to explain it is treated in other papers

micro heterogeneity of firms and the stability of industrial growth abstract in the micro macro m m model moses real swedish firms make independent decisions in markets schumpeterian innovative activities and wicksellian capital market disequilibria generate a growth cycle production and investment decisions in firms are dynamically coordinated by markets for products labor and capital under different market regimes as to speed intensity of competitive processes and of innovative activity by varying market regime ceteris par leux long term growth rates of the economy can be generated at cliffe as much as between the industrial countries during the last 50 years high speed market processes increase output growth for long periods but make the model economy sensitive to disturbances that eventually generate a severe depression simulation results suggest the importance for stable macroeconomic growth of a steady input of innovative technical change through new investment new entry and exit to preserve micro diversity of structures

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

commodity price fluctuations price dependent delays and nonlinearities as explanatory factors this paper develops a price adjustment model for a single commodity market with state dependent production and storage delays conditions for the equilibrium price to be stable are derived in terms of a variety of economic parameters when stability of the equilibrium price is lost a hopf bifurcation occurs giving rise to an oscillatory commodity price with a period between two and four times the equilibrium production storage delay

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

argentina growth resumption sustainability and environment abstract this paper analyzes the sustainability of the current growth process in argentina taking into account macroeconomic consistency and environmental constraints the economy appears to be generating an unsustainable current account deficit and a relative price distortion in favor of nontradables impeding a needed increase in exports resolution of the main environmental problems would absorb around 10 of savings over the next 10 years the saving scarcity suggests that a gradualist policy giving priority to the urban environment should be implemented

chaotic dynamics in credit constrained emerging economies abstract this paper analyzes the role of financial development as a source of endogenous instability in small open economies by assuming that firms face credit constraints our model displays a complex dynamic behavior with high period cycles or even chaotic dynamic patterns for intermediate values of the parameter representing the level of financial development of the economy we derive sufficient conditions for global stability and we prove that chaos appears via a border collision bifurcation the basic implication of our model is that economies experiencing a process of financial development are more unstable than both very underdeveloped and very developed economies

a puzzle for adaptive theory abstract over the life cycle aspirations for material goods grow commensurately with consumer wealth but aspirations for marriage and the number and quality of children do not change much the puzzle is why there is this difference between life domains in the extent to which aspirations adapt to actual circumstances the findings come from a cohort analysis of 1978 and 1994 survey responses on the good life

on the complicated price dynamics of a simple one dimensional discontinuous financial market model with heterogeneous interacting traders abstract we develop a financial market model with heterogeneous interacting agents market makers adjust prices with respect to excess demand chartists believe in the persistence of bull and bear markets and fundamentalists bet on mean reversion moreover speculators trade asymmetrically in over and undervalued markets and while some of them determine the size of their orders via linear trading rules others always trade the same amount of assets the dynamics of our model is driven by a one dimensional discontinuous map despite the simplicity of our model analytical graphical and numerical analysis reveals a surprisingly rich set of interesting dynamical behaviors

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

complex dynamics in a simple macro disequilibrium model abstract this study analyzes disequilibrium dynamics in a simple macro economic model constructed with micro foundation in which the behavior of individual economic agents concerning consumption labor supply employment output supply and the formation of expectation can be described by very simple and conventional monotonic functions it is demonstrated that despite that simplicity complex nonlinear dynamics may appear through the interaction of those individual behavior in different markets

dilemmas of structural adjustment and environmental policies under instability post 1980 turkey abstract the turkish structural adjustment since 1980 has been associated with chronic instability since the late 1980s the weaknesses in the fiscal system and the premature external liberalization emerge as the main factors hindering the passage toward stable growth enforced and erratic distributional changes and relative stagnation of capital accumulation have undermined the growth potential of the economy further it is demonstrated that existing market structures may negate environmental policies based on market incentives these observations as well as those on the interactions of the market system and the environment create strong arguments in favor of an active state

is trade policy for sale congressional voting on recent trade bills this paper examines voting by u s representatives onthe north american free trade agreement the uruguayround agreement and most favored nation status forchina using recent political economy models of tradepolicy to formulate an empirical specification ofcongressional voting behavior we find evidence thatcampaign contributions influenced legislators voteson the nafta and uruguay round bills labor groupcontributions were associated with votes against freertrade while business contributions were associatedwith votes in favor of freer trade economicconditions in each member s district as well as thebroad policy views of the legislators also affectedrepresentatives voting decisions

differential savings factor shares and endogenous growth cycles abstract the paper analyzes the dynamic properties of the neoclassical one sector growth model with differential savings in the sense of kaldor pasinetti the economy exhibits unstable steady states and fluctuations if the income distribution varies sufficiently and if shareholders save more than workers the paper analyzes in detail the dynamics for the case with a fixed proportions technology as well as with a smooth approximation if the savings propensities differ by an arbitrarily small amount the system exhibits topological chaos in the sense of li and yorke for an open set of production functions the analytical results are supplemented by numerical experiments

africa s economic performance limitations of the current consensus historical and micro survey evidence as well as the standard data from international organizations support less pessimistic conclusions on africa s development performance than those reached by many social scientists the changes that have benefited women over the last four decades are highlighted a discussion of growth in agricultural production follows however the complexity and the brutality of processes of social and economic change in sub saharan african economies are also stressed the theoretical implications of these complexities have not been adequately analyzed by world bank economists the bank s recent efforts to reassess its policies are therefore unlikely to achieve the results anticipated

editorial the revival of the liberal creed the imf and the world bank in a globalized economy abstract this editorial reviews problems arising from the popular washington consensus economic package as economies become more globalized and the reasons why they occur suggestions for improving the performance of the institutions behind the policies the world bank and international monetary fund are provided

endogenous cycles in a stiglitz weiss economy the literature on financial imperfections and business cycles has focused onpropagation mechanisms in this paper we model a purereversion mechanism such that the economy may converge to a two period equilibrium cycle this mechanism confirms that financial imperfections may have a dramatic amplification effect unlike in some related models contracts are complete indexation is not assumed away the welfare properties of a possible stabilizing policy are analyzed the model itself is a dynamic extension of the well known stiglitz weiss model of lending under moral hazard although stylized the model still captures some important features of credit cycles

durable capital and chaos in competitive business cycles abstract this study constructs an example of chaotic optimal accumulation that results from the existence of the limitation of capital depreciation an example is an extension of the model developed by weitzman

non linear structure of a metzlerian inventory cycle model abstract this study considers optimizing behavior of an inventory holding firm its main purpose is to investigate a consistent microeconomic foundation of the non linear macrodynamic model that generates inventory cycles it solves present value maximization problems under two different specifications of expectation formations one is specifying expectation formation independently of the optimizing process of the firm i call it a myopic perfect formation of expectation the other is incorporating the expectation formation in the optimizing process i call it a dynamic perfect formation of expectation the analysis demonstrates that the firm with the myopic perfect formation can posses sufficient nonlinearity for generation of cyclical macrodynamics whereas the firm with the dynamic perfect formation cannot these results suggest that the myopic perfect treatment of expectations of economic agents can be a source of macro fluctuations like inventory cycles