endogenous business cycles and systematic stabilization policy we study the effects of fiscal policy rules on the determinacy of rational expectations equilibrium in a perfectly competitive monetary model with constant returns government spending implies a distortion of the monetary steady state due to the implied taxation we show that policy rules that let the gnp share of government spending depend sufficiently negatively on increases in gnp stabilize the economy with respect to endogenous fluctuations for arbitrarily little distortion of the steady state at which stabilization occurs the rules do not involve lump sum taxation negative income taxation or exact knowledge of the economy s laissez faire steady state

money taxes and efficiency when sunspots matter abstract this paper examines the impact monetary redistribution policies have on the amount of sunspot induced volatility in an economy a dynamic model of segmented asset markets is presented in which the tax transfer policy determines in a continuous way the influence sunspots can have on the general price level and on consumption if the policy leads to a transfer of resources across segmentation lines there exist equilibria in which sunspots affect consumption the primary result is that there is an efficiency cost of taxation larger transfers lead to larger fluctuations in consumption the paper also shows that in many cases improvements in asset markets that decrease consumption volatility simultaneously increase price level volatility journal of economic literature classification numbers d84 e31 e44 h21

optimal fiscal policy under multiple equilibria abstract we study optimal fiscal policy in an economy where i search frictions create a coordination problem and generate multiple pareto ranked equilibria and ii the government finances the provision of a public good by taxing market activity the government must choose the tax rate before it knows which equilibrium will obtain and therefore an important part of the problem is determining how the policy will affect the equilibrium selection process we show that when the equilibrium selection rule is based on the concept of risk dominance higher tax rates make coordination on the pareto superior outcome less likely as a result taking equilibrium selection effects into account leads to a lower optimal tax rate

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

capital labor substitution and competitive nonlinear endogenous business cycles abstract we develop simple geometrical methods to study local indeterminacy bifurcations and stochastic sunspot equilibria near a steady state in nonlinear two dimensional economic models we present in particular a simple constructive geometrical characterization of the support of stochastic sunspot equilibria not only arbitrarily near a steady state but also along local bifurcations these methods are applied to a simple aggregative model to study in particular the influence of capital labor substitution and of the aggregate labor supply wage elasticity on the occurrence of competitive endogenous deterministic or stochastic fluctuations journal of economic literature classification numbers e32 c62

sunspot equilibria and periodic cycles under idiosyncratic uncertainty abstract this paper investigates how some intrinsic uncertainty affects the existence of sunspot equilibria and deterministic cycles in an overlapping generations model in the model there exists an intrinsic idiosyncratic uncertainty under which each individual has a small probability of losing consumption goods due to the law of large numbers this uncertainty causes no fundamental macroeconomic fluctuation however since it may change the dynamic stability the model may have both stationary sunspot equilibria and deterministic cycles even if the degree of relative risk aversion is small in particular these equilibria can exist even if the probability of loss is negligible

the e correspondence principle we present a new application of samuelson s correspondence principle to the analysis of comparative dynamics in stochastic rational expectations models our version which we call the e correspondence principle applies to rational expectations equilibria that are stable under least squares and closely related learning rules with this technique it is sometimes possible to study without explicitly solving for the equilibrium how qualitative properties of the equilibrium are affected by changes in the model parameters applications to overlapping generations and new keynesian models illustrate the potential of the technique

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

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

time and uncertainty in overlapping generations economies this paper shows the general reversibility of every perfect foresight equilibrium of an overlapping generations economy it then shows and characterizes the exist ence of reversible sunspot equilibria in these economies as well which seems to be at odds with our intuition about the irreversibility of a tree of events although the paper establishes also that such reversible stochastic equilibria constitute a negligible subset of all the equilibria of their class their mere existence may be considered somewhat puzzling for this intuition

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

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

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

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

monetary policy transmission in a model with animal spirits and house price booms and busts abstract can monetary policy trigger pronounced boom bust cycles in house prices and create persistent business cycles we address this question by building heuristics into an otherwise standard dsge model as a result monetary policy sets off waves of optimism and pessimism animal spirits that drive house prices that in turn have strong repercussions on the business cycle we compare our findings to a standard model with rational expectations by means of impulse responses we suggest that a standard taylor rule is not well suited to maintain macroeconomic stability instead an augmented rule that incorporates house prices is shown to be superior

dynamic determinacy and the existence of sunspot equilibria this paper relates the existence of stationary sunspot equilibria in the vicinity of a conventional stationary state to the phase diagram surrounding the latter we find that the local condition required for a unique equilibrium path returning to the stationary state following any slight disturbance of initial conditions is also sufficient to exclude stationary sunspot equilibria in the stationary state s immediate vicinity in that sense an eigenvalue condition familiar from dynamic analysis can tell us something about the possibilities of local sunspot activity as well journal of

chaos sunspots and automatic stabilizers abstract we consider a real business cycle model with an externality in production depending on parameter values the model has sunspot equilibria cyclical and chaotic equilibria and equilibria with deterministic or stochastic regime switching we study the implications of this model environment for automatic stabilizer tax systems stabilization is desirable because the efficient allocations are characterized by constant employment and output growth we identify an automatic stabilizer income tax subsidy schedule with two properties i it specifies the tax rate to be an increasing function of aggregate employment and ii earnings are subsidized when aggregate employment is at its efficient level the first feature eliminates inefficient fluctuating equilibria while the second induces agents to internalize the externality

keynesian issues and economic theory recent research helped in clarifying the nature of short run price and quantity adjustments in keynesian macroeconomic models and the possible causes of a persistent excess labour supply it is argued however that theories involving imperfect competition and real wage rigidities generate classical unemployment where multipliers act through supply side effects while nominal inertia seems to be at the root of truly keynesian multipliers the appraisal also contains a nontechnical presentation of recent models of endogenous expectations driven business fluctuations cycles sunspots monetary policy can then have persistent real effects under complete information money as a sunspot

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

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

imperfectly competitive cycles with keynesian and walrasian features abstract we consider a multi sector overlapping generations model with oligopolistic firms in the output markets and wage setting trade unions in the labour markets a coordination problem between firms creates multiple temporary equilibria which are either walrasian or of the keynesian unemployment type there exist many deterministic and stochastic equilibrium cycles fluctuating between keynesian recession and walrasian boom periods with arbitrarily long phases in each regime the cycles are in accordance with certain empirical regularities money is neutral and superneutral but appropriate countercyclical fiscal policies stabilize the cycles in a textbook keynesian way

sunspot equilibria rational bubbles in a model of money in the utility function abstract sunspot equilibria are constructed in brock s 1975 model of money in the utility function serial correlations of real balances and the nominal interest rate in these equilibria can be either positive or negative the example here suggests that local sunspots are more likely to exist when the agent s discount rate is small and that serial correlations in local sunspots when they exist are inversely related to the rate of money growth it is also shown that stationary sunspots may exist even when equilibrium cycles do not

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

free access versus private property in a resource income distributions compared distributions of income are compared under the alternative regimes of free access to and private property in a resource it is shown that in several analytically distinct cases all those deprived of free access on conversion of a resource to private property can be better off even though no compensating transfers are made this resu lt can hold even if the granting of private property rights also conf ers monopoly or monopsony power copyright 1987 by university of chicago press

monetary stability and liquidity crises the role of the lender of last resort we study an economy where agents are subject to liquidity demand shocks and banks arise endogenously to insure consumers against these shocks in this environment we evaluate the desirability of a lender of last resort who can provide liquidity loans to banks in distress in the absence of a lender of last resort the economy has a unique stationary equilibrium the introduction of unlimited and costless lender of last resort services allows the economy to achieve a steady state allocation that is pareto optimal however this economy also displays a continuum of hyperin ationary equilibria we then explore restrictions on the provision of lender of last resort services that rule out such monetary instability while preserving some of the e ciency obtained by unrestricted lender of last resort services when the lender of last resort charges an interest rate on liquidity loans the economy has a unique steady state equilibrium and when the interest rate charged is high enough no hyperin ationary equilibria arise finally when the lender of last resort faces an upper bound on loanable funds there is again a unique long run equilibrium and when the upper bound on loanable funds is small enough hyperin ationary equilibria are ruled out

the economic effects of restrictions on government budget deficits abstract in overlapping generations economies with perfect financial markets and lump sum taxation restrictions on the government budget deficit do not limit the set of achievable allocations for economies in which the tax instruments are distortionary and limited in number this strong form of irrelevance does not hold even if markets are perfect we propose a weaker but natural definition of irrelevance in which only a finite but arbitrarily large number of restrictions near the baseline deficit are considered we show that if the government can use only anonymous consumption taxes there is weak irrelevance of the deficit restrictions if the number of tax instruments is large relative to the number of policy goals journal of economic literature classification numbers d51 d91 e32

the elusive character of fiscal sustainability abstractwe assess the sustainability of public finances in oecd countries using unit root and cointegration analysis controlling for endogenous breaks results deem fiscal sustainability as rather elusive since we find lack of cointegration absence of sustainability between government revenues and expenditures except for austria canada france germany japan netherlands sweden and uk improvements of the primary balance after worsening debt ratios only for australia belgium germany ireland netherlands and the uk and granger causality from government debt to primary balances for 12 countries suggesting ricardian regimes

rational random walks the paper examines within the framework of a multi dimensional one step forward looking model a special category of rational expectations equilibria their support is infinite with two accumulation points steady states the stochastic motion of the system is of random walk type a general strategy for an existence proof associated with the study of a dynamical systemstresses necessary conditions in a simple overlapping generations model the proof is made complete no backwards bending labour supply is required in the pure sunspot case by continuity heteroclinic random walk equilibria are also shown to exist when shocks are real i introduction many economic models consider exogenous variables that follow stochastic processes of a random walk type the present paper considers a category of rational expectation equilibria in which the path of endogenous variables exhibits a similar qualitative feature the state of the system walks randomly furthermore this random walk takes place between two steady states of the system we call such equilibria random walk because of the temporal stochastic process followed by the equilibrium state heteroclinic because the support of the process connects two steady states in the state space equilibria the paper defines and discusses such equilibria and proposes a general methodology for assessing their existence it shows on a simple example that they do exist they may be either of sunspot type in the case where fluctuations are driven by beliefs only or extrinsic in cass shell 1983 terminology or non sunspot when some underlying fundamentals actually follow a random walk although the study has an exploratory dimension it strongly suggests that the random walk rational expectation equilibria under scrutiny exist within a large class of models in particular an explicit example of sunspot random walk equilibria is exhibited in a subclass of overlapping generations models that do not have traditional sunspot equilibria i e sunspot equilibria triggered by stationary markov processes finally when

legal restrictions sunspots and cycles abstract an economy in which legal restrictions prevent private agents from issuing close substitutes for money is examined specifically in a model with borrowing and lending agents are prevented from acquiring privately issued liabilities in amounts smaller than some minimum dollar denomination an economy is then constructed which has no sunspot equilibria absent such a restriction in the presence of the restriction however conditions sufficient to rule out equilibrium 2 cycles also imply the existence of stationary sunspot equilibria this is the case even though all agents have savings functions that are non decreasing in relevant rates of return

nonlinear business cycle modelling abstract literature which employs nonlinearities to explain economic fluctuations commonly called business cycles is surveyed relaxation of the linearity assumption significantly increases the range of possible dynamic solution paths and introduces the possibility that business cycles are endogenously determined the dominant post war modelling strategy has been the frisch 1933 and slutsky 1937 inspired one of developing essentially log linear economic models which produce damped cycles or monotonic damping to propagate the energy provided by repeated random or autocorrelated shocks the cycle is exogenously driven since it would die out in the absence of shocks deterministic nonstochastic nonlinear models can produce a wide range of endogenous fluctuations including stable limit cycles growth cycles and chaotic output which have the appearance of random fluctuations further the same model can produce qualitatively different outputs according to starting and parameter values if the possibility of shocks to parameters is admitted then behaviour can change abruptly following shocks evidence on the existence of nonlinearities and chaos in macroeconomic time series is assessed and alternative approaches to modelling dynamic economic development related to the work of keynes marx schumpeter and shackle are discussed their ideas have not proved readily amenable to mathematical modelling but attempts to encapsulate some of them are reviewed