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

characterizing efficiency in stochastic overlapping generations models abstract we introduce uncertainty about production in diamond s olg model we compare any two feasible consumption production allocations using stochastic ordering and define two types of efficient allocations given initial capital stock for stationary allocations it is shown that a necessary and sufficient condition for efficiency type i is that e log r is greater or equal to log 1 n where r generates the stationary interest factors corresponding to this allocation n is the population growth rate a complete characterization of type ii efficient allocations is derived using the property of cyclical monotonicity between each generation s consumption allocation and the relevant interest rates

market distortions and local indeterminacy a general approach we provide a methodology to study the role of market distortions on the emergence of indeterminacy and bifurcations it consists in introducing general specifications for the elasticities of the crucial functions defining the aggregate equilibrium dynamics of the model this allows us to study how market distortions influence the range of values for the elasticity of input substitution under which local indeterminacy and bifurcations occur highlighting the main channels and classes of distortions responsible for indeterminacy most of the specific market imperfections considered in the related literature are particular cases of our framework comparing them we obtain several equivalence results in terms of local dynamic properties applying this methodology to the woodford 30 framework we find that distortions in the capital market per se do not play a major role we further show that for empirically plausible values of elasticity of substitution between inputs indeterminacy requires a minimal degree of distortions this degree seems to be high under output market distortions while with labor market distortions the required degree is empirically plausible

tax policy and aggregate demand management under catching up with the joneses this paper examines the role for tax policies in productivity shock driven economies with catching up with the joneses utility functions the optimal tax policy is shown to affect the economy countercyclically via procyclical taxes i e cooling down the economy with higher taxes when it is overheating in booms and stimulating the economy with lower taxes in recessions to keep consumption up thus models with catching up with the joneses utility functions call for traditional keynesian demand management policies but for rather unorthodox reasons

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

continuous time sunspot equilibria and dynamics in a model of growth abstract this article is concerned with the existence of sunspot equilibria in a continuous time growth setting it brings alternative approaches in the self fulfilling prophecies literature continuous time global dynamics and non stationarity the main contribution of the use of continuous time methods is to allow for a complete understanding of the global dynamical properties of these stochastic equilibria within a non stationary economy in this model fluctuations in growth rates occur through a self fulfilling prophecies mechanism journal of economic literature classification numbers e12 e32 o41

indeterminacy and stabilization policy abstract it has been shown that a one sector real business cycle model with sufficient increasing returns in production may possess an indeterminate steady state that can be exploited to generate business cycles driven by animal spirits of agents this paper shows how an income tax schedule that exhibits a progressivity feature can ensure saddle path stability in such a framework and thereby stabilize the economy against sunspot fluctuations conversely an economy with a flat or regressive tax schedule is more susceptible to indeterminacy journal of economic literature classification numbers e32 e62

debt deficits and finite horizons the stochastic case abstract we introduce aggregate uncertainty and complete markets into blanchard s 1985 perpetual youth model we derive a simple expression for the pricing kernel that can be used to close a variety of equilibrium models in which the set of agents changes over time

multiple steady states and endogenous fluctuations with increasing returns to scale in production abstract the purpose of this paper is to study the influence of the elasticity of capital labor substitution and of the labor supply elasticity on the existence of multiple pareto ranked stationary equilibria local indeterminacy bifurcations and expectations driven fluctuations in economies with external and internal increasing returns to scale in production this is done through general geometrical methods that do not depend upon particular specifications for preferences and technology for the sake of concreteness the analysis focuses on the model with heterogeneous agents and financial constraints presented in woodford j econ theory 40 1986 128 137 and extended by grandmont pintus and de vilder capital labor substitution and competitive nonlinear endogenous business cycles crest working paper 9728 1997 to account for capital labor substitution increasing returns to scale are incorporated in two different market structures an economy with aggregate production externalities and perfectly competitive markets an economy with increasing returns internal to the firm and imperfect competition in the product s market s only journal of economic literature classification numbers c61 e32

stochastic olg models market structure and optimality for a general class of pure exchange olg economies under uncertainty we provide a complete characterization of the efficency properties of competitive equilibria when markets are only sequentially complete and the criterion of efficency is conditional pareto optimality we also consider a particular case in which markets fail to be even sequentially complete and provide a characterization when the criterion of efficency is weakened to ex post pareto optimality

intergenerational risk sharing via social security when financial markets are incomplete this paper develops an overlapping generations model with stochastic production and incomplete markets to assess whether the introduction of an unfunded social security system can lead to a pareto improvement even if the initial equilibrium is neither production ine cient in the spirit of diamond 1965 nor dynamically ine cient in the spirit of samuelson 1957 when returns to capital and wages are imperfectly correlated and subject to aggregate shocks then the consumption variance of all generations can be reduced if private markets or government policies enable them to pool their labor and capital incomes a social security system that endows retired households with a claim to labor income may serve as an e ective tool to share aggregate risk between gener

dynamic effects of government expenditure in a finance constrained economy abstract this paper introduces constant government expenditure in woodford s finance constrained model j econ theory 1986 with capital labor substitution as presented in grandmont pintus and de vilder j econ theory 1998 and investigates how government expenditure influences local dynamics near multiple steady states depending upon the elasticity of substitution between capital and labor in production

on the role of labor supply for the optimal size of social security abstract the paper studies the welfare effects of a social security system in a stylized overlapping generations economy with random production and capital accumulation different welfare concepts including long run optimality social optimality and time consistency are employed to determine the optimal size of the system when labor supply is exogenous a unique contribution level can be identified which is optimal according to all three concepts when labor supply is endogenous however this result generically fails to hold and the long run optimal solution is only constrained socially optimal while the time consistent policy may even lead to an inefficient equilibrium

optimality in stochastic olg models theory for tests we consider general olg economies under uncertainty with short maturity assets and with dividend paying assets of infinite maturity and fiat money and study the optimality properties of equilibria with a sequence of asset markets that are sequentially complete we provide necessary and sufficient conditions in terms of asset prices and dividends for equilibria to be conditionally pareto optimal these results provide a theoretical basis for empirical investigation

the cass criterion the net dividend criterion and optimality abstract abel mankiw summers and zeckhauser assessing dynamic efficiency theory and evidence rev econ stud 56 1989 1 20 propose the net dividend criterion as an easy to use sufficient condition for optimality in general stochastic overlapping generations economies with production we provide examples based on the criterion due to cass on capital overaccumulation in the aggregative neoclassical model of economic growth a complete characterization j econ theory 4 1972 200 223 and its extensions the usual tools for such problems to show that the net dividend criterion need not give the right answer we identify the flaw in their proof we also provide an alternative condition which by an argument unrelated to theirs is a sufficient condition for optimality when dividends are nonnegative and then argue that the condition is not innocuous since it cannot be verified in actual economies

stationary monetary equilibria in overlapping generations models with incomplete markets abstract the objective of this paper is to study the stationary monetary equilibria of a stochastic overlapping generations model with a general incomplete asset structure it is proved that a stationary equilibrium with a nonzero price of money generically exists and is locally isolated when there is outside money for an open set of economies there is an equilibrium with positive money prices in all states the equilibrium is also given a neat characterisation in terms of the properties of the underlying state prices with only inside money there will instead be a continuum of equilibria journal of economic literature classification numbers d52 d90 e40

taste for variety and optimum production patterns in monopolistic competition abstract many positive and normative results in models using the monopolistic competition framework of the dixit stiglitz spence type depend on the value of an important parameter the taste for variety in these models however the taste for variety is linked in a close but arbitrary manner to the degree of market power of monopolistic competitors in this paper we make a simple modification to the basic model which clearly disentangles taste for variety and market power we then show how this changes the usual comparisons between social optimum and market outcomes

a characterization of inefficiency in stochastic overlapping generations economies in this paper we provide a characterization of interim inefficiency in stochastic economies of overlapping generations under possibly sequentially incomplete markets with respect to the established body of results in the literature we remove the hypothesis of two period horizons by considering longer though uniformly bounded horizons for generations the characterization exploits a suitably modified cass criterion grounded on the long run behavior of compounded safe interest rates and independent of the length of horizons of generations thus the hypothesis of two period horizons is purely heuristic in establishing a criterion for inefficiency in addition for sequentially incomplete markets we adopt a suitable notion of unambiguous inefficiency separating the inefficient intertemporal allocation of resources from incomplete risk sharing unambiguous inefficiency reduces to inefficiency when markets are sequentially complete

balanced budget rules distortionary taxes and aggregate instability a traditional argument against a balanced budget fiscal policy rule is that it amplifies business cycles by stimulating aggregate demand during booms via tax cuts and higher public expenditures and by reducing demand during recessions through a corresponding fiscal contraction this paper suggests an additional source of instability that may arise from this type of fiscal policy rule it shows that within the standard neoclassical growth model a balanced budget rule can make expectations of higher tax rates self fulfilling if the fiscal authority relies heavily on changes in labor income taxes to eliminate short run fiscal imbalances calibrated versions of the model show that indeterminacy occurs for income tax rates that are empirically plausible for the u s economy and other group of seven countries

earnings and consumption dynamics a nonlinear panel data framework we develop a new quantile based panel data framework to study the nature of income persistence and the transmission of income shocks to consumption log earnings are the sum of a general markovian persistent component and a transitory innovation the persistence of past shocks to earnings is allowed to vary according to the size and sign of the current shock consumption is modeled as an age dependent nonlinear function of assets unobservable tastes and the two earnings components we establish the nonparametric identification of the nonlinear earnings process and of the consumption policy rule exploiting the enhanced consumption and asset data in recent waves of the panel study of income dynamics we find that the earnings process features nonlinear persistence and conditional skewness we confirm these results using population register data from norway we then show that the impact of earnings shocks varies substantially across earnings histories and that this nonlinearity drives heterogeneous consumption responses the framework provides new empirical measures of partial insurance in which the transmission of income shocks to consumption varies systematically with assets the level of the shock and the history of past shocks

asset prices debt constraints and inefficiency abstract we consider possibly non stationary economies with endogenous solvency constraints under uncertainty over an infinite horizon as in alvarez and jermann 2000 5 a sort of cass criterion cass 1972 10 completely characterizes constrained inefficiency under the hypothesis of uniform gains from risk sharing which is always satisfied in stationary economies when the autarchy is constrained inefficient uniform gains from risk sharing also guarantee a finite value of the intertemporal aggregate endowment at a constrained optimum hence no equilibrium exhibits a null interest rate in the long run finally constrained inefficiency occurs if and only if there exists a feasible redistribution producing a welfare improvement at all contingencies

sunspots and the business cycle in a finance constrained economy abstract this paper examines the cyclical properties of a finance constrained economy populated by two classes of households with heterogeneous preferences and featuring social increasing returns to scale the model exhibits indeterminacy for externalities mild enough so that the labor demand curve is downward sloping furthermore simulation results show that endogenous fluctuations driven by expectations are quantitatively relevant in opposition to standard real business cycles and sunspot models with single type of households our finance constrained economy reveals to be able to mimic both an acyclical pattern of the real wage and strong procyclical movements of aggregate consumption journal of economic literature classification numbers e2 e32

endogenous market incompleteness without market frictions dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies abstract in this paper we show that within the set of stochastic three period lived olg economies with productive assets such as land markets are necessarily sequentially incomplete and agents in the model do not share risk optimally we start by characterizing perfect risk sharing and find that it requires state dependent consumption claims which depend only on the exogenous shock realizations we show then that the recursive competitive equilibrium of any overlapping generations economy with weakly more than three generations is not strongly stationary this then allows us to show directly that there are short run pareto improvements possible in terms of risk sharing and hence that the recursive competitive equilibrium is not pareto optimal we then show that a financial reform which eliminates the equity asset and replaces it with zero net supply insurance contracts arrow securities will implement to pareto optimal stochastic steady state known to exist in the model finally we also show via numerical simulations that a system of government taxes and transfers can lead to a pareto improvement over the competitive equilibrium in the model

a complete characterization of pareto optimality for general olg economies abstract in the context of general pure exchange olg economies where agents can have heterogeneous longevities we provide both sufficient and necessary conditions for pareto optimality of competitive equilibria for the case in which all agents live for the same number of periods we find that these conditions are equivalent we also find this equivalence when agents can have different lifetimes but in this case we need to impose particular restrictions on relative equilibrium prices moreover we show that without these conditions on prices the equivalence and hence a full characterization is not necessarily obtained

dominant root characterization of pareto optimality and the existence of optimal equilibria in stochastic overlapping generations models abstract we characterize pareto optimality of interior stationary allocations in single good overlapping generations models with stochastic aggregate shocks and heterogeneous but recurring generations an interior stationary allocation is pareto optimal if and only if it is an equilibrium allocation and the associated contingent claims price matrix has a dominant root less than or equal to unity we then use this characterization to show that there always exists an optimal equilibrium with or without valued fiat money

social security and risk sharing abstract in this paper we identify conditions under which the introduction of a pay as you go social security system is ex ante pareto improving in a stochastic olg economy with capital accumulation and land we argue that these conditions are consistent with realistic specifications of the parameters of the economy in our model financial markets are complete and competitive equilibria interim pareto efficient therefore a welfare improvement can only be obtained if agents welfare is evaluated ex ante and arises from an improvement in intergenerational risk sharing we also examine the optimal size of a given social security system as well as its optimal reform

efficiency and prices in economies of overlapping generations abstract in a general economy of overlapping generations i introduce a notion of uniform inefficiency corresponding to the occurrence of a pareto improvement with a small uniform destruction of resources g debreu the coefficient of resource utilization econometrica 19 1951 273 292 i provide a necessary and sufficient condition for uniform inefficiency in terms of prices at a competitive equilibrium an allocation is uniformly inefficient if and only if the relative price of the aggregate endowment in a given period into the aggregate endowment up to that period does not vanish over periods of trade a sort of modified cass criterion d cass on capital overaccumulation in the aggregative neoclassical model of economic growth a complete characterization j econ theory 4 1972 200 223 minimal assumptions on fundamentals are needed for such a complete characterization furthermore proofs reduce to simple and short direct arguments finally i verify that uniform inefficiency is preserved under perturbations a property that might fail for the canonical notion of inefficiency remarkably an allocation is uniformly inefficient if and only if a non vanishing redistribution like a social security mechanism is welfare improving

on the interaction between risk sharing and capital accumulation in a stochastic olg model with production abstract we analyze the interaction between risk sharing and capital accumulation in a stochastic olg model with production we give a complete characterization of interim pareto optimal competitive equilibrium allocations furthermore we provide tests of pareto optimality suboptimality based on risky rates of return only

the cyclical behavior of marginal cost and price the author examines the cyclical behavior of price marginal cost margins for u s manufac turing after 1956 short run marginal cost is markedly procyclical this is primarily due to procyclical overtime payments incurred beca use employment is not perfectly flexible in most industries output price fails to respond to the cyclical movement in marginal cost so price marginal cost margins are markedly countercyclical the res ults contradict business cycle theories that explain low production i n a recession by a high real cost of producing they support theories that explain low production in a recession by the inability of firms to sell their output copyright 1987 by american economic association

indeterminacy and endogenous fluctuations with arbitrarily small externalities abstract in this paper we study the occurrence of local indeterminacy endogenous fluctuations and bifurcations in a simple non monetary 2 period overlapping generations economy in which people do not consume when young with capital labor substitution elastic labor supply and productive externalities we show that in contrast with the local dynamics generated by many one sector models of capital accumulation studied in the current literature local indeterminacy and therefore stationary stochastic equilibria driven by self fulfilling beliefs sunspots as well as multiple stationary equilibria are pervasive phenomena when the elasticity of input substitution is large and when the size of externalities is arbitrarily small we also demonstrate that when externalities are arbitrarily small the cobb douglas production function often used for its analytical tractability in many models is structurally unstable it is always associated with uniqueness of the steady state but any small perturbation of the elasticity of input substitution leads to the existence of two stationary equilibria which may be close to each other with the consequence that the dynamics may be qualitatively very different from those originated in the unit elasticity case journal of economic literature classification numbers e32 c62

non linear endogenous fluctuations with free entry and variable markups abstract the paper explores the effects of markup variability associated with free entry of cournotian firms on the occurrence of local indeterminacy local hopf bifurcations and multiplicity of steady states it uses an overlapping generations model with capital in which differentiated intermediate goods are produced with constant marginal cost plus a positive fixed cost if the markup factor were constant the case of no free entry or the case of zero fixed costs leading to the perfectly competitive outcome no local endogenous fluctuations or multiplicity of steady states can emerge unless factors of production are complementary on the contrary with any positive variable market power indeterminacy and multiplicity of steady states is possible for any value of the elasticity of technological substitution and local hopf bifurcations may also emerge provided variable market power is high enough

labor income dynamics and the insurance from taxes transfers and the family article i nfo what do labor income dynamics look like over the life cycle what is the relative importance of persistent shocks transitoryshocksandheterogeneousprofiles to what extent dotaxes transfers and thefamilyattenuate these various factors in the evolution of life cycle inequality in this paper we use rich norwegian population panel data to answer these important questions we let individuals with different education levels have a sepa rate income process and within each skill group we allow for non stationarity in age and time heterogeneous experience profiles and shocksof varying persistence we findthattheincomeprocesses differ systematically by age skill level and their interaction to accurately describe labor income dynamics over the life cycle it is neces sary toallow for heterogeneity by education levelsand account for non stationarity inage and time our findings suggest that the redistributive nature of the norwegian tax transfer system plays a key role in attenuating the magnitude and persistence of income shocks especially among the low skilled by comparison spouse s income matters less for the dynamics of inequality over the life cycle

cooperation in stochastic olg games abstract this paper builds on cremer s quart j econ 101 1986 33 seminal analysis which shows that almost complete cooperation can be achieved as an equilibrium in a game played by overlapping generations of players if the institution in which players cooperate is infinitely lived we analyze a similar model in which the costs of cooperation are subject to random shocks even if these random shocks are very small the range of parameters for which cooperation can be sustained is decreased considerably in comparison to the deterministic case furthermore we show how the efficient outcome can be approximated if the level of cooperation can be varied continuously and the cooperation technology has decreasing or constant returns to scale while this is not possible in the case of increasing returns to scale

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

income dynamics when shocks occur during the year abstract this paper suggests a persistent income process specification where income flows may shift during the year the variance of persistent shocks is shown to be consistently estimated also with traditional specifications restricting shocks to occur only between years

animal spirits technology shocks and the business cycle the last few years have witnessed a revival of business cycle models in which beliefs of agents have played a leading role in explaining economic fluctuations 1 most of these models involve strong economy wide increasing returns to scale in order for sunspot equilibria to exist in a recent paper however basu and fernald 1996 present evidence that returns to scale are far from evenly distributed across the u s economy in particular they report that scale economies are present mainly in the domain of durable goods production in the nondurable goods sector of the u s economy evidence of increasing returns to scale cannot be found

informational diversity over time and the optimality of monetary equilibria abstract the temporal realizations of a random state variable in an overlapping generations model create an informational diversity between members of different generations and require a reexamination of the optimality that competitive equilibria might display in such an environment using an optimality criterion that reflects this informational diversity we prove the optimality of competitive equilibrium in a model with a fixed stock of fiat money a single spot market and good endowments that follow a markov process the need for an optimality criterion that incorporates informational diversity is further motivated by studying the same model with the operation of complete contingent commodities markets

rational expectations in the overlapping generations model abstract this paper reports results on the character of the rational expectations equilibria of a stochastic overlapping generations model with heterogenous markets the model considered is a stationary overlapping generations model in which the endowments of young agents are subject to i i d random shocks the main result shown is that if there are l 1 commodities traded in every period then for most preferences the rational expectations equilibrium stochastic process of prices and allocations necessarily exhibits serial correlation this is in marked contrast to the one commodity model in which there always exists an equilibrium which is measure isomorphic to the endowment process

income variance dynamics and heterogeneity recent theoretical work has shown the importance of measuring microeconomic uncertainty for models of both general and partial equilibrium under imperfect insurance in this paper the assumption of i i d income innovations used in previous empirical studies is removed and the focus of the analysis is placed on models for the conditional variance of income shocks which is related to the measure of risk emphasized by the theory we first discriminate amongst various models of earnings determination that separate income shocks into idiosyncratic transitory and permanent components we allow for education and time specific differences in the stochastic process for earnings and for measurement error the conditional variance of the income shocks is modelled as a parsimonious arch process with both observable and unobserved heterogeneity the empirical analysis is conducted on data drawn from the 1967 1992 panel study of income dynamics we find strong evidence of sizeable arch effects as well as evidence of unobserved heterogeneity in the variances

existence and optimality of currency equilibrium in stochastic overlapping generations models the pure endowment case abstract we consider a pure exchange stochastic overlapping generations economy sufficient conditions for the existence of a monetary equilibrium and a characterization of optimality are provided it is shown that in a monetary equilibrium currency provides partial insurance and that the equilibrium allocation is optimal it is also shown that if an allocation is optimal the contingent claim prices associated with it are such that in an average sense the present value of the social endowment is bounded

stationary equilibria with incomplete markets and overlapping generations recent work on general equilibrium models with incomplete financial markets has demonstrated that when assets pay off in units of account equilibrium prices and allocations are indeterminate the equilibria in such models are also generically constrained suboptimal a central planner can typically reallocate assets in such a way as to pareto dominate the competitive equilibrium in this paper the authors consider an overlapping generations model with incomplete markets in which one asset is fiat money they show that when outside money has value in equilibrium the stationary equilibrium prices and allocations are both locally isolated and constrained optimal copyright 1992 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association