Deviant generations, Ricardian equivalence, and growth cycles

Two equilibrium possibilities are known to obtain in a standard overlapping-generations model with dynastic preferences: either the altruistic bequest motive is operative for every generation (in which case, Ricardian equivalence obtains) or it is not, for any generation. Dynamic equilibria, where the bequest motive is occasionally operative, cannot emerge. This paper studies bequest-giving behavior and out-of-steady-state bequest and growth dynamics in a Ak model with intra- and inter-generational consumption externalities. These externalities, by their very presence, do not destroy Ricardian equivalence. They may, however, give rise to deviant generations—generations that do not leave a bequest having received an inheritance, and vice versa—and that seals the fate for Ricardian equivalence. Consumption externalities may also generate interesting indeterminacies and endogenous growth cycles that did not exist otherwise.     

Population aging,the costs of health care for the elderly and growth

Employing an overlapping-generations model with endogenous growth in which altruistic young agents take care of the health level of their aged parents at risk of illness, this paper examines how population aging influences the long-run growth rate of the economy. We show that life expectancy, when relatively low (high), positively (negatively) affects economic growth. This paper also investigates public policy on long-term care and demonstrates the existence of an intergenerational conflict between current and future generations. We also point out that population aging may mitigate the extent of this conflict.     

Existence of a Pareto-optimal equilibrium in nearly-stationary overlapping-generations economies

Summary In overlapping-generations models of fiat money, the existence of a Pareto-optimal equilibrium — which defines an optimal quantity of money — is more general than well-known counter-examples suggest. Those examples, having no optimal equilibrium just because there are small variations in households' tastes and endowments across generations, are not typical. On the contrary: For an open-dense, full-measure subset of smooth stationary economies and an open-dense subset of continuous stationary economies, introducing small variations in tastes and endowments across generations preserves the existence of an optimal equilibrium. Put simply, optimal equilibria generically exist for nearly-stationary economies.I thank Scott Freeman, Katsuhiko Kawai, and two referees for proofreading this text; all lead to clarifications.     

A Characterization of the Dynamical System in a Two-sector Overlapping-generations Model: The Case of Unbounded Growth

This paper characterizes perfect-foresight equilibria in a two-sector overlapping-generations economy for the case of unbounded growth. The analysis demonstrates that gross substitutability in consumption is not sufficient to ensure the determinacy of equilibrium. Unlike Boldrin and Rustichini (1994), indeterminacy of equilibria can arise within the framework of an overlapping-generations model with convex technology. The finite time horizon of agents is the source of such indeterminacy.
JEL Classification Number: 041.     

Stone–Geary preferences in overlapping generations economies under pure exchange: A note

We incorporate Stone–Geary preferences into an overlapping generations economy under pure exchange, and explore stability, indeterminacy, and cycles with positive levels of saving and nonnegative public debt. A stable nontrivial steady state exists for parameter values, for which there does not exist equilibrium in the model with purely logarithmic utility function. We also show the possibility of a period-doubling bifurcation (a two-cycle).     

Sraffian Indeterminacy in General Equilibrium

The indeterminacy claim for competitive price systems made by Sraffa (1960) is examined by placing Sraffa's work in an intertemporal general equilibrium model. We show that indeterminacy occurs at a natural type of equilibrium. Moreover, the presence of linear activities instead of a differentiable technology is crucial and the indeterminacy is constructed, as in Sraffa, by fixing some or all of the economy's aggregate quantities. On the other hand, an extra condition, that some factors have inelastic excess demand is necessary, and, unlike Sraffa's model, relative prices must be allowed to vary through time. Sraffian indeterminacy and the generic finiteness of the number of equilibria are reconciled by showing that indeterminacy occurs at a measure-zero set of endowments. We use an overlapping-generations model to show that these endowments nevertheless arise systematically and that indeterminacy does not occur when relative prices are constant through time.     

Demographic structure and capital accumulation

This paper develops an overlapping-generations (OLG) model to analyze the consequences of demographic structure changes induced by an exogenous shift in the birth rate. We first show that a finite growth rate of the population that maximizes long-run capital per capita exists. Then, we examine the theoretical properties of this growth rate by showing that: (i) it corresponds to the demographic structure such that the average ages of capital holders and workers are equal; (ii) it is associated to an efficient steady state; (iii) it increases with compulsory transfers from younger to older generations. Finally, we explain why standard OLG models do not exhibit such a growth rate.     

Environmental Abatement and Intergenerational Distribution

This paper employs an overlapping-generations model to explore the impactof public abatement on private investment and the intergenerationaldistribution of welfare. Whereas public abatement benefits the oldestgenerations in terms of non-environmental welfare, future generations gainmost in terms of environment welfare. The overall benefits tend to besmallest for generations born at the time of the unanticipated policy shock.Public debt policy, however, can be employed to ensure that welfare gainsare distributed more equally across the various generations. Such a policyimplies that natural capital crowds-out man-made capital.     

Age-specific entrepreneurship and PAYG: Public pensions in Germany

We present new empirical evidence on the distribution of earnings, income and wealth among entrepreneurs in Germany. We document that both earnings and income are more concentrated among entrepreneurs than among workers and describe a large-scale overlapping-generations model that replicates the age-earnings profiles of these two household types. As an application, we compute the equilibrium effects of a reform of the German pay-as-you-go pension system in which entrepreneurs must also contribute and receive a pension. We show that in the presence of mobility between workers and entrepreneurs, the expected lifetime utility of all newborn households unanimously declines due to the general equilibrium effects of lower aggregate savings, and welfare losses amount to approximately 0.7% of total consumption. In addition, the integration of self-employed workers into the social security system in Germany does not help to improve its fiscal sustainability, and only an increase in the retirement age to 70 years will help to finance pensions at the present level beyond the year 2050.     

Endogenous, Efficient Long-Run Cyclical Unemployment, Endogenous Long-Run Growth, and Division of Labor

The paper uses a dynamic equilibrium model to explain the concurrence of economic growth and business cycles. Introducing durable goods into a model with ex-ante identical consumer–producers and economies of specialized learning-by-doing, the author shows that when job-shifting costs, economies of specialized learning-by-doing, and trading efficiency are sufficiently large, a dynamic equilibrium with business cycles and unemployment might be Pareto superior to noncyclical growth patterns. Long-run cyclical unemployment still exists when the credit market is imperfect. Extending the model into overlapping generations framework, the author shows that complete division of labor with business cycles would still occur in equilibrium.     

Should I Stay or Should I Go? On Relative Deprivation and Migration Dynamics

An overlapping-generations model for rural to urban labor migration is developed. In the migration decision the potential migrants consider both the absolute income gain and the relative deprivation associated with moving to town. It is shown that the relative deprivation mechanism introduces a positive externality between generations of migrants that can generate dual equilibria.     

Chaotic Equilibria in a Small, Open, Overlapping-Generations Economy with Child–Parent Externality

This paper presents a simple overlapping-generations model of a small open economy with child–parent externality that exhibits chaotic equilibrium dynamics.     

Population ageing and inflation with endogenous money creation

This paper models a mechanism through which population ageing may induce a deflationary process. We propose an overlapping-generations model (OLG) with money created by credits (inside money) and intergenerational trade. The model links demographic factors, such as fertility rates and longevity, to prices. We show that lower fertility rates lead to smaller demand for credit and lower money creation, which in turn cause a decline in prices. Changes in longevity affect prices through real savings and the capital market. Furthermore, a few links between interest rates and inflation are addressed; they arise in the general equilibrium and are not thoroughly discussed in literature. Long-run results are derived analytically; short-run dynamics are simulated numerically.     

ENDOGENOUS FLUCTUATIONS IN TWO‐COUNTRY MODELS*

This paper investigates the interlinkage in the business cycles of large‐country economies in a free‐trade equilibrium. We consider a two‐country, two‐good, two‐factor general equilibrium model with Cobb‐Douglas technologies and linear preferences. We also assume decreasing returns to scale in the consumption good sector. We first identify the determinants of each country's global accumulation pattern in autarky equilibrium, and secondly we show how a country's business cycles may spread throughout the world once trade opens. We thus give capital intensity conditions for local and global stability of competitive equilibrium paths.     

The robustness of optimal equilibrium among overlapping generations

Summary. We combine and strengthen optimality and robustness theorems for the overlapping-generations model of money. Roughly, we find a Pareto-optimal monetary equilibrium of a generic stationary economy that is near an optimal monetary equilibrium of each nearby non-stationary economy. Since the nearby equilibria are monetary, the general problem of macroeconomic stabilization reduces to maintaining the money supply. And since the nearby equilibria are optimal, stabilization is socially desirable. Received: October 27, 1997; revised version: March 25, 1998     

Growth and welfare effects of stabilizing innovation cycles

We consider a simple model of innovation where equilibrium cycles may arise and show that, whenever actual capital accumulation falls below its balanced growth path, subsidizing innovators by taxing consumers has stabilizing effects, promotes sustained growth and increases welfare. Further, if the steady state is unstable under laissez faire, the introduction of the subsidy can make the steady state stable. Such a policy has beneficial effects as it fosters output growth along the transitional adjustment path, and increases the welfare of current and future generations.     

Endogenous market incompleteness without market frictions: Dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies

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.     

Erratic accumulation

We study a simple, deterministic overlapping-generations model with capital accumulation where the discount rate of each generation is positively related to its lifetime wealth. We show that the trajectories for the capital stock can be periodic of arbitrary high order or totally aperiodic and chaotic and even ergodic.     

Residential Mobility and the Housing Market in a Two-sector Neoclassical Growth Model

The impact of residential mobility and competitive housing markets on long run growth is examined using a two-sector general equilibrium overlapping-generations model in continuous time. There is an infinity of agents with finite lives who adjust their housing consumption by moving, which is costly. We explore the model's steady-state properties, first with a free housing market, then under rent control when the market clears through restrictions on the frequency of moves. Rent controls do not just reduce welfare; they may increase the steady-state capital-labor ratio.     

Imperfectly competitive cycles with Keynesian and Walrasian features

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.