Overlapping Generations Economy Research Articles

Economic Growth in a Cooperative Economy

Abstract We develop and formalise an equilibrium concept for a dynamic economy in which production takes place in worker cooperatives. The concept rules out allocations of workers to cooperatives in which a worker in one cooperative could move to a different cooperative and make both herself and the existing workers in the receiving cooperative better off. It also rules out allocations in which workers in a cooperative would be made better off by some of the other workers leaving. We also provide a minimum-information equilibrium-selection criterion, which refines our equilibrium concept. We illustrate the application of our concept and refinement in the context of an overlapping-generation economy with specific preferences and technology. The cooperative economy follows a dynamic path qualitatively similar to the path followed by a capitalist economy, featuring gradual convergence to a steady state with constant output. However, the cooperative economy features a static inefficiency, in that, for a given aggregate capital stock, firm size is smaller than what a social planner would choose. On the other hand, the cooperative economy cannot be dynamically inefficient and could accumulate capital at a rate that is higher or lower than the capitalist economy. As a result, steady-state income per worker could be higher or lower in the cooperative economy. We also present an illustrative calibration, which quantitatively compares steady-state incomes and welfare in a cooperative and in a capitalist economy.

Old-age support policy and fertility with strategic bequest motives

This paper presents an analysis of the effects of public old-age support on individuals’ fertility decisions and on the long-term equilibrium in an overlapping generation economy with strategic bequest motives. Parents must pay their adult children at least the reservation wage to receive informal old-age support from them (individual rationality constraint). Formal old-age support is financed through wage taxes on children. The increased present value of formal old-age support tends to increase old-age utility, thereby decreasing the family support demand and decreasing savings for the old age. The increased wage tax reduces the opportunity cost of child-rearing time, thereby increasing the fertility rate. The effects of increased formal old-age support on per-worker capital and labor are indeterminate, as is the effect on the long-term lifetime utility of individuals. A strategic bequest motive might engender a higher fertility rate than that of the social optimum.

Sraffian indeterminacy of steady‐state equilibria in the Walrasian general equilibrium framework

AbstractIn contrast to Mandler's generic determinacy of steady‐state equilibria, we first show that any non‐trivial steady‐state equilibrium is indeterminate under a general overlapping generation (OLG) economy with a fixed Leontief technique. We also check that this indeterminacy is generic. These results are obtained by explicitly introducing a general model of every generation's utility function and individual optimization program to the OLG economy, which also verifies that Mandler's claim on generic determinacy is invalid. We also argue the distinctiveness of our results in comparison with the standard literature of OLG indeterminacy.

Difficulties in testing for capital overaccumulation

This paper reconsiders the question of testing for the presence of Pareto suboptimal capital overaccumulation in overlapping generations economies. The paper allows generation‐specific technology shocks to evolve over time according to a stationary Markov chain, and assumes that an econometrician observes a finite sample of aggregate quantities. In this setting, any statistical test of the null hypothesis of capital overaccumulation with size less than one also has zero power against the alternative hypothesis of a dynamically efficient steady state. This result means that the standard assessments of capital overaccumulation based on US aggregate quantity data should be viewed as inconclusive.

Wealth preference and rational bubbles

In this paper, we show that rational bubbles can exist within a neoclassical economy, provided that households derive utility from holding wealth. Hence, we provide a microfoundation for bubbles that relies on a frictionless economy with an infinitely-lived representative household. While our bubbly equilibria are very similar to those obtained by Tirole (1985) in an overlapping generation economy, the underlying mechanism is fundamentally different. Instead of relying on an exchange across heterogeneous households, the bubble relies on the representative household’s willingness to accumulate wealth without the intention of spending it. Turning to public debt, we carefully review the similarities and the differences between rational bubbles and Ponzi schemes. We establish that the Ricardian equivalence must hold in any of our equilibria. Finally, within a monetary economy, we show that the preference for wealth is fundamentally different from money-in-the-utility-function.

Optimal climate and fiscal policy in an OLG economy

AbstractThis paper develops a climate–economy model to study the joint design of optimal climate and fiscal policies in economies with overlapping generations (OLGs). I demonstrate how capital taxation, if optimal, drives a wedge between the market costs of carbon (the net present value of marginal damages using the market interest rate) and the Pigouvian tax (the net present value of marginal damages using the consumption discount rate of successive OLGs). In contrast to deterministic infinitely lived representative agent models, at the optimum, the capital income tax is positive, the carbon price equals the market costs of carbon but it falls short of the Pigouvian tax when (i) preferences are not separable over consumption and leisure; and (ii) labor income taxes cannot be age‐dependent. I also show that restrictions on climate change policy provide a novel rationale for positive capital income taxes.

Overlapping-Generations Economies under Uncertainty: Dynamic Inefficiency/Efficiency with Multiple Assets and no Labour

Overlapping-Generations Economies under Uncertainty: Dynamic Inefficiency/Efficiency with Multiple Assets and no Labour

Renewable resource and harvesting cost in a simple monetary overlapping generation economy

The literature has shown that the long-term preservation of renewable resources is ensured in two situations: (1) when the resource can be used as a store of value, and (2) when households are altruistic. This article shows that there is a third situation in which renewable resources are preserved in the long term: when harvesting is costly. To prove this, a monetary overlapping-generations economy is developed, in which a renewable resource is held by a representative household living through two periods. In his youth, he inherits the resource from his parents and decides how much to harvest. Income from the sale of the harvest is saved entirely in fiat currency to finance consumption in old age. It is assumed that harvesting takes time (harvesting cost), and so the young household has to trade off leisure for harvesting. In this simple context, we show that the resource level can be different from zero in the long term (resource preservation). In particular, we observe that two stationary states can coexist: one with a low resource level (overexploitation) and the other with a high resource level (underexploitation). Moreover, with a sufficiently productive harvesting technology, cycles of period two can emerge around each stationary state (flip bifurcation), as well as local indeterminacy around the stationary state with the highest resource level. In this sense, the cost of harvesting seems to be both a source of preservation and a source of resource fluctuations.JEL classification: E32, O44, Q20.

A tractable overlapping generations structure for quantitative DSGE models

This paper develops a novel tractable overlapping generations (OLG) structure whose aggregate equations resemble a model of an infinitely lived representative agent, except that there are no aggregate transversality conditions in the OLG economy. The main assumptions are complete markets and time-invariant (but age-dependent) consumption shares of age-groups. The tractability of the OLG structure here distinguishes it from conventional OLG models – the present structure is suitable for quantitative dynamic stochastic general equilibrium (DSGE) macro models. Importantly, the OLG structure here maintains key predictions of standard OLG models, namely the possibility of low real interest rates and of equilibrium indeterminacy. • This paper develops a novel tractable overlapping generations (OLG) structure. • Aggregate equations resemble a model of an infinitely lived representative agent. • However, there are no aggregate transversality conditions in the OLG economy. • The OLG structure here is much more tractable than conventional OLG models. • Thus, the present OLG structure is suitable for quantitative DSGE macro models.

Fair Allocations in an Overlapping Generations Economy,

This paper investigates fair (i.e., envy-free and efficient) allocations in an overlapping generations economy without production and with two-period lived agents. We show that there is a conflict between no-envy and efficiency when all generations have identical preferences. This conflict crucially depends on the size of the given young age consumption of the initial old generation relative to the young age consumption at the golden-rule. We then show that there exist non-stationary preferences for which such a conflict does not arise, regardless of the young age consumption of the initial old generation. JEL Classifications: D60, D63, D70

Insurance-adjusted valuation, decision making, and capital return

Although the insurance industry has a significant economic role, few theoretical studies link insurance with the overlapping generations economy. This study suggests a new overlapping generations model that includes insurance in the agents' economic decisions under the uncertainty of financial losses. In this insurance model, we derive risk-averse workers' optimal insurance purchases and consumption based on the insurance-adjusted valuations, which are the present value of the income streams minus insurance premiums paid in the future. The theoretical equilibrium model predicts capital returns, wealth, labor supply, etc. Our findings show that higher workforce and technological progress increase private insurance demand and reduce the capital-output ratio, and higher losses as a fraction of output increase social insurance demand and reduce the capital-output ratio via numerical comparative statics.

Risk-adjusted valuation in the worker's economic decision making

We suggest a risk-adjusted valuation approach for workers at retirement risk to make decisions in an overlapping generations economy. The risk-averse workers use greater weights than expected, so-called risk-adjusted probability, on their retirement cash flows to assess the residual lifetime income. This method can be consistently applied to value financial and non-financial assets, and on the risk-adjusted valuations, the workers will make optimal investments. To predict capital returns and economic variables, comparative statics will be numerically implemented via demographic structure, preference, and social security policy by aggregating workers’ decisions.

To seed, or not to seed? An endogenous labor supply approach in a simple overlapping generation economy

ABSTRACTWithin this paper, we develop a simple overlapping generations model with a renewable resource (forest) in the spirit of Koskela et al. (2002). Seeding activities (more broadly, forestry) are introduced in the form of a domestic production as well as a joy‐of‐giving bequest motive regarding the resource. In this simple framework, we show that altruism always guarantee a positive resource level at the steady state. However, studying the dynamics, we point out that the stability of the steady state crucially depends upon both altruism and forestry productivity: under low forestry productivity the steady state is always stable, while under high forestry productivity two period cycles (flip bifurcation) can emerge near the steady state if and only if altruism is sufficiently high which raises the question of resource preservation and leads to the conclusion that the road to hell is paved with good intentions.

Social security and endogenous demographic change: child support and retirement policies

AbstractThis paper studies retirement and child support policies in a small, open, overlapping-generations economy with PAYG social security and endogenous retirement and fertility decisions. It demonstrates that neither fertility nor retirement choices necessarily coincide with socially optimal allocation, because agents do not take into account the externalities of fertility and the elderly labor supply in the economy as a whole. It shows that governments can realize the first-best allocation by introducing a child allowance scheme and a subsidy to incentivize the labor supply of older workers. As an alternative to subsidizing the elderly labor supply, we show that the first-best allocation can also be achieved by controlling the retirement age. Finally, the model is simulated in order to study whether the policies devoted to realizing the social optimum in a market economy could be a Pareto improvement.

OUTWARD HABITS AND ENVIRONMENTAL QUALITY IN AN OVERLAPPING GENERATIONS MODEL

Outward habit formation affects consumption decisions. Since consumption displays a negative environmental externality, outward habits has as well an (adverse) effect on the environment. This research paper centers around the theoretical linkage between the combination of both externalities (environmental deterioration and outward habits). The objective of this study is to examine the impacts of outward habits on the state of the environment in the context of an overlapping generations economy. In our study, environmental quality is a public good negatively affected by consumption activity and positively affected by maintenance investment. With outward habit formation, the build-up level of average past consumption in the economy at large influences the current utility of an individual consumer. Thus, individuals draw utility not only from their own level of current consumption, but also from its level relative to the average consumption in the economy. How does outward habit influence the state of the environment? We analyze this question using an overlapping generations model with outward habit and environmental quality in the utility function. In steady state equilibrium allocation, we show that whether outward habits are destructive to the environment depends on the degrees of outward habit formation and the size of the economy.

Social Security and Endogenous Demographic Change: Child Support and Retirement Policies

This paper studies retirement and child support policies in a small, open, overlapping-generations economy with PAYG social security and endogenous retirement and fertility decisions. It demonstrates that neither fertility nor retirement choices necessarily coincide with socially optimal allocation, because agents do not take into account the externalities of fertility and the elderly labor supply in the economy as a whole. It shows that governments can realize the first-best allocation by introducing a child allowance scheme and a subsidy to incentivize the labor supply of older workers. As an alternative to subsidizing the elderly labor supply, we show that the first-best allocation can also be achieved by controlling the retirement age. Finally, the model is simulated in order to study whether the policies devoted to realizing the social optimum in a market economy could be a Pareto improvement.

Social Security Reform and Growth in an Overlapping Generations Economy with Heterogeneous Agents

Considerable attention has been paid to the many problems inherent to the US Social Security system over the past several decades. This study investigates the redistributive and efficiency consequences of introducing a subsidy-based pension system in an endogenous growth setting with income and mortality inequality. My analysis suggests that both current and future generations are better off without Social Security regardless of skill level. More significantly, I find that replacing the US Social Security system with capital subsidies is Pareto optimal for all generations and skill groups for a given set of subsidy rates. The existence of income and mortality inequality reduces the range of Pareto optimal capital subsidy rates, implying that a public pension system based on capital subsidies is less costly to implement in an economy with inequality than in an economy with homogeneous agents.

Why must it always be so Real with tax evasion?

We provide an alternative theoretical explanation to the tax evasion-inflation relationship by endogenizing the discount factor in an overlapping generations economy. When the discount factor is a positive function of public expenditure, i.e., discounting is endogenous, then an increase in inflation leads to an increase seigniorage, and hence the discount factor via the rise in public expenditure. In consequence, old age consumption increases in importance such that tax evasion among young-age agents increases to enhance the interest income from savings.

On the Anatomy of Medical Progress Within an Overlapping Generations Economy

We study medical progress within a two-sector economy of overlapping generations subject to endogenous mortality. Individuals demand health care with a view to lowering mortality over their life-cycle. We characterise the individual optimum and the general equilibrium, and study the impact of a major medical innovation leading to an improvement in the effectiveness of health care. We find that general equilibrium effects dampen strongly the increase in health care usage following medical innovation. Moreover, an increase in savings offsets the negative impact on GDP per capita of a decline in the support ratio. Finally, we show that the reallocation of resources between the final goods and health care sector, following the innovation, plays a crucial role in shaping the general equilibrium impact.

Taxation of capital income in overlapping generations economies

AbstractWhether capital income should be taxed in overlapping generations economies is vividly discussed. It is shown that intergenerational lump‐sum taxes cannot implement the Golden Rule allocation when agents have private information on their earnings potential. Hence, the seminal Atkinson–Stiglitz result that optimal income taxation pre‐empts any role for indirect taxation cannot be interpreted to imply that capital income taxation (affecting intertemporal relative prices) should not be taxed. Specifically, capital income should unambiguously be taxed in small open economies, and the optimal tax rate depends inversely on the elasticity of total savings to disposable income and the after‐tax rate of return.