Equilibrium dynamics under lump-sum taxation in an exchange economy with skewed endowments

I explore the dynamics in overlapping generations models with pure exchange and lump-sum taxes, when the second period after tax endowment is negative, and contrast the characteristics of equilibria to those of models with positive after tax endowments. In particular, if the intertemporal elasticity of substitution is less than unity, there can be only a two cycle or stable (ie indeterminate) equilibria for certain parameter values. With this value for that elasticity chaos and a cycle of any order can occur in a model with regular endowments. In a sense the lump-sum taxation in this model operates as a stabilizing device. The precise stability condition holds with a small discount factor and in economies with relatively high taxes in the first period. If the intertemporal elasticity of substitution is greater than unity, the steady state equilibria are unstable, and thus determinate, as is the case with the regular model.overlapping generations economy; saving; cycles; lump-sum taxation

The effects of aging population on the sustainability of fiscal policy

We study the effects of aging population on the sustainability of fiscal policy in overlapping generations models with government debt and a pay-as-you-go pension system. The smaller the population growth rate, the lower the maximum sustainable level of deficits. When the utility function is of a specific form, an increase in the payroll tax rate and the replacement rate decreases the level of maximum sustainable deficits; except in the case when pension depends on the wage level prevailing during the working period. The ratio of the deficits in two economies with different population growth rates is characterized with numerical examples.aging; pensions; overlapping generations; fiscal policy

Stabilizing Competitive Cycles with Distortionary Taxation

We utilize a simple overlapping generations model with a balanced budget rule to study the effect of distortionary taxation on cycles and local stability of equilibria. We show that under proportional taxation there is a critical tax rate above which cycles will vanish, while in the case of linearly progressive taxation there is a critical level of exemption below which cycles will vanish as well. Hence, a sufficiently high tax rate and a low tax progression eliminate cycles. If the lifetime utility function is quasi-linear, increasing the tax rate can cause the economy to become locally unstable both with proportional and linearly progressive taxation so that tax exemption does not matter. Finally, if the lifetime utility function is not quasi-linear, for small tax rates an increase in progression can locally destabilize the economy.overlapping generations, cycles, stabilizing taxation

Stability and Dynamics in an Overlapping Generations Economy under Flexible Wage Negotiation and Capital Accumulation

We analyze the stability and dynamics of an overlapping generations model under imperfectly competitive labour markets without population growth and with perfect foresight. Under right-to-manage wage bargaining we assume that wage is negotiated after the decision on the capital stock. With Cobb-Douglas utility and production functions the steady state is unique and the steady state capital stock depends on the trade union’s bargaining power. This is because higher bargaining power of the trade union will induce workers to save more thus boosting the capital stock, ceteris paribus. Finally, we show that the steady state equilibrium is a saddle point.overlapping generations economy, capital accumulation, flexible wage negotiation, stability and dynamics

The Effects of the Size of the Public Sector on Fertility

We construct a simple exchange economy overlapping generations model in which there are along with a public social security various private insurance schemes to explore fertility and the effects of various variables on it. In the private system parents can invest in children and benefit from their support (care and income support) in the old age. An introduction of the public system will lower the incentive to have children, i.e. the fertility will be lower. This is an important negative externality of public pension system. We test some of the model's basic implications using long historical panel data from 11 countries for the period 1750-1995. In addition, two other data sets, the WDI (World Bank) and MZES (Manheim University) are used to reinforce the empirical results that are obtained with historical data. These analyses show that, opposite to common beliefs, there is a positive relationship between ageing and fertility if we control for the key determinants of fertility (size of the public sector, level of income, education and infant mortality). By contrast there is a strong negative relationship between the size of the public sector and fertility. The same is true in terms of income and education while the fertility effect of infant mortality is clearly positive.fertility, pensions, overlapping generations

Saddles, Indeterminacy and Bifurcations in an Overlapping Generations Economy with a Renewable Resource

No abstract.

Saddles, Indeterminacy and Bifurcations in an Overlapping Generations Economy with a Renewable Resource

We incorporate a renewable resource into an overlapping generations model with standard, well-behaved utility and constant returns to scale production functions. Besides being a factor of production the resource serves as a store of value. We characterize dynamics, efficiency and stability of steady state equilibria and show that the nature of steady state equilibrium depends on the value of the intertemporal elasticity of substitution in consumption. In particular, if that elasticity is at least half, but not exactly one, stationary equilibria are saddle points. The stationary equilibrium is stable when the intertemporal elasticity of substitution is unity. For smaller values of that elasticity we use a parametric example to demonstrate the existence of stable equilibria (indeterminacy) and a subcritical flip bifurcation. Hence, an overlapping generations economy with a renewable resource can display cycles and indeterminacy even in the absence of externalities or imperfect competition.Overlapping generations, renewable resources, bifurcations