Complex equilibrium dynamics in a simple OLG model of neoclassical growth with endogenous retirement age and public pensions

We analyse the steady-state equilibrium dynamics of the conventional overlapping generations economy à la Diamond (1965) with pay-as-you-go public pensions and second period of life divided between working and retirement time in a proportion dependent on the individual health status (a rather realistic assumption especially in the current world with high longevity). In contrast to an economy without public health spending – which is always stable with monotonic trajectories –, an economy with tax-financed health care services (which in turn affect the individual health status and hence the length of the retirement time) may experience complex equilibrium dynamics with deterministic chaotic business cycles and, in particular, complicated dynamical phenomena, such as multiple “bubblings” may occur when crucial economic parameters change. Interestingly, it is shown that increasing the size of PAYG pensions, although initially may trigger chaotic cycles, eventually works for stability.Health; Old-age workers; OLG model; Perfect foresight; Public PAYG pensions

Fertility and PAYG pensions in the overlapping generations model

This article analyses how long-run pay-as-you-go public pensions react to a change in fertility in the basic overlapping generations model of neoclassical growth. While it would seem well established both in the academic and political debates that the decline in fertility represents a “demographic time bomb” for the sustainability of public pensions, it is shown that a falling birth rate need not necessarily cause long-run pension benefit to fall.Fertility; PAYG pensions; OLG model

A two-sector OLG economy: economic growth and demographic behaviour

We analyse an overlapping generations economy with two sectors of production: a capital-intensive commodity sector and a labour-intensive services sector. First, we consider an economy with exogenous population and study the effects of a change in the individual preference for old-aged services that causes a reallocation of labour between sectors on per capita income. Then, we compare the results with the standard Diamond (1965) style one-sector economy. Second, we endogenise fertility founding that a reallocation of labour in favour of the services sector causes an additional beneficial effect on per capita income with respect to the model with exogenous population. Third, we further introduce endogenous lifetime through public health investments, showing that multiple regimes of development may exist. In this context, the a rise in the preference for old-aged services may help escaping from poverty.Fertility, Life expectancy; OLG model; Public health expenditure; Services market

Endogenous fertility and development traps with endogenous lifetime

We extend the literature on endogenous lifetime and economic growth by Chakraborty (2004) and Bunzel and Qiao (2005) to endogenous fertility. It is shown that development traps due to under investments in health can never appear when fertility is an economic decision variable.Endogenous fertility; Health; Life expectancy; OLG model

Endogenous fertility, endogenous lifetime and economic growth: the role of child policies

We examine the effects of child policies on both the transitional dynamics and long-run demo-economic outcomes in the conventional overlapping generations model of neoclassical growth extended with endogenous longevity and endogenous fertility. The government invests in public health (Chakraborty, 2004) and the individual survival probability at the end of youth depends on health expenditure through an S-shaped longevity function. This may give rise to four steady states and, hence, development traps are possible. However, poverty or prosperity may not depend on initial conditions, while being the result of a child policy design. In particular, a child tax can be used to effectively allow those economies that were entrapped into poverty to prosper irrespective of where they start from.Child policy; Endogenous fertility; Health; Life expectancy; OLG model

From the Malthusian to the Modern Growth Regime in an OLG Model with Unions

The passage from the Malthusian Regime to the Modern Regime has been theoretically investigated only in recent times and the understanding of this process is still incomplete. This paper develops a neoclassical OLG model of neoclassical growth which embodies a stylised fact emerged in the second half of the XIX century, especially in European countries, that is the unionisation of labour markets and the diffusion of unemployment insurance systems. The results of this paper suggest that, differently from the previous literature, the diffusion of trade unions - which, causing a simultaneous increase of wages and unemployment, on the one hand reversed the effects of wage on fertility and on the other hand enhanced savings, capital accumulation and output in the long-run - may have triggered or at least favoured the passage.Economic Growth

Monopoly union, unemployment benefits and labour taxes: The unemployment problem revisited

Unemployment is undoubtedly one of the most important concerns in developed countries, especially in Europe. Most of the related economic literature has discussed the possible influence of unemployment benefits on unemployment and welfare, assuming a lump-sum type benefit system, while the more realistic earnings-related (replacement rate) regime has been scarcely considered. Applying a fairly standard monopoly union model, we show that when unemployment benefit is related to the existing wage, the rate of unemployment can be reduced by increasing both the replacement rate and the labour tax.

Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes

This study analyses the dynamics of a two-dimensional overlapping generations economy with endogenous labour supply à la Reichlin (1986) and aspirations, i.e. effective consumption by individuals of the current generation depends on the standard of living (based on consumption experience) of those that belong to the previous generation. We show that the relative importance of aspirations in utility is responsible for the existence of either one (normalised) steady state or two steady states. In particular, when the relative degree of aspiration is fairly high, the supply of labour becomes higher than those corresponding to the normalised steady state because individuals want to increase the amount of time spent at work when they are young in order to increase consumption possibilities when they are old, since the relative importance of past consumption is high in such a case. As regards local stability, the normalised steady state can be determinate or indeterminate and can undergo either a transcritical bifurcation or supercritical flip bifurcation depending on the intensity of the taste externality. Moreover, some interesting global dynamic properties emerge: indeed, when the relative importance of aspirations is strong enough, cyclical or quasi-cyclical behaviour and/or coexistence of attractors may occur. In particular, this last phenomena may cause global indeterminacy even if the stationary equilibria are locally determinate.Aspirations; Indeterminacy; Labour supply; OLG model; Nonlinear dynamics

PAYG pensions, tax-cum-subsidy and optimality

Using a simple OLG small open economy with endogenous fertility we show that the command optimum can be decentralised in a market setting using both a PAYG transfer from the young (old) to the old (young) and a tax-cum-subsidy (subsidy-cum-tax) policy, to redistribute within the working age generation. The latter instrument, in fact, reduces (increases) the opportunity cost of bearing children and, hence, stimulates (depresses) fertility. The policy implications are straightforward: when PAYG transfers exist and child rearing is time consuming, a tax-cum-subsidy (subsidy-cum-tax) policy can be used to internalise the externality of children, while also representing a Pareto improvement.Overlapping generations; PAYG Pensions; Small open economy; Tax-cum-subsidy

On economic growth and minimum wages

We offer an analysis of the existence of a positive relationship between minimum wages and economic growth in a simple one-sector overlapping generations economy where the usual Romer-typed knowledge spill-over mechanism in production represents the engine of endogenous growth, in the case of both homogeneous and heterogeneous (i.e., skilled and unskilled) labour. Assuming also the existence of unemployment benefits financed with consumption taxes not conditioned on age at a balanced budget, it is shown that minimum wages may stimulate economic growth and welfare despite the unemployment occurrence. Moreover, a growth-maximising minimum wage can exist. A straightforward message, therefore, is that a combination of minimum wage and unemployment benefit policies can appropriately be used to promote balanced growth and welfare.Endogenous growth; Minimum wage; Unemployment; OLG model