Pension,possible phaseout,and endogenous fertility in general equilibrium

The rich literature on Pay-As-You-Go (PAYG)-type pensions provides a notion that when pension return is dominated by the market return, generally it is impossible to phase pension out without hurting any generation. We show that PAYG pensions can indeed be phased out in a much richer framework where fertility is endogenous and general equilibrium effects are present. Interestingly, the factor that helps us to phase the pension out in a Pareto way is hidden in the structure of PAYG pension itself. Individualistic agents fail to recognize the benefits of their fertility decision on these programs and, therefore, end up in an allocation that is strictly dominated by the allocations that internalize this externality. Exploiting this positive externality, competitive economy can improve its allocations and can reach the planner's steady-state in finite time where each generation secures as much utility as in the competitive equilibrium. Clearly, it is possible to transition in a Pareto way to an economy either with no pension or with pensions whose return is not dominated by market return.     

Fertility,Intra‐Generational Redistribution,and Social Security Sustainability

Incorporating heterogeneity in preference to having children into an overlapping generations model of a small open economy, we examine the effects of changes in the size of pay‐as‐you‐go (PAYG) social security on fertility choices of individuals and population growth of the economy. It is shown that PAYG social security will raise population growth by increasing the number of individuals who have children and the number of children parents have if the system involves redistribution between retirees with different contributions, whereas, if it has no redistribution, PAYG social security does not affect the fertility decisions of individuals.     

Child policy ineffectiveness in an overlapping generations small open economy with human capital accumulation and public education

Motivated by the recent decrease in the number of children experienced in several developed countries, in this paper we consider a small open economy model with overlapping generations, endogenous fertility and human capital formation through public education, and look at the role the government can play in affecting fertility through the widely used child allowance policy. Contrary to conventional view, we show that the public provision of child allowances is fertility-neutral in the long run, that is it is not effective as a pro-natalist policy, while also reducing human capital accumulation. In contrast, the financing of the public education system is beneficial to both fertility and human capital. These results hold in the cases of both fixed and time cost of children.     

Ageing,fertility, and growth

This paper analyses the interaction between human capital accumulation, fertility, and labour participation of families in the presence of technology shocks. Altruistic families spend time on the education of their children to increase their level of human capital. Compensating transfers through negative bequests are blocked by an active bequest constraint. Productivity shocks increase the opportunity costs of children and may cause a drop in fertility, which results in population ageing. We investigate the effects of ageing on allocation and welfare in the presence of a Pay-As-You-Go (PAYG) pension system.     

The Optimal Level of Debt in an OLG Model with Endogenous Fertility

Abstract. In the present work we extend Diamond's OLG model by allowing for endogenous fertility and look at the consequences of such an extension on the rules for optimal public debt issuing. In particular, we show that the condition according to which the rate of growth of population should be higher than the interest rate is no longer sufficient for obtaining welfare improvements via debt increases and that the level of optimal debt is, ceteris paribus, lower than the one arising with exogenous fertility. Finally, a sensitivity analysis shows that the optimal level of debt is higher the lower the capital share, the higher individuals' degree of patience, the bigger the child‐rearing cost and the lower the preference for children. On policy grounds we argue that debt‐tightening policies may be optimal in the long run provided that the cost of rearing children does not increase (or, if anything, does decrease).     

Social security and demographic trends: Theory and evidence from the international experience

The worldwide problem with pay-as-you-go, defined-benefits social security systems is not just financial. Through a dynamic, overlapping-generations model where forming a family and bearing and educating children are choice variables, we show that social security taxes and benefits generate incentives to reduce both family formation and fertility, and that these effects cannot be fully neutralized by counteracting inter-temporal or intergenerational transfers within families. We implement the model using calibrated simulations as well as panel data from 57 countries over 32 years. We find that PAYG tax measures account for a non-trivial part of the downward trends in family formation and fertility worldwide, especially in OECD countries.     

Growth and welfare effects of monetary policy with endogenous fertility

This paper investigates the economic growth and social welfare implications of monetary policy in an endogenous growth model with endogenous fertility. We show that, in the money-in-the-utility-function framework, endogenous fertility governs the validity of money superneutrality, the transitional dynamics of an anticipated monetary policy, and the optimal monetary policy. Along a balanced growth path, monetary growth increases fertility and reduces the economic growth rate if consumption and real balances are complements or are independent. However, monetary expansion may decrease fertility and increase economic growth if consumption and real balances are substitutes. Generally speaking, the superneutrality of money does not hold in the presence of endogenous fertility. More importantly, with endogenous fertility, the Friedman (1969) rule is no longer a welfare-maximizing monetary policy. We also show that an anticipated inflation induces the transitional dynamics of fertility and the economic growth rate even though the intertemporal elasticity of substitution equals unity. This differs from the conventional notion in the existing literature.     

Input versus output taxation in an experimental international economy

This paper presents the results of a policy oriented macroeconomic experiment involving an ‘international’ economy with a relatively small ‘home’ country and a large ‘foreign’ country. It compares the economic performance of two alternative tax systems: a wage tax system and a sales-tax-cum-labor-subsidy system. The two systems are applied to the small country, while the wage tax system always obtains in the large country. The main result is that the sales tax system outperforms the wage tax system, using standard economic indicators. Moreover, it turns out that under the sales tax system economic activities appear to be moving toward the ‘better’ of two theoretical equilibria. It is argued that producers’ reluctance to incur costs up-front while being uncertain about product prices can explain these results. Several pieces of evidence are provided to support this claim. The results strongly suggest that behavioral aspects should be taken into account also in applied macroeconomic models.     

Quasi-hyperbolic discounting and social security systems

Hyperbolic discounting has become a common assumption for modeling bounded rationality with respect to individual savings decisions. We examine the effects of hyperbolic discounting on the comparison of alternative social security systems. We show that this form of bounded rationality breaks the equivalence between funded and pay-as-you-go (PAYG) systems established in Sheshinski and Weiss [Sheshinski, E., Weiss, Y., 1981. Uncertainty and optimal social security. Quarterly Journal of Economics 95, 189-206]. Intergenerational transfers within a PAYG economy are usually secured by the social security system and independent of longevity, whereas this is not the case for the funded economy. The savings level under hyperbolic discounting is lower than under exponential discounting [Laibson et al., 1998], but the ratio between the savings level under hyperbolic discounting within a funded economy and a PAYG economy depends on the effectiveness of the commitment devices. It is shown that if individuals are hyperbolic discounters, then in a PAYG economy any change in the mandated level of intergenerational transfers is neutralized by individuals’ voluntary bequests. This does not apply to a funded system.     

Endogenous fertility and growth in a model with old age support

Summary. This paper examines the interrelationship between capital accumulation, fertility, and growth by introducing an endogenous fertility decision into Diamond's (1965) neoclassical growth model. Under the assumptions that children provide old age support and that individuals incur a variable time cost of raising children, it investigates the potential for cyclical fluctuations in the capital-labor ratio and fertility, as well as for development trap phenomena to be observed. It is shown that when capital and labor are highly substitutable in production, there is a unique steady state equilibrium, and either damped or undamped oscillations in fertility and the capital-labor ratio may occur. However, when the elasticity of substitution between capital and labor is less than one, two steady state equilibria may exist; one with a high capital-labor ratio and a high rate of population growth, and the other with a lower capital-labor ratio as well as a lower population growth rate. The former is a saddle, while the latter may be either a source or a sink. In the latter case development traps are possible. Received: June 16, 1997; revised version: December 18, 1997     

Policy effects on transitional welfare in an overlapping generations model: A pay-as-you-go pension reconsidered

We study the welfare effects of a pay-as-you-go (PAYG) pension system in transition, as well as in the steady state, by showing how the total welfare effects are determined by a cumulative effect on capital. Theoretical studies have shown that the introduction of a PAYG pension system reduces steady-state welfare under dynamic efficiency. Nevertheless, such pension systems have been widely adopted in the real world. To explain this, we algebraically and graphically prove that the PAYG pension system could be Pareto-improving in transition under dynamic efficiency. Similarly, it is acknowledged that this pension system should be introduced under dynamic inefficiency because it improves steady-state welfare. However, we show that the PAYG pension system may be Pareto-deteriorating in transition. Our findings imply that governments adopt PAYG pension systems to achieve policy targets other than long-run welfare maximization.     

War finance and the baby boom

In this paper, I extend the Barro–Becker model of endogenous fertility to incorporate specific fiscal policies and use it to study the effects of the fiscal policy changes following WWII on fertility in the United States. The US government went through large changes in fiscal policy after the beginning of WWII. The marginal income tax rate for an average American jumped from 4% on average before 1940 to approximately 25% during the war and stayed around 20% afterwards. The government debt–GDP ratio jumped from approximately 30% on average before WWII to 108% in 1946 and then dropped gradually in the following two decades to about 30% again at the end of 1960s. I find that the dramatic increase in the marginal income tax rate was an important cause of the postwar baby boom in the US because it lowered the after-tax wage and thus the opportunity cost of child-rearing. I also find that the differential change in taxes by income was an important reason why the baby boom was more pronounced among richer households (as documented by Jones and Tertilt, 2008). Furthermore, I argue that the government's debt policy may also matter for understanding fertility choices because government debt implies a tax burden on children in the future and thus affects their utility, which is a key determinant of current fertility choice in the Barro–Becker model. The results of a computational experiment show that the US government's postwar debt policy also contributed to the baby boom, but its quantitative importance is relatively small.     

Optimal social security tax with myopic agents

Myopic agents lack the foresight to save for their own old age. It is generally believed that correcting myopia is a rationale for a pay-as-you-go (PAYG) pension system. This view has been supported by existing literature showing that the optimal PAYG social security tax should increase when people are more myopic. In this paper we obtain new results opposed to the traditional view. By establishing a very standard general equilibrium OLG model with myopic agents and endogenized marginal product of capital, we show that the optimal social security tax should be lower when people are more myopic. Our numerical analysis also shows that the welfare cost of the social security tax increases with people's degree of myopia. These results suggest that correcting myopia is not a clear rationale for the PAYG social security.     

The consumption tax in the presence of altruistic cash and human capital bequests with endogenous fertility decisions

We provide an analysis of the consumption tax policy in the presence of cash bequests, human capital investments in children, and endogenous fertility decisions. It is shown that the consumption tax is no longer neutral if the tax rate is constant over the taxpayer's life cycle, labor supply is exogenous, and the parent expects the offspring to pay the same tax rate, if the number of children is chosen optimally by the parent. Neutrality breaks down because the shadow prices of both bequests and fertility are interlinked; it is more expensive to produce a child the larger either bequest is and it is more expensive to make a bequest of either type to each child the larger the number of children produced. Several examples are provided where imposing the consumption tax induces an increase in the number of children produced and a decrease in net capital formation.     

Child participation,nature of work,and fertility demand: a theoretical analysis

A model of utility maximization with home production of children and standard of living is used to analyze the fertility behavior of a subsistence farming household in an agricultural lesser developed country. Assuming children as both consumer and producer goods, and assuming a prestige cost of their participation in labor force, the author derived alternative levels of fertility demand. The following different conditions of child participation were identified depending upon the size of the prestige cost and the resultant net gain from child work: (1) participation in wage-labor, if marginal child income from the family farm is less than marginal wage income; (2) participation in family farm works only, if the larger wage income is neutralized by a higher prestige cost, implying a lower child contribution; (3) participation in family farm works only, if its marginal child income is greater than wage income, thus providing the largest child contribution; and (4) no participation in labor force at all, implied by a very high prestige cost and resulting in no child contribution. The household demands a larger number of children under conditions (1) and (3) than under conditions (2) and (4). The results are then used to draw inferences regarding fertility behavior across different landholding households. It appears that landholding reduces fertility initially, increases it at the intermediate levels, and then decreases it when the household becomes a non-cultivating rental income earner. The nonmonotonic landholding-fertility relationship explains the contradictory empirical evidence which exists in the literature while also suggesting important implications for fertility regulation policy.     

Temptation and social security in a dynastic framework

We investigate welfare and aggregate implications of a pay-as-you-go (PAYG) social security system in a dynastic framework in which individuals have self-control problems. The presence of self-control problems induces individuals to save less because of their urge for temptation towards current consumption. Individuals' efforts to balance between the short-term urge for temptation and the long-term commitment for consumption smoothing result in self-control costs. In this environment PAYG social security works as a self-control cost reducing device. In contrast, the presence of altruism induces individuals to save more. This in turn mitigates the adverse effects of self-control problems and PAYG social security on savings but magnifies the self-control costs. We find that in our environment the adverse welfare effects of a PAYG system are further mitigated relative to the environments that incorporate altruism and self control issues separately. However, the level of mitigation is quite modest.     

The optimal linear income tax with tax credits contingent on fertility

The literature on the optimal linear income tax is extended by incorporating tax credits contingent on the number of dependents the taxpayer is responsible for. The choice over how many dependents to be responsible for is made endogenous by allowing taxpayers a choice over their own fertility. Formulae are derived governing the government's optimal choice of the labor income tax rate and the tax credit contingent on fertility. It is also shown that if the government chooses its policy based on the belief that fertility behavior is exogenous when it is actually endogenous, then a suboptimal policy will be chosen. If certain conditions are fulfilled the government will choose a labor income tax rate lower than that which is actually optimal.     

Gender Power,Fertility, and Family Policy

The birth of children often shifts the balance of power within a family. If family decisions are made according to the welfare function of the spouses, this shift in power might cause a time‐consistency problem. In a model of cooperative family decision‐making, we show that this problem can lead to a systematic downward bias in fertility. By keeping fertility low, spouses mitigate the ex ante undesired shift in the balance of power that results from the presence of children. This provides scope for welfare‐enhancing policy intervention. We discuss to what extent existing family policy measures are suitable for overcoming the bias.     

The American frontier: Technology versus immigration

How important was international immigration for the US and its demography during the nineteenth century? This paper investigates, quantitatively, its effect on the westward movement of population and the regional and secular changes in fertility. Beside immigration, two alternative forces are considered: technological progress and the land policy (the Homestead Act). An optimal growth model with endogenous fertility and migration is calibrated, and counterfactual experiments reveal that the main driving forces were productivity growth and the declining cost of transportation. International immigration played a lesser role.     

Public provision of private child goods

This paper analyzes the public provision of private goods for children in a politico-economic model with endogenous fertility. The government provides every child with goods that can also be purchased by parents in private markets, and the level of provision is determined by majority rule. Households with many children benefit from the public provision more than those with fewer children; thus, a political conflict arises between them. The distribution of the number of children across households, which is a crucial factor for determining which group is politically dominant, is endogenously determined by households' fertility decision. The sequential interaction between fertility and political decisions might lead to multiple equilibria: equilibrium with high fertility and low-private/public-spending ratio and equilibrium with low fertility and high-private/public-spending ratio. Our model could explain the large differences in fertility and structure of child-related spending across countries.