Economic Growth and Social Security

外生生育率通常在解释现收现付社会保障制度的存在及其影响的模型中被假设。我们假设内生生育在两代重叠的简单模型中是允许的，即年轻人照顾老人。社会保障水平被建模为政府最优分配问题的解。社会保障福利被认为取决于个人生育率。我们的研究表明，尽管在实践中不能实现最优配置，但个人遵循政府设定的社会保障水平，达到可持续的次优稳态。此外，我们还证明了可持续的稳定状态比没有社会保障制度的稳定状态具有更高的效用。面对人口增长的下降，现收现付的公共养老金的未来会怎样？一种普遍的观点是悲观的，因为未来的年轻人可能会选择摆脱越来越多的老年人的负担。然而，在包含内生人口增长和经济变量之间相互作用的简单模型中，公共养老金本身是人口增长下降的一个促成因素。在该模型中，此类养老金是可持续的，并改善了稳定的国家福利。这些结果也向许多发展中国家提供了重要的信息，在这些国家，向老年人的转移仍然发生在家庭内部，因为主要的老年支助和人口过剩是一个共同问题。我们的研究结果表明，向社会保障体系迈进将改善福利，并将导致生育率下降。因此，即使提高了个人的福利水平，人口过剩问题也可以得到解决。

Exogenous fertility has usually been assumed in models of explaining the existence and effects of pay-as-you-go social security system. We assume that endogenous fertility is allowed in a two overlapping generations simple model with the young caring for the old. The social security level is modeled as a solution of an optimal allocation problem by the government. Social security benefit is assumed to be conditional on individual fertility.We have shown that, although the optimal allocation cannot be achieved in practice, individuals follow the social security level set by the government and reach a sustainable sub-optimal steady state. Furthermore, we have also shown that the sustainable steady state has higher utility than that of the steady state without a social security system.What is the future of pay-as-you-go public pensions in the face of declining population growth? One common view is pessimistic, in that the future young may choose to shed the burden of a larger and larger number of elderly. However in simple model, which incorporates interactions between endogenous population growth and economic variables,public pensions are themselves a contributing factor to the decline in population growth. In the model, such pensions are sustainable and improve steady state welfare.These results also provide importanr messages to many developing countries where transfers to the old still occur within families as the major old-age support and over-population is a common problem. Our results imply that moving towards a social security system would be welfare-improving, and would lead to declining fertility. Thus the over-population problem can be solved even with improved welfare on an individual level.