Economic Growth and Social Security

在解释现收现付社会保障制度的存在和影响的模型中，通常假设外生生育率。我们假设，在两代重叠的简单模型中，允许内生生育，年轻人照顾老年人。社会保障水平被政府建模为最优分配问题的解决方案。假设社会保障福利是以个体生育能力为条件的，虽然在实践中不能实现最优分配，但个体遵循政府设定的社会保障水平，达到一个可持续的次优稳定状态。此外，我们还表明，可持续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。在人口增长不断下降的情况下，现收现付制公共养老金的未来是什么？一种普遍的看法是悲观的，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，公共养老金本身就是人口增长下降的一个促成因素。在该模型中，这种养老金是可持续的，并改善了稳定状态下的福利。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，因为主要的养老支持和人口过剩是一个常见的问题。我们的结果表明，迈向社会保障体系将改善福利，并将导致生育率下降。因此，即使在个人层面上改善福利，人口过剩的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.