Social security and endogenous demographic change: child support and retirement policies*

This paper studies retirement and child support policies in a small, open, overlapping-generations economy with PAYG social security and endogenous retirement and fertility decisions. It demonstrates that neither fertility nor retirement choices necessarily coincide with socially optimal allocation, because agents do not take into account the externalities of fertility and the elderly labor supply in the economy as a whole. It shows that governments can realize the first-best allocation by introducing a child allowance scheme and a subsidy to incentivize the labor supply of older workers. As an alternative to subsidizing the elderly labor supply, we show that the first-best allocation can also be achieved by controlling the retirement age. Finally, the model is simulated in order to study whether the policies devoted to realizing the social optimum in a market economy could be a Pareto improvement.

PAY-AS-YOU-GO PENSIONS AND ENDOGENOUS RETIREMENT

This paper revisits two classic results in standard overlapping generations models with a pay-as-you-go (PAYG) pension system. Firstly, a PAYG system crowds out private savings and reduces the overall capital stock. Secondly, in dynamically efficient economies, a PAYG system will reduce steady-state welfare. These classic results have been derived and exposed in models with no retirement decision. However, by allowing for endogenous retirement, and without taking recourse to any frictions, uncertainty, or myopia, it is shown that a PAYG system may be neutral and may even increase the capital–labor ratio. In particular, it is shown that the effect of the pension contribution rate on capital intensity depends on the elasticity of substitution between consumption and leisure. If the elasticity of substitution is between 0 and 1, an increase in the contribution rate will increase capital intensity. Moreover, it is shown that the result regarding welfare may also be overturned. An increase in the PAYG contribution rate may increase steady-state welfare.

OPTIMAL PAY-AS-YOU-GO SOCIAL SECURITY WITH ENDOGENOUS RETIREMENT

This paper considers an overlapping-generations model with pay-as-you-go social security and retirement decision making by an old agent. In addition, this paper assumes that labor productivity depreciates. Under this setting, socially optimal allocations are examined. The first-best allocation is an allocation that maximizes welfare when a social planner distributes resources and forces an old agent to work and retire as she wants. The second-best allocation is one that maximizes welfare when a social planner can use only pay-as-you-go social security in a decentralized economy. This paper finds a range of an old agent's labor productivity such that the first-best allocation is achieved in a decentralized economy. This finding differs from that in Michel and Pestieau [“Social security and early retirement in an overlapping-generations growth model”, Annals of Economics & Finance, 2013], which notes that the first-best allocation cannot be achieved in a decentralized economy.

The future of Spanish pensions

We use an overlapping generations model economy with endogenous retirement to study the 2011 and 2013 reforms of the Spanish public pension system. These reforms delay the legal retirement ages, increase the contributivity of the system, and adopt a sustainability factor and a pension revualuation index that effectively transform the Spanish pension system into a defined-contribution pension system. We find that these reforms improve the sustainability of Spanish pensions substantially, and that they limit the tax increases that would have been necessary to finance the pension system deficits. But these results are achieved at the expense of large reductions in the real value of the average pension. This reduction is progressive and, by 2050, the average pension is approximately 30% smaller in real terms than what it would have been under the pension system rules that prevailed in 2010. We also show that these reforms are costly in welfare terms and that households born between 1950 and 1970, young disabled workers who are alive at the time of the reform, and future cohorts bear the highest welfare costs. The substantial reduction of pensions and the high welfare costs that these reforms bring about lead us to conjecture that further reforms lurk in the future of Spanish pensions.

MORTALITY DECLINE, RETIREMENT AGE, AND AGGREGATE SAVINGS

We use an overlapping-generations model with endogenous retirement and saving to study the trade-off between saving and retirement age in response to mortality decline. When life expectancy increases by one year, people delay retirement by about four months. With this magnitude of delay in retirement age, the percentage of lifetime spent in working decreases, and people have to save more for postretirement years. Neither the pure form of sole adjustment through savings nor the proportionality hypothesis is consistent with our results, but the proportionality hypothesis is a better rule of thumb in predicting future behavior. Our choice of the modified Boucekkine et al. (2002) survival function gives a convenient one-to-one correspondence between life expectancy increase and a change in the survival parameter.