امنیت اجتماعی و باروری درونی: حقوق بازنشستگی و کمک هزینه فرزند به عنوان دوقلوهای به هم چسبیده

This paper analyses public pensions and child support in a model with endogenous fertility. We show that the individual fertility choice may not coincide with the social optimum, due to the existence of external effects of children on society as a whole. The market outcome without government intervention is efficient, however, as the externalities exactly cancel out in that case. If the government wants to redistribute towards the old, it cannot replicate the command optimum by merely applying lump-sum transfers, but rather needs a child allowance scheme to effectively alter the number of offspring. Finally, we analyse whether a Pareto-improving social security reform is possible. It is shown that merely reducing the PAYG-scheme cannot be Pareto-improving, but the introduction of a child allowance scheme can be.

As many societies will experience an ageing population in the near future, concerns about the feasibility of current pension and health care arrangements are growing. This demographic shift is caused both by a decrease in the number of children and increasing longevity. As to the first aspect, a lower rate of fertility seems to be the result of a choice that individuals make, viz. how many children to have. This endogeneity of fertility has important implications for the economy, and can therefore significantly affect the results of analyses concerning for instance social security reform. This paper analyses the effects of social security arrangements in a society where fertility is endogenous, and looks at the role the government can play in improving welfare. It is organised as follows. Section 2 pictures some recent demographic trends and population prospects, and dwells on the explanation of the fertility rate from an economic perspective. Section 3 presents the basic model. We will consider a small open economy where individuals derive utility from material consumption and raising their children. Section 4 describes the command optimum for this economy. As was argued in Cigno (1993), we find that there are two opposite externalities of children involved. Firstly, an additional child implies a higher future output, and secondly, it reduces the capital–labour ratio (or per capita debt in a small open economy). Parents who do not take these externalities into account are likely to give birth to a (socially) suboptimal number of children. We show, however, that the market solution without any form of government intervention is Pareto-efficient as both externalities then exactly cancel out. But if the government redistributes between generations, the command optimum cannot be replicated by merely applying lump-sum transfers. Rather, an additional instrument is required that induces substitution effects so as to effectively alter the number of children chosen by households. In particular, if the government redistributes from the young to the old, children on balance involve a positive externality and a system of child allowances in addition to the transfer scheme makes the achievement of the first-best outcome possible. We show this for the specific case of pay-as-you-go (PAYG) transfers, but this conclusion can readily be generalised to all other types of intergenerational redistribution. An international comparison of generational accounts (Kotlikoff and Leibfritz, 1998) shows that many countries do indeed transfer large amounts of resources from the yet unborn to current generations.1 If, however, resources are transferred in the opposite direction, i.e. from the old to the young, the net external effect of offspring is negative and a tax per child is necessary to achieve Pareto-efficiency. A similar conclusion is drawn by Harford (1998), where children entail a (negative) pollution externality created by their consumption of particular commodities in the future. Section 5 analyses whether social security reforms can be implemented in a Pareto-improving way, i.e. without utility loss for any generation, if one starts from a situation in which there only exists a PAYG-pension scheme. We first discuss the effects of introducing a system of child allowances that internalises the positive net externality that offspring generates in this setting. We show that introducing such a system is a Pareto-improvement if the subsidy per child is not too high. Next, we elaborate on the effect of reducing the size of the PAYG-scheme. Such a social security reform is discussed in many western countries in reaction to the ageing of the population they experience. This discussion is based on the notion that a lower PAYG-tax would be optimal in the long run when the economy is characterised by dynamic efficiency. It is well-known, however, that such a decrease in the size of PAYG-scheme is not Pareto-improving when fertility is exogenous (see Verbon (1988), and Breyer (1989)), unless there is some externality involved. If abolishing the PAYG-scheme goes along with the elimination of a negative external effect, as for example the distortion of the labour–leisure choice caused by a PAYG-tax as in Homburg (1990), then a Pareto-improving transition to a funded system is possible. Likewise, such a transition can be achieved if the increase in savings that results when the PAYG-scheme is reduced has positive external effects (as in Belan et al. (1998), and Corneo and Marquardt (2000), who assume endogenous growth2). One would therefore conjecture that downsizing the PAYG-scheme yields a Pareto-improvement when fertility is endogenous since it would decrease the external effect of the pension system on the number of offspring. A positive welfare effect would thus be realised that enables the Pareto-improving transition to funded pensions which is not possible if fertility is exogenous. Yet, we prove that just like in the models of Verbon (1988) and Breyer (1989) with exogenous fertility, merely reducing the PAYG-tax does not allow for a Pareto-improvement. Section 6 winds up with some concluding remarks.

Both a smaller family size and increasing longevity imply serious challenges for modern western societies with extensive social security programmes. How to best deal with these is a question that cannot be answered unambiguously, as many studies have already pointed out. Still, most economists analyse the economic consequences of population ageing without paying much attention to the underlying causes. These stem to a large extent from the fact that in modern societies, fertility is the endogenous source of population growth, i.e. family size is something people can decide upon, besides savings and material consumption. Moreover, the existence of PAYG-financed social security arrangements implies that the investment element of a child is socialised. Fertility choice is therefore only based on the direct utility that a household gets from its offspring, neglecting the fact that progeny benefits all in society. Apparently, children are to some extent a public good and consequently involve externalities. Because individuals typically do not take these into account when deciding on their family size, the rate of population growth may deviate from its socially optimal value. We show, however, that the market outcome without any form of government intervention is efficient. That is, the number of offspring is socially optimal if the government does not redistribute between generations. On the other hand, in a society with a PAYG-pension scheme, the number of offspring will be too low if there is no child allowance. In that case, an appropriate child subsidy is required to replicate the command optimum. So pensions and child allowances are like Siamese twins: you should see neither of them or both together, but never one without the other. In many societies with an extensive PAYG-scheme the general feeling is that, in view of ageing, the existing pension scheme is too generous. But downsizing the system is difficult because this comes at the cost of lower utility for at least one generation. We have shown that even if initially, as a consequence of the PAYG-scheme, the number of children is too low, it cannot be a Pareto-improvement to merely reduce the generosity of the public pension scheme. Pareto-improvements can only be realised by internalising the external effect due to the existing redistribution scheme through introduction of a child allowance scheme. This suggests a simple policy advice for countries with extensive PAYG-schemes but no child subsidy: these countries should introduce a child allowance scheme so as to broaden the tax base for the PAYG-scheme.