This paper investigates the effect of a change in life expectancy (i.e., longevity) on fertility in a standard OLG economy. The main result is that, in contrast with other papers, an increase in the longevity rate may increase the fertility rate as well. It is shown that such a result holds when the cost of rearing children in terms of goods and services (rather than in terms of forgone wages) matters. In particular, such a result depends on the relative “strength” of the capital in the technology as compared with the “strength” of the parsimony. Moreover it is shown, again in contrast with other papers, that with an unfunded social security system it is more likely that a longer life may increase the fertility. The latter result is even more likely in the presence of child subsidy policies, which are widespread in developed countries. In conclusion, we argue that in countries having a population with a high longevity, a high capital share, a large unfunded social security, and child subsidy policies (such as Italy), a further increase of longevity may increase fertility in the long run and thus partially alleviate the peril of the so-called “demographic bomb.” 1. Introduction In the recent years longevity and fertility have been primary policy concerns, especially in the developed countries in which the population aging affects public budget (e.g., pensions and health cares) and labour market. As a consequence, there is a vast recent literature considering the role of longevity in dynamic models. Among the recent papers, De La Croix and Licandro [1] consider the role of rising longevity on schooling decisions in the early stages of life. Zhang et al. [2] consider a model with public education and imperfect annuity markets, where a decline in mortality affects growth. Cipriani and Makris [3] consider the role of expectations of longevity on economic outcomes in an overlapping generations model where longevity of one generation depends on the average human capital level of the same generation. However while De la Croix and Licandro [1] and Zhang et al. [2] assume exogenous longevity and Cipriani and Makris [3] focus on an endogenous mechanism determining longevity, they abstract from the fertility issue and thus from the possible effects of longevity on fertility. The latter issue, although it seems to be crucial for determining the long run population growth, has been investigated by few papers. Among these, the seminal paper by Ehrlich and Lui [4] found that rising longevity promotes growth by rising human capital investment in children and by reducing
References
[1]
While Yakita introduces in the Diamond’s model also an externality à la Romer for generating endogenous rather than exogenous growth, we preserve the neoclassical exogenous growth Diamond’s model. The findings of this paper does not depend on whether growth is endogenous or exogenous.
[2]
The endogenous choice of fertility is motivated according to the so-called weak altruism of parents towards their children; that is, parents choose the number of their children as a “consumption” good ([7, 10, 14]). By contrast, Ehrlich and Lui [4] assume that parents invest in the quantity (and in the human capital) of their children in order to secure old-age insurance.
[3]
Since a better understanding of the relationship longevity-fertility in as simple as possible models is a preliminary task, I have not embarked in developing more refined models: this allowed me, in the present paper, for focusing on a key ingredient as a responsible of opposite effects, such as the form of the cost of rearing children. Of course the effects of a longer life on fertility may be rather complicated in the cases in which, for instance, parents derive utility from their children’s utility, leave unintended or voluntary bequests, invest in the children’s human capital, and so on, but I abstracted from the vast literature which considers such cases.
[4]
For instance, in Italy this cost has been estimated to be, for each child and for each month, 252？€, 212？€, and 233？€ for the age classes 0–5, 6–14, and 15–18 years, respectively (this amounts to say that the per child cost is around 25% of a labourer’s average wage). Therefore, our assumption amounts to say that, loosely speaking, parents take into account only this cost when they decide whether to have or not a child, independently of whether they receive a high or a low wage (while they assume that the forgone work hours for child caring are included in the amount allowed, without forgone wages, by the family laws (e.g., parental leaves)).
[5]
This sharp contrast with the previous results show that the type of the cost of rearing children is crucial for determining the effect of a longer life on the long-run fertility rates.
[6]
I refer to the book of de-la-Croix and Michel [12, ch. 1] for a thorough analysis of the basic OLG growth model.
[7]
It is assumed that (i) the private annuity market is competitive and the companies are risk neutral; (ii) individuals are willing to invest their assets in such insurance companies, given the hypothesis of absence of bequests.
[8]
Note that with constant return to scale the use of a representative firm (instead of heterogeneous firms) is justified since the number of firms does not matter and does not affect production, given that firms adopt the same technology.
[9]
Adding exogenous growth in labour productivity does not alter any of the substantive conclusions of the model and, hence, it is not included here.
[10]
The price of output has been normalised to unity.
[11]
I thank an anonymous referee to have suggested to clarify the dynamic interaction between firms and agents from different generations.
[12]
This assumption is not strictly necessary, because the maximization target of the firm is essentially a static one, and thus we might, alternatively, also assume that firms live forever.
[13]
Note that, as known, in the standard Diamond’s model under Cobb-Douglas production function and logarithmic utility function, the existence, uniqueness and stability of the equilibrium are always preserved and this also holds in the present model which extends the Diamond’s model with endogenous fertility choices and exogenous longevity.
[14]
For the sake of precision, Result 1 holds provided that the share of capital is not rather unrealistically low. Indeed, simulations revealed that a positive effect of pensions on fertility might occur only if the capital share is significantly below 0.33 (which is the standard value of the capital share in most papers) and in any case only if the contribution rate is very low: for instance, even in the case of an unrealistically low value of the capital share about 0.15 the positive effect would only hold for contribution rates lower than 0.01 (for given realistic values of and ).
[15]
As to the issue of the relationship between pension systems and low fertility in Europe, see, for instance, Cigno and Werding [15].
[16]
Child policies have been investigated, although in a different context, for instance, by Fanti and Gori [8, 16].
[17]
For economy of space, the standard passages, equal to those in Sections 2 and 4, are omitted.
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