تعادل جمعیتی - اقتصادی زمانی که سن مادری آندوژن است

In this article, we study the joint dynamics of the demography and the economy. We explore how economic conditions affect fertility choices, and in return how the population growth rate affects both financial and labor markets. Our main contribution is to consider a realistic demographic setup that allows characterizing the age at which individuals decide to give birth to their children. In such a framework, we aim at studying the existence of an equilibrium. We notably prove there exists a monetary steady state if the average age of consumers is greater than the average age of producers.

In demographics, there is a long tradition of modeling population dynamics, dating back to the pioneer works of Lotka, 1907 and Lotka, 1922. Stable population theory studies the dynamics of an age distribution once fertility and mortality patterns are held constant. Generalizations have then been proposed to take into account deterministic or stochastic changes in fertility and mortality. We propose to extend the traditional stable population model to endogenous fertility behaviors hinging on a trade-off between the utility derived from having children and the costs they induce. A key variable affecting both utility and costs is the age at which women become mothers. As pointed out by Gustafsson (2001), it is notably the age at first birth that is the main explanatory variable for the rapid decrease in fertility in developed countries. Using the data from the Human Fertility Database (2010), it is striking to see the negative correlation between the cohort’s mean first maternal age and their total fertility rate. For instance, in the US, the mean age was slightly greater than 24 for cohorts born in 1918 as well as for those born in 1956, while it reached 22 and less for the cohorts, born between 1934 and 1940, that participated to the post-war baby-boom. In Fig. 1 are represented the dynamics of the mean age at first birth and of the total fertility rates for cohorts born between 1918 and 1966.We consider an overlapping generations model with continuous trading in which individuals work, consume and decide the age at motherhood. This choice affects labor participation and aggregate economic variables. We study the monetary equilibrium such that aggregate assets are positive. The main departure from Samuelson (1958) and the subsequent literature is that the population growth rate is endogenous. The intertemporal equilibrium is shown to be the solution of a non-linear functional differential equation of mixed-type. The dynamics is indeed affected by discrete delays and advances. As in Boucekkine et al. (2002) and d’Albis and Augeraud-Véron (2007), delays are generated by the vintage structure of the population while advances rely on the expectations of the individuals. Moreover, with an endogenous age at motherhood, some of the delays and advances are state-dependent. We characterize the steady states of our economy and focus on the monetary steady state. It is indeed well-known in the Samuelson (1958) setting that monetary steady states always appear as candidates for the equilibrium. In our framework with endogenous fertility, we show that it is not necessarily the case and that it depends on the marginal impact of the age at motherhood on human wealth. Moreover, we show that the condition initially exhibited by Arthur and McNicoll (1978) in a framework with exogenous population growth rate, still holds and is even necessary and sufficient for the existence of the monetary steady state. This condition says that the difference between the average age of consumers weighted by their consumptions and the average age of producers weighted by their earnings should be strictly positive. We finally show that the population growth rate obtained at the monetary equilibrium is always lower than the one that would be chosen by a social planner, upon existence of this latter solution. Section 2 presents the model describing the individual life-cycle behavior and the aggregation of both the population and the economy. Section 3 studies the monetary equilibrium. Section 4 concludes

Fertility choices involve three strongly interrelated decisions: the timing and spacing of births, the number of children and the quality of children. Since Becker (1960), the literature has extensively studied the tradeoff between child quality and quantity, but the first decision is much less discussed, in spite of the fact that its consequences on population growth are well documented empirically (see for instance Gustafsson, 2001). The novelty of this paper is to propose an endogenous determination of the age at motherhood. We represent this age by the age at first birth and suppose, in accordance to empirical works (Heckman and Walker, 1990), that the number of children is a decreasing function of this age. The central mechanism allowing to endogenize the age at motherhood is the comparison between the enjoyment the mother derives from spending time with her children and the opportunity cost of raising them, taking the form of a wage penalty. Recent papers endogenizing the age at motherhood have done it indirectly, considering that this age is a by-product of educational choices: when the mother decides to invest in her own human capital, she postpones childbearing until she has completed her education (de la Croix and Licandro, 2009). This work could be extended in two directions. First, the analysis of the dynamics of the model could allow us to get insights on the consequences of changes in variables affecting the tempo of childbearing, as economic policies aimed at reducing the opportunity cost of raising children. Following d’Albis and Augeraud-Véron (2008), it is possible to conjecture that the economy would experience long run fluctuations. Secondly, the model could be enriched by introducing the mother’s educational choices as in de la Croix and Licandro (2009), and an uncertain lifetime, which would allow us to analyze the interplay between fertility choices and mortality. The methodology developed here could then help to better understand the demographic transition