Development, fertility and childbearing age: A Unified Growth Theory

Abstract

During the last century, fertility has exhibited, in industrialized economies, two distinct trends: the cohort total fertility rate follows a decreasing pattern, while the cohort average age at motherhood exhibits a U-shaped pattern. This paper proposes a Unified Growth Theory aimed at rationalizing those two demographic stylized facts. We develop a three-period OLG model with two periods of fertility, and show how a traditional economy, where individuals do not invest in education, and where income rises push towards advancing births, can progressively converge towards a modern economy, where individuals invest in education, and where income rises encourage postponing births. Our findings are illustrated numerically by replicating the dynamics of the quantum and the tempo of births for cohorts 1906–1975 of the Human Fertility Database.

Introduction

In the 20th century, growth theorists paid particular attention to interactions between, on the one hand, the production of goods, and, on the other hand, fertility behavior, that is, the production of men. When studying those interactions, they have mainly focused on one aspect of fertility: the number or quantum of births. From that perspective, the key stylized fact to be explained is the declining trend in fertility.¹ That decline is illustrated on Fig. 1, which shows the cohort total fertility rate (hereafter, TFR) for cohorts of women aged 40 in industrialized countries. That fertility decline was explained through various channels, such as the rise in the opportunity costs of children (Barro and Becker, 1989), a shift from investment in children's quantity towards children's quality caused by lower infant mortality (Ehrlich and Lui, 1991, Doepke, 2005, Bhattacharya and Chakraborty, 2012), a rise in the return to education (Galor and Weil, 2000), a rise in women's relative wages (Galor and Weil, 1996), and the rise of contraception (Bhattacharya and Chakraborty, 2017, Strulik, 2017).

Although those models cast substantial light on interactions between fertility and development, their exclusive emphasis on the quantum of births leaves aside another important aspect of fertility, which has a strong impact on economic development: the timing or tempo of births. Studying the tempo of births – and not only the quantum of births – matters for understanding long-run economic development, because of two distinct reasons.

First, theoretical papers, such as Happel et al. (1984), Cigno and Ermisch (1989) and Gustafsson (2001), studied, at the microeconomic level, the mechanisms by which the birth timing decision is related to education and labor supply decisions. A lower wage early in the career reduces the opportunity cost of an early birth, and pushes towards more early births (substitution effect), but limits also the purchasing power, which pushes towards fewer early births (income effect). Moreover, investing in education raises the purchasing power in the future (which pushes towards more late births), but, at the same time, raises also the opportunity cost of future children (which pushes towards fewer late births). Those strong interactions between birth timing, education and labor decisions at the temporary equilibrium motivate the study, in a dynamic model, of how development affects – and is affected by – birth timing.

Second, there is also strong empirical evidence supporting the existence of complex, multiple interactions between the tempo of births and various economic variables, with causal relations going in both directions. Demographic studies show that the tempo of births is strongly correlated with the education level, which affects the human capital accumulation process (see Smallwood, 2002, Lappegard and Ronsen, 2005, Robert-Bobée et al., 2006). Moreover, several works, such as Schulz (1985), Heckman and Walker (1990) and Tasiran (1995), show that a rise in women's wages tends to favor a postponement of births.² There is also evidence that the wage level is affected by the timing of births (see Miller, 2009, Joshi, 1990, Joshi, 1998; Dankmeyer, 1996).

The timing of births has varied significantly during the 20th century, as illustrated on Fig. 2, which shows the cohort mean age at motherhood by age 40 (hereafter, MAM).³ Whereas patterns differ across countries, Fig. 2 reveals an important stylized fact: the MAM exhibits, across cohorts, a U-shaped pattern. The MAM has been first decreasing for cohorts born before 1940/1950, and, then, has been increasing for later cohorts.⁴

The U-shaped pattern for the MAM raises several questions. A first question concerns the economic causes and consequences of that non-monotonic pattern. How can one explain that economic development is associated first with advancing births, and, then, with postponing births? How can one relate this stylized fact with income and substitution effects, and with the education decision? Another key question concerns the relation between the dynamics of the quantum of births (Fig. 1) and the tempo of births (Fig. 2). Why is it the case that, at a time of strong fertility decline, cohorts tended to advance births, and, then, tended to postpone births once total fertility was stabilized?

The goal of this paper is precisely to cast some light on the relation between the quantum of births, the tempo of births, and economic development. For that purpose, we propose to adopt a Unified Growth Theory approach. As pioneered by Galor (see Galor and Moav, 2002, Galor, 2010), Unified Growth Theory pays a particular attention to the relation between quantitative changes (i.e. changes in numbers) and qualitative changes (i.e. changes in the form of relations between variables).⁵ Qualitative changes are studied by means of regime shifts, which are achieved as the economy develops, and which cause major changes in the relations between fundamental variables. The fact, shown on Fig. 2, that development was first associated with an advancement of births, and, then, with a postponement of births, can be regarded as a major qualitative change. Our paper aims at developing a single unified framework of analysis to understand the relation between development and birth timing, and, as such, can be regarded as a contribution to Unified Growth Theory.⁶

For that purpose, this paper develops a three-period overlapping generations (OLG) model with lifecycle fertility, that is, with two fertility periods (instead of one as usually assumed). In our model, individuals decide not only the quantum of births, but, also, how they allocate those births along their lifecycle, that is, the tempo of births. In order to study the interactions between birth timing and education, we also assume that individuals choose how much they invest in their education when being young, which will affect their future productivity.

Anticipating our results, we show, using a general model with additively separable preferences, that there exist conditions on preferences such that, depending on the prevailing level of human capital, the temporary equilibrium takes three distinct forms, which correspond to three distinct regimes. In each of those regimes, a rise in human capital pushes towards fewer births. However, those regimes differ regarding the relation between human capital and the timing of births. In the first regime, which prevails for low levels of human capital, individuals do not invest in education, and rises in human capital push them towards advancing births (a decline of the MAM). In the second regime, which is achieved once human capital crosses a first threshold, individuals start investing in education, but education remains so low that human capital accumulation still makes individuals advance births. Then, once human capital is sufficiently high, and reaches a second threshold, the economy enters a third regime, where human capital accumulation leads to postponing births (a rise in the MAM).

Whereas the last, modern regime (with declining TFR and births postponement) was studied in the literature (see Iyigun, 2000), a merit of this paper is to highlight the existence of two anterior regimes, where the decline of the TFR is associated not with the postponement of births, but with the advancement of births. In particular, the second regime, which exhibits increasing education and births advancement, has received little attention so far, but plays a key role in the transition from a traditional economy with a high TFR and a decreasing MAM to a modern economy with a low TFR and an increasing MAM.

The conditions on preferences leading to the existence of those regimes have three main aspects, which admit intuitive economic interpretation. First, those conditions guarantee that, as human capital accumulates, the substitution effect dominates the income effect for both early and late fertility rates (leading to a fall of TFR). Second, the conditions on preferences are such that, beyond some threshold for human capital, the level of education becomes positive and increasing with human capital. Third, standard assumptions on preferences imply also that the level of education tends to weaken the strength of the substitution effect with respect to the income effect for late births only. This latter property explains that, once education reaches a sufficiently high level, the tendency to advance births as human capital accumulates (which prevails for low levels of human capital) is replaced by a tendency to postpone births, leading to the U-shaped curve for the MAM.

Our dynamic lifecycle fertility model can thus rationalize both the decrease in fertility and the U-shaped pattern of the mean age at motherhood. That rationalization of the non-monotonic relation between development and birth timing is achieved by means of regime shifts as the economy develops, without having to rely on exogenous shocks. Besides this analytical finding, we also explore the capacity of our model to replicate numerically the dynamics of the quantum and the tempo of births. Using data for 28 countries from the Human Fertility Database (cohorts 1906–1975), we show that our model can, with some degree of approximation, fit the patterns of the TFR and the MAM.

Our paper is related to several branches of the literature. First of all, it complements microeconomic studies of birth timing, such as Happel et al. (1984), Cigno and Ermisch (1989) and Gustafsson (2001), which examine birth timing decisions in a static setting, whereas we propose to draw the corollaries of those decisions for long-run dynamics. Second, we also complement the literature focusing on the relation between birth timing and long-run development. In a pioneer paper, Iyigun (2000) showed, by means of a 3-period OLG model with two fertility periods, that human capital accumulation leads to the postponement of births. While Iyigun's paper rationalizes the increasing part of the U-shaped curve for the MAM, our paper provides a rationalization for the entire U-shaped curve, including its decreasing segment.⁷ Our paper complements also other papers, such as, in continuous time, D'Albis et al. (2010), and, in discrete time, Momota and Horii (2013) and Pestieau and Ponthiere, 2014, Pestieau and Ponthiere, 2015. Those papers examined the relation between, on the one hand, physical capital accumulation, and, on the other hand, the quantum and tempo of births.⁸ Whereas those papers paid attention to the existence and stability of a stationary equilibrium under several fertility periods, our paper adopts, on the contrary, a Unified Growth Theory approach, where regime shifts are used to rationalize the non-monotonic pattern exhibited by the tempo of births.

The rest of the paper is organized as follows. Section 2 has a closer look at the data, and examines the statistical significance and the robustness of the stylized facts concerning the quantum and the tempo of births, as well as the relation between fertility behavior and education. The model is presented in Section 3. Section 4 characterizes the temporary equilibrium, and examines the distinct regimes. Long-run dynamics is studied in Section 5. An analytical example is developed in Section 6. Section 7 illustrates our findings numerically, by focusing on cohorts of the Human Fertility Database. Section 8 concludes.