Endogenous Growth, Population Dynamics, and Economic Structure: Long-Run Macroeconomics When Demography Matters

Abstract

Even long-run macroeconomic growth models that allow for endogenous growth rely on simplistic assumptions regarding demographic regimes. This paper develops a model with more realistic variation in such regimes, including both excessively high and excessively low levels of average fertility. Variations in the structure of the market economy shape these population dynamics, and these trends in turn affect macroeconomic outcomes. Like early overlapping generations models of the type proposed by Paul A. Samuelson, our approach points to market failures and the importance of social institutions and nonmarket relationships that influence transfers between the old and the young, and the costs of childbearing. It also highlights current demographic imbalances at the country level and points to the need to develop open-economy extensions of this model that can capture the effects of population redistribution through immigration.

HIGHLIGHTS

• Demographic trends affect macroeconomic outcomes, and vice versa.

• These dynamics challenge the assumption that individual decisions generate sustainable outcomes.

• In the long run, below-replacement fertility can have serious economic consequences.

• The macroeconomic model outlined here suggests that costs of caring for dependents should be more equitably shared.

KEYWORDS:

• Macroeconomics
• endogenous growth
• returns to scale
• demography
• population growth
• social reproduction

JEL Codes:

• E1
• J10
• H3

INTRODUCTION

Population growth is a prominent feature of long-run economic growth models but is seldom integrated in a convincing way. Changes in the size of the labor force are typically treated as exogenous or, as a result of an assumption of constant returns, inconsequential. In this paper, we outline an endogenous growth model in which demographics matter. Because this model allows for endogenous fertility and variations in economic structure, it links macroeconomic dynamics with changes in the level and the distribution of the costs of reproduction (defined broadly as the cost of producing and maintaining human capabilities; Walters 1995; Folbre and Heintz 2017). It sets the stage for an approach to reproductive decision making that goes beyond individual utility maximization and builds on early overlapping generations models (Samuelson 1958; Cigno 1993) by emphasizing the effect of nonmarket institutions shaped by the relative bargaining power of groups based on gender, age, citizenship, and other dimensions of collective identity.

Economies feature distinct demographic patterns. At the global level, we see some economies struggling with the potential problem of a “surplus” population, while others fear the possibility of their populations shrinking. In North America, Western Europe, and some parts of Asia, many higher-income countries are faced with the prospect of below-replacement fertility and aging populations. This raises concerns about the future of their cultures and the trajectories of their economies. In contrast, other countries, particularly lower-income countries in Sub-Saharan Africa and South Asia, have high fertility rates and large youth populations, with fewer working-age adults per child to generate income and perform unpaid care work. This limits the resources available to invest in the next generation.

The model presented here encompasses both demographic regimes. Unlike most growth models with endogenous fertility, negative population growth is a possible long-run outcome. Economies may gravitate toward a situation of below-replacement fertility and stagnant growth of per capita income. But other dynamics are possible. Economies with different productive characteristics, as reflected in variations in the returns to factors of production, may have high, positive fertility rates, but potentially unstable population dynamics that have negative consequences for per capita market incomes.

ENDOGENOUS GROWTH AND POPULATION DYNAMICS

Most models in the original Robert M. Solow (1956) tradition assume constant returns to scale and exogenous population growth rates. Within these models, constant returns to scale preclude population dynamics from affecting per capita market output, even when population growth changes. Shifts in population dynamics, which correspond in these models to changes in the employed paid labor force, affect aggregate output but not per capita income. By contrast, endogenous growth theory allows for a different relationship between an economy’s population dynamics and per capita market income, adopting an assumption of increasing returns that alters the relationship between demographics and macroeconomic outcomes.

For instance, in Paul M. Romer’s (1990) theory of endogenous technological change, the non-rival nature of knowledge and ideas introduces economies of scale, yielding a result in which growth rate of market output per worker varies with the population (Jones 1999). An increase in the absolute size of the population raises the per capita growth rate. This connection between the size of the population and the growth rate of per capita income raises questions. Why would countries with large populations necessarily grow more rapidly? Other endogenous growth models yield different relationships between population dynamics and per capita outcomes. Charles I. Jones (1995) proposes a model in which changes in the size of the population affect the level of market income per capita, but not its growth rate. Logically, this implies that the growth of per capita income is positively correlated with the population growth rate.

Endogenous growth models create scope for demographics to affect per capita macroeconomic outcomes. However, many of these models still treat fertility and population dynamics as exogenous. Demographic changes occur outside of and are independent of the machinations of the growth process.

Some growth models do endogenize population dynamics. Robert J. Barro and Gary S. Becker (1989) represent an early, and influential, effort to include fertility decisions in a neoclassical growth model across an infinite time horizon. Oded Galor and David N. Weil (1996) offer an alternative growth model with endogenous fertility, one based on overlapping generations instead of dynastic utility maximization. In both models, fertility choices are the result of maximizing a unitary utility function. Other growth models incorporate bargaining dynamics into their models (Doepke and Tertilt 2016; Agénor 2017). In these approaches, women’s bargaining power is either exogenously given or related to the returns to their productive attributes in the paid labor market. Instead of a unitary utility function, women and men have different exogenous preferences and the models assume that women innately care more for their children than do men.¹

Yet these models also fall short for a number of reasons. They foreclose the possibility of below-replacement fertility and negative population growth. They assume that households are identical and representative, and that all women participate in childbearing and have the same fertility rate. The models also assume that, if households have children, the minimum number of children is equal to the number of adults. For instance, in models with two-adult households, this implies that if households have children, they have at least two (in some models, individuals replicate themselves so that each individual has at least one child). This, combined with the assumption that households are identical, sets a lower bound of zero on population growth.

Furthermore, in their emphasis on individual utility optimization, many of these models ignore the possibility that individuals may engage in collective action with others to establish social institutions and public policies that affect intergenerational and inter-gender transfers of time and money. Paul A. Samuelson (1958) explicitly emphasized the importance of what he variously termed social collusion, social coercion, and social contracts. Alessandro Cigno (1993) has observed that intra-family contracts for intergenerational transfers are easily disrupted by the development of markets for capital and labor.

This paper presents a model that combines elements of endogenous growth theory with endogenous fertility choice and population dynamics. Variations in the structure of the market economy are represented as differences in returns to the human inputs into market production: decreasing, constant, or increasing. Depending on these structural characteristics, the model generates distinct outcomes. It allows for below-replacement fertility and negative population growth as a possible equilibrium. It also can produce outcomes with high fertility in an unstable equilibrium, allowing for a high fertility “trap” with low, and declining, per capita incomes. While the micro-foundations are not developed here, these outcomes strengthen the argument that individual optimization of fertility decisions is unlikely to invariably generate a stable long-run equilibrium growth path with constantly rising per capita market incomes.

Duncan K. Foley (2000) explores similar themes and the connections between demographics and economic structure, captured by increasing or decreasing returns to labor. Foley describes two stable equilibriums at the global level – a low-income “Malthusian” outcome and a high-income “Smithian” alternative – in which the level of the population is stable (that is, fertility rates remain at replacement). In Foley’s framework, fertility responds negatively to increases in per capita market income, and technology is subject to exogenous shocks. Economic structure is endogenous and is simply a function of the size of the global population – a larger population allows for greater specialization, up to a point. The model presented here takes a different approach, allowing for endogenous technology and fertility, but taking the economic structures of particular economies as exogenous. In our model, unlike Foley’s, the long-run equilibrium is not self-correcting with a return to replacement fertility and a tendency toward below-replacement fertility is possible.

THE MODEL

This growth model loosely adapts an approach sketched out by Jones (1999) that focuses on population dynamics within an endogenous growth framework. We introduce endogenous fertility into this framework. Therefore, in the model presented here, there are two endogenously produced factors of production: human beings (labor) and knowledge that reflects technical know-how.

Assume that the production of market goods and services is described by the following relationship: (1) $Y=(\lambda AhL{)}^{\sigma }$(1) Y is aggregate output, L represents the potential labor force (working-age population), λ is the fraction of the potential labor force engaged in paid employment, h is the average cumulative investment in human capacities per working-age adult, and A reflects the current state of knowledge that can enhance the productivity of labor.² No restrictions are placed on the variable σ except that it must be greater than zero. This allows the model to explore increasing, decreasing, or constant returns to the human inputs in market production: labor augmented by human capacities and technology. Equation 1 only reflects aggregate market income. For the purposes of this model, all nonmarket production is assumed to be dedicated to care work that produces new human beings. Adding nonmarket production that supplements market income and household consumption is certainly possible, but it would not change the core dynamics of the model. Although nonmarket production that supplements household consumption has been excluded for the purposes of exposition, market income per capita should not be considered an accurate indicator of averagewelfare.

Average participation in market work, λ, responds to the returns to labor, which are assumed to be proportional to market income per working-age adult.³ (2) $\lambda =a{\left(\frac{Y}{L}\right)}^v{\lambda }_0$(2) The variable v indicates the responsiveness of participation in market work to market income, and a is a scaling parameter. Participation rates vary widely across countries at the same level of average market income due to structural factors, such as gender roles, norms, and the household division of labor. The variable λ₀ captures these factors. If participation in paid work is unresponsive to market income, that is, a = 1 and v = 0, labor force participation is constant and determined entirely by social structures and institutions.

The relationship between the working-age population and the total population is given by: (3) $L=wN$(3) N represents the total population, and w is the working-age population as a share of the total.

We define human capacities along the same lines as Elissa Braunstein, Irene van Staveren, and Daniele Tavani (2011). These refer to individual attributes that improve productive contributions. Human capacities are not innate but must be built in the course of a person’s life. They include formal education and training, that is, the traditional categories of human capital, but also emotional maturity, leadership, the ability to work collaboratively, cultivated creativity, good health, and other similar attributes.

In standard growth models, A typically represents the current state of technology – that is, the output of concerted efforts at research and development. Here the variable is interpreted more broadly as the stock of knowledge that can be used to boost productivity. This includes new inventions and product innovations. But it could also include better ways of organizing production, improved management techniques, and knowledge generated by a process of learning-by-doing.

The generation of new productive know-how depends on the average cumulative investments made in human capacities and is given by the following differential equation: (4) $\dot{A}=\delta h{A}^{\phi }$(4) In Equation 4, δ is assumed to be greater than zero and 0 < φ < 1. Because of the restrictions placed on φ, knowledge is accumulated over time, but at a decreasing rate (that is, as the stock of knowledge expands, it becomes increasingly difficult to come up with something innovative). This assumption follows Jones (1999).⁴

One feature of Equations 1 and 4 is that the generation of productivity-enhancing know-how has broad-based impacts. As discussed by Romer (1990), knowledge is a non-rival good, and excludability, that is, designing an enforceable set of property rights, can be difficult and costly. In these respects, knowledge shares many of the characteristics of a public good. In this model, the benefits of knowledge production spill over across individual firms and producers. They have macroeconomic impacts and, because of the existence of non-rivalness and positive externalities, an argument can be made for public investment in human capacities that fuel on-going innovations in the way we do things.

The population growth rate is also assumed to be endogenous and represented by the following differential equation. (5) $\dot{N}=\mu {\left(s\frac{Y}{L}\right)}^{-\tau }N-mN$(5) Equation 5 has two components – a birth rate term reflecting gross additions to the population due to fertility decisions (the first term on the righthand side) and losses to the population due to mortality. Total deaths (mN) are assumed to be a constant share (m) of the population. Equation 5 assumes that population growth responds inversely to the expected net cost of children to women. Women are assumed to make fertility decisions based on preferences, norms, and the expected net costs of raising children. The expected costs of children are influenced by bargaining dynamics within the household, the number of working-age adults present (for example, two-parent versus single parent households), economies of scale associated with household formation, and women’s degree of specialization in unpaid care. Children also may provide benefits to women and the households in which they live (for example, adult children may transfer income to support aging parents). Therefore, we assume that fertility rates respond to the net costs of children, taking into account these benefits. Other institutional factors, such as the enjoyment of reproductive rights and the availability of contraception, influence women’s ability to exercise agency with regard to fertility decisions.

One component of the cost of children is the opportunity cost of investing in children – that is, the foregone market expenditures that could have been enjoyed if time and money were not spent on raising children. Therefore, the cost of children is assumed to rise with market income per working adult (Y/L). The parameter τ captures the responsiveness of changes in population to this opportunity cost. The variable s in Equation 5 is a scale parameter that captures the size of these opportunity costs for women. For example, a gender wage gap would reduce women’s earnings relative to men’s and lower their opportunity cost of women specializing (at least in part) in nonmarket care work. This would be captured in a lower value for s. If labor market segregation declined and new opportunities for paid employment opened up to women, the value of s would rise. Changing norms in which men shouldered a larger share of the responsibility for raising children could be reflected in a lower value for s.

Different societies exhibit distinct norms that influence gender roles and the expression of preferences. For instance, pro-natalist norms, which place greater value on childbearing and women’s role as mothers, may be associated with higher fertility rates even when the expected net cost of children to women does not vary. The parameter μ in Equation 5 captures the effects of these norms on fertility rates and population growth.

To focus on the dynamics of the simple model, Equation 5 assumes a closed economy with no net migration (we discuss the issue of migration later). Mortality rates also typically change in the course of economic development, leading to an increase in life expectancy that affects the size of the total population. Falling mortality rates and increasing life expectancy would be associated with an aging population, with the share of the population in higher-age cohorts growing over time.⁵ The model does not consider these changes in mortality rates or life expectancy in order to emphasize its core results. When the population growth rate changes over time, the share of the working-age population, w, will also change. However, we are initially focused on determining a steady state growth rate, when the rate of population growth is constant. With a constant population growth rate, we assume a constant w. Shifts in w would affect the rate of adjustment toward a steady-state population growth rate, an issue discussedlater.

Transfers of both time and money affect the costs of children. If relatives take care of children after school, this represents a transfer of time that has real value and can reduce the individual cost of children. Similarly, public services (such as childcare services) or family support grants also represent transfers that affect the private, individual cost of children. In some cases, the existence of such transfers could be modeled as a reduction in the size of s. But the impact of transfers could be more far-reaching with respect to the simple formulation presented here. A system of transfers of time, money, and services may alter the relationship presented in Equation 5. To the extent that the opportunity cost of children is delinked from personal, private income, Equation 5 would have to be modified. For example, the cost of raising children could be socialized in such a way that increases in per capita income might actually encourage higher fertility. We discuss alternative approaches later, but for the present analysis the costs of children are assumed to rise with average marketincome.

In order to focus on population dynamics within an endogenous growth model, we assume that h, the average cumulative investment in human capacities, is determined exogenously. To the extent that h is primarily determined by policy choices, this assumption is warranted. However, many aspects of human capacities would be determined by factors similar to those that influence fertility choices. In addition, household expenditures on education, care services, and health are important inputs into developing human capacities. Nevertheless, to keep the focus on the relationships of primary interest in this particular exercise, we make the simplifying assumption that h is exogenous (and can be used to illustrate policy choices around investment in human capacities). If we treat the average (that is, per capita) investment in human capacities as exogenous, this implies that the share of market income that is dedicated to maintaining human capabilities will change with the dynamics of the model. This occurs because the growth rates of aggregate market output and population areendogenous.

THE DYNAMICS OF THE MODEL

From Equation 4, it is straight-forward to derive an expression for the growth rate of productivity-enhancing knowledge, g_A (6) $g_A=\frac{\delta h}{A^{1-\phi }}$(6) and of the steady-state, where the growth rate of knowledge production is constant and has no tendency to accelerate or decelerate: (7) $g_A^{\ast }=\frac{g_h}{1-\phi }$(7) We define g_y to be the growth rate of market income per working-age adult (Y/L). As discussed earlier, in the steady state, we assume that the working-age population grows, in the long-run, at the same rate as the total population.⁶ Furthermore, as a first step, we take the population growth rate, n, to be constant – but we relax this assumption shortly. Equations 1, 2, and 7 give us an expression for g_y when knowledge production is in a steady-state: (8) $g_y^{\ast }=\frac{\sigma g_h\left(2-\phi \right)+\left(\sigma -1\right)\left(1-\phi \right)n}{\left(1-\phi \right)\left(1-v\sigma \right)}$(8) The expression in Equation 8 presents a relationship between the steady-state growth rate of income per working-age adult and the population growth rate. Here the returns to the human factors of production in market production come into play. If there are decreasing returns, 0< σ < 1, then there is a negative relationship between the population growth rate and the growth rate of average market income. If there are constant returns, σ = 1, the population growth rate has no impact on the growth rate of average income. Finally, if there are increasing returns, σ > 1, then there is a positive relationship between the population growth rate and the growth rate in average market income.

For the purposes of this model, the determination of the returns to human inputs happens at the aggregate level, consistent with the idea of external economies first proposed by Allyn A. Young (1928). As economies grow and diversify, producers become increasingly specialized in ways that generate broad productivity benefits through spill-over and clustering effects. Therefore, we would expect more developed, diverse economies to exhibit increasing returns. Note that increasing returns can exist at the aggregate level, even if individual firms experience constant returns to scale (Romer 1986). This occurs because of the existence of positive externalities that benefit industries or clusters of firms. In contrast, economies that are not diversified and depend to a large extent on fixed resources for production (for example, land) are more likely to be characterized by decreasing returns. Within this model, these two types of economies – increasing returns and decreasing returns – exhibit dramatically different population dynamics.

Equation 8 showed the relationship between the steady-state growth rate of income per working-age adult and the population growth rate when the population growth rate was taken to be exogenous. But, in this model, the population growth rate is endogenous, as presented in Equation 5. Dividing both sides of Equation 4 by the size of the population, N, give us: (9) $\frac{\dot{N}}{N}=n=\mu {\left(s\frac{Y}{L}\right)}^{-\tau }-m$(9) Equation 9 tells us that the population growth rate is the difference between the birth rate minus a constant mortality rate, the rate of deaths in the population. Since the mortality rate is constant, the population growth rate will also be constant (that is, in a steady-state) when the birth rate (that is, the gross additions to the population relative to the size of the population) does not change.

From average market incomes implied from Equation 1, average participation in paid employment from Equation 2 and the gross additions to the population expression from Equation 9, and we derive an expression for steady-state population growth rate, this time taking g_A to be exogenous: (10) $n^{\ast }=\frac{\sigma }{\left(1-\sigma \right)}{g}_A+\frac{\sigma }{\left(1-\sigma \right)}{g}_h$(10) Equations 7 and 10 give us expressions for the steady-state growth rate of the two produced factors of production: productivity-enhancing knowledge and people. When these expressions hold simultaneously, we have a description of the growth path of this model economy: (11) $n^{\ast }=\frac{\sigma \left(2-\phi \right)}{\left(1-\sigma \right)\left(1-\phi \right)}{g}_h$(11) As Equation 11 indicates, the nature of this steady-state, however, depends on σ which determines whether the economy is exhibiting increasing, decreasing, or constant returns to human factors of production.

THE STEADY STATE

The case of increasing returns

If there are increasing returns, σ > 1, and the coefficient on the g_A term in Equation 8 is negative. The intercept with the horizontal axis, that is, when g_A = 0, is also negative. Figure 1 shows a graph of Equations 7 and 10 when there are increasing returns to human factors of production. The horizontal line, g*_A, is given by Equation 6 and the downward sloping line, n*, is given by Equation 9. The steady-state for this model is shown by the intersection of the two lines, at point S. Note that this model predicts a negative population growth rate in the steady-state – that is, an economy that exhibits increasing returns will gravitate toward a situation of below-replacement fertility (this steady state solution is also captured in Equation 11).

Figure 1 Steady state equilibrium, increasing returns case

Using Equations 1, 7, and 10, with a bit of manipulation, we can show that the steady state equilibrium would be one in which average growth of market income were zero. This occurs because an exogenous increase in market income would raise the cost of children, all other things being equal, and slow the population growth rate. In an increasing returns economy, a lower population growth rate reduces the growth rate of average market incomes.

An examination of the dynamics of g_A and n when they take on values other than their steady-state values shows that the steady state with below-replacement fertility is a stable equilibrium (see phase diagram in Figure 1). What this suggests is that in increasing returns economies, positive population growth rates will initially be associated with positive growth rates in market income per working-age adult (see Equation 8 for the intuition). However, as average market incomes increase, so do the cost of children, putting downward pressure on the population growth rate until it eventually turns negative. This movement toward the steady-state may be extremely slow – it could take generations – so Figure 1 may be better interpreted as illustrating a tendency toward a steady-state, rather than a rapidly established equilibrium.

As noted previously, changes in population growth due to shifts in fertility rates can affect the working age population’s share of the total population. This could have implications for the adjustment to long-run equilibrium in the model. Figure 2 plots the fertility rate against the working-age share of the population in 2018 for 193 countries. When the fertility rate is above replacement (that is, a value greater than 2), falling fertility is associated with a larger working-age share. For fertility rates below replacement, the relationship is ambiguous and depends on other demographic dynamics, such as mortality rates, not modeled in this analysis. This would suggest that when population growth rates are declining and approaching zero, the reduction in the growth rate of the working-age population would be less than the decrease in the growth rate of the population as a whole, thereby affecting the speed of adjustment toward the long-run equilibrium. Specifically, for increasing-returns economies, a more rapid increase in the working-age population would raise average market incomes, relative to the case of a constant working-age share of the population, and cause fertility to fall more rapidly (for example, this could be interpreted as a version of a “demographic dividend”).

Figure 2 Fertility rates and working-age population as share of total population, 2018Source: World Development Indicators Database, World Bank, Washington, DC.

In this simple presentation, we assume that the average cumulative investment in human capacities, h, is exogenously determined. What would happen if the growth rate of h were increased? A positive growth rate for h would mean that the human capacities of children would be greater, on average, than those of their parents. The higher the growth rate of h, the bigger this difference would be. Following an increase in g_h, we would expect an increase in per capita market incomes in the short-run as the growth rate in average market incomes initially rises. However, this has a feedback effect on fertility rates and would lower the population growth rate. Lower population growth rates subsequently slow average income growth. The steady-state population growth rate would become increasingly negative as h increases (see Figure 3 in which the dotted lines correspond to the steady state values of g_A and n when the growth rate of h increases).

Figure 3 Steady state equilibrium, increasing returns with shift in g_h

The case of decreasing returns

The case of a decreasing returns economy, 0 < σ < 1, looks quite different from the case of increasing returns (Figure 4). Now the n* line, illustrating the combinations of g_A and n for which there is no tendency for n to change, is upward sloping. The steady state occurs when the population growth rate is positive. With decreasing returns, a positive population growth rate puts downward pressure on average market incomes. To some extent ongoing investments in human capacities, if they are forthcoming, can counteract the effect of high population growth.

Figure 4 Steady state equilibrium, decreasing returns case

The difficulty with the model’s steady state under decreasing returns is that the steady state is no longer stable. If the population growth rate exceeds the steady state equilibrium, this places downward pressure on average market incomes (similar to a Malthusian argument) and encourages higher, not lower, fertility rates. There is no automatic equilibrating mechanism and decreasing returns economies could face a high fertility “trap.” Under these conditions, an external intervention is needed to address high and increasing fertility rates. For instance, an exogenous increase in investments in human capacities (a “big push”) could shift the economy toward the steady-state path.

Structural change

This simple model assumes that a country falls into one of three categories: increasing returns, decreasing returns, or constant returns. However, the process of economic development has been described (along the lines of Kuznets [2013] and Kaldor [2007]) as one of structural change – in which economies diversify and begin to exhibit increasing returns. In the simple model presented here, this would manifest itself as an increase in the value of σ and it would alter the nature of the n* curve. When 0 < σ < 1, the steady-state n* curve would be upward sloping as in Figure 4. As σ increases, the slope of the n* curve would flatten until it began to slope downward, as in Figure 1. As the curve flattens, we would expect that, at some point, there would be downward pressure on the population growth rate. That downward pressure would continue as the economy began to exhibit increasing returns. As the process of structural change continues, the economy would eventually move toward below-replacementfertility.

BELOW-REPLACEMENT FERTILITY

This model shows that, when the expected net cost of children rises with per capita income and when increasing returns to scale are present, an economy moves toward negative population growth (that is, below-replacement fertility) and low (or zero) growth in average market incomes. Again – we acknowledge that average market incomes are not an adequate indicator of welfare. The distinction between levels and growth rates is important here. Although per capita incomes may stagnate (that is, have a low growth rate), the level of per capita income in diversified economies exhibiting increasing returns to human factors of production can still be quite high. Market income per capita will be higher still when participation in market production is responsive to changes in average income (see Equations 2 and 8). This would occur, for example, when fertility falls due to the rising cost of children causing a larger share of women to enter the paid labor force.

However, below-replacement fertility generates potential problems not captured in this model. For instance, economies that currently have below-replacement fertility rates also have aging populations. This can create growing demand for care services, higher health expenditures, and pressures on public pension systems – all of which have macroeconomic consequences. A population that is slowly dwindling may generate other social concerns beyond a simple consideration of the average size of market incomes.

What can be done? One possibility is to reduce the expected burden to women of raising children. This could be achieved, for instance, by reducing the size of s in Equation 5 through various policy measures (that is, partially subsidizing the cost of childcare or better enforcement of male child support responsibilities). This would generate an increase in the population growth rate in the short-run. But as long as the cost of children is proportional to private market incomes (that is, the opportunity costs of having children is reflected in a reduction in the discretionary use of that income for other purposes) downward pressures on population growth rates will continue in the long-run. An alternative would be to transform the relationship in Equation 5. For instance, taxes could be collected from the entire working age population (parents and non-parents) in order to finance family support policies for caregivers with children. This would significantly weaken the link between the cost of children and private market incomes in ways that would change the population dynamics of the model. Rather than socializing the costs of children, another possibility would be to adopt extreme patriarchal institutions in which women have no access to paid employment and no economic alternatives outside of specializing in unpaid work. This arrangement would also sever the relationship between fertility decisions and opportunities in the market economy.

There is another way to delink population dynamics from the costs of children and market incomes. Countries with below-replacement fertility could import adults from other countries. Since the costs of raising immigrants from infants to adults would have been incurred in another country, there is no direct connection between the domestic cost of raising children and increases in the population associated with immigration. Indeed, higher levels of market income per working age adult could attract immigrants to countries with below-replacement fertility, depending on the costs of such immigration. Although this offers one solution to the challenge of below-replacement fertility, it is important to acknowledge that the receiving country benefits from this inflow of people while parents in the sending country bear the costs. To some extent international transfers (remittances) may offset these costs. Nevertheless, allowing for the international movement of people complicates the distribution of the costs of social reproduction.

CONCLUSIONS AND WAY FORWARD

Long ago, Paul A. Samuelson expressed concern that individual optimization in the absence of social contracts could lead to unfortunate demographic and therefore, unfortunate economic outcomes (1958, 1975). Our very different model leads to similar conclusions driven partly by macroeconomic dynamics. Structural features of the market economy, captured by variations in returns to human factors of production, can affect population dynamics and macroeconomic outcomes in a framework that includes endogenous fertility choices. Demographic trends affect macroeconomic outcomes.

Standard microeconomic foundations take the household as the unit of analysis, assuming that married couples are the primary decisionmakers. However, the process of economic development is often associated with significant changes in household structure, including less intergenerational co-residence, fewer stable marital unions, and increases in the percentage of families supported by mothers alone. As a result, households become increasingly heterogeneous both within between countries. Furthermore, improvements in women’s access to independent market income tend to amplify their influence on household decision making.

Macroeconomic dynamics, as well as individual decisions and social institutions, contribute to significant differences in population dynamics, with some countries experiencing below-replacement fertility and aging populations and others experiencing high fertility and a youth bulge. Our model suggests the need for public policies to move away from the current regime of social reproduction, in which women bear most of the private costs of raising the next generation and caring for the elderly, to one in which the costs of caring for dependents are more equitably shared and more generously socialized. It also highlights current demographic imbalances at the country level and points to the need to develop open-economy extensions of this model that can capture the effects of population redistribution through immigration.

The two equilibriums examined in this paper are unsettling with regard to the implications for long-run macroeconomic stability. Below-replacement fertility cannot continue indefinitely in a closed economy because populations would eventually approach zero. The high fertility, low per capita trap can only be escaped through greater investment in human capacities and structural change. Unlike the “Malthusian” and “Smithian” scenarios proposed by Foley (2000), the market economy has no self-correcting mechanism to keep fertility rates precisely at replacement levels. A range of social and institutional factors lying outside of, but interacting with, the market economy influence fertility decisions and investments in human beings. This model suggests that shifting the economy onto a more stable and sustainable path requires changes to these non-marketprocesses.

Adopting a global perspective raises issues beyond a consideration of immigration and the redistribution of populations. While some national economies may exhibit increasing returns, environmental constraints could limit the expansion of production at the global level. If the capacity of the global ecosystem to assimilate the byproducts of market production is limited (for example, the case of greenhouse gases), then increasing returns may not ultimately hold for the world economy. The possibility of decreasing returns at the global level as production expands introduces another coordination problem – the population dynamics that contribute to national-level macroeconomic performance may be harm the global economy as a whole. In an elaboration of the model, global environmental constraints could feed back into country-level population dynamics.

The simple macroeconomic model presented here could be extended in a number of other ways. It would relatively easy to include physical capital accumulation in the basic model – our expectation is that it would not meaningfully change the results. At present, the treatment of investments in human capacities is rudimentary and could be conceptualized more fully. A top priority for future research should be the development of a more explicit microeconomic foundation for demographic decisions that leaves room for individual optimization but also emphasizes the impact of social institutions and public policies on family care provision.

ACKNOWLEDGMENTS

We gratefully acknowledge comments and criticisms from members of the Gender and Macroeconomics working group and the support of the Hewlett Foundation. Special thanks to Robert Blecker and Tom Michl for their insights and feedback.

Additional information

Notes on contributors

James Heintz

James Heintz is Andrew Glyn Professor of Economics, University of Massachusetts Amherst and Political Economy Research Institute.

Nancy Folbre

Nancy Folbre is Professor Emerita of Economics, University of Massachusetts Amherst, Director of the Program on Gender and Care Work of the Political Economy Research Institute, and Senior Fellow of the Levy Economics Institute at Bard College in the United States.

Notes

1 In the model presented in Pierre-Richard Agénor (2017), women care more about investments in their children’s health outcomes relative to current consumption compared to men. Similarly, in their discussion of growth and household bargaining, Matthias Doepke and Michèle Tertilt (2016) assume that women care more about child welfare than men.

2 This is a long-run model and does not consider cyclical unemployment or short-term fluctuations of aggregate demand around the long-run trend. The model could accommodate long-run structural unemployment, but if structural unemployment is assumed to be a fixed share of the paid labor force based on exogenous institutional factors, it will not affect the dynamic analysis of this exercise.

3 The idea that wages, that is, returns to labor, are proportional to average labor productivity is consistent with structural macroeconomic models in which firms price products based on a fixed mark-up over unit labor costs.

4  Variations on the specification of the technology/know-how production function are evident in the literature on growth models with endogenous technological change. The specification used in this model assumes that technological progress slows with higher values of A (that is, there is decreasing marginal productivity). Other approaches assume that past discoveries contribute to accelerating technological change, that is, φ > 1 or that marginal productivity increases along with A.

5 Changes in the age composition of the population may have further macroeconomic implications that are not explored in this model but discussed later.

6 As mentioned earlier, this is equivalent to assuming that the working-age population’s share of the total population is constant in long-run equilibrium.