First published on Mar 13, 2024
The fundamental phenomenon that requires elucidation is the substantial and widespread reduction in fertility rates that has occurred throughout the course of the demographic transition. Prior to the onset of the industrial revolution, and even at its earliest stages, large families were a common occurrence; indeed, both sets of my own grandparents had the privilege of growing up alongside ten siblings. At a certain point, as if by some inexplicable transformation, a decline in fertility rates began to emerge, manifesting itself across every regions and every nation, concomitant with a significant rise in economic prosperity. As economic growth accelerated, fertility exhibited a downward trend. Around the beginning of the twentieth century, fertility commenced a precipitous decline, with the majority of countries experiencing rates well below four children per woman before the outbreak of the First World War. Following a brief recovery during the post-war baby boom, fertility rates once again declined, eventually stabilizing at a level between 1.4 and 2.1 in the latter part of the twentieth century. In the present day, we find ourselves in a situation where more affluent and highly educated parents from the upper-middle and upper classes are opting to have fewer children compared to their less prosperous working-class counterparts, but this is entirely perplexing -- at least to me. If I were richer, I'd surely enjoy more children. Indeed, some research aims at figuring this out, and it does appear that fertility tends to rise when there is an exogenous increase in men’s income.
This is a problem, for a lot of reasons. One major, very tangible, reason is that this implies the population is aging: more retired people, so more people who need hospice, with fewer young people to work and provide. But another even more major reason is that humanity could truly go extinct if we keep reproducing below the replacement rate -- although it'd take a while.
Yes, I did say we could go extinct. To illustrate, here's a toy model. Imagine a very simple society.
Given these conditions, the transition from one generation to the next for the population of religious and secular individuals can be described by a matrix multiplication. If we define the state vector as $\mathbf{v} = [r, s]^T$, where $r$ and $s$ represent the number of religious and secular individuals, respectively, then the transition matrix $\mathbf{M}$ can be formulated based on the provided reproductive and transmission rates.
The elements of the transition matrix can be defined as follows, based on the given probabilities and fertility rates:
Therefore, the transition matrix is:
$$ \mathbf{M} = \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} 1.5 \times 0.6 & 1.5 \times 0.4 \\ 0 & 0.5 \end{pmatrix} = \begin{pmatrix} 0.9 & 0.6 \\ 0 & 0.5 \end{pmatrix} $$
The largest eigenvalue of this matrix, $\lambda$, is indicative of the long-term growth rate of the population:
$$ \lambda = \frac{(a+d) + \sqrt{(a+d)^2 - 4(ad - bc)}}{2} $$
In particular, if $\lambda > 1$, the population grows; if it is equal to $1$, it'll be stable; otherwise, it'll shrink.
In this particular case, it looks like $\lambda \approx 0.9$, and thus the population shrinks, even if religious women are much more strongly suited towards having many children. Notably, even if $c \neq 0$, but still small (as intuitively I expect it to be), we'll see shrinking, and we'll die. That is to say, even if fertility is HIGHLY HERITABLE, and we have a select bunch of people reproducing at magnificent rates (3 >> 1), we'll still see shrinkage.
One idea, introduced by Becker in 1960, is to consider children as goods, where quantity and quality (investment) matter. In this case, a wealthier parent, for instance, might spend more on their childrens wardrobe (investment), and if such demand for quality is elastic with respect to income, then you might well see the number of children decline. In the United States, in particular, a trend towards investing in education emerged and coincided with a decline in fertility, supporting the idea of a quantity-quality tradeoff. A trivial model can be generated by, say, considering a log-utility function, attaching some weights, and solving for the parents optimal fertility and education. In such a model, as children are normal goods, an exogenous increase in wealth increases fertility (as intuition suggests, this is the income effect); however, children are costly in terms of time, so that an increase in the wage makes children more costly relative to consumption, and an increase in the wage makes child quality cheaper relative to child quantity, and in combination, these two effects lead to a decline in fertility in wage.
In the United States, a model that provides financial incentives for having children might seem appealing to some, given the widespread concerns about the costs of college, rent, healthcare, and other expenses. Many people wonder how they can afford to have children at all, let alone provide them with a high quality of life. However, the argument that financial assistance alone can solve the problem of low fertility rates is overly simplistic. Hungary, for example, spent 5% of its GDP on family support programs, yet failed to significantly boost fertility rates. Similarly, Spain has implemented various government programs to encourage childbearing, but these efforts have been largely ineffective. Other affluent countries face the same fertility challenges, and financial assistance does not appear to be making a substantial difference.
Some conservative commentators argue that the decline in fertility rates can be attributed to societal changes brought about by second-wave feminism, such as the introduction of no-fault divorce, the normalization of sexual relations outside of marriage, and the erosion of marriage as the primary framework for family structure. This viewpoint is even shared by some self-identified feminist authors, like Louise Perry in her book "The Case Against the Sexual Revolution."
However, this, too, falls short when considering countries like South Korea and Japan, which lag behind in terms of gender equality but still experience extremely low fertility rates. Conversely, Scandinavian nations, known for their progress in promoting egalitarian gender norms, also face low fertility rates, although not to the same extent as Japan and South Korea. While the widespread availability of contraceptives has likely had some impact on fertility rates, it is clear that the issue is more complex than any single factor can explain. In fact, that's precisely why the problem is so interesting!
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