JACOB FAJNOR – APRIL 18TH, 2018
Economic theory offers great insights into why fertility in recent history behaves contrary to common sense predictions. Yet, pinning down an exact model that universally predicts the childbearing behavior can be troublesome as childbearing behavior in the United States has not followed a consistent pattern in recent economic history.
The first question to tackle is how a population’s total fertility rate (number of children per woman) reacts to income. The behavior of total fertility rates (TFR) is dependent on whether households view children as normal or inferior goods. While this terminology may sound sadistic, understanding how fertility reacts to changes in income will allow us to make predictions about how fertility will behave in the future. In the United States, many two parent households enjoy raising children and therefore maximize the number of children they have. As incomes rise, we expect the average household to have additional children. However, this behavior is not consistent, as in some periods of economic boom, we can see that the TFR fell. For example, in the 1920’s the TFR fell by approximately 1.3 children per woman . This suggests that children may be inferior goods: as income rises, demand for children decreases. Yet, thirty years later in the Baby Boom, we see that fertility increased during a period of strong growth.
The reason that the demand for children is inconsistent is because children, in addition to their monetary costs, also come with an opportunity cost. If we assume that all of a family’s income is spent on either children (school books, baby food, clothes, etc.) or goods (a second car, a vacation home, etc.), then we can compute indifference curves to model how a family prefer combinations of good and children. For simplicity we will represent utility with a Cobb-Douglas function (U(x, y) = xay1-a) where “x” represents kids, “y” are goods, and a is a constant. To find each families’ optimum combination of children and goods, we can use the time-cost of children function. This function gives us a key insight into the inconsistent “pricing” behavior of children: X = wT + I – (p+wc)N. The function defines income as wages (w*T (time)) plus outside income (I) (capital gain from investments, a monetary gift, winning the lottery, etc.). minus the fixed costs of children (p) (school fees, toys, medical bills) plus the opportunity cost of raising your children (w*c) times the number of children (N) set equal to the amount we spend of goods (X). The function demonstrates that changes in outside income, and the fixed cost of children will have a direct and predictable effect on the number of children. Perhaps more importantly, this equation demonstrates that increases in wage income increase our willingness and ability to have children while also increasing the opportunity cost of raising children. The opportunity cost of raising your children is the reason fertility does not have a fixed relationship with economic well-being. As one’s income increases, the opportunity cost of spending time away from work to be with one’s kids grows larger and larger.
This answers why in the 1920’s, fertility decreased with an increase in economic prosperity: the opportunity cost presented by the wage rate doubling in the 1920’s made children more expensive, lowering the fertility rate. But how did good economic times bring about higher fertility as seen in the 1950’s? If the fixed cost of children (p) exceeds the opportunity cost (wc) then our demand for children behaves as if children are a normal good. As wages rise, the opportunity cost of raising children grows larger and larger making it more expensive to raise the same number of children as they would have with lower incomes. Therefore, the TFR will decrease as families substitute additional children with goods as their income increases in order to maximize their utility. One of the most effective strategies for raising total fertility rate of developed countries with low fertility rates, such as Japan, is the implementation of professional child care. Child care allows parents to work and raise children at the same time, so the opportunity cost of children is capped at the fees of the child care and does not rise or fall with your wage. The implementation of child care services in nations such as Japan could help raise the fertility rate back to the replacement rate (2 children per couple) if wages remain high in the future. This fertility rate will stabilize population growth which, in turn, can ease the implementation of social programs such as inter-generational wealth transfer programs.
The time-cost model does leave some unanswered questions. It mostly describes fertility rates at the microeconomic level, household to household, and becomes difficult to evaluate if we extrapolate its principles to entire populations. For instance, not all families optimize utility at the same fertility rates, because all goods do not have a fixed cost. The amount that a family wishes to “invest” in their children may also alter the predicted fertility rate. The choice to send a child to private school may lead to the family not having another child, changing predicted fertility rate. Finally, estimating the “fixed” cost of children is nearly impossible to do. However, the relationship presented between fertility and economic prosperity gives us new insights into explaining population trends over the course of history as well as predict demographic transitions in developing nations.
Featured Image Source: Parents magazine
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