Here comes the long-awaited discussion on the economic modeling of parental investment in children. It took us two classes to cover the classic quality-quantity tradeoff theory and its recent empirical tests.
Becker and Tomes (1976) model the parents’ utility as a function of the number of children, the quality of each child (assumed to be equal), and other goods produced in the family (“Z goods”). Costs of raising children is multiplicative in the quantity and quality of children because of “equal concern”. The resulting conditions indicate that shadow price of children is endogenous because the number of children is a choice variable. While this model provided a basic framework to think about fertility decisions, it has two important flaws. First, counter-factual questions are hard to make sense because “n” and “q” are jointly determined. Second, they assume costless transfers between children in terms of income and other outcomes to achieve equality. This assumption might be plausible for outcomes like welfare or happiness, which are difficult to take from one person to another. By contrast, Behrman, Pollak and Taubman (1982) addressed equal concern in aspects other than income. They incorporated endowment as complementary to education (i.e. parental investment) and argued that equal concern would not necessarily lead to equal investments.
For empirical results on the topic, Schultz (2001) provides a comprehensive account of the opportunity costs of having children. A clever strategy mentioned in the paper is to use labor market conditions that affect the career prospects of the male but not the female to identify the costs of having children. It is also important that opportunity cost may not be the whole story: the increasing bargaining power in the family might allow women to have their desired number of children, which could be fewer than what their husbands want.
Researchers have used data from developed and developing countries to test the quantity-quality tradeoff and differential investment by gender. In class we touched upon a few papers on “If parents’ income expands, how do they allocate the additional money towards investments in their children?” Paxson and Shady (2010) assessed the “intent to treat” effects of cash transfers on the health of children; De Brauw and Hodinott (2011) investigated whether taking away the school enrollment conditions hurt the effectiveness of the cash transfer program in Mexico. But it is important to bear in mind that the benefits and costs of enrollment are not examined in their paper. The goal of the policy is to increase enrollment.
I think there should be more research on fertility and child investment decisions in a dynamic framework. Parents might time their births to reap the most benefits from scale economies, and the gender of firstborn might affect subsequent childbearing decisions. There is a lot to be learned.