This is the first post of a series of reflective essays on fertility choice/human investment models in economics. My goal for this semester is to present a model of parental investment in children under birth planning policies, hopefully with empirically testable hypotheses.
I look at how parents invest in children given multiple constraints. In addition to the usual budget constraint, parents are limited to two children and have to pay a fine if they decide to have a second child. The amount of the fine represents the difficulty of having a second child (i.e. the level of enforcement of One Child Policy). A zero fine suggests that it is legitimate to have a second child, while a fine going to infinity implies that having a second child is strictly prohibited. China’s OCP yields a perfect context to study how parents make fertility decisions and allocate their resources among their children given birth restrictions.
The classic Becker model (Becker 1994, Becker and Tomes 1986) makes two assumptions of parents’ fertility choices that I think are unrealistic. First, it assumes that parents put equal weight on children’s consumption (the only “utility” by the children in the unitary utility function). This is hardly realistic in developing countries where there is a strong preference for sons over daughters. Second, it assumes that “quality of children” can be purchased at a fixed price. This is key to the famous “quality-quantity tradeoff” result. What we observe more often is that parents need to devote time to their children and invest in their education and health in order to enhance the children’s abilities. Some question the unitary model assumption, but bargaining models are hard to estimate empirically. For the bargaining approach, see papers by Chiappori and Browning and the “separate spheres” paper by Shelly Lundberg and her coauthors.
A paragraph from Alderman and King (1998) elucidate the importance of preference:
There are issues not only of the efficiency of the investment, but also of the intra household allocation of the expected benefits. Preferences, then, matter for two distinct reasons. First, learning may contribute directly towards the welfare of the child and of parents, over and above its productive return as an investment. That is, learning may be a consumption good. Second, the decision-makers’ preference for equity among-est children influences how investments in education are allocated to children with different expected rates of return.
There are several ways to incorporate gender bias in the model. One can assume different marginal utility from sons’ and daughters’ consumption (or outcome variable, in general), or even put substitution/complementarity assumptions by restraining the second-order derivatives. A model with remittances can allow for different contribution rates from children to parents. Some papers also assume different labor market returns of parents’ investment by the gender of the child.
One piece of advice for graduate students who are trying to get identifiable information which requires IRB approval: don’t expect the data to arrive any time soon. Work on the theory first so that you will have something to present if your data request gets stuck in the administrative files.