Science Magazine has published an interesting blurb about a Demography piece that claims that China's One Child Policy reduced this nation's total population by a billion people. How? The piece claims that by the year 2060 that there would have been an extra billion people in China in the absence of the policy! We all agree that it is crucial to measure the causal effects of this policy but how does one do this?
There is a fundamental missing data problem. For every woman in China during the years when the policy was in place, how many children would she have had in the absence of this constraint? If she would have had the same number of children then the policy wasn't binding!
By estimating a structural econometrics model, one can conduct such a policy counter-factual. Hilary Clinton only had one child. My wife only has one child. Some women choose to have only 1 child (even without a government restriction).
Facts:
1. women's wages rise with education and among the highly educated, people with STEM and quantitative degrees earn more
2. A child's quality is an increasing function of the time that parents spend with the child. This time effect is diluted if the parent has multiple children.
3. urbanites urban higher wages than rural people
4. Chinese apartments in cities are highly expensive and an extra bedroom is extremely costly.
These 4 facts yield several predictions;
For the most educated urban women in China, the government's policy is less likely to bind. For those who value child quality (having the next Einstein), the government's policy is less likely to bind. So, this policy was really binding for farmers. Middle class people who are urbanized are unlikely to be able to afford to have a second child. Why? The woman would sacrifice too much urban labor income and their rent for the two bedroom apartment would be too high.
As China's urbanization and educational attainment accelerated, the one child policy becomes less and less binding as more women aspire to be the Chinese version of Hilary Clinton.
A structural model would take a formal stand on a woman's utility function (defined over private consumption, quantity of children and quality of children) and would take an explicit stand on the production function of child quality as a function of market inputs and parental time. By living in a city, the same person has a higher wage (and thus a higher opportunity cost of having a child) and will face higher rents for an extra bedroom. The researcher would solve for the optimal fertility with and without the one child policy constraint. This constraint states that the family cannot have more than 1 child but if the optimal fertility is 1 child then the policy isn't binding.
My claim is that education and urbanization rise in China, this is not a binding constraint. There would not be an extra billion people in China without this policy.
For some formal academic research on fertility read these.