On the measurement of total fertility rate: With understanding on the impacts of population policies

Fertility rate is an important indicator about the present state and future change of a society. However, it is not easy to accurately measure fertility rate, especially when fertility rates change substantially.

When a woman is over her reproductive age, we can be certain about  her total fertility rate. However, the fertility rates of the general population may differ significantly from those who have already pass their reproductive age. Historical fertility rates are  lagging indicators of current and future fertility rates.

Currently, total fertility rate is the most commonly used measurement of fertility. To reduce the impact of time lagging, total fertility rate is defined in the following way: The number of children who would be born per woman if she were to pass through the childbearing years bearing children according to a current schedule of age-specific fertility rates.

This definition used the sum of the current age-specific fertility rates as the total fertility rate of the population. This method reduces the impact of time lagging. When fertility rates are near stationary, this method provides an accurate measure of fertility rates. However, when fertility rates change rapidly, this method does not track the change of future fertility rates timely. We will use an example of a hypothetical animal to discuss this problem.

Suppose the life long fertility rate per female is three. On average, each female will give birth one offspring per year, for three consecutive years. Then, a sudden social change  occurs. The life long fertility rate of the younger cohorts becomes one. For the younger cohorts, on average, each female will give birth one fourth offspring per year, for four consecutive years. This change of fertility patterns models the change of fertility patterns in many human societies. On average, women have less children. Their reproductive periods are extended. What will be the observed total fertility rates during this period of demographic transition?

For the first year when the life long fertility rate of a young cohort turns to one, the annual birth rate of that cohort is 1/4. The annual birth rate of two elder cohorts is 1. The measured total fertility rate is 1+1+1/4=2.25. For the second year, the life long fertility rate of two young cohorts turns to one, the annual birth rate of that two cohort is 1/4. The annual birth rate of the remaining elder cohort is 1. The measured total fertility rate is 1+1/4+1/4=1.5. For the third year, the life long fertility rate of three young cohorts turns to one, the annual birth rate of that three cohorts is 1/4. The elder cohorts all pass the reproductive age. The measured total fertility rate is 1/4+1/4+1/4=0.75. For the fourth year, the life long fertility rate of four young cohorts turns to one, the annual birth rate of that four cohorts is 1/4. The measured total fertility rate is 1/4+1/4+1/4+1/4=1.

Overall, during the period of fertility change, the measured total fertility rates are 2.25, 1.5, 0.75 and 1 respectively.  For the first two years, measured total fertility rates underestimate the magnitude of change of life long fertility rate. For the third year, measured total fertility rate overestimates the magnitude of change of life long fertility rate. For the fourth year, the transformation to the new fertility pattern  completes. The measured total fertility is an accurate representation of new life long fertility rate.

This pattern is very similar to the changes of measured total fertility rate over time in many countries under demographic changes. The total fertility rate in Japan continue to decline until the year 2005, when it reached the minimum value of 1.26. After that, the measured total fertility rate climbed back a little bit. The total fertility rates in many countries exhibit similar patterns. Usually, the increases of fertility rates in these countries are attributed to pro birth policies implemented by the governments. From our discussion, this pattern can be simply attributed, at least in part, to the measurement problem during the transitional period of change of fertility patterns.

We will further discuss the impacts of fertility enhancing policies. Usually the adoption of a new policy will satisfy a pent up demand and hence have a significant short term impact on the increase of fertility. However, the cost associated with the policy is long term. This may damp fertility over long term. For example, recently Japanese government announced free daycare. The cost of running daycare will be paid by the increase of sales tax from 8% to 10%. This pro birth policy is generally regarded to increase fertility. Indeed, the new policy will encourage many people who look forward to free daycare to have babies. This will indeed push up short term fertility rate. However, the increase of sales tax is permanent. This will reduce the purchasing capacity of the general population, including the young people in their reproductive age. As the tax and transfer system generates a lot of waste in the process, it is not certain if the overall impact of this policy on the fertility rate is positive.

Fertility rate is an extremely important measurement of long term social well-being. Yet the measured total fertility rates often exhibit serious time lagging. Occasionally, they give false signals on the effectiveness of government policies. Are there any methods to reduce to relieve or reduce these problems?

We can study the specific birth rates of different age cohorts and compare with historical data to understand the change of patterns. We can also study fertility as a function of other social and economic parameters. While the developed functions are not perfect, they may improve the forecasting of the change in fertility rate. By adopting a theoretical approach on the relation among different factors, we may better estimate the overall impact of the policy. This will help us better prepare for the future.