A Posteriori

Attempts to grapple with and elucidate empirical knowledge

Replacement and Population Momentum October 4, 2009

Filed under: Public Policy — Rāhul @ 17:53

China implemented the one-child policy back in 1979, under which most of the country’s couples were encouraged, and some would say compelled, to have only one child. Even though many Chinese parents, as decided by geography or ethnic minority status, were allowed to have more than 1 child, on the average, Chinese families had less than 2 children per woman. Indeed by 2005, the fertility rate of mainland Chinese women has fallen to about 1.75. But, China’s population continues to increase even today, as can be seen from Fig: 1 below, courtesy Wikipedia.

Fig: 1 Growth of China's population

Fig: 1 Growth of China's population

Replacement fertility rate of a group is defined as the average number of children a newborn girl needs to give birth to in her life so that the population of her group remains constant. At first glance, this number seems like it should be around 2, so that the children born would replace (at the risk of sounding rather inhumane) their parents. But, unfortunately, not all baby girls live long enough to be of childbearing age, which means the Replacement fertiliy rate has to be a little higher than 2. Also, as the sex ratio at birth in most places in the world is skewed towards boys, less than half of the children born are girls who will give birth to the next generation. So, to have the replacement number of girls, the replacement fertility rate has to be a little higher still. Obviously, since infant/child mortality rates and sex ratio at birth differ widely across the world, the amount by which the Replacement fertility rate is above 2 is different in different countries. According to Wikipedia, while the number is around 2.1 for most developed countries, it ranges from 2.5 to 3.3 in developing countries.  So, when fertility rate in China is so low, how does population still increase?

To understand why changes in fertility don’t immediately translate to changes in population, let’s see what is the immediate reason for changes in population. The net-population growth is the difference between the total of births and immigration and the total of deaths and emigration. Migrations, being independent of fertility, obviously do not affect how fertility rate affects population. Then, the question is whether replacement fertility during a particular year guarantees equality between total births and deaths. It is easy to see that it doesn’t. Even after a few years of replacement fertility, the society only guarantees that the number of births is equal to the number of births X years ago, where X is the average childbearing age of women in that society. But, the number of deaths is different! It will be the number of births Y years ago, where Y is the life span of the society. If the society had a growing population in the near past, then X would be greater than Y and so the population will continue to increase despite the achievement of fertility at or below replacement levels. Similarly, population will continue to fall for a few years in countries like Russia, which has a declining population now, even if they achieve Replacement fertility. This whole phenomenon where Population lags behind fertility rate trends is called Population Momentum.

It is evident that if fertility rate continues to be low, the Chinese population eventually has to fall. When will this happen? When the one-child policy has continued for long enough that the total number of births in the current year (in the future) is less than than the number of births Y years before current, the population will begin to fall. As births are falling each year and the number of deaths Y years ago increasing each year, that day will come soon. Of course, Chinese policymakers will find it prudent to reverse the policy, at least partially, much before that day as the dependency ratio in China is rapidly increasing, threatening to curtail economic growth as the average working age Chinese will have to support more and more retired seniors.

Policy-making is intensely intricate and dependent of good data collection and analysis. Leaving aside for another venue the morality of an overly planned state, one can’t but admire how intelligent data analysis can lead to policies that can quickly uplift hundreds of millions from poverty, as seen in China today.

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