On a Special Property of the Total Fertility Rate

Lei Lu, Independent Consultant

In demography, the (period) total fertility rate (TFR) is an important and commonly used measure of period fertility. Demographers have studied the TFR for many decades and gained a lot of knowledge about the indicator. In this paper, the author studied a special property of the TFR, i.e. the relationship between the TFR of a total population and the TFRs of the concerned two sub-populations. Both graphical and mathematical analyses were conducted on the relationships. The analyses showed that, theoretically speaking, the TFR of a total population may (i) fall between the TFRs of the concerned two sub-populations, or (ii) be larger (or smaller) than both of the TFRs of the concerned two sub-populations. The paper also established general criteria for judging the different relationships and provided a demographic interpretation of the “paradox”. An actual case was provided to show that the “paradox” did have happened in reality.