# Formula for Cohort Fertility Rate

I understand the definition of Cohort Fertility Rate as the average number of live births that a woman born in a particular year has had by the end of her reproductive life. But is there a formula to calculate it? I tried googling but in vain. I have seen formula for many other fertility indicators like CBR, IMR etc. All of them have some formula for direct computation but I couldn't find any such idea for CFR. If there isn't any formula then please direct me to the mechanism of its calculation.

• Seems like you could derive this? I think you would need: (1) age, year specific fertility rates and (2) age, year specific mortality rates. There may be a bit of trickiness at the interaction of fertility and mortality within a year, but I imagine getting that right doesn't matter for rich countries with low mortality rates. – Matthew Gunn Jun 11 '16 at 2:59

• Let $d_{a,t}$ be the mortality rate for women age $a$ in year $t$.
• Let $x_{a,b}$ be the fraction of women age $a$ that were born in year $b$ and still alive.
• Let $f_{a,t}$ be the fertility rate for women age $a$ in year $t$. One hundred percent of women born are alive, hence: $x_{0,b} = 1$. Then we have: $$x_{a+1,b} = (1 - d_{a,a+b}) x_{a,b}$$ Let $l_{a,b}$ be live births for women age $a$ and born in year $b$. You might want to think about this more, but somewhere to start might be:
$$l_{a,b} = f_{a,a+b} x_{a+1,b} \quad \text{<--- assumes all women that die don't give birth... probably not right}$$
Then lifetime cohort fertility would be: $$c_b = \sum_a l_{a,b}$$
• Yeah, the latter assumption creates a problem especially when we are dealing with developing and under-developed countries data. $x_{a+1,b}$ factor creates a problem in the $l_{a,b}$ formula. – Dark_Knight Jun 11 '16 at 16:20