I estimated the number of Australian births as 250,000. The actual number of births, according to the Australian Institute of Family Studies, it's around 310,000. Where did I go wrong?
My estimate was 25 million times 0.8 children per person lifetime divided by lifetime of 80 years.
The actual total fertility rate is 1.74 per woman, giving a birth rate of around half this of 0.87 per person which is significantly higher than I estimated. Even if I use a rate of 0.9, then my estimate is 280,000, about 10% too low.
The key assumption was smoothing out the person lifetime; that we'll get one eightieth of the population. Women in Australia tend to have children in an age range of about 20-40 (and later in more recent times). Looking at the ABS Australian Demographics people of this age range are about 29% of the population, rather than 25% based on a smooth age assumtpion. This is an uplift of 1.16 times, which is slightly too much, but illustrates a closer look at demographics is likely to explain the difference.