How is population growth predicted?
It's possible that the stories about drastic drops in Japan refer to working-age population, not the population itself. 

This is a link to the U.S. Census methodology.

I have only casually looked at these data over the years, but I would summarise the general idea as follows.


We already have the current population distribution. We work with the data based on the number of people in each age cohort.
We have estimates of life expectancy based on age, and actuaries spend a lot of time working on developing projections. (The defined benefit pension and life insurance industry depend upon such actuarial projections.)
We usually have a good idea of the birth rate, based on the characteristics of under-30 population. Even if we miss, it takes a long time for the errors to really add up. (People have to reach puberty before the prediction error compounds.)
This covers the existing population; what remains to do is estimate the effect of net migration.


For the developed countries, the big unknown is typically net immigration. In the euro area, the collapse of economies has often caused a considerable amount of emigration.

Outside of net immigration, the only thing that could cause the projections to off is a massive change in the death rate (or birth mortality). Birth rates tend to be slow-moving; the baby boom after World War II was a response to highly unusual earlier conditions (Great Depression, WWII). Life expectancy is another wild card, but it is unclear how much it will change.