The study is done by The Lancet, one of the world's most reputable medical journals. So they must have done some thorough research on the topic.
No? Let's crunch some numbers.
India's TFR is already close to replacement level at 2.2, and will likely to continue to fall as India develops and urbanize. India's population will probably start shrinking in a generation's time, assuming no major changes in life expectancy.
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Definitely possible if you do the math. There's still 80 years away to 2100, which is around 3-4 generation's time.
Assuming China's TFR is 1.6 on average for the next 80 years, each generation will be around 1.6/2.1=
76% the size of the previous generation. Compounded by 3 generations, the third generation would be around only 0.76^3=
44% of today's generation.
And this is based on very optimistic projections. According to the National Bureau of Statistics of China, China's TFR is only 1.05 in 2015. They have stopped compiling after that.
https://www.caixinglobal.com/2016-1...hinas-plunging-fertility-rates-101003748.html
Maybe China's TFR has risen after the relaxation of one-child policy, but most experts estimate the current TFR is around 1.2-1.3, not too different from other East Asian countries. Birth rates continue to fall after the second year of the relaxation of the OCP.
https://www.caixinglobal.com/2018-11-02/chart-of-the-day-chinas-slipping-birth-rate-101342166.html
It's unlikely to see a major uptick in China's TFR in the foreseeable future. China will continue to urbanize, and younger generations of Chinese women will continue to get more educated and participate in the workforce.
According to Chinese state media, China's working-age population is projected to fall by 100 million in just 15 years' time.
http://en.people.cn/n3/2020/0103/c90000-9645794.html
Since those entering the labor force by 2035 have already been born by 2019, this figure should be very accurate.
So back to your question, China's population shrinking by 50% (or even more) in 80 years' time is a very distinct possibility.