Okay, more on this.

China's 2020 Census showed 253 million kids ages 0-14.

Prior official data showed 239 million births 2006-2020.

Interpolating survey-reported ASFRs onto best-guess populations yields just 185 million births in that period.
So who do we trust?

Is the Census correct that there were 253 million kids ages 0-14, and so prior birth estimates were too low by *14 million*?
That could be true. But walking that birth estimate back onto the childbearing population produces pretty high ASFR estimates.
So here's a comparison of TFRs. One line is basically, TFRs according to censuses, large, high-quality surveys, and reconstruction of birth histories.
Here's the relevant birth count estimates. Huge differences!
Here's that birth chart again, but here I add in "how many people who were born in each year were counted in late surveys and censuses." Alas I can't find 2010 official counts by specific age group.
Smoothing the data out from all those sample surveys and censuses, here it is simplified. You can see that official births track census data pretty closely until the 1990s. Sample surveys are always low but have reliable trend vs. official. Until VERY recently!
So in the latest official data you have this massive decline in births in recent years, but it doesn't really show up at all in the sample survey data.
China also publishes official estimates of the under-15 population. Here it is, compared to their pre-2020-census-results birth estimates over the lagged 15 year period and their revised estimates.
China's official birth tallies have persistently run "ahead" of their estimated 0-14 population, implying net emigration + mortality at very high rates. Here's implied net migration + mortality rates using old and new birth data vs. official under-15 population.
This is obviously wrong. China did not lose *15%* of the babies born 1995-2010 before they were counted in the 2010 census. That would imply either like least-developing-country levels of child death, or ***30 million*** Chinese children moving abroad.
Moreover, you can see in this graph the official population has big jumps. Those are census or major survey years where they make revisions. They don't go back and fix prior years. As a result, we can GUESS what 2010 census results WOULD HAVE shown in the missing years!
Basically, the 0-14 population was GREATLY REDUCED in the 2010 census vs. prior counts. See that jump down in 2010?
Which number is "true" is irrelevant. What it tells us is that if we had 2010 census data by specific year of age, it probably would NOT show a much higher birth rate in the late 1990s than the census data shows here.
As a result, it is extremely implausible that true births in the late 1990s and early 2000s were as high as the official birth data indicate.
To complicate things further, the 0-14 population jumped back UPWARDS in 2020... even though if we toss in the sample-survey estimates for each year, the 0-14 population is WAY lower.
There's a plausible story for why official births and young child populations would be overstated: localities can get more money for schools by having more kids.
There is also a plausible story for why direct surveys of fertility would be understated up through 2015: it's a bad idea to admit you had kids that are legally dispreferred.
However, it's not clear why the sample surveys would have a downward bias on, say, 12 year olds. Hiding a kid that old is very hard.
It can be done. But probably not by 50 million households.
All that to say....

With the censuses before 2020 and sample surveys we have pretty strong agreement on low births. Censuses and sample surveys both separately query child population and fertility, and both methods in both sources produce low birth estimates.
The sample survey is lower, almost certainly too low. But this is likely because of a base population problem not a rate problem, since the censuses produce similar rates.
So I think the best approach is: get a base population you think is plausible-ish-enough, use ASFRs from sample surveys and censuses, try to smooth out series breaks, apply those calculations to the base population, disregard official births as propaganda.

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