The empirical data doesn't support this. The nations with the strongest economies are also the nations with among the lowest birth rates, and it has been that way for decades. To highlight one specific example, China's birth rate fell even as its economy took off over the past 30 years. And they did not experience high rates of immigration either.
It's probably a short-term good to zero out your birthrate. That way you have tons of working age people who aren't busy being parents and can do economically useful labor.
But in forty years when those people get too old to work and there's no younger generation to replace them (and take care of them), you're gonna have a really bad time.
My hunch is that contraception is still new enough that countries like the US haven't quite reached the "have a really bad time" side of that curve, but we are fast approaching it. It's going to be rough in the US when all the Boomers retire and start consuming healthcare while there aren't enough young people paying into Social Security to support it.
You're addressing a different, more specific question, which is "what will happen to a nation with a strong economy when their birth rate declines?" Answering this is more dependent on longitudinal data. It's fine if you think there's not enough data yet, although I'll point out that that should preclude you from making predictions too...
> It's going to be rough in the US when all the Boomers retire and start consuming healthcare while there aren't enough young people paying into Social Security to support it.
There is really nothing about Social Security that depends on a certain ratio of people. The only things that need to match are the intakes and outlays, in dollars. If a shrinking working population is accompanied by sufficient productivity growth, total economic output will continue to grow and Social Security will remain solvent.
I wouldn't worry about the Boomers specifically; they're already outnumbered about 2:1 by Gen X plus Millenials, and that ratio is growing as older Boomers start to pass away.
Payroll taxes increase the effective tax burden on younger working families in their prime reproductive years, which means they can no longer afford to have the same number of kids, or to have kids as early. When younger workers are taxed, the less affordable it is to create new generations of younger workers, and fertility rates decrease.
The best thing the United States could do to address this would be to eliminate FICA \ self-employment taxes and fund social security out of a general income tax which taxed capital gains and dividends at the same rate as labor income. An even better solution would be fund it via a national real-estate property tax or national land value tax, and not to raise it from taxes on earnings at all, as Thomas Paine originally proposed in Agrarian Justice.
Now, I know and you probably know that it is actually run like a transfer program, where the payroll taxes from working people in 2018 are turned right around and sent out as checks to retired people in 2018.
But here's the thing: so are 401k's. The money you spend to buy investments in 2018 doesn't go into a vault; it is transferred to people who are selling investments... people like current retirees who are drawing down their 401k. And then when you're retired in 2048 (or whenever), and you're drawing down your 401k, you'll be getting your money transferred from people who are buying investments... people like younger workers building their nest egg.
Retirement programs are just collections of promises... that's all a financial asset is, a claim against future income. Social Security is a different kind of asset, but it still works fundamentally the same way; you pay into it while working, to create a claim against future payroll tax income when you're retired.
https://www.mitpressjournals.org/doi/abs/10.1162/rest.89.1.1...
But imagine that their population falls slowly, as automation increases their per-capita productivity. Imagine a future China with 1 million people, but the average person can produce 1,000x the economic value that the average person can today.
standard disclaimers about correlation not correlating with causation apply both ways.