has a blog post and a long comment on Amish demographics. There are now somewhere approaching a quarter of a million Amish in the U.S., up from less than 10,000 a century ago. At the current growth rate of doubling every twenty years, there would be approaching eight million Amish by 2110. (Warning: Projections 100 years into the future not likely to turn out right.)
My impression is that the Amish are not a major drain on the taxpayers the way the polygamous Fundamentalist Mormons are, who put their junior wives on welfare and run a lot of scams
to get federal and state funds for the their town on the Utah-Arizona border. Of course, an all-Amish country wouldn`t work due to the pacifism of the Amish.
Somebody might wish to create a model of the optimal sect for increase in share of the population. The components would consist of:
1. Fertility rates
2. Retention rates
3. Conversion rates
4. Death rates (which usually are pretty much the same these days, as long as the sect doesn`t oppose vaccination, or whatever).
The Amish, for example, have quite high fertility rates, high but not 100% retention rates, and very low conversion rates. There are probably trade-offs between the different components.
It seems plausible that the human race in 3000 A.D. will largely be descended from cultures that achieved optimal combinations of these trade-offs for population growth.