[Sherman Logan]

Not an unreasonable assumption. However, I think the birth rate for both white and black Americans dropped off in the second half of the 19th century, down from the explosive growth rate of the previous two centuries.

Your projection of course assumes the exact same birth rate in 1860 to 1900 as in 1820 to 1860. Even a quite small drop in birth rate would throw the numbers off a lot.

Here’s a paper that looks very interesting. Frankly, I don’t have time to thrash about in its weeds, but changes in both death and birth rates from the 1st to the 2nd half of the 19th century would significantly impact the number alive in 1900 vs. 1860.

http://www.nber.org/papers/h0056

[MUDDOG]

The paper is short on statistical tables. There are a few at the end, but the only rates he gives are birth and infant mortality rates, and for blacks, not even that before 1850.

The World Almanac data I used gives a multiplier of 2.5 for black population from 1820 to 1860. Given the starting population of 1.77 million, that means every 0.1 in the multiplier translates to 177,000, i.e., if the natural increase was a multiplier of 2.4 (out of the total multiplier of 2.5), that would still leave 177,000 imported.

What I did is all back of the envelope stuff. Like you, I've got other things to do! But I think a serious study of the demographics could narrow the estimates down to the point of some validity.

[MUDDOG]

BTW here are his black birthrates per thousand per annum:

1850s: 58.5

1860s: 55.0

1870s: 55.4

1880s: 51.9

1890: 48.1

1900: 44.4

(It's only in 1890 that he starts breaking it out by year rather than aggregated by decade, for blacks.)

So it looks like the average black birthrate betwen 1860 and 1900 is about 52. Let's increase the 1850s rate on the assumption it was higher for the whole period 1820-1860, let's say 62.

So without adjusting for deaths, that would mean the ratio of natural increase between periods was 62/52, or 1.2 higher in 1820-1860 than in 1860-1900.

So we take the 2.0 multiplier of 1860-1900 and adjust it by 1.2 times to get 2.4 as the natural increase to apply to 1820 to 1860.

So we get for 1820-1860 a natural increase multiplier of 2.4, which subtracted from the total multiplier of 2.5, leaves for imports of slaves, 177,000.

That's about 200,000 slaves imported between 1820 and 1860.

Maybe that's not unreasonable.