Ansley J. Coale, Norfleet W. Rives, Jr., A Statistical Reconstruction of the Black Population of the United States 1880-1970: Estimates of True Numbers by Age and Sex, Birth Rates, and Total Fertility, Population Index, Vol. 39, No. 1 (Jan., 1973), pp. 3-36
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Coale et al. (1973) studied this question.