This article rigorously derives the properties of the regression of births on child deaths. It is shown how the raw regression coefficient may be corrected for the effects of fertility on mortality so that the rate at which dead children are replaced may be estimated. The method is applied to data from Colombia. It is found that the mortality rate differs across individuals and is correlated with fertility. Such conditions vitiate the use of birth intervals and parity progression ratios yet can be dealt with using the new method. On average each death produces 0.2 new births as a direct result of the death. Fertility hoarding may raise the total fertility response to roughly one-half birth per death.

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