Evaluation of the Olsen technique for estimating the fertility response to child mortality

In a previous issue of this journal, Olsen proposed a technique for quantifying the fertility response to child mortality. To estimate the extent of child replacement, one needs data only on the number of children ever born and the number of child deaths for each woman. The technique involves first running a regression of the number of births on the number of deaths and then correcting the regression coefficient in order to obtain a consistent estimate of replacement. Here we evaluate the performance of the technique by seeing how well it works on a simulated set of reproductive histories for which we known the true extent of replacement. In passing, we derive an extension of the technique to handle the situation in which replacement strategies are heterogeneous. We conclude that the technique performs very well, especially in those cases where the stochastic structure of the data can be diagnosed.