A competing risks approach to the two-sex problem

The measurement of nuptiality rates is complicated by the fact that a marriage can be attributed both to the woman and the man involved. This is an example of the so called two-sex problem of mathematical demography. Several theoretical solutions have been proposed, but none has found universal acceptance. We introduce an individual level stochastic model based on competing risks ideas. The model shows explicitly how behavioral factors influence the accuracy of the various models. Although the product model is shown to be the only one that is invariant with respect to the units in which time and age are measured, different behavioral considerations may lead to different definitions of the population at risk. We show that the marriage models are only expected to differ empirically, if the numbers of marriageables vary abruptly in close ages. In an attempt to use data analysis to determine the best fitting risk population, we apply moving averages, approximately polynomial models, and subspace fitting models to Finnish age-specific marriage data, mostly from 1989. The results are conflicting. Depending on the criterium used, different models provide the best fit. We also study the role of the models in the forecasting of marriages. In some circumstances, an erroneous choice of the population at risk model can be compensated by a particular forecasting method.