Multistage Model of First Marriage and Birth: An Extension of the Coale-McNeil Nuputiality Model

Ryuichi Kaneko, National Institute of Population and Social Security Research, Japan

In this study, I first focus on the potential profile of the Coale-McNeil nuptiality model (CM model) as a multistage model of vital events such as the first marriage and birth separated by birth order. The convolution structure of the CM model can be regarded as an expression of a multistage process consisting of attainment of marriageable age, and several waiting time to the goal. This interpretable nature of the CM model is carefully examined here and the corresponding equivalent convolution model is presented. The critical problem is that the assumption of the model over independence between the sub-processes is not satisfied in the reality according to my survey results. Hence I proposed new model by introducing liner relationships among parameters so that realistic associations of the sub-processes be reproduced. It is applicable to describe latent processes such as age at becoming marriageable and marriage market population, for instance.