Modeling and Forecasting First Marriage: A Latent Function Approach

Nan Li, United Nations
Zheng Wu, University of Victoria

Hernes (1972) proposed a deductive model for diffusion processes and applied it to first marriage. Using a latent function, we generalize the Hernes model and base the assumption on observation. The Hernes model has a linear latent function, and hence is the simplest among the generalized Hernes models that are capable of dealing with diffusion processes of which the latent functions may be nonlinear. The linear latent function gives two advantages to the Hernes model. First, forecasts are based on linear extensions of historically linear trends, and the confidence intervals of forecasts are obtained analytically. Second, the starting and ending ages of the model could be chosen less arbitrarily by identifying outliers of a linear trend, which can hardly be done in nonlinear models. We use data on first marriage from Canada and the U.S. to demonstrate these advantages, and forecast decline and delay in first marriage for Canadian cohorts.