Aiming at an Unobserved Moving Target: A Simple Nonlinear Model of Fertility

Jose A. Ortega, Universidad Autonoma de Madrid and Universidad de Salamanca

Ronald Lee introduced a simple nonlinear model of fertility which could capture many of the characteristic features of US fertility change such as the intensity of the baby-boom and bust compared to cohort fertility. The moving target model described period fertility as a fixed proportion of the gap between a (moving) target fertility, and current cohort fertility. In this paper we explore an alternative model where the desired fertility level is unobserved and estimated from data. This produces an array of simple nonlinear models of US fertility: fixed proportion, age-specific fixed proportion, time-varying fixed proportion, time-varying age-specific proportion. The different models are presented and estimated using US data and the forecasting performance of the models is evaluated. These models provide an interesting and useful alternative to the simpler models based purely in historical trends, pure cohort fertility, and to the more complex models of parity-specific fertility quantum and tempo.