Prediction and error propagation in cohort diffusion models

Mikko Myrskylä, Max Planck Institute for Demographic Research

We study prediction and error propagation in the Gompertz, logistic, and Hernes diffusion models. We show that the models can be treated in a unifying framework in which the models are linearized with respect to cohort age and predictions and prediction variance are derived from the underlying linear process. We develop and compare different methods for deriving predictions from the underlying linear process and show that a midpoint method, which has not been used in cohort diffusion models, improves accuracy over standard methods. For an important special case, random walk with drift, we develop an analytical prediction variance estimator and study its accuracy with respect to a Monte Carlo estimator. Simulation studies and empirical applications to first births and marriages show that the analytical estimator is accurate, allowing forecasters to make precise the level of within-model prediction uncertainty.