Prediction and Error Propagation in Cohort Diffusion Models

Mikko Myrskylä, University of Pennsylvania
Joshua R. Goldstein, Max Planck Institute for Demographic Research

We study prediction and error propagation in the Gompertz, logistic and Hernes cohort diffusion models. We show that the linearized forms of these models can be modeled as a random walk with drift and that predictions and prediction error estimates can be derived from the random walk model. We develop and compare different methods for deriving predictions from the underlying random walk model. We also develop an analytic variance estimator for the prediction variance and study its accuracy with respect to a Monte Carlo estimator. Simulation studies and empirical applications to first births and marriages show that the analytic estimator is accurate, allowing forecasters to make precise the level of "within-model" uncertainty that should be attached to their forecasts, a level that should be viewed as a lowerbound of the total uncertainty, which could include departure from the model.