Estimation under exact linear time-varying constraints, with an application to population projections

Estimation problems sometimes have inherent constraints which, when used, increase efficiency. When these constraints vary over time, the Kalman filter provides a convenient method of imposing them. This paper applies the Kalman filter to the problem of estimating state (provincial) populations given annual national population and national net arrivals, together with actual state populations in census years. An advantage with this approach is that the resulting projections can be evaluated by the provision of standard errors and the quality of one step ahead predictions. With the author’s data the method seems to perform well for population projections, but poorly for net arrivals.