We present a new way to model age-specific demographic variables, using the example of age-specific mortality in the United States, building on the LeeCarter approach and extending it in several dimensions. We incorporate covariates and model their dynamics jointly with the latent variables underlying mortality of all age classes. In contrast to previous models, a similar development of adjacent age groups is assured, allowing for consistent forecasts. We develop an appropriate Markov chain Monte Carlo algorithm to estimate the parameters and the latent variables in an efficient one-step procedure. Via the Bayesian approach we are able to assess uncertainty intuitively by constructing error bands for the forecasts. We observe that in particular parameter uncertainty is important for long-run forecasts. This implies that existing forecasting methods, which ignore certain sources of uncertainty, may yield misleadingly sure predictions. To test the forecast ability of our model we perform in-sample and out-of-sample forecasts up to 2050, revealing that covariates can help improve the forecasts for particular age classes. A structural analysis of the relationship between age-specific mortality and covariates is conducted in a companion paper.
Demography age-specific mortality LeeCarter stochastic Bayesian state space models forecasts