State space time series modelling of the Dutch Labour Force Survey: Model selection and mean squared errors estimation

Structural time series models are a powerful technique for variance reduction in the framework of small area estimation (SAE) based on repeatedly conducted surveys. Statistics Netherlands implemented a structural time series model to produce monthly figures about the labour force with the Dutch Labour Force Survey (DLFS). Such models, however, contain unknown hyperparameters that have to be estimated before the Kalman filter can be launched to estimate state variables of the model. This paper describes a simulation aimed at studying the properties of hyperparameter estimators in the model. Simulating distributions of the hyperparameter estimators under different model specifications complements standard model diagnostics for state space models. Uncertainty around the model hyperparameters is another major issue. To account for hyperparameter uncertainty in the mean squared errors (MSE) estimates of the DLFS, several estimation approaches known in the literature are considered in a simulation. Apart from the MSE bias comparison, this paper also provides insight into the variances and MSEs of the MSE estimators considered.