Multivariate state space approach to variance reduction in series with level and variance breaks due to survey redesigns

Statistics Netherlands applies a design-based estimation procedure to produce road transportation figures. Frequent survey redesigns caused discontinuities in these series which obstruct the comparability of figures over time. Reductions in the sample size and changes in the sample design resulted in variance breaks and unacceptably large sampling errors in the recent part of the series. Both problems are addressed and solved simultaneously. Discontinuities and small sample sizes are accounted for by using a multivariate structural time series model that borrows strength over time and space. The paper illustrates an increased precision when we move from univariate models to a multivariate model where the domains are jointly modelled. This increase is especially significant in the most recent period when sample sizes become smaller, with standard errors of the design-based estimator of the target variables being reduced by 40-70% with the model-based approach.