Improving Efficiency of Model Based Estimation in Longitudinal Surveys Through the Use of Historical Data

In this context, supposing a sampling survey framework and a model-based approach, the attention has been focused on the main features of the optimal prediction strategy for a population mean, which implies knowledge of some model parameters and functions, normally unknown. In particular, a wrong specification of the model individual variances may lead to a serious loss of efficiency of estimates. For this reason, we have proposed some techniques for the estimation of model variances, which instead of being put equal to given a priori functions, can be estimated through historical data concerning past survey occasions. A time series of past observations is almost always available, especially in a longitudinal survey context. Usefulness of the technique proposed has been tested through an empirical attempt, concerning the quarterly wholesale trade survey carried out by ISTAT (Italian National Statistical Institute) in the period 2005-2010. In this framework, the problem consists in minimising magnitude of revisions, given by the differences between preliminary estimates (based on the sub-sample of quick respondents) and final estimates (which take into account late respondents as well). Main results show that model variances estimation through historical data lead to efficiency gains which cannot be neglected. This outcome was confirmed by a further exercise, based on 1000 random replications of late responses.