The efficiency of rotating-panel designs in an analysis-of-variance model

In this paper we consider the relative efficiency of rotating-panel designs in analysis-of-variance models. Throughout we assume that the parameter of interest is a linear combination of period means in the analysis-of-variance model. Results from spectral theory are used to obtain manageable expressions for the variance of the BLUE of this parameter. Relative efficiencies of the BLUE for rotating panels with different rotation periods are presented, e.g., for the period means themselves, of differences, or of averages of means. Moreover we present bounds on the relative efficiency which are valid irrespective of the parameter of interest. The analysis shows that the gains from choosing an optimal rotation design can be quite substantial, even if the cost of a reinterview equals the cost of a first observation. In many cases either the smallest or the highest possible rotation period is optimal. The analysis is illustrated with an empirical example concerning monthly consumer expenditures on food and clothing.