On Precision in Estimates of Change over Time where Samples are Positively Coordinated by Permanent Random Numbers

Measures of period-to-period change are key statistics for many economy surveys. To improve the precision of these estimates of change, the majority of the business surveys at Statistics Sweden select stratified simple random samples (STSI) at different points in time, ensuring positive correlation between samples (overlapping samples) by using permanent random numbers (PRN). Statistics Sweden normally selects positively coordinated STSIs drawn from an updated Business Register (BR). In these samples, the industry strata are usually stratified further within industry into size strata. When the most recent sampling frame contains updated classification variables for all units, enterprises can change stratum between two sampling occasions. A drawback of the coordinated sample selection procedure is that the desired correlation between the two samples decreases if the proportion of enterprises that change strata is substantial. Consequently, the sample design must anticipate the potential effect of stratum changes between samples. This article presents a study that examines how the design of a repeated business survey affects the precision in estimates of change over time using the Turnover in the Service Sector survey conducted by Statistics Sweden as an example.