Comparison of Variance Estimators for the Consumer Price Index

Estimates of sampling errors are of importance for survey designers when allocating sample sizes, in production as a tool for output editing and for users of statistics in decision making. The use of two-dimensional designs with elements of non-probability sampling methods, annually updated samples and complex estimators creates problems when estimating sampling variances for CPI-statistics. In this paper the character of variation in price changes is studied by use of analysis of variance models with one locality and one item effect and an error corresponding to the selection of product offers. This yields valuable information for the sample allocation work. Variance estimators in analytical forms, expressed in schemes of resampling procedures and model based formulas are tested in a large simulation study. A random groups method is proposed. This method makes it possible to estimate the variance for complex functions of index links such as e.g. the annual change of quarterly average inflation rates. .