Multilateral indices in official price statistics and a new additive splicing method

A substitution of the traditional data sources allows National Statistical Institutes to collect large samples of product items with corresponding prices recorded over more frequent time periods. For some product categories, a frequent replacement of product items requires a dynamic approach to define a product sample that can be achieved by a monthly update of the sample. In a month-on-month comparison of price changes, bilateral indices must be chained that can lead to a chain drift bias. Multilateral methods are designed to reduce the chain drift, albeit not completely eliminate it. A disadvantage of multilateral methods is its ambiguous interpretability and a revision problem. The main objective of this paper is to show an implementation of multilateral methods for official price statistics in practice. The multilateral GEKS method is decomposed into elementary components that identifies the effect of successive price relatives used in its compilation. An importance of the decomposition is shown when interpreting the GEKS index in the context of official price statistics. We demonstrate that it can lead to an inaccurate public dissemination of the consumer price index. Moreover, we propose a new method for the splice extension that is required to avoid the revision of previously published indices. The method uses a Stein-type shrinkage estimator for the splice extension that is applied additively to the last published index. In the empirical study, we use web scraped data, which are obtained from the Slovak market, for comparison of bilateral and multilateral indices.