Evolution of the GEKS index

Jacek Białek
Statistika, 106(3): 276–293
https://doi.org/10.54694/stat.2025.58

Abstract

The GEKS index is a well-known multilateral index used by many statisticians to measure inflation based on scanner data. As a rule, it is assumed that the underlying index within the GEKS formula satisfies the time reversal test. Most often, this underlying index is assumed to be superlative, and therefore, the GEKS index based on the Fisher, Tornqvist (GEKS-T or CCDI) or Walsh (GEKS-W) formulas are most often considered. However, the ’classic’ GEKS index does not meet the stringent identity test. Unfortunately, most of the known multilateral indices do not meet the time reversal test, which many researchers consider a weakness. This paper reviews both well-known and lesser-known modifications and generalizations of the GEKS index. We discuss three new and general classes of indices based on the GEKS method, as well as some special cases of these classes, which include the GEKS, GEKS-T, and GEKS-W indices and, additionally, the GEKS-L and GEKS-GL indices. One class uses elasticity of substitution, so it is close to the economic approach, while another class - like the multilateral Geary-Khamis index- uses quality-adjusted prices and quantities. Not all the GEKS modifications discussed require the underlying index to meet the time reversal test. It should be noted that in cases where this assumption has been dropped, an identity test has been gained. We present the basic axiomatic properties of the proposed indices and compare them empirically based on real and available scanner datasets. The simulation study verifies the impact of price and quantity volatilities on the differences between the price indices discussed.

Keywords
inflation measurement, Consumer Price Index (CPI), scanner data, multilateral indices, identity test, GEKS method