1 Elementary Indexes April 29, 2020 Erwin Diewert,1 Discussion Paper 20-06, Vancouver School of Economics, The University of British Columbia, Vancouver, Canada V6T 1L4. Abstract Elementary indexes are indexes that are used by national statistical agencies to construct a subindex of a national Consumer Price Index (CPI) at the first stage of aggregation. Usually, only price information is available to the National Statistical Office. The main elementary indexes that have been used over the years are the Carli, Dutot and Jevons indexes. These indexes are compared to each other using Taylor series approximations to the indexes. An axiomatic or test approach to elementary indexes is also described. Finally, Irving Fisher’s rectification procedure that converts an elementary index into an index which satisfies the time reversal test is discussed. Key Words: Superlative indexes, elementary indexes, the consumer price index, Fisher, Carli, Dutot and Jevons price indexes, the test approach to index number theory, Fisher’s time rectification procedure. Journal of Economic Literature Classification: C43, E31. 1 University of British Columbia and University of New South Wales. Email:
[email protected] . This is a draft of Chapter 6 of Consumer Price Index Theory. This chapter draws heavily on Chapter 20 of the Consumer Price Index Manual; see ILO IMF OECD UNECE Eurostat World Bank (2004; 355-371). The author thanks Carsten Boldsen, Kevin Fox, Ronald Johnson, Claude Lamboray and Chihiro Shimizu for helpful comments. 2 1. Introduction In all countries, the calculation of a Consumer Price Index proceeds in two (or more) stages. In the first stage of calculation, elementary price indexes are calculated for the elementary expenditure aggregates of a CPI.