Post-Laspeyres: The Case for a New Formula for Compiling Consumer Price Indexes

Consumer price indexes (CPIs) are compiled at the higher (weighted) level using Laspeyres-type arithmetic averages. This paper questions the suitability of such formulas and considers two counterpart alternatives that use geometric averaging, the Geometric Young and the (price-updated) Geometric Lowe. The paper provides a formal decomposition and understanding of the differences between the two. Empirical results are provided using United States CPI data. The findings lead to advocacy of variants of a hybrid formula suggested by Lent and Dorfman (2009) that substantially reduces bias from Laspeyres-type indexes. Most national statistical offices (NSOs) use in practice what they often describe as “Laspeyres-type” index formulas for aggregating their consumer price index (CPI) at the higher (weighted) level. These Laspeyres-type indexes include the Young and the Lowe indexes, both of which have serious shortcomings. It is argued here that Laspeyres-type indexes can be replaced at little cost by more suitable formulas that use the same data and can be compiled in real time. A Laspeyres price index can be defined as a period 0-weighted arithmetic average of price changes between periods 0 and t. However, it takes time to compile the results of a household expenditure survey, so in practice statistical agencies use a prior period b survey weights to rebase a CPI that runs from the price reference period 0 (b < 0 < t). The Young index has as its weights the preceding survey period b expenditure shares and the Lowe index uses period b weights price-updated (and normalized) to the price reference period 0. Laspeyres is exceptionally used in practice for compiling CPIs.