consumers alter their spending patterns when faced with changes in relative prices.

In the 1920s American economist Irving Fisher proposed what he called an “ideal” index that is formed as the geometric mean (the square root of the product) of Laspeyres and Paasche indexes and thus incorporates information about consumer spending patterns from both the base and comparison periods (see Fisher, 1922). In a 1924 article (not available in English until 1939), Russian economist Alexander Konus formally showed how to construct a cost-of-living index as the ratio of the minimum costs required for a consumer to achieve a given standard of living. He also established the relationships between the Laspeyres index and the cost-of-living index for the reference period’s standard of living and between the Paasche index and the cost-of-living index for the comparison period. In 1976 W. Erwin Diewert demonstrated that a class of indexes could be constructed using only information on actual quantities and prices in the two periods that would closely approximate a Konus cost-of-living index (see Chapter 2) for some standard of living intermediate between those in the base and comparison periods and would do so for any pattern of (stable) consumer tastes. He labeled such measures superlative indexes. The Fisher ideal index is one of many possible formulations of a superlative index, all of which involve some form of averaging base period and comparison period weights.

Two Levels of Index Construction Underlying the CPI

Familiarity with several key aspects of the way BLS gathers and combines individual price data into an overall index is necessary for understanding how the substitution issue affects the CPI.8 The BLS collects roughly 80,000 individual prices each month from over 21,000 retail outlets in various geographic areas around the country. For a few CPI categories, it also collects data from 7,300 housing units. The individual prices are classified into 218 categories (termed strata) that represent the various types of goods that consumers buy. From the individual item prices that have been collected, separate price indexes are then computed for each stratum in each area, with weights based on the importance in consumer spending of each of the items included in the stratum.9 This process is called lower-level aggregation. The resulting 218 strata indexes are in turn com-


Though this report details various aspects of CPI construction, we do not provide a unified top-to-bottom description. For this, we recommend the primer in Shapiro and Wilcox (1996:95-102) as well as the documentation on the BLS’s CPI web page.


This is an oversimplification. The individual items that are priced in each store are selected by a sampling process designed so that the probability for selection is proportional to the importance of that type of good in overall consumer expenditures. A simple average of the prices in each stratum thus produces what is, in effect, a weighted index for the stratum.

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