The Consumer Price Index: Underlying Concepts and Caveats

Article excerpt

In 1927, Irving Fisher, in The Making of Index Numbers, wrote:

Most people have at least a rudimentary idea of a "high cost of living" or of a "low level of prices," but usually have very little idea of how the height of the high cost or the lowness of the low level is to be measured. It is to measure sure such magnitudes that "index numbers" were invented.(1)

The Consumer Price Index (CPI), produced by the Bureau of Labor Statistics, serves as an approximation of an ideal cost-of-living index (CLI).(2) The CPI is "a measure of the average change in the prices paid by urban consumers for a fixed market basket of goods and services." Measuring price change through the use of a fixed market basket has a long history, dating to the early 1700's.3 The theory underlying the CLI is much more recent, having been developed by A. A. Konus in 1924.(4)

This article reviews how the theory of the CLI provides the conceptual foundation for the CPI and the caveats governing the use of the CPI as an approximation for a CLI. To understand these warnings it is necessary to know the sources of measurement errors in prices and weights that unavoidably impede the construction of the CPI. If the measurement error is systematic, then a systematic difference may exist between the computed CPI and the true CLI, which would, in turn, affect the measured rate of price change. In this article such systematic differences are called systematic effects(5)

A description of some of the prominent features of the structure and market dynamics of prices is useful because they are relevant to understanding sources of measurement error. First, consumers face a large number of different products; those who design indexes must aggregate the prices of nonidentical products into groups or strata. Second, within a product stratum, consumers face a variety of prices arising from such factors as differences in the production technology of manufacturers and the location of retail outlets. Third, price changes stem from market dynamics such as entry and exit of firms, and the expansion of existing firms. Fourth, prices routinely oscillate, due to, among other reasons, seasonal factors and periodic sales.

Although BLS uses procedures to account for these influences, the task is complicated by the frequency of price change induced by them. Firms cannot change prices without cost; for example, costs are associated with changing price lists ("menu" costs). Firms therefore change their prices when the benefit of the change exceeds the cost. Consequently, the observed price oscillation among retail firms depends on the pressure for price change arising from the influences mentioned earlier and the costs of price change for a given firm.

Conceptual framework underlying the CPI

The measurement of the change in the cost of living stemming from a change in price is based on an assessment of how a change in the price of goods and services affects consumers' well-being. Consumer well-being can be defined as the level of utility achieved by the consumer through the consumption of goods and services. The underlying assumption is that consumers choose the bundle of goods and services that maximizes their utility for a given expenditure level or, equivalently, minimizes expenditures to achieve a given level of utility.

Because a cost-of-living index measures how price changes affect a consumer, one can look at how the minimum expenditure necessary to obtain a certain level of utility responds to price changes. Let the minimum expenditure needed to achieve the level of utility u be denoted by E(p;u), where p denotes the set of prices of goods and services. The cost of living index for a consumer between period t and the base period b can be expressed as a ratio of the minimum expenditures:


The level of utility in the base period underpins the comparison between the two expenditure levels. …