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December 1993, Vol. 116, No. 12

The commodity substitution effect in CPI data, 1982-91

Ana M. Aizcorbe and Patrick C. Jackman

The Consumer Price Index (CLI) is a measure and of the average price change of a fixed market basket of goods and services purchased by the average household. The market basket contains a sample of items-food, clothing, shelter, fuels, and other goods and services-that people buy for day-to-day living. While it is often referred to as a "cost-of-living index" (CLI), and indeed was so titled until 1945, the CLI is not in general a CLI. A CLI is defined as the ratio of the minimum expenditure required to attain a particular level of satisfaction in two price situations; a comparison period and the base period.1 The CLI, a modified Laspeyres index, holds the standard of living constant (in the span between major revisions) by keeping quantities fixed, but allows prices to vary. In addition, over an extended period of time the CLI is a chain index, because the expenditure pattern of consumers is updated and sequentially linked into the index at approximately 10-year intervals.2 The restriction imposed on the CLI, by keeping the quantities fixed and not allowing substitution among goods in response to relative price change, results in a substitution effect,3 or a divergence between the CLI (or any other index with fixed quantity weights) and the CLI. In the case of a Laspeyres index, the effect is such that it is greater than or equal to the true cost of living. Indeed, as is well known a Laspeyres index is an upper bound to the true CLI.

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1 See Robert A. Pollak, The Theory of the Cost-of-Living Index (England, Oxford University Press, 1989).

2 For example, the present expenditure pattern reflected in the official CPI is a 3-year average - 1982-84 - and was introduced in December 1986. Thus, the period immediately prior to and including December 1986 was based on 1972-73 expenditures, while the period from December 1986 was based on 1982-84 expenditures.

3 Economic literature generally refers to this effect as "substitution bias." We have chosen to characterize the difference between the CPI and CLI as the substitution effect to avoid confusion with other types of biases associated with price indexes, such as sampling bias.

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