Choice of formula for the measurement of inflation does matter. In January 1999 the formula principally used for aggregating price changes for the U.S. consumer price index (CPI) at the lower level of aggregation was changed from an arithmetic to a geometric mean. The effect of the change has been estimated by the Bureau of Labor Statistics (BLS) (2001) to have reduced the annual rate of increase by approximately 0.2 percentage points. Following estimates from the Boskin Commission‘s Report on the U.S. CPI (Boskin et. al, 1996 and 1998), this implied a cumulative additional national debt from over-indexing the budget of more than $200 billion over a twelve year period up to the mid-1990s.
These lower‘ level aggregation formulas are applied to samples of prices from outlets of finely-defined goods such as varieties of apples and are the building blocks of a CPI. The differences between these formulas are seen below to be primarily determined by changes in price dispersion while the desirability of the geometric (Jevons) index against the arithmetic (Dutot) index will be shown to be determined by the absolute level of price dispersion.
The Schultze and Mackie (2002) report on the U.S. CPI recommended the use of a trailing superlative index instead of the Laspeyres index since it would capture weighted upper level substitution effects. One such superlative index which has much to commend it (Diewert, 1997 and 2003a) is the Fisher index, a geometric mean of Laspeyres and Paasche. Boskin estimated that upper level substitution accounted for 0.15 percentage points bias in the U.S. CPI. Changes in price dispersion will be seen to account for some of the differences between these formulas.
Although the Laspeyres formula is commonly thought to be the formula used for the U.S. and other CPIs at the upper level, the expenditure weights for a comparison, say between periods 0 and t, relate to a previous time period b, as opposed to period 0, since it takes time to compile the information from an expenditure survey for the weights. A resulting practically-used index is a Young index which is shown below to be biased (Diewert, 2003a), the extent of which depends again on changes in price dispersion.
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Why Price Index Number Formulas Differ: Economic Theory And Evidence On Price Dispersion
