This paper demonstrates that random sampling error in CPI price and
expenditure data at the item-area level can have a distorting
effect on empirical cost-of-living indexes computed using those
data. In particular, the expected values of the Fisher Ideal and
Tornqvist indexes can be distorted downward by random error in
basic index relatives. This, in turn, can cause the estimated
Laspeyres substitution bias in the CPI to be overestimated. The
issue is illustrated empirically using CPI data for the period 1987
through 1995. Estimated substitution bias is sharply higher in each
year when smaller CPI "replicate" samples are used to compute
indexes than when the full samples-which are subject to less
sampling error-are employed. To address this problem, the paper
derives and applies a composite-estimation approach, in which CPI
item-area indexes are replaced by a weighted average of those
indexes and the U.S.-level item indexes. This approach causes the
estimated superlative index values to be higher, and the estimated
substitution bias consequently lower. For example, in a comparison
of annual chain Laspeyres indexes to chain Fisher Ideal indexes the
adjusted estimate of substitution bias is about 0.08 percentage
point rather than the roughly 0.12 percentage point previously
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