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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes
stating their true magnitude, the statistical discrepancy (which measures the excess of the independently collected gross domestic income relative to gross domestic expenditures) would tend to be a substantially larger (positive) number than it typically is.
Most of the NIPA consumer expenditure data are grouped into detailed categories that can be associated with one or a combination of several CPI strata price indexes. These expenditure categories are then deflated, principally with the use of the CPI price indexes, to produce quantity indexes of real consumption outlays for each category. The detailed price and quantity indexes are aggregated into annual and quarterly Fisher indexes for total consumption and its major subcategories.23 Fisher quantity and price indexes have the desirable property that an index of current dollar expenditures divided by a Fisher price index produces the corresponding Fisher quantity index.
The quarterly data are available shortly after the quarter ends. Inflation and output changes for each year or quarter reflect the weights of the beginning and ending periods in the comparison. The Fisher price and quantity indexes are superlative indexes and take approximate account of the effect of consumer substitution among the individual strata categories of goods in response to changes in relative prices. For this as well as other reasons, the measured inflation rate is a little lower and the output increase a little higher than would be the case with Laspeyres weighting.24
Even though the overall CPI is not itself used as an output deflator for consumption expenditures, its individual components are the critical elements (along with the estimates of current dollar expenditures) in measuring what is happening to the level and structure of national output. Decisions about how to deal with such problems as quality change and new goods thus feed into the aggregate measures through the individual price indexes.
The estimation of national output data through the deflation of current dollar expenditures for the individual components of consumption requires either that the individual strata indexes used for deflators be themselves aggregated from individual prices with expenditure weights or that the individual prices be selected with the sampling procedure based on expenditure weights. That is, they must be plutocratic indexes. If the research into alternative data collection tech-
The annual Fisher indexes are based on weights in adjacent years and (in a very recent change in methodology) the quarterly indexes on weights in adjacent quarters. The quarterly indexes through the most recent completed year are adjusted so that their annual average corresponds to the annual indexes.
BLS recently switched to geometric averaging of individual prices for calculating the individual indexes for strata that account for about 61 percent of the weight in the CPI. Analysis led the agency to conclude that in these strata substitution among goods in response to price changes was large enough to warrant that geometric weights would be superior to arithmetic weights for approximating the effects of substitution behavior on the cost of living.