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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes
“ideal” index, which is the geometric mean of the Paasche and the Laspeyres. But the Fisher index cannot be produced any faster than its least timely component, so its production lag is as great as that of the Paasche index. As we show below, there are other indexes that may be more timely than the Fisher ideal, but that still do a better job of approximating a COLI than does the Laspeyres.
For constructing COLI price indexes, as for other economic statistics, there is a tradeoff between timeliness and accuracy. For some purposes, a longer wait is an acceptable price to pay for greater accuracy and closer conformity to a theoretically desirable concept. Moreover, technical and statistical innovations in data collection—such as scanner data—will likely reduce the lag in the future, at least for some components of the CPI. (Bar codes for rent, cars, haircuts, and medical care are still some way off!) As always, much depends on the purpose to which the CPI is to be put. Policy makers and many others value rapid availability, so the BLS puts a good deal of weight on timely production of the index. An index for compensating social security beneficiaries, or for adjusting income tax brackets, can presumably wait longer, though probably not 3 years.
THE THEORY OF PRICE INDEXES AND ITS CRITICS
There is a large literature in economics on the theory of price indexes. We present no more than is needed for use in this report. Much of the relevant literature makes free use of mathematics. While it is possible to give a useful verbal discussion of the main issues, clarity requires some use of formulas. We provide a verbal discussion in the main text and support the argument with a technical note that contains the most important equations. We begin with the basket price index because the ideas are more straightforward and because Laspeyres and Paasche indexes provide useful starting points for thinking about cost-of-living indexes.
Basket Price Indexes
A price index is needed because there are many goods and services in the economy, each with its own price, and each with its own rate of change in price. If all prices in the economy changed at the same rate, there would be no need to construct an index because the ratio of prices in the two periods would be the same for all goods, and any one would summarize all others. Price indexes are needed because prices do not move at the same rate. Because relative prices change over time, a way must be found to combine (or aggregate) all the changes into a reasonable measure of overall price change. This aggregation needs to take into account how much is spent on each good, so that price changes for goods on which more is spent get greater weight. One simple way to do so is to calculate a basket price index.
Beginning with a list of actual purchases in the base period, the total cost of this basket in the reference period can be calculated, as can its total cost in the