to be the conceptual basis. Nevertheless, both the test and stochastic approaches have intuitive appeal, and they are often useful for illuminating the properties of specific indexes or for dealing with technical issues that are not otherwise easily addressed. Given the many purposes to which price indexes are put, it is often helpful to have more than one conceptual framework.
It is useful at the outset to put these concepts in context. Note first that general discussions of price index numbers are often cast in terms of two situations, usually labeled the reference and the comparison. The two situations might be geographical locations—Los Angeles versus New York, or the United States versus India—but in the case of the CPI, the two situations are different time periods, typically a reference period that is held fixed for a number of years, and a series of later periods ending with the “current” period, which in practice is a period in the recent past. The CPI is produced on a schedule that, together with the availability of the underlying data, puts constraints on what is possible. In particular, the BLS is able to collect data on prices with a much shorter lag than is possible for collecting data on the quantities of items purchased. The monthly CPI is published quickly: for example, the October 1999 CPI was published on November 17, 1999. However, the basket that was priced for this CPI came from Consumer Expenditure Surveys that collected data during 1993, 1994, and 1995 and was therefore a little more than 5 years old on average. In the past, the basket had been updated infrequently, only once a decade. Although the BLS has undertaken to shorten the time between updates, baskets available for pricing are always likely to be several years old, at least in the absence of some radical new technology, such as the extensive use of scanner data or automatic computer-based reporting of sales from retailers.
The availability of data places limits on what can be achieved within any given conceptual approach to the CPI. To stay with the current production schedule, a basket price index approach must use a base that is considerably earlier than the comparison period. The BLS can compute basket indexes relative to any base period in which quantity (or expenditure) data are available, but no later. Any methodology that requires a current basket to compute the current price index can generate price indexes only with a lag of 2-3 years. To see the implications of this, think about the two most familiar forms of the basket price index, the Laspeyres price index and the Paasche price index. In the Laspeyres, the base period basket is priced in both base and current periods—the base period is also the reference period—and the price index is the ratio of the basket’s cost at current prices and at base period prices. No information is required on the current basket. The Paasche index, by contrast, works with the current basket; it is defined as the ratio of the cost of the current basket at current and reference period prices. Because quantity information comes more slowly than price information, the production of a Paasche price index requires a longer time lag than does the production of a Laspeyres. A Laspeyres index can be thought of as an approximation to a COLI. Better approximations are possible using information on both the reference period and current period baskets. One such approximation is Fisher’s