price relatives, and statistical agencies are quite successful in collecting information on prices in a timely manner. However, while the Laspeyres price index requires information on base period expenditure shares, the , the Paasche index requires information on current period expenditure shares, the With present methods of data collection, it is not possible to have accurate information on current period expenditure shares in a timely manner. Thus, from a practical point of view, the preferred fixed-basket price index is the Laspeyres price index since it can be evaluated in a timely manner. We note another advantage of the Laspeyres price index over its Paasche counterpart in the context of indexation of incomes below.
After a lag of about 2 years, it becomes feasible to evaluate the Paasche price index.1 Hence, in the context of making price comparisons over the long run, we have (at least) two different measures of price change between periods 0 and t: the Laspeyres estimate of price change, , and the Paasche estimate of price change, . These are conceptually different, because they price different bundles over time, and in some cases the distinction may be important, and statistical agencies might wish to make both of these indexes available to the public. However, suppose that for practical or political reasons we need a single estimate of price change between periods 0 and t; is there a “best” such estimate? Obviously, there are many possible approaches to answering this question. We consider two simple and intuitive approaches.
The first way of combining the Paasche and Laspeyres measures of price change is to take some sort of an average, which we write in the form so that we can write the new index as
We want this average to treat both price indexes symmetrically, to be positive, to be linearly homogeneous in both price indexes, and to be equal to either one when they are the same. In addition, we would like our new index to satisfy the time reversal test, which says that a price index from 0 to t should be the reciprocal of the price index from t to 0, so that