changes in relative prices—pork prices rise a lot and beef prices only a little— consumers try to minimize the effect of the price rise on their living standards: they shift their purchases, buying fewer of the goods whose relative prices have risen and more of those whose relative prices have fallen. This substitution allows them to improve their living standards relative to what would have been the case had they been constrained to maintain their old buying patterns in the face of the price changes. The traditional Laspeyres version of the fixed-basket index takes no account of these possibilities since it simply weights both sets of prices by the reference period quantities. As a consequence, the Laspeyres index tends to overstate the rise in the cost of maintaining the reference period’s standard of living.

An alternative weighting scheme is the Paasche index, which uses as weights the quantities purchased in the ending, or comparison, period. It measures the percentage difference in expenditures between what it would cost the household to buy the comparison period quantities at the old prices and what it costs at the new ones. But because the comparison period quantities already incorporate the household’s substitution in favor of goods whose prices have risen the least, the Paasche index understates the cost of maintaining the comparison period’s standard of living at the old prices. Equivalently, the Paasche index understates the change in the household’s cost of living, as evaluated at the comparison period’s standard of living.

If substitution behavior plays a major role in explaining changes in quantities purchased between the reference and comparison periods, goods that have experienced relatively large price increases will tend to receive higher weights in the Laspeyres than in the Paasche index, and the opposite will be true for goods that have experienced relative price decreases. Thus, the Paasche index typically tends to produce a lower estimate of average price increase than the Laspeyres index.

Notice, however, that the Laspeyres index overstates the cost of maintaining the reference period’s standard of living while the Paasche index understates the cost of maintaining the comparison period’s standard of living. Under conditions in which those two standards of living are significantly different—due perhaps to the size and pattern of the relative price changes or to changes in the incomes and tastes of consumers between the two periods—it is conceptually possible that the change in quantities is not dominated by the effects of substitution behavior. In that case the Laspeyres might produce a lower estimate of price increase than the Paasche. Nevertheless, empirical studies have shown that when the actual inflation measures produced by the two types of indexes are compared over various historical periods, Laspeyres indexes consistently produce a higher measured rate of inflation than Paasche indexes. This finding is widely interpreted as a testament to the importance of substitution behavior by individual households. Similarly, the magnitude of the differences between the two estimates is usually thought to depend on how much relative prices have changed and how much



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