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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes
calculation of conventional price indexes. . . shows substantial pitfalls of mechanically applying price indexes to such data.” The superlative index is intended to capture reductions in the cost of living as consumers substitute goods that have decreased in price for those that have increased. However, the superlative index calculated by the authors fails to produce this result (the superlative index grew faster). Feenstra and Shapiro (2001:22) concluded:
The consumer behavior that generates these data cannot correspond to the static utility maximization that provides the foundation for superlative index numbers. Our tabulations suggest that the index numbers do not properly account for consumer behavior in response to sales. In particular, the chained Tornqvist gives too much weight to price increases that follow the end of sales.
The authors go on to explain that their findings reflect purchases made for storage rather than immediate consumption. In other words, purchases and consumption do not track in a parallel fashion, particularly for items that can be stored. As such, the consumer does not face as much an increase in price (after sales) as the raw data imply. In addition, advertising contributes to the breakdown of the law of demand that is assumed under the superlative index approach: “If advertisements cause consumers to purchase a [larger] quantity than would be consistent with static maximization of a time-invariant utility function, superlative index numbers will not accurately measure the cost of living” (Feenstra and Shapiro, 2001:22). On the basis of their findings, they conclude that unit values might provide a good approximation for construction of a COLI but should be adjusted to reflect consumption and should be adjusted to account for storage costs.11
Many of the general advantages of scanner data noted above may also help to address other CPI biases. For instance, scanner data allow for quicker and more accurate identification of both new goods and item attrition (and, as such, could have the capability to reduce new goods bias), as well as of outlet substitution patterns. Furthermore, scanner technology generates more detailed data for hedonic regression and other quality adjustment methods (although quality change bias is probably less of an issue for food items—the potential may be greater in areas such as consumer electronics) and also produces empirical evidence that may allow researchers to estimate the impact of quantity (and other types of) discount pricing on index growth.
Triplett (1998) provides a simple demonstration of several other problems with using high-frequency data to produce a chained superlative index.