. "4 Evolving Market Baskets: Adjusting Indexes to Account for Quality Change." At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes. Washington, DC: The National Academies Press, 2002.
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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes
procedure assumes that for any two periods, t and u, ht(z) = Ktuhu(z) for all characteristics bundles z, where Ktu depends on t and u but not on z. That is, between any two periods the prices of all models (actual and potential) are assumed to differ by the same percentage. If this assumption is correct and the hedonic function is correctly specified, the characteristics variables pick up all price changes driven by quality changes in the menu of varieties on the market and coefficients on the time dummies pick up the residual pure price change. The index—interpreted as the price ratio net of the quality component captured by the characteristics variables—is produced directly from the difference in the time dummy coefficients from period to period. If the dummy variable for the base period is omitted, as is standard, the antilogarithm of the time dummy coefficient for any other period t gives the ratio of the price(s) of the good in question in period t to the price(s) in the base period.21 Similarly, the antilog of the difference between the time dummy coefficients for any two periods gives the price relative between those periods.
Under the time dummy method, a single regression covering all periods must be run each time the index is produced. Since regression coefficients involving the characteristics are held constant across periods, changes in marginal cost ratios or in consumer demand patterns are assumed to be negligible. Thus, the basic relationship between product characteristics and relative prices (as well as the mix of characteristics available at market) must be stable in order to accurately isolate the price component associated with quality change over successive periods. This stability is what allows time dummy coefficients to be interpreted as the pure price effect.22
The key problem with the time dummy approach is that, for product areas in which quality change bias is likely to be an issue, the relationship between price and characteristics often changes rapidly. As an example, it is unlikely that consumers value, on the margin, a 10 percent increase in computer hard drive memory the same now as a year or two ago. If regression coefficients assumed to be
Triplett (2001b:6-7) notes that the dummy variable method, when specified in a double-log or semilog functional form, produces a price index based on the geometric mean formula. Since statistical agencies have begun moving toward using the geometric mean formula to construct elementary item indexes (for other reasons), time dummy approaches have become more consistent with the prevailing methodology.
The problem of obsolete regression coefficients on characteristics is not unique to the time dummy approach. Certainly, the coefficients produced by the indirect approach, if not updated, are also susceptible to the same problem. However, the magnitude of the effect that the changing “true” relationship between characteristics and price can have on the index is more limited for the indirect approach. An index that is adjusted with the indirect hedonic approach will typically be less volatile because it is only affected by those variables representing characteristics whose values have changed from one period to the next. By contrast, all product characteristic variables that experience a divergences between their estimated and “true” relationship to price affect the time dummy coefficients and, in turn, any index derived from them.