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COPYRIGHT 2004 American Statistical Association
Matched-model price indexes generally overestimate quality-adjusted prices, because the price/performance ratio of models sold in consecutive periods is worse than that of new models. This "unrepresentativeness" of the sample potentially might be reduced by obtaining higher-frequency data, thus increasing the fraction of models that are matched. We propose a set of comformable indexes to test this hypothesis. Using computer prices from the Buy Direct press, we find, contrary to initial expectations, that the bias in the matched-model price index increases with the sampling frequency. The bias is reduced if the high-frequency index is constructed using only long-lived models. These results suggest that models that last for only a brief time are models for which the price/performance ratio has deteriorated very rapidly. Thus increasing the sampling frequency without purging short-lived models actually increases the selection bias.
KEY WORDS: Personal computers; Quality-adjusted consumer price index.
1. INTRODUCTION
The accurate measurement of quality-adjusted price changes is an important element in the construction of aggregate changes in the cost of living and the measurement of productivity increases. This is particularly important for products characterized by rapid technological change and performance improvement. Indeed, recent estimates indicate that half or more of the (upward) bias in the consumer price index (CPI) is due to inadequate measurement of quality improvements. Reducing this bias in the CPI has been the subject of recent research by Abraham, Greenlees, and Moulton (1998), Moulton and Moses (1997), Moulton and Stewart (1999), and Reinsdorf (1999). Greenlees (1999) demonstrated that even random sampling errors can impart a negative bias in the CPI when superlative indexes are used. A related literature, to which Hausman (1999) has made the most recent contribution, discusses how to incorporate new products in the CPI.
This article explains that a more-intensive data collection effort designed to improve the quality of a price index constructed from price changes of identical models can actually have the opposite effect. In particular, we have shown using data from the personal computer market that increasing the sampling frequency (i.e, collecting data on a monthly rather than quarterly basis) will result in an upwardly biased matched-model-based price index. We show that this result is driven by the fact that a high-frequency index includes short-lived models with very rapidly deteriorating price-performance ratios.
Of the many approaches to control for quality change in the construction of price indexes, the two most prominent are matched-model analysis and hedonic regressions. A price index based on matched-model analysis is derived by calculating the change in the average price for models offered in both of two periods. In hedonic regression analysis, one assumes that the price of a product is a function of its quality characteristics. Price indexes obtained from hedonic regressions are derived by calculating the change in "imputed" prices between the two periods.
Matched-model analysis has been widely perceived to lead to an underestimate of improvements in the price/quality ratio (Gordon 1990, chap. 6; Triplett 1986). This perception is based on the conjecture that new models are on the price/quality frontier, whereas existing models, on which the construction of the price index is based, are progressively falling behind the price/quality frontier. Indeed, Berndt, Griliches, and Rappaport (1995), Berndt and Griliches (1993), and Cole et al. (1986) have provided some evidence suggesting that prices of existing models are higher, after adjusting for quality, than prices of newly introduced models. Because a matched-model index is based on the price changes of existing models only, it will overestimate the price index. Hedonic regression methods take into account all available observations and estimate changes in quality by "pricing" the attributes of each model using the hedonic coefficients. However, there is no unique way to construct such an index, because the index is dependent on the specification of the hedonic regression. Therefore, a unique "hedonic price index" does not exist. Often, however, different hedonic regression-based price indexes yield similar results. (We henceforth abstract from any theoretical issues concerning the economic meaning of the specification for any regression-based or other price indexes, and refer the reader to Dhrymes 1971; Fisher and Shell 1971; Triplett 1971, 1989, and Feenstra 1995 for stimulating discussions on this subject.)
Essentially, the choice between the two types of indexes involves a trade-off between a well-defined index with selection bias and an ambiguously defined index with no selection bias. The recent literature prefers the unbiased hedonic approach. (We note, parenthetically, that both indexes could exhibit bias due to unobserved technical change.) However, most of the research comparing the types of indexes has used annual data. Using annual data means that only a very small fraction of models can be used in constructing the matched-model price index. This factor may contribute to the poor performance of this index because of both the high variance due to small samples and the bias resulting from the unrepresentativeness of the sample since only very long-lived models are included. In principle, both of these factors would be greatly diminished if high-frequency data were used to construct a matched-model index, because then a higher fraction of the models would be included. Indeed, one might argue that a more representative, high-frequency matched-model index could be preferable to the ambiguously defined hedonic-based indexes. This approach to increasing the sample size might also be preferable to the alternative approach of "matching" models that are not identical. This latter approach decreases the bias due to the unrepresentativeness of the sample but creates a new source of bias in the presence of a systematic and incremental "drift" toward slightly better models (see Triplett 1986).
In this article we test the possibility that higher sampling frequencies reduce the bias of the matched-model price index using a very high-frequency dataset of personal computers advertised in the Buy Direct press. In particular, the high-frequency aspect of the data allows us to investigate not only whether price indexes based on matched-model analysis differ from those based on hedonic regression, but also whether these differences (if any) become less pronounced as the interval between successive price sampling periods decreases. The personal computer industry is characterized by high model turnover and technical change: It is the ideal industry in which to study the effects of increased frequency of data collection on matched model price index performance. Indeed, Cole et al. (1986) have documented that the discrepancy between matched-model and regression-based indexes is highest for products and time periods that are characterized by rapid technical advances. In addition, we investigate the robustness of the hedonic-based indexes to regression specification.
For the comparison between the matched-model and hedonic regression based indexes to be meaningful, the two sets of indexes must be defined in a conformable way. Two indexes are defined to be conformable to one another if they yield identical results when all models are offered in all periods. In this article, we extend the theory of price indexes by formulating such a set of conformable matched-model and regression-based price indexes.
Our results show that (a) the regression-based indexes do not differ dramatically over the course of our sample period; (b) the matched-model-based indexes differ from each other and from the regression based indexes; and, to our initial surprise, (c) the difference between the matched-model-based and regression-based indexes increases with sampling frequency. A matched-model index based on monthly data yields price declines that are much lower than those obtained from regression-based indexes. A matched-model index based on bimonthly data (i.e., an index constructed by "throwing away" the data from every other month) yields price declines that are higher than the monthly matched-model index but lower than the regression-based indexes. Quarterly and semiannual price indexes follow the same pattern; the lower the sampling frequency, the higher the estimated price decline, but not as high as the declines estimated by the regression indexes. These patterns are robust to excluding observations that correspond to "overpriced" models (i.e., models with prices in the top quartile of prices after controlling for observed characteristics) and excluding a model during the last month that it is offered for sale. In contrast, the bias of the monthly matched-model index is reduced by a factor of 2 when only very long-lived models are included in the sample.
The foregoing results suggest that the selection bias is increased when models that survive for only a short period are included in the construction of a matched-model index. The intuition for this result is as follows. Discontinued models are models with price/performance ratios that have fallen far below the frontier. Hence models that last only 2...
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