Hedonic price indexes with unobserved product characteristics, and application to personal computers.

We show that hedonic price indexes may be biased when not all product characteristics are observed. We derive two primary sources of bias. The first source is a classical selection problem that arises due to changes over time in the values of unobserved characteristics. The second comes from changes in the implicit prices of unobserved characteristics. Next we show that the bias can be corrected for under fairly general assumptions using extensions of factor analysis methods. We test our methods empirically using a new comprehensive monthly dataset for desktop personal computer systems. For these data, we find that the standard hedonic index has a slight upward bias of approximately 1.4% per year. We also find that omitting an important characteristic (CPU benchmark) causes a large bias in the index with standard methods, but that this bias is essentially eliminated when the proposed correction is applied.

KEY WORDS: Factor analysis.

1. INTRODUCTION

In recent years, U.S. statistical agencies have dramatically increased their use of hedonic methods in constructing official price indexes. Although the first use of hedonic methods in the consumer price index did not occur until 1987, according to Landefeld and Grimm (2000), approximately 18% of U.S. GDP final expenditures are now deflated using indexes created using hedonic methods, and this number is rapidly growing (see Moulton 2001). Other official indexes, such as the Census Bureau's single-family housing index and the BEA computer price index, used hedonic methods before their adoption in the consumer price index.

Hedonic methods are being introduced into official indexes to correct for two well-known problems with traditional matched-model methods. First, in markets with rapid product turnover, the matched-model index cannot be properly calculated, because it is impossible to measure the prices of new products before they enter and of old products after they exit. Pakes (2003) showed that if the matched-model index is calculated only for those products that remain in the sample, then it is subject to a selection bias, because the products that exit tend to be the ones that are less profitable. Second, the matched-model index does not account for quality change. All price changes, even those associated with improvements in some product characteristics, go into the index.

A long-standing problem with hedonic methods that has been widely recognized (Court 1939; Griliches 1961; Triplett 1969; Griliches and Ohta 1986) but remains unresolved is that typically not all product characteristics are observable by researchers constructing price indexes. The importance of unobserved characteristics has been demonstrated in recent work on demand estimation (e.g., Berry, Levinsohn, and Pakes 1995; Nevo 2001; Bajari and Benkard 2003). Another indication that unobserved characteristics may be important is the fact that it is often the case that hedonic price regressions have a low goodness of fit as measured by the R2. For example, Pakes (2003) reported [[??].sup.2]'s for computers in the range of .26-.52, and Cockburn and Anis (1998) reported [[??].sup.2]'s for arthritis drugs in the range of .26-.29. Very low [[??].sup.2]'s are not always the case. For example, Berndt, Griliches, and Rappaport (1995) reported [[??].sup.2]'s of .77-.83 for computers, and Griliches (1961) reported R2's in the range of .84-.97 for automobiles.

These observations motivate our three main research questions. First, what explains the errors made in the typical hedonic price regression? Candidate explanations include measurement error in prices, unobserved product characteristics, and approximation error due to functional form. The answer to this question is important, because if price regression errors reflect, for example, only measurement error in prices, then all of the assumptions of standard hedonic methods are satisfied. Second, if the hedonic regression errors reflect unobserved product characteristics, then to what extent is there a bias in the price index? Finally, is it possible to construct hedonic price indexes that fully account for unobserved characteristics?