Quality-corrected price indices: the case of the Dutch new passenger car market, 1990–1999

Abstract

Market dynamics and technological developments constitute a major challenge to the proper measurement of the price evolution of durable goods. In this study, hedonic methods are used to estimate quality-corrected price indices of new passenger cars in the Netherlands, 1990–1999. Use is made of a huge set of price, quantity and quality information about 11,000 car models, obtained from different sources. During the observation period the nominal price level of all available car models increased about 20% on average, while the shares of car models with airbags, tinted glass and power steering increased from almost nothing to about 90%. Matched model price indices and the official CPI for new passenger cars, which partially account for quality-adjustments, estimate the price increase to be equal to 10.6–14.2% respectively 11.2% for the 1990–1999 period. By contrast, the hedonic Fisher-like price indices based on the preferred annually estimated brand-weighted semi-log hedonic model, lead to price changes varying from  + 2.3% to  − 3.4% (depending on the choice of weight variable, and the use of fixed or varying reference periods in the index construction) and thereby fall 8.9 to 14.6 percentage points below the official figures, over the period 1990–1999. The pooled adjacent-years model holds an intermediate position with a predicted quality-corrected price decrease of 1.8% over the observation period, which is 13.0 points below the CPI.

Acknowledgements

This study has been part of the joint research project Price and volume measurement of goods and services of Statistics Netherlands (SN) and EUR. The authors gratefully acknowledge the role of SN in making available the required data and providing field specific support. They also acknowledge the contributions of ANWB and RDC in this respect. A.P.J. Abrahamse, B.M. Balk, J.S. Cramer, J. de Haan and L. Hoven are thanked for comments on previous drafts. The usual disclaimers apply.

Notes

 ANWB refers to the Royal Dutch Touring Club, which attends to the interests of tourists an road users in the Netherlands. RDC refers to the RAI Datacentre, which is responsible for car registrations in the Netherlands.

 The relatively high percentage of matching car models in 1999 is due to the fact that this year has only been observed for the first five months. If the introduction of new car models primarily takes place during the fall, then the actual percentage of matching models for 1999 will be much lower.

 The unit value price index

for the matched set is defined as:

 =  

(all summations over the matched set

, and ignoring the subscript Typ). This can be re-written to obtain

, which shows that

is similar to the Laspeyres matched model price relative apart from the factor (

), which incidentally shows that the unit value price index is not suited to measure pure price developments unless sales volume shares are constant.

 Hedonic methods have been frequently applied to the measurement of car prices. See Fisher et al. 1962; Griliches, 1964; Cagan, 1965; Cramer, 1966; Dhrymes, 1971; Hall, 1971; Cowling and Cubbin, 1971; Boyle and Hogarty, 1975; Friedlander et al. 1983; Mertens and Ginsburgh, 1985; Ginsburgh and Vanhamme, 1989; Mertens, 1990; Santos and Coimbra, 1995; Verboven, 1996; and recently Harhoff, 2002, Van Mulligen, 2002, and Tomat, 2002. In addition they have been applied to a wide variety of durable goods like refrigerators (Dhrymes, 1967), washing machines (Gavett, 1967; Silver and Heravi, 2001) and houses (Bailey et al. 1963; Musgrave, 1969; and recently Hoffmann and Kurz, 2002, and Bover and Velilla, 2002). Formalizations of the hedonic models are found in Rosen (1974), Triplett (1986), Feenstra (1995), Fixler and Zieschang (1993), Berry et al. (1995) and Goldberg (1995).

 The J-tests are performed by adding the predicted values of the alternative (H ₁)-specification, say z, to the model specification under H ₀. The H ₀-specification is maintained if the estimated parameter  α  of z in this regression does not differ significantly from zero; under H ₀:

. In addition to these J-tests, F-tests have been performed to evaluate the contribution of both the regular and the log-transformed continuous variables in a super model containing both types of variables next to the dummy characteristics. These F-tests do not give a definite result, but the F-values evaluating the contribution of the regular continuous variables, are substantially larger than those evaluating the impact of the log-transformed continuous variables.

 More precisely, the relative use of a weighting variable w ₀ against a competing variable w ₁ is examined as follows. First, the (annual or pooled) hedonic regressions are performed weighted by w ₀. Secondly, the residuals

from these regressions are squared and divided by their mean square error MSE, yielding

. Thirdly, the e _i are regressed on w ₁. Fourthly, half the regression sum of squares gives the Breusch–Pagan test statistic BP=SSR / 2, which is  χ ²(1)-distributed. If the e _i would be regressed on all three competing weighting variables together, then the required degrees of freedom in the last step would be equal to 3.

 Two remarks: first, in this study we abstract from the biased estimation of the expected price when least squares estimation of the log-transformed models is adopted; see Teekens and Koerts (1972) who demonstrate this point. Secondly, for the semi-log and double-log hedonic models, the order of exponentiation (of

) and averaging (of the

) may be important. Here, we interpret

as the characterization of a typical car model, of which the price development is estimated by various hedonic price indices. Alternatively, one might first impute the prices of all car models in the sample (leading to

), and subsequently determine their average (leading to

). The latter might be interpreted as the typical (imputed) price of the entire sample. Bode and Van Dalen (2002b) show that this alternative approach generates price index values that are slightly below those obtained with (11)–(14); the difference in AAG amounts to 0.2–0.4 percentage points. In the case of linear hedonic models, both issues are irrelevant.

 The corresponding calculations for a linear specification are less trivial. In the linear model, the estimated effects are interpreted as the quality-corrected (absolute) price differences between current and reference period (either t=0 or the preceding year t  −  1):

;

. These differences need to be divided by an estimate of the average price level in the reference period,

or

. The required estimates are obtained by substituting the (weighted) averages of the quality indicators (including age and vintage) and the estimated implicit prices into the hedonic models. This yields three indices for each pooled model, depending on the estimation period used to calculate the averages: the current period, the base period or the entire observation period. Examples are given in Bode and Van Dalen (2002b).

 To prove the point for the annually-estimated semi-log regressions, model (8) is slightly reformulated to become:

,

, and

is a row vector with technical characteristics including a 1 to represent the intercept. For convenience, let

an (K  +  1)  ×  n matrix to summarize the car characteristics and  ι  a n-vector with ones. Least squares estimation yields

, and

, where the

denote vectors with log-transformed prices. From this, the hedonic prices are imputed as:

; where h _ij is element (i, j) of the hat-matrix

. The  ≡  − sign is used to reflect the imputation practice, which ignores the fact that the least-squares predictors

are biased estimators of the expected price at given characteristics,

(see Teekens and Koerts, 1972; and Goldberger, 1968). Similarly,

. The imputed hedonic price relative for car i is therefore equal to:

. The geometric mean of these relatives is:

, which is the unweighted geometric mean matched model price relative. The last step makes use of the fact that

, which follows from the property of the hat-matrix that

; so for each row j:

. If a linear hedonic model is used, the same identity holds with respect to the arithmetic average. A similar proof based on a time dummy hedonic model can be found in Diewert (2001).

 In addition to these three identifiers the use of a fourth key EURuitv has been considered consisting of EURtyp plus 10 other make descriptors. (1) Primary type descriptors, like  ‘ L ’ ,  ‘ XL ’  or  ‘ GLS ’ . (2) Secondary type descriptors, like  ‘ FIRST ’  or  ‘ VOLCANO ’ . (3) Horse power (in kwh). (4) Number of valves,  ‘ 12V ’ ,  ‘ 16V ’ , etc. (5) Number of cylinders,  ‘ V4 ’ ,  ‘ V5 ’ ,  ‘ V6 ’ , etc. (6) Number of doors,  ‘ 2D ’ ,  ‘ 3D ’ ,  ‘ 4D ’  or  ‘ 5D ’ . (7) Four-wheel drive. (8) Four-wheel steering. (9) Roof type (hard or soft). (10) Long wheel base. Eventually, we did not use this key because it strongly increased the number of non-matching car models, and consequently the amount of unused volume information. In our defence, many of these characteristics correlate with the type characteristics defined in EURtyp, like horse power with cylinder content, and number of doors with type of body.