Age Effects, Unobserved Characteristics and Hedonic Price Indexes: The Spanish Car Market in the 1990's

This paper computes and compares alternative quality-adjusted price indexes for new cars in Spain in the period 1990-2000. The proposed hedonic approach simultaneously controls for time-invariant unobserved product effects and time-variant unobserved quality changes, that are assumed to be captured by model age effects. The results show that the non-adjusted price index largely overstates the increase in the cost of living induced by changes in car prices and that previous evidence for this market have not measured the real extent of that bias, probably due to the omission of controls for unobservables. It is also shown that omitting age effects can also lead to misleading conclusions. The estimated price indexes give also some insights on what could have been the determinants of price evolution in the Spanish car market.


Introduction
The consumer price index (CPI) is an economic magnitude of major interest in economic policy. From a microeconomic point of view in ‡ation increases consumer's cost of living.
One immediate macroeconomic implication is the pressure to increase wages, which in turn has a direct impact on competitiveness. The CPI is also the basis for measuring growth and productivity in real terms, not to mention its in ‡uence in the evolution of interest rates and other …nancial variables governing for instance investment decisions at the micro and macro levels, which also in ‡uence growth rates. In this context, the correct measurement of consumer price's changes is a fundamental issue (Boskin et al. (1998)).
The CPI is usually measured as a weighted average of the prices of a …xed basket of goods representing consumer expenditure. However, the report of the Boskin Commission has established that one of the major drawbacks of this methodology is the inability to cope with the quality change and new product biases (Boskin (1996)), therefore overstating the increase in the cost of living (Boskin et al. (1998)). The recommendations of the Boskin report have in ‡uenced statistical agencies to take the steps toward making the CPI a better approximation of a true cost of living index. They have also served to renew the interest on hedonic regressions and hedonic price indexes as a potential way of controlling for those biases. The recent literature has mainly focused on durable goods where quality upgrading is frequent and product replacement is high, such as for example cars (Reis and Silva (2006), Matas and Raymond (2009), Dalen and Bode (2004)), computers (Pakes (2003), Brown (2000)), domestic appliances (Ioannidis and Silver (2003), Silver and Heravi (2004)) or electronic devices (Chwelos et al. (2008)). These types of goods usually have a large weight in the CPI (specially in the case of cars) and therefore any adjustment in price indexes for those categories may have a relevant impact on the CPI.
Hedonic price indexes are constructed based on a hedonic regression where the price of the good is explained by its characteristics. The coe¢ cients of this regression are a sort of prices for characteristics that may be used to construct an index of quality change. The price change of the good is then adjusted by this quality change to build a price index free of quality or new product biases. Most of the literature considers hedonic regressions with observed product characteristics, while the impact of omitted unobserved product characteristics have received very little attention. Most authors rely on brand or make dummies hoping that this will be enough to control for product unobservables. However, Benkard and Bajari (2005) and Requena-Silvente and Walker (2006) show, using di¤erent methodologies, that not including speci…c controls for unobserved e¤ects can induce a signi…cant bias in hedonic price indexes.
In this paper, following Requena-Silvente and Walker (2006) I construct a hedonic price index for cars in Spain in the 1990's controlling for time-invariant product unobservables. I extend their approach to control also for time-variant unobserved factors by including age or cohort controls. This has already been proposed in the literature (see for example the application to the Dutch car market of Dalen and Bode (2004) and the references therein) but the simultaneous inclusion of age and …xed e¤ects has not been tried before. As usual in this literature I …nd that price indexes are larger than quality-adjusted prices, but also that …xed e¤ects play an important role that will be misleading unless we control for age e¤ects. In particular, it is shown that in the absence of cohort e¤ects just controlling for time-invariant unobservables tends to overstate the hedonic price index by a large amount.
The hedonic methodology dates back at least to the 1930's with the pioneering work of Court (1939) followed by the later contributions of Griliches starting from 1961. Since then, there have been theoretical and methodological developments (see Triplett (2004) or Pakes (2003) for a general perspective) and many empirical applications (see for example Bover and Izquierdo (2003) for an overview by product categories). It is not the purpose of this article to provide a full review of the literature so I will concentrate on those aspects closer to the scope of the paper.
Regarding the estimation of hedonic equations, Benkard and Bajari (2005) make clear that the potential e¤ects of omitting unobserved product characteristics over the qualityadjusted hedonic price index, although recognized, have not been tackled adequately (p.61). They propose a method based on factor analysis to correct for these biases and they apply it to the US personal computer market …nding that not taking into account unobserved e¤ects induces an upward bias in the hedonic index of about 1.4% per year. An alternative approach proposed by Requena-Silvente and Walker (2006) controls for product unobservables by introducing model dummies in the hedonic regressions. In their application to the UK car market they …nd that the contribution of …xed e¤ects to the value of cars has fallen since the 1970's, suggesting a downward bias in the hedonic index.
The automobile sector has been widely studied in the hedonic price index literature, probably as a consequence of the important weight that automobiles have in consumer price indexes. Among the papers that have computed hedonic prices indexes for cars for di¤erent countries and periods of time we have: i) For the US: Court (1939), Griliches (1961) between 1954-1960, Triplett (1969) between 1960-1965and Ohta (1987) for used cars between 1970-1983 ii) For the UK: Cowling and Cubbin (1972) between 1956-1968, Murray and Sarantis (1999) between 1977-1991and Requena-Silvente and Walker (2006 between 1971-1998. iii) For the Netherlands: Kroonenberg and Cramer (1974) between 1964-1971and Dalen and Bode (2004) between 1990-1999. iv) For Portugal Reis and Silva (2006) between1997-2001. v) For Italy Tomat (2002Tomat ( ) between 1988Tomat ( -1998 Regarding the Spanish market Izquierdo et al. (2001) have computed hedonic prices for new cars using monthly data for the period 1997-2000. Their hedonic regressions explain prices as a function of quality indexes, constructed from a comprehensive set of 35 observed characteristics, in order to avoid the collinearity problems common to this methodology (Pakes (2003)). The main …nding is that quality corrected prices are 3.1% lower per year as compared to the price index computed by the Spanish National Statistics O¢ ce. Matas and Raymond (2009) o¤er estimates for the period 1981-2005 but using yearly, instead of monthly, data. They perform standard hedonic regressions but they also propose two di¤erent smoothing techniques to deal with the parameter instability caused by collinearity. They do not address directly the problem of product unobservables, assuming that they may be captured by brand dummies. Their results show that not controlling for quality improvements overestimates nominal price increases at an average rate of 8.8% per year for this 25 years. For the period 1997-2001 they estimate a gap of around 2.85% per year, in line with the results of Izquierdo et al. (2001), although a bit smaller.
The rest of the paper is organized as follows: Section 2 describes de data and the quality improvement process of cars in Spain. Section 3 explains the methodology followed in the hedonic regressions. Section 4 presents the price indexes to be computed. Section 5 shows and discuss the results. Finally, section 6 concludes.
2 Quality improvement patterns for cars in Spain during the 1990' s 2.1 Data Description I use a unique data set of monthly registrations of new cars in Spain from January 1990 to December 2000. These data were initially collected by, and …rst used in Moral (1999) 1 , who also provides a thorough description of the data base. It includes information on listed nominal and real prices and characteristics such as car size (length, width, luggage capacity), power, maximum speed, fuel consumption, and equipment (dummies for air conditioner, anti-lock braking system, power steering, central door locking and electric windows). It also has information on model age and on the geographical origin of the brand producing the model. Table 1 describes the set of characteristics.
The unit of observation is the car model. Car models often have several variants or subvariants. In the data, a given model denomination is associated with the characteristics of its most popular variant. Therefore, the variation in characteristics over time is due to the variation of the characteristics of the representative variant (and not due to a change on the variant chosen). The number of registrations for a model are, however, the sum of registrations of all variants. Some …lters were introduced to exclude super luxury models, e.g., Ferrari or Rolls Royce. Models with fewer than 10 registrations per month are also excluded. Nevertheless, the data set accounts for more than 99.9% of car registrations during the sample period.
Models are classi…ed in segments following industry sources 2 . In particular, I consider the following classi…cation in eight segments: Small-Mini, Small, Compact, Intermediate, High Intermediate, Luxury, Sport, and Minivan. The segments from Small-Mini to Luxury correspond to vertical product di¤erentiation, while Sport and Minivan can be identi…ed with the horizontal one. These two segments include cars of di¤erent levels of quality, all of them having in common that they are designed to serve a more speci…c purpose.

The evolution of automobile characteristics and prices
One of the most salient features of the Spanish car market in the 1990's is the intense process of product entry and replacement. The number of products increases steadily over the period due to the entry of new …rms (mainly from Asia) and the expansion of the product range of incumbents. We can therefore say that the market is characterized by an scenario of increased competition, specially from Asian manufacturers (Jaumandreu and Moral (2008)). The evolution of prices and car characteristics suggests that non-price competition is the strategy followed by the majority of …rms. The average price of cars in real terms increases all over the period, except for Asian models (Figure 1), which may be due to the fact that at the beginning of the sample period Asian producers were concentrating mainly on models of the upper-class segments. As they expanded their range of products to cover segments of lower quality it is natural that the global average price decreases. The initial decline in prices ( Figure 2) can be attributed to the context of economic crisis at the beginning of the decade in Spain. The quality of cars, measured by the amount of each characteristic, clearly increases all over the period, perhaps more in the case of non-Asian models. Figures 3 to 6 plot the evolution of engine power and air conditioning, which are representative of the general pattern of change of the other characteristics. 3;4 The general trend goes toward larger, faster and more powerful cars but with smaller luggage capacity and higher consumption rates. This is particularly marked in the case of European models, probably as a response to the increased competition from Asian models in the second half of the decade. The average Asian car seems to follow the opposite pattern, but as mentioned before, this is mainly a consequence of the fact that the earlier Asian cars were concentrated in the upper-quality segments. After 1995 the Spanish market witnesses an intense wave of entries by Asian makers, mainly in the medium and lower quality segments. Nevertheless, Spanish, European and American manufacturers contribute also very actively to the enlargement of the number of models o¤ered in Spain.
The evolution of car amenities such as air conditioning, power steering, etc. follows a similar pattern, although in this case it is very clear that improvements in these characteristics are always introduced in the upper-class segments and they eventually spread over the rest. It is important to clarify that the Minivan and Small-Mini segments became popular during this period so that the variety and number of models increased signi…cantly. As a consequence the average characteristics varied a lot due to the intense entry process, specially at the beginning of the sample period.
In summary, it seems clear that the automobile sector in Spain experienced a remarkable improvement in quality which a simple price index would ignore, thus overstating the increase in the cost of living attributed to car purchases. Therefore, the application of hedonic regression techniques to the computation of price indexes seems to be clearly justi…ed.

Hedonic regressions
The hedonic regression methodology is aimed at explaining price variations by the change in product characteristics. Its practical implementation requires choosing and justify-3 These …gures are omitted here for the sake of brevity. They are available from the author upon request. 4 All the …gures presented here are weighted by unit sales. ing assumptions regarding model speci…cation, functional form of the hedonic function, parameter constancy or weighting. The next subsections address each of these issues.

Model speci…cation
The most basic hedonic speci…cation relates price to characteristics: where 0 is an intercept, X i is a row vector of product i observed characteristics, is the vector of implicit prices and " i is some iid error term. In some cases the researcher may have access to a thorough set of product characteristics, comprehensive enough to justify the assumption that there remains no unobserved characteristic and the model is well speci…ed. However, in most cases the set of characteristics is much more limited and observability becomes an issue. And even if we had such an exhaustive set of characteristics we could always think of factors like reliability, consumer's perception of quality or reputation that have an e¤ect on prices but are not speci…cally captured by any combination of technical characteristics. If these factors are also correlated with the observed characteristics then their omission would make the estimation of 0 s inconsistent. One approach that has become common to address this problem consists on adding brand or make dummies, hoping that reputation or reliability will be adequately captured: where Brand is a row vector of make dummies taking value 1 in the position corresponding to the brand of product i and zero otherwise. This set of dummies may be augmented in some cases, like the automobile sector, with the addition of segment dummies: where Seg is interpreted in the same manner than Brand , but now for segments. Unfortunately, even with brand or segment dummies there may remain unobserved factors speci…c to model i. One possible solution would be to introduce product speci…c dummies ( ) to capture such e¤ects: However, if the number of products is large this approach could be problematic due to the lack of degrees of freedom. An alternative solution would specify a model with a time-invariant product …xed e¤ect ( i ): The estimated prices for characteristics, , would be the same in approaches 4 and 5 (Cameron and Trivedi (2005) section 21.6.4, p.732). Approaches 1-3 are common in the literature and approach 4 has been proposed by Requena-Silvente and Walker (2006). In this paper I will compare the results from all of them, but using the speci…cation 5 instead of 4.
Regarding the choice of characteristics in X the common approach has been using as many as there are available. However, the potential collinearity between many of these characteristics can induce some problems in the estimation of 's , notably the appearance of "wrong" signs or parameter instability. Nevertheless, following Pakes (2003), these problems have not been a particular source of worry in the literature. Therefore, in my empirical speci…cation I will be using all characteristics listed in Table 1. 5 Among them, the role of age deserves particular attention.
The variable age, measures the age of the product, i.e., the period of time elapsed since it was …rstly introduced in the market. So, for a given year, the variable age informs about the vintage of the product and its particular level of technical change (for example, older products could be technically less developed). But age also informs about the degree of obsolescence of the product, or its reputation among consumers (older products could be seen as more successful). In summary, the age can be informative about product speci…c (quality) characteristics that cannot be inferred from the observed technical speci…cations and that can also be time-variant (see the discussion in Dalen and Bode (2004)). Therefore introducing age as an explanatory variable can help in controlling for unobserved e¤ects in combination with i in expression 5. The latter would control for time-invariant product speci…c unobserved e¤ects, while the former would capture the time-variant ones that are common to the products of the same age. After these controls are introduced it does not seem implausible to assume that all relevant sources of (time-variant or -invariant) unobserved product heterogeneity are being accounted for.
If product unobservables are really an issue then the estimation of expressions 1-3 should yield biased estimates of . The introduction or not of age would just a¤ect the size of the bias. In speci…cation 5 however, the omission of age could introduce some bias and its inclusion should remove it. If the time-variant unobserved e¤ects are correlated with X then omitting them would induce correlation between X and the error term. The size and direction of these biases are empirical questions that depend on the correspondent estimates of the e¤ects.

Functional form of the hedonic function
In the previous subsections linear expressions of the hedonic regression have been used for simplicity in the exposition. However, the relation between prices and characteristics could follow any general functional form: . Nevertheless, the literature has focused on linear relations but allowing for the possibility of transforming the data to have a more ‡exible speci…cation. The usual approach has consisted on applying a Box-Cox transformation to the dependent and/or the right hand side variables and estimating the transformation parameters consistent with the data. It turns out that in most cases the Box-Cox parameters are close enough to 0 or 1 to safely assume semi-log, log-log or simple linear speci…cations. Therefore, most of the work of functional form selection reduces to determining the best suitable transformation of the data.
Regarding the automobile industry previous studies have found that a semi-log spec-i…cation (taking logs on the price and leaving the right hand side variables unchanged) is the one that best …ts the data, it is the case of Dalen and Bode (2004) or Requena-Silvente and Walker (2006). For the Spanish market, Matas and Raymond (2009) also …nd the semi-log the most adequate choice. That will also be the one I will use in this paper. This choice is sustained by the fact that the maximum likelihood estimates for the parameters of the Box-Cox transform on a regression of price on characteristics for the whole sample yield a parameter of 0:013 (p-value 0:116) for price and 1:14 for the right hand side variables (the dummies are excluded from the transformation). Therefore the assumption of linearity for right hand side variables and logs for price does not seem unreasonable. 6

Parameter constancy and the use of weights in hedonic regressions
The hedonic price index methods can be applied following di¤erent estimation strategies that are basically di¤erentiated by the sample size they use: 1. The time dummy variable (TDV) method …ts the hedonic regression to the whole sample, adding to the model speci…cation a set of time dummies. The idea is that the coe¢ cient of the dummy of say, period t, will represent the growth in the price index from the initial period to time t net of quality changes, which are controlled for through the variation of characteristics. The main drawback of this method is that it restricts the coe¢ cients (prices) of characteristics to be constant over the whole sample period. Even if one could consider that this assumption would be reasonable for short sample periods or in contexts where consumer perception and valuation of quality remain constant over time, the truth is that in the literature parameter constancy is most often rejected by Chow tests of structural break. The case of the automobile industry is not an exception.
2. The adjacent period (AP) method can be seen as a re…nement of the TDV where parameter constancy is assumed to hold only for two consecutive periods and a dummy is added to capture the quality-adjusted price increase of the second period with respect to the …rst one. A whole index series can then be constructed by chaining the time dummies coe¢ cients.
3. The single period equation (SP) method allows the prices of characteristics to vary from period to period. Its parameter estimates can then be used to construct indexes of quality change which serve to correct the quality bias of the non-adjusted price index. One potential drawback of this approach is, as mentioned before, the parameter instability on the estimated prices of characteristics. However, the quality-adjusted price indexes constructed from them seem to be quite robust in general (Pakes (2003)).
In this study I will follow the single period equation approach, that has gained in popularity precisely because it avoids the assumption of parameter constancy, which is not recommended unless it is sustained by the data (Triplett (2004) p.61). This is generally not a problem in the AP method, however this paper is aimed at assessing the impact of unobservables on price indexes, rather than comparing the results of SP and AP methods 7 (see again for examples Triplett (2004) pp.61-63).
Another point of debate in the hedonic literature is whether the hedonic regressions should be weighted or not. In this respect, and following the recommendations in Triplett (2004) I will make use of weights to avoid an excessive impact of prices of products whose market share is low because they are viewed as less satisfactory by consumers. The price variation of these type of goods should have less importance than other more successful 7 For the same reason I will not consider here the matched model approach. models. 8

Estimation issues
Taking into account all considerations of the previous subsections, the …nal hedonic spec-i…cations to be taken to the data are: LGC + 4 HP + 5 maxSp + 6 Age + (6) + 7 AC + 8 ABS + 9 P ST + 10 CDL + 11 EW + " ln p = 0 + 1 C90 + 2 CarSize + 3 LGC + 4 HP + 5 maxSp + 6 Age + (7) LGC + 4 HP + 5 maxSp + 6 Age + (8) LGC + 4 HP + 5 maxSp + 6 Age + (9) + 7 AC + 8 ABS + 9 P ST + 10 CDL + 11 EW + + " where Brand and SEG denote sets of dummies to control for brand and segment e¤ects, respectively. Assuming that observed characteristics are exogenous, expressions 6 -8 can be estimated period to period by ordinary least squares. Expression 9 requires at least two periods to control for the unobserved component . Therefore, in the estimation of 9 I follow the approach proposed in Matas and Raymond (2009) of taking moving samples of order h. They suggest this procedure as a way to smooth the estimated coe¢ cients of single period hedonic regressions, that tend to be erratic from period to period. This method has the added advantage of providing enough time observations for the application of the within estimator 9 in equation 9. It should be clari…ed that this approach allows di¤erent prices for characteristics every period, except for the …rst h 1 periods. What is assumed is that the coe¢ cients of period t can be satisfactorily estimated by pooling all periods from t h + 1 to t. In this subsample the prices for characteristics from t h + 1 to t 1 are held equal to those in period t. Next, for the estimation of period t + 1 the coe¢ cients of t + 1 will be assumed to hold for the previous t h + 2 to t periods, and so on. So, contrary to what happens in the AP or TDV approaches, holding the coe¢ cients constant is a manner of improving the estimation of the per-period coe¢ cients. It is assumed that for the estimation of t the previous t h + 1 periods contain useful information, and that we can take advantage of it even if we "temporarily" impose the coe¢ cients of period t over the previous t h + 1 periods.
In the AP or TDV methods the sample remains constant and so do the coe¢ cients within the sample. The order of the moving sample, h, should be of a size just enough to control for the …xed e¤ect, and not too large to avoid an excessive smoothing. For the empirical application I have chosen h = 12 because for shorter samples many of the characteristics are usually constant and therefore their coe¢ cients could not be separately identi…ed from the …xed e¤ect. Recall that we are using here monthly data and that even if there is a signi…cant rate of product change and improvement, many models do not experiment changes in their technical speci…cations from one month to the next one. 10 By …xing h = 12 we are assuming a one-year moving sample 11 , which may be seen as a bit ad-hoc but which is also consistent with all studies using yearly data to estimate hedonic prices 9 The within estimator for a …xed e¤ects model is an ordinary least squares estimator of a model where the original variables are substituted by their within transformation, which consists on subtracting to each variable its time mean, i.e, for a variable y it its within transformation is: y w it = y it 1 T P T t=1 y it , where T is the number of time periods for the cross-section unit i. The within transformation is therefore a way of removing the …xed e¤ect from the data. 10 This is also the main reason for not computing price indexes using the AP hedonic approach. 11 The hedonic indexes are quite robust to the choice of h. For instance, there is not much di¤erence between those computed for values of h = 6; 12; 24 . However, for h = 6 still many characteristics remained constant preventing the estimation of their hedonic prices, and h = 24 seems perhaps a too long period to impose the equality of parameters to the moving sample. for characteristics. 12 To make the results more comparable I will estimate speci…cations 6 -8 using the moving sample of order 12 13 4 Quality-adjusted price indexes I use a unit sales weighted Laspeyres geometric index 14 , as proposed in Feenstra (1995), to measure the price increase of automobiles. The quality-adjusted index for model i is therefore de…ned as: where Q it = (X it X it 1 ) t represents the quality correction and can be interpreted as a characteristics quantity index (Triplett (2004) p.60). Notice that all time-invariant characteristics, such as brand and segment dummies or individual …xed e¤ects, cancel out in Q it . Thus, the di¤erences between the alternative quality-adjusted price indexes proposed come from the di¤erent estimates of 's in each speci…cation. In order to mitigate the potential impact of coe¢ cient instability in the single period hedonic regressions over the indexes I smooth the 's using a weighted moving average of coe¢ cients or order k = 3 as proposed in Matas and Raymond (2009). 15 Therefore, the smoothed coe¢ cient for characteristic j in period t is: smooth jt = t 1^ jt 1 + t^ jt + t+1^ jt+1 12 Although it is true that in these cases there is no alternative choice given the data constraints. 13 The hedonic indexes from 6 -8 computed using single period hedonic regressions are virtually identical to those using the moving sample.
14 One advantage of using characteristics price indexes is that the functional form of the hedonic speci-…cation is not linked to the index number formula (Triplett (2004), p.60). If we were following the TDV or AP approaches the use of semi-log hedonic speci…cations would imply that a geometric index would be a must rather than a choice. 15 It must be said, however, that smoothing does not have any signi…cative impact over the hedonic price indexes because the results were essentially identical for orders of smoothing of 3, 7, 13 and 1 (no smoothing).
where^ jt denotes the estimate of jt and t = The aggregated index is the weighted sum: where n t is the number of models in period t and s it is the market share of model i in period t, such that nt X i=1 s it = 1. This is the kind of approach followed by the Spanish National Statistics O¢ ce (see for example Izquierdo et al. (2001)). The indexes (11) are then chained to construct a whole series.
I use as reference the non-quality-adjusted index, comparing it to adjusted indexes from each of the four speci…cations (6 -9).

Results
The hedonic speci…cations 6-9 were estimated for each period. 16 The estimated coe¢ cients had in general the right sign, although a few variables showed reversed signs for certain periods, most likely due to the collinearity between characteristics frequently reported in the literature (Pakes (2003)). The size of coe¢ cients (in absolute value) also varies over time, but changes tend to be smooth from period to period. 17 This may be a consequence of having monthly regressions, because even if we can expect parameter instability (as usually found in the literature), it should be smaller between two consecutive months than between two consecutive years. It is not unreasonable to expect that consumers'valuation of characteristics do not change much within a year, and that would be consistent with obtaining very similar results for price indexes using di¤erent orders of smoothing of the hedonic parameters.
The quality-adjusted hedonic price indexes resulting from the estimation of speci…ca- 16 Given the choice of h and k, the …nal number of periods available for hedonic regressions is T = 132 h + 1 = 121 and for the computation of indexes is T = 132 h k + 2 = 119. The …gures take as base period the …rst one available, i.e., t = h + k 1 = 14 (February 1991). 17 The presentation of results from the estimation of the single period hedonic regressions is omitted due to the exaggerate length of the tables, but they are available from the author. tions 6-9 are presented in Figure 7, the non-adjusted index is also included for comparison. 18 We can see that correcting for quality using dummies for brand or segment has a strong impact, in line with the results generally reported in the literature and similar to those reported by Izquierdo et al. (2001) or Matas and Raymond (2009) for the Spanish market. The important …nding is however that not taking into account unobserved e¤ects largely overestimates the dummy-corrected indexes. Indeed, the index coming from the …xed e¤ects speci…cation shows that quality-adjusted prices remained basically constant for the whole period. By the end of 2000 the di¤erence between the …xed-e¤ects-and the brand-dummies-corrected indexes is about 18% and the di¤erence with respect to the non-adjusted index is around 35%. This represents an average year-on-year di¤erence of 1:8% and 3:5%, respectively. Taking into account that the purchase price of new cars had at that time a weight of 5:27% in the Spanish consumer price index 19 (IPC) we can say that omitting observed and unobserved quality improvements in automobiles would have led to an overestimation of the IPC of almost a 0:2% per year during the 1990's.
Interestingly, the omission of age e¤ects has a striking in ‡uence over the …xed-e¤ectsadjusted hedonic index. Actually, not including model age as an additional characteristic would lead to opposite conclusions as the adjusted and non-adjusted indexes would follow similar patterns. This result shows that the omission of time-variant unobserved e¤ects can be an important source of bias, which would be more relevant in the case of …xed e¤ects speci…cation than in the dummy variables one. As discussed in subsection 3.1 we can expect that not introducing age in speci…cations 6-8 would just a¤ect the size of the bias of hedonic coe¢ cients, while in speci…cation 9 that omission would give rise to some bias. The results without age e¤ects show a similar pattern than those reported for the UK by Requena-Silvente and Walker (2006). They …nd that …xed e¤ects push-up the hedonic index with respect to the brand dummies case and they attribute the result to the fact that the value of unobserved components is decreasing over time. In our case it seems that age e¤ects are in general positive, 20 suggesting that the quality of cars perceived by the consumers is improving even if this is not re ‡ected in the characteristics observed by the econometrician (Dalen and Bode (2004)). Therefore, the omission of age e¤ects would tend to underestimate quality improvement thus overestimating quality-adjusted prices.
The estimated age coe¢ cients in the …xed e¤ects speci…cation are much larger 21 than the corresponding coe¢ cients in the dummy speci…cations, so their omission also induces a much larger upward bias in the quality-adjusted index in the …xed e¤ects case than in the brand and brand-segment dummies cases. In particular, the hedonic coe¢ cients of age under …xed e¤ects take their largest values between January 1993 and April 1996. Their omission determines the strikingly di¤erent pattern of the hedonic price index between …gures 7 and 8 in that period.
I have used the coe¢ cient estimates of the hedonic speci…cations to construct price indexes by car model geographic origin and segment. 22;23 The objective is to determine whether the behavior of prices is determined by the evolution of any particular type of models. Figures 9-12 report the results for car models from Spain, Europe (excluding Spain), Asia and America. Asian cars are clearly leaders in (…xed e¤ects) quality-adjusted price reductions with a 20% drop in the whole sample period. American cars also reduced their quality-adjusted price while the Spanish and European ones increased between 3% and 8% . However, for making comparisons we must take into account that the average price at the initial period was di¤erent across geographic origins. Asian cars where on 20 The coe¢ cient of age is positive for most of the per-period regressions. It is negative for periods 18 to 47 (June 1991 to November 1993) and 131-132 (November to December 2000) in the brand dummies speci…cation; for periods 18 to 65 (June 1991 to July 1994), 97 to 107 (January to November 1998) and 131-132 in the brand and segment dummies speci…cation; for periods 28 to 35 (April 1992 to November 1992) and 95 to 120 (November 1997to December 1999 in the …xed e¤ects speci…cation. Therefore, we can say that the pattern of signs for age e¤ects is similar across speci…cations. It is also consistent with previous evidence: Dalen and Bode (2004) also …nd positive age e¤ects that change to negative between 1990 and 1994 for the Dutch car market. 21 Around ten times larger. 22 This means that no segment-or origin-speci…c hedonic regressions were run to construct these indexes. The scarcity of observations in several classes prevents the implementation of this approach. This is also the reason for some volatile patterns displayed for example in segments like Minivan or Small-Mini, or for car models original from Spain. In these cases and for some periods, due to the relatively small number of products, the entry or exit of just one product can have an big impact on the index. 23 These are all weighted indexes. The weights sum to 1 within each class considered. For example, in the …gure for European cars ( Figure 10) the weights assigned to each model are per period market shares conditional on being a European car. average most expensive at the beginning of the sample (Figure 1) and we could expect that as more models were introduced in lower-class segments the average price would fall even if the quality improvement was not too high. So let's look for example at the beginning of 1995, where the average real price of Asian and European cars was roughly the same, around 12000 Euro. The real price of Asian cars remained roughly constant, while European cars increased around a 10%. In the same period, …xed e¤ects, qualityadjusted prices for Asian cars fell by a 7% while European ones fell by less than 4% Therefore, even starting from similar price ranges, Asian cars seem to have improved in quality faster than the rest. The increasing competitive pressure from these models may have served to discipline the European makers towards better products to retain their market shares. Figure 10 shows that between mid-1995 and the end of 1997 the …xed e¤ects quality-adjusted price of European cars fell down sharply after three years of increase (the brand and segment dummies approaches also show that pattern, although it spreads over two more years, until the end of 1999), probably as a response to the wave of entry of models from Asian manufacturers that took place after 1995. Spanish and American models kept their …xed e¤ects quality-adjusted prices more or less constant (Figures 9 and 12). These indexes show however some jumps that can be attributed to the smaller number of models in these categories, specially for Spanish cars, that make the indexes more sensitive to product entry or exit.
The indexes for each segment shown in …gures 13 to 15 have been computed following the same approach than for the by-origin …gures. To make the exposition more concise, I present only the results for the most popular segments, the Small, Compact and High-Intermediate, that account for around 70% of the market. However, their examination does not indicate that there is a speci…c segment leading price reductions. Qualityadjusted prices tend to increase in the …rst half of the sample and then start to decrease around 1995. The intensity of price increases and decreases is obviously di¤erent across segments but the general impression is that both trends are roughly uniformly distributed across segments.

Concluding remarks
The use of hedonic regressions to compute quality-adjusted price indexes is nowadays a common practice in the economics literature. Nevertheless, the impact of unobserved product characteristics in that analysis has been largely neglected. Based on Requena-Silvente and Walker (2006)  Extending the analysis to the segment and geographical origin level leads to two additional conclusions: First, that the patterns of price evolution are similar across segments, such that price increases or decreases seem to be distributed uniformly across segments, i.e., price increases or decreases do not seem to be concentrated on a particular segment.
Second, the price decrease of both the non-adjusted and the adjusted price indexes in the second half of the decade seems to be motivated by the strength of competition after an intense wave of new entries of Asian models. Asian cars show by far the largest price reductions, specially due to their strong quality improvements. It seems plausible to interpret the price reductions of Spanish and European incumbents as a response to that pressure, although a more formal analysis would be needed to clearly determine to what extent this is the case.   1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 Small   1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 Small  1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 1990 1995 2000 Small      1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Non adjusted index Fixed effec ts Brand dummies

Index
Brand and segment dummies No dummies nor fixed effects Figure 11: Hedonic price indexes by origin of car model: Asia