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**QUALITY-ADJUSTED PRICE INDEXES FOR MAINSTREAM NEW PASSENGER CARS**

**IN THE US (2000-2016)**

**Contents**

1. Introduction

2. Literature review

2.1. Traditional “matched model” method

2.2. Hedonic price analysis

2.3. Identification problem: Simultaneity

3. Estimating procedure

3.1. To pool or not to pool

3.2. Functional form of the hedonic equation

3.3. Characteristics variables representing quality

3.4. Multicollinearity and heteroskedasticity

4. Empirical results

5. Conclusion

Bibliography

Appendix

The relationship between price and quality of goods is one of the most important underlying feature forming the structure of our economies. In the field of economics, the attempt to analyze this price-quality relationship for durable, differentiated goods have varied between two major methodologies, namely the “matched model” method and the hedonic price analysis. This paper, serving the automobile industry in the US from 2000 – 2016, adopts the latter with the use of time dummy variables in a pooled equation, which is more preferable and considered the standard approach in investigating the effects that quality improvements have on price variations, and forming price indexes which are of crucial importance in estimating inflation.

In essence, the hedonic price analysis approach takes to separable characteristics representing quality of a particular heterogeneous good to explain for changes in prices of that good over time. This approach has been widely applied for a variety of industries, most notably housing, computer and mobile phone. Interest in using hedonic analysis for the car industry started soon enough in the US by Court (1939), revived by Griliches (1961) and recently has been spreading to other countries, see Matas & Raymond (2009), Murray & Sarantis (1999), Reis & Santos Silva (2006), Shiratsuka (1995), Dalen & Bode (2004). Surprisingly enough, while the automobile industry plays an extremely critical role to the US economy as demonstrated multiple times and most notably through the bailouts of General Motors and Chrysler as a result of the 2007 financial crisis, most hedonic pricing papers concerning cars in the US have stopped looking further than the 1990s with one of the most recent being Arguea, Hsiao & Taylor (1994). It is worth mentioning that since then, passenger cars in the US have seen numerous improvements in their quality, with brand new features being introduced and once considered premium features only present in luxury cars now gradually making their way to mainstream ones. Furthermore, their nominal prices have gone up by 28.04% over the period of 2000-2016.

For that reason, this paper serves a purpose to provide another, updated look into the price-quality situation of the car industry in the US from 2000 – 2016 with a complete set of data. The focus is put more on the demand side than supply since the data collected includes manufacturers’ suggested retail prices (MSRP) rather than producer prices, which is necessarily lower. Tripplet (2004) remarks that using consumer prices to assess producer costs or vice versa could bring up some errors though small in the estimated effects. Therefore, explanatory variables should be chosen accordingly as to what customers want from a car and are willing to pay for.

Specifically, the first objective of this paper is to confirm that quality improvements have indeed been made to the car industry by providing a numerical indicator. Secondly, we want to find out whether (CPI-deflated) prices of cars in the US recently have increased or decreased after controlling for relatively new quality improvements by manufacturers that are unknown to previous periods, by forming price indexes. Also, as a by-product, a closer analysis into which kinds of features that are desired by consumers when considering buying a new car can be obtained, providing some level of insights for marketing activities. With respect to availability of data, this paper only includes mainstream cars (net exotic and luxury cars), as they are better at accounting for buyers’ rationality (more of car characteristics is better) when choosing a car, whereas luxury buyers are often heavily influenced by aesthetic styling and other sensuous features (for example, softness of leather, interior wood textures, concierge services satisfaction, etc.) which are hard to measure quantitatively. Mainstream cars also frequently account for more than 90% of annual automotive sales in the US.

This paper is structured as follows. Section 2 briefly summaries the literature and theory of hedonic pricing analysis as a more preferable alternative to the conventional “matched model” method. Section 3 outlines the estimation procedure, concerning the choice of car characteristics, choice of functional form for the hedonic regression, and other econometric issues. Section 4 lays out empirical results and remarks. The final section wraps up the main findings of this paper.

To see why hedonic pricing analysis is a more appropriate method to form price indexes controlling for quality improvements, it is necessary to consider its older alternative, called “matched model”. As its name suggests, the procedure involves only models the specifications of which remain unchanged between two subsequent time periods. Naturally, any price variations recorded between these periods are solely attributed to pure price changes and not from innovations of the product itself. The underlying assumption of this method is that, an improved version of a good possesses different quality to its predecessor, thus should be treated as a different good and eliminated from the sample. On the other hand, when a product is discontinued, another product deemed identical is added to the sample as an attempt to ‘match’ the outgoing model.

Consequently, this rather obsolete practice runs into two typical errors. Firstly, it is very possible to exclude models that after a long enough time span can actually incorporate price movements. On the contrary, an ‘identical’ product added as a successor to a disappearing one might not be exactly identical, and at least some of the price changes extracted from these are actually from quality improvements. Trying to correct for one bias leads to a higher probability of making the other. More details about this method can be acquired in Pakes (2003) and Berndt (1991).

Hedonic price analysis, which this paper utilizes, tackles this tradeoff with a regression analysis detailed below.

One of the first studies to establish that price variations between different varieties of a product reflect their quality differentials belongs to Waugh (1929). His work concerns prices of asparagus, attributable to his selected variables representing quality:

pit=αi0+βi1Greenit+βi2NoStalksit+βi3Disperseit+μit

where relative prices

pitis the result of actual price of asparagus lot

iat date

t, divided by the average price of asparagus at date

tto eliminate seasonal and day-to-day price variations. Clearly, this does not measure the price-quality relationship over time, but rather at a given point in time.

To include the effects of the passage of time into price determination, Court (1939) study of automobile prices adds among quality/characteristics variables (namely, WEIGHT, LENGTH and HORSEPOWER), dummy variables

Ditrepresenting the year in which a model was introduced:

logpi=α0+α1tDit+β1WEIGHT+β2WHEELBASE+β3HORSEPOWER+μi

This equation estimated through OLS allows for separating the effects in percentage of quality changes on price changes from those of time, and thus sets out a way to form a price index for time

tby taking the antilogarithm of that period’s respective estimated

α1t. This comes from the fact that

α1t, as the derivatives of log prices with respect to time dummy variables, measure the effects of simply being in each time period on log of prices, after holding other independent variables constant (the intercept

α0refers to the base year). Suppose two automobiles identical in quality were introduced at different prices in both the base period and at period

t. Then the difference in their logarithmic prices is

α1t(or its estimated value to be exact) and only happens because of different time periods.

The fundamental assumption embraced by Court and later studies within the hedonic literature in conducting this type of analysis is that the product is regarded as a bundle of certain characteristics, which appears in such a hedonic function as Eq.X as independent variables. When customers purchase a product, they are actually buying these characteristics that they desire, which is grouped altogether into the product itself. All else equal, the more of a characteristic that are incorporated into the good, the higher the utility level gained to the customers. Court focused on this notion as it was intended to be more concerned about the demand side. This framework allows for a very important interpretation of the coefficients accompanying explanatory quality variables which can be derived as the first derivatives of the hedonic function with respect to those variables: they are the implicit marginal prices of the characteristics. Or in other words, these coefficients indicate the value of characteristics that users are willing to pay for.

As Berndt (1991) points out, the hedonic method is suitable for industries where characteristics of the products are separable and observable, with the most notable examples being computer, housing, mobile phone and automobile. Since Court (1939), there have been some variations of his method developed in the hedonic literature which are comprehensively detailed in Tripplet (2004). However, most of them are still based heavily on the foundation work of Court, which is now frequently dubbed the “time dummy variable method” and widely used for its straightforward interpretation.

As expected, even when this paper follows what Court (1939) originally intended by looking from the demand side, specifically choosing demand-oriented quality variables to explain for variations in manufacturers’ suggested retail price and finding customers’ valuations for quality, in general as with any other prices, implicit prices (in the hedonic case, the estimated coefficients accompanying quality variables) are a result of interactions between supply and demand. This could potentially lead to an identification problem: the implicit prices output from the regression contain not only information about how much consumers value those characteristics, but also how much they cost to the producers to include more features or improve upon what is already present on their automobiles. In other words, the results from Court and other hedonic studies focusing on the demand side then could be suspected to be upward-biased when not accounting for the effects of supply on (implicit) prices. The debate about this simultaneity was settled by Rosen (1974) by confirming that it is indeed the case that hedonic functions are not uniquely useful in measuring the marginal benefit that customers enjoy when buying a better product, but also the marginal cost that producers incur when trying to enhance their offerings. However, Rosen also noted that one could not extract either a demand function or a supply function from the hedonic function. Nevertheless, since it is very difficult to separate between the effects of supply and demand on prices, Tripplet (2004) suggests that it is necessary to interpret the implicit prices as both customers’ valuation toward and producers’ cost of improvements in the product’s characteristics.

In light of the findings from Rosen (1974), it should still be noted that his dual interpretation of implicit prices is made under the assumptions of competition with a lot of producers, and there are no niche markets. As Berndt (1983) remarks, these two assumptions ensure that producers are price takers since they have no market power over each other either as a result of competition, or from an innovation that could open a brand new submarket thus no incentive to develop one. Then the supply curve will be completely flat (perfectly price elastic), and the price determined by the intersection of the demand and supply curves will always equal marginal cost and also average cost. In realistic conditions, the automobile industry is hardly a perfectly competitive market. In fact, this industry is widely accepted as an oligopoly, where most of the market share is distributed among only a portion of manufacturers, products are differentiated and barrier to entry is high. Therefore, the assumptions imposed by Rosen (1974) are sufficiently violated to be applied to the automobile market.

With competition mostly done not through pricing in an oligopoly, it would be perhaps not too far-fetched to consider the opposite case to Rosen’s assumptions in which supply is perfectly or highly price inelastic and thus nearly vertically fixed. In such a situation, prices are determined solely or mostly by the demand curve’s movements and reveal only the magnitude of market’s valuations of quality. This paper relies mainly on this assumption to show implicit prices as consumers’ valuations of automobile characteristics. The idea has also been explored by Hall (1971) in an application to the US pickup truck market.

This paper utilizes the standard time dummy variable method invented by Court (1939) in the semi-logarithmic form as outlined in Section 2.2, with the natural log of CPI-deflated prices as the dependent variable and selected variables depicting automobile characteristics, which will be further discussed in Section 3.2, as explanatory variables, along with dummy variables corresponding to year 2001 – 2016 (2000 serves as base year). The equation is estimated using a single, pooled regression for all the 17 periods that this paper is concerned with.

Another popular alternative hedonic method has been considered, such as the “adjacent period” approach. Both these adjacent and pooled approaches have been applied by Izquierdo, Licandro & Maydeu (2001), Reis & Santos Silva (2006), Matas & Raymond (2009), Dalen & Bode (2004), Raff & Trajtenberg (1997), Tripplet (1969) for the automobile industry in various countries, to test the hypothesis of constant coefficients that the pooled regression implies, with mixed results. If a single regression is to be carried out for all of the periods, an important assumption automatically follows, that is the coefficients do not change for the whole period. In the case of the hedonic literature in general and price index construction for automobiles in particular, that means the implicit prices for characteristics do not change over the years, and in the final period customers still value the characteristics the same as they do any previous period. Meanwhile, the adjacent method only holds the estimated coefficients fixed for any two consecutive periods, which some could say is a much more relaxed assumption.

For this paper, only the pooled regression is performed and its results are reported in Section 4, for several reasons. First of all, suppose we allow for the possibility of an incident facing the demand side happening during 2000 – 2016 that could have altered customers’ willingness to pay for the characteristics. A tax break or raise is supposed to do this, as pointed out by Matas and Raymond (2009). During the concerned period, conveniently there was no tax change US for automobiles detected in the. However, the event of the financial crisis in 2007 might also bring about a structural break to the estimated coefficients. As people become poorer, their implicit valuations for cars’ characteristics may change as well. To test for the null hypothesis of stable coefficients before and after 2007, a Chow test, which was detailed in Chow (1960) to investigate the stability of coefficients estimated using two different data sets, has been conducted and yields failure to reject the hypothesis at 5% significance level. Moreover, there was not a technical breakthrough that could have changed the characteristics’ costs facing car manufacturers. A popular example of which was the invention of mass production, happening first with the Ford Model T. This phenomenon has been discussed at some length by Raff & Trajtenberg (1997).

The choice of functional form for the hedonic regression should also be put into attention. Most prior work relating to hedonic analysis have involved three typical function forms for their regressions: linear, semi-log (transforming the dependent variable into log form) and log-log forms. Among these, the semi-log form is the most popular choice for studies applied not only to the automobile industry as demonstrated by Murray & Sarantis (1999), Reis & Santos Silva (2006), Dalen & Bode (2004) and several others, but to other industries as well. This popularity has also been remarked in Gordon (1990).

As Rosen (1974) points out, the choice of functional form for the hedonic regression equation should be empirically examined so that the form actually fits the data best. One proposed method given by Berndt (1991) is using the Box-Cox procedure as guidance in choosing among linear, semi-log, log-log, transforming both sides of the equation by different parameters, and transforming both sides by a single parameter (the parameters are non-linear and to be estimated). However, this paper finds that the Box-Cox transformation soundly rejects all options, an inclusiveness that is also acknowledged by Tripplet (2004). Therefore, the semi-log form has been selected for regression, which yields slightly higher goodness of fit (R^{2}) and produces likelihood not statistically inferior to the others, a result that is in line with previous studies. This functional form for the regression equation also provides easy coefficient interpretations.

Another reason to be in favor of a non-linear hedonic function rather than a linear one is also given by Rosen (1974), who noted that with the presence of arbitrage in the market, the hedonic function should be presented in a linear form. Arbitrage here is defined as follows: suppose a car producer charges different prices for 1 unit of torque for pickup trucks and sport sedans. Then, if users were free to substitute between these two engines into their trucks and sedans, prices for 1 unit of torque would then be forced to become equal, hence linearity. This logic has also been argued for by Arguea, Hsiao & Taylor (1994) but criticized by Tripplet (2004) in terms of the plausibility of the assumption of arbitrage in real conditions. In the case of automobiles, it may be costly to substitute engines between cars for an average owner. These costs include advanced technical knowledge of cars’ working mechanism, time, skills and monetary costs of going to a mechanic, which most of the time render such substitution virtually impossible for typical car owners.

Explicitly, the hedonic function used in this study is:

logPit=α0+βXi+∑k=116γkDτ+k+εit

where:

Pitis the real price (deflated by new vehicles CPI) of car model i at time t. At period 0 (base year 2000), t = τ.

Xiis a vector comprised of characteristics.

Dτ+kis a vector of dummy variables for each year (except the base year).

As hedonic price analysis adopts a core assumption that heterogeneous products are essentially a bundle of characteristics and these characteristics while representing quality drive price changes, it is important to specify these characteristics, and what qualities they stand for. As per the hedonic literature defines and applied to the automobile industry, these characteristics must be costly for the cars manufacturer to improve or add into their cars, and must provide a certain level of value, or utility, for consumers to be willing to pay extra for instead of going for another car. In addition, as Tripplet (2004) noted, there are no major econometric rule restricting the choice of quality variables other than knowing the product technically (One should ask a question: What makes a car a car?) and applying marketing insights to suspect which variables to include in the regression (What do customers want from a car?).

The first hedonic study produced by Court (1939), as previously outlined in Section 2.2, included only 3 quality variables: weight, wheelbase and horsepower. Given his emphasis on the demand side and how much simpler cars were designed back then, one could quickly point out that this is hardly an adequate set of variables to be applied in modern times. However, the same logic used to choose variables still holds: these variables are characteristics of a car that represent quality. Though not explicitly expressed by Court, it could be implicitly understood that a heavier car is considered safer than a lighter one, while a longer wheelbase (the distance from the 2 axles) contributes to a more spacious interior thus more comfort. Horsepower directly refers to performance and are still widely present in recent hedonic studies concerning cars.

Since Court (1939), cars have drastically evolved in every aspect and become an extremely complex durable product. As such, there are now many new measures to quantify safety, comfort, performance and other traits as well, most have been recognized in more recent studies. Raff & Trajtenberg (1997) while investigating the price-quality situation of the US automobile industry from 1906 – 1940 use wheelbase, horsepower, engine displacement, clutch type, brake type, drive type, suspension type and rear axle type to describe cars in that period. Matas and Raymond (2009) studying 1981 – 2005 Spain market define automotive quality in terms of performance, ease of drive, size, comfort, fuel efficiency and safety, perceived by variables including engine displacement, ratio of power per weight, automatic transmission, power steering, number of doors, air conditioning, electric powered windows, diesel engine, antilock braking system.

Recent developments in the automobile industry call for an update to the set of quality variables when applied to mainstream cars. Many features appearing in previous studies indicating that their presence increases prices compared to prices of cars that do not have them, now have become standard in all cars, both due to new regulations and competition. For example, it became mandatory for passenger cars in the US to have frontal airbags in 1998. The antilock braking system though not mandated to be equipped on passenger cars, but all models come standard with it as a basic safety feature. Therefore, it would not provide any meaningful result to include those now standard features as dummy variables in this study, as done in many others previously. Meanwhile, other characteristics once only appearing on luxury cars (for instance, heated seats, sunroof, cruise control, etc.) are now gradually making their way to appear more often in affordable vehicles, and are included for analysis.

Since we are focusing on the demand side, and with respect to data availability, it is important to set out which characteristics a customer with average knowledge about cars is looking for when they intend to buy one. Performance is measured by maximum horsepower in hundreds (or how fast a car could go) and maximum torque in hundreds (how strong can it pull/tow) produced by the engine. Some studies use the ratios of horsepower/weight and torque/weight to assess a car’s performance. While this could be a better indicator for speed and strength in a strictly technical debate, most car buyers do not calculate these kinds of ratio to compare between cars. Moreover, while popular in many previous automotive hedonic pricing studies, wheelbase should be deemed less meaningful in measuring interior space than front leg room, which is the distance between the farthest possible point of the front seatback to the pedals, and rear leg room, which is the distance between the rear seatback to the front seat. The whole measurement of these two characteristics are dedicated to more space thus more comfort for passengers, while only part of the wheelbase is made for the enjoyment of users and the rest is to cover other mechanical components. It is possible for a car to have a longer wheelbase, but less leg rooms if these mechanical components or panels are made too thick. For this reason, front leg room and rear leg room are chosen to measure comfort, instead of wheelbase. Some of the more technically advanced aspects such as ones included in Raff & Trajtenberg (1997) might be more useful when looking at the supply side as they are far too technical. Reis & Santos Silva (2006) provides a rather comprehensive list of vehicles characteristics that are more relevant to the purpose of this paper.

Another problem that the hedonic literature has to deal with is durability of the product. Surely this is something that customers value and producers have to spend more money into research and development to improve. However, there is not really a direct way to quantify durability, especially when data on warranty coverage is not available at the time this paper is carried out. To partly make durability observable, a dummy variable that receives value unity when a car is made by a Japanese manufacturer is included. This comes from a rather conventional thinking widely adopted by car shoppers, that a Japanese car is somewhat more durable than others and runs into less problem during their service. This is not without some proof to back it up though, as Japanese manufacturers and models frequently top reputable annual Initial Quality Study and Vehicle Dependability Study surveys taken by industry-recognized market research company JD Power[1]. Berndt (1991) calls the practice of using dummy variables indicating a particular manufacture or country of origins to portray durability in a hedonic regression “make effects”. Based on Reis & Santos Silva’s (2006) selection of variables and current available data, a full list of characteristics variables and their respective quality traits that this paper uses to test their significance is summarized in Table X.

As with any other research taking on regression to analyze data, omitted variable is a problem worth mentioning. If there is a characteristic that is significant in explaining price variations and thus should be included in the regression but is not, then the estimated coefficients will be biased upwards from its true value. Basically, the effects that should have been attributed to the omitted variable to explain for variations in prices are now in part wrongly assigned to explanatory variables already included. Especially for hedonic estimations, it is impossible to enumerate all the relevant characteristics variables. A Ramsey Regression Specification Error test (RESET) indicates that the specification set out in Section 3.2 for the hedonic function does not run into endogeneity caused by missing variable(s), confirming the adequacy of the variables set. The test, invented by Ramsey (1969), also rules out the need to transform explanatory variables into non-linear (reciprocal or squared) forms.

Since automobile is an extremely complex product in terms of engineering components, it is very easy for some of the selected independent variables to be linearly correlated with each other. In fact, multicollinearity has been widely detected in hedonic studies and is a major econometric issue. Tripplet (2004) argues that multicollinearity in hedonic regressions comes from two sources: engineering relations between variables, and from the sample. The former is inevitable: there are certain forces of physics and nature in play that dictate the technical relationship between some members of the characteristics set. For example, horsepower and torque is related by the formula:

Horsepower=(Torque ×RPM)/5252, though RPM (revolutions per minute – how fast an engine revs) varies between different cars. Another demonstration of multicollinearity is that as an engine makes more power, it also requires more fuel to do so, all else equal. Understandably, customers would prefer more fuel economy so they pay more for additional miles per gallon consumed and car makers must incur costs to improve this area, so its coefficient from hedonic regression should be expected to be positive. However, more expensive cars are likely to have more horsepower, thus reducing its fuel economy, all else equal. This is why some hedonic research has reported a negative sign for fuel economy, as experienced by Matas & Raymond (2009).

The second source of multicollinearity comes from sample type itself, which in hedonic research is either model-based or transaction-based. Tripplet (2004) remarks that the latter will induce a higher level of multicollinearity. Automobile manufacturers often diversify their product portfolio. Suppose that through varying RPM, a producer can create car models that have high torque but low horsepower for the sake of towing, and other models with high horsepower but low torque in favor of acceleration. If the data comes from a scanner that records transactions between dealers and buyers (including horsepower and torque information of the cars), more multicollinearity could happen because buyers also tend to want more horsepower when they pay more to choose a car with higher torque. Therefore, car shoppers often concentrate in the middle of the distribution of models. In other words, they tend to buy a car with more of every characteristic, and this kind of cars will receive most sales and appear most often in the sample, driving sample multicollinearity up. Generally, a model-based dataset that does not rely on sales or transactions suffers less from multicollinearity. To deal with this source of multicollinearity, other than increasing the sample size and correcting for errors in data as suggested by Tripplet (2004), the most plausible is to use a dataset that utilizes solely vehicles’ specifications and does not come from transactions. This is the kind of sample that this study uses for estimation. Data is extracted from Edmunds.com, an industry-recognized automotive website that provides trust-worthy specifications for each model included in the sample. There are more than 400 models reported from 2000 – 2016, coming from more than 30 makes. This sample is sufficiently larger than many previous automotive hedonic research.

Another effect of multicollinearity is that it tends to blow up standard errors, leading to a higher probability of rejecting statistical significance of the estimated coefficients. The results reported in Section 4 and Table X show that most of the explanatory variables are significant at 95% confidence level, probably thanks to sample size and quality. All coefficients show their expected signs. Upon multicollinearity inspection, correlations between independent variables are well on par with other automotive hedonic studies.

One kind of criticism that hedonic studies have often received is that they occasionally suffer from heteroskedasticity. The OLS method used to estimate the hedonic function requires that the residuals must display constant variance, or homoskedasticity, to become efficient and BLUE. The presence of heteroskedasticity on the other hand biases the standard errors, though it causes no bias nor leads to inconsistency of the estimated coefficients (Woolridge, 2002). It should be noted that heteroskedasticity is mainly again an unwanted econometric issue emerging from using a transaction sample, as Tripplet (2004) remarks. Best-selling models will reasonably have more variances in their transaction prices compared to slower selling models, since the actual prices that buyers have to pay for their cars, even for an exactly same model, vary from sales person to another, from dealer to dealer and even from region to region within a same country. This comes from the fact that cars are generally not a liquid asset (Boyes & Melvin, 2000), therefore people have different valuations toward a same car. Since a transaction-based sample uses only the average price from all the transactions for a particular car, it could be argued that not much variance from the top-selling models is retained, relatively to that of slower selling models. Therefore, to deal with heteroskedasticity, a standard practice recommended by Berndt (1991) is to multiply both sides of the hedonic function with the square root of sales, or use Generalized Least Squares which gives more weight to models with higher sales volumes (low residual variance) and less weight to models with low sales volumes (high residual variance) to compensate. Upon inspection using a Breusch-Pagan test, the sample used for this paper is not affected by heteroskedasticity, since the data is originally extracted from car makers’ websites and brochures (model-based), in which for each model there is only a single price listed regardless of the sales numbers, not the arithmetic mean price from transactions. As an additional note, using a semi-log functional form for the hedonic equation also helps with lowering heteroskedasticity in this case as a side effect, as Tripplet (2004) remarks.

The estimation results from a single regression covering the whole annual period from 2000 – 2016 are displayed in Table X. Overall, the high goodness of fit (0.9827) indicates that most of the variations in log of prices have been explained for by the variations in quality characteristics. This R-squared statistic is on par with other automotive hedonic studies (see Dalen & Bode (2004), Shiratsuka (1995), Izquierdo, Licandro & Maydeu (2001), Murray & Sarantis (1999), Matas & Raymond (2009), Hogarty (1975) and Raff & Trajtenberg (1997)). The Ramsey RESET test, Breusch-Pagan test, and Chow test for omitted variable, heteroskedasticity and coefficient stability respectively all return favorable result at 5% significance level. These tests confirm that the regression specification set out in Section 2 is proper, and the coefficients, or implicit prices of characteristics and time dummy variables are BLUE.

The quality coefficients provide percentage price changes when a characteristic is marginally improved by 1 unit or when a car is added with a feature that is represented by a dummy variable. Overall, all the quality coefficients display their expected signs. For instance, for performance variables, for an exact same car with an additional 100 horsepower or 100 pound-feet of torque, the price would go up respectively 8.12% and 6.62%. This is relatively high in magnitude, probably could be explained for by driving etiquette in the US where drivers often accelerate quite hard and thus require more horsepower and torque. These numbers are higher than what have been found for horsepower and torque in EU markets (Dalen & Bode, 2004) or (Murray & Sarantis, (1999), Japan (Shiratsuka, 1995) and the US in previous time (Raff & Trajtenberg, (1997) where/when people conventionally have a somewhat ‘calmer’ driving manner, possibly due to lower speed limits imposed at those times and places.

Surprisingly, number of airbags are found to be statistically insignificant even though it is an important passive safety device in cars. One possible explanation for this could be that shortly after early 2000s, most cars in the US have been equipped with a number of airbags and this started to become such a norm in all cars that customers stopped paying attention to this measure of safety. Most cars come standard with 7 airbags (including 2 frontal airbags, 2 side airbags, 2 curtain airbags and a knee airbag for the driver) regardless of the segment and price. Manufacturers may have found this quantity of airbags enough to pass the government’s crash tests and protect all body parts of passenger, then also stopped incorporating more of them into their products. Consequently, number of airbag is no longer considered a good measure of safety in customers’ consideration. On a side note, Murray (1999) found braking distance to be also insignificant, so it would be interesting for later studies to explore which other continuous safety features are good at representing safety. On the other hand, other safety features included for this study that are blind spot monitoring system, advanced lighting system (xenon and LED headlights) compared to traditional halogen that gives better visibility on road, and all-wheel drive system that provides extra traction and prevents skidding all show their expected positive coefficient.

All other comfort variables show positive effects on log of prices, which is expected. The coefficient on fuel economy (measured as miles per gallon) show that it has a pleasant positive sign and is statistically significance, indicating that multicollinearity has been controlled in the sample. Hogarty (1975) while investigating the US car market from 1957 – 1971 found out that miles per gallon was not significant. His provided rationale for that result was that American did not care much about fuel economy since they had been much accustomed to cheap gas prices. Drastically higher gas prices in subsequent periods might have made American more attentive to fuel consumption when buying cars, forcing manufacturers to find ways to improve this area, including technical innovations to enhance engine efficiency while converting combustion into power as well as reduce friction along the drivetrain. Another hypothesis intended for inference, which is Japanese cars are charged more possibly for their reputation of being reliable, is also confirmed to be not able to reject. This could lay the ground for Japanese auto makers to establish a pricing strategy that set their prices slightly higher than manufacturers from other countries-of-origin, since customers are willing to pay extra in belief that their cars will be in service longer.

In general, most of the annual average values for quality variables have increased from 2000 to 2016, confirming that car makers have indeed made improvements to their cars. Remarkably, together with horsepower and torque, rear leg room, front leg room, cargo space, all-wheel drive system, ground clearance all have increased in average over the period. Apart from quality improvements, this could also be partly explained for by American customers’ preference for SUV and crossover vehicles that started in the early 2000s. These vehicles have more of those characteristics than traditional sedans and coupes and thus are deemed more practical and more desirable in mainstream car market. The surge of demand for SUVs and crossovers perhaps have urged manufacturers to includes more of them into their portfolio, driving their sample average values up during the period. Evolution of car characteristics in annual average values is shown in Figure X.

Nevertheless, it is necessary to form a numerical indicator to show how much better cars today are from cars last year. From 2000 – 2016, the crude (or nominal) price index rose by an annual average rate of 2.14% per year, or 28% for the whole period. During the same years, the CPI-deflated average prices have gone up around 24%, or at a rate of 1.97% per year. Meanwhile, the quality-adjusted price index has experienced a 1.47% decrease per year, or fallen by more than 23%. To put this into perspective, this means that a 2000 average car model at a price of $23,214 without any improvements in quality would have cost only $18,316 in 2016. Following a method suggested by Raff & Trajtenberg (1997), we can compute that cars in the US have seen an average quality change of 3.44% per year (1.97% minus -1.47%). The positive number confirms that cars were better than they had been. This result is equivalent to seeing around 43% of (the magnitude of) price changes as coming from quality improvements, and the rest 57% coming from pure price changes itself. The idea is that (real) price changes themselves could be broken down into two contributors, which are quality changes and quality-corrected price changes (or could be regarded as pure price changes), and is a sum of these two. As a result, quality changes can be quantitatively measured as the difference between price changes and pure/quality-corrected price changes:

%∆Quality= %∆Real prices-%∆Quality-adjusted prices

Nominal, CPI-deflated and quality-adjusted price indexes are given in Table X. Raff & Trajtenberg (1997) reported an average decrease rate of 2% per year for real prices for US market from 1906 and 1940. He also concluded that improvements on quality during 1906 – 1940 were made at a change rate of 2%, which is 42% lower than our estimated 3.44%. The fact that positive quality enhancements were made at a faster rate in 2000s, but real prices decreased rather than increased in 1900s indicates that quality-adjusted prices must have decreased by quite large an amount in annual percentage terms in the earlier period. Indeed, Raff & Trajtenberg reported that quality-corrected prices were decreasing at 5% per year, and noted that this estimate is a very sizable rate of change. It is worth noting that the phenomenal invention of mass production started by Ford with its Model T in 1908 and soon followed by other car makers might have biased the price drops brought about in that period. A Model T, frequently claiming more than half the market share at the time, had a nominal price tag of $850 in 1908, then only $260 in 1925. There was no such major technical breakthrough taking place from 2000 that could have led to price volatility anywhere that rate reported by Raff & Trajtenberg. Nonetheless, a comparison between this paper’s findings and those from Raff & Trajtenberg indicates that more successful efforts to make cars better have been made during 2000 – 2016 than from 1906 – 1940 (Unfortunately, Hogarty (1975), Atkinson & Halvorsen (1984) and Arguea, Hsiao & Taylor (1994) while all studying the US automobile market in their corresponding times, did not construct price indexes that would perhaps make for a more useful comparison).

**5.** **Conclusion**

This paper is an update to the hedonic literature in general and to automobile price index construction in particular by providing a more recent investigation into the mainstream US market (excluding luxury and exotic vehicles) from 2000 – 2016. The aim is to estimate customers’ valuations for certain car quality characteristics and forming a price index after controlling for quality improvements. Mainstream cars frequently account for more than 90% annual sales and are better at reflecting buyers’ rationality for quantifiable characteristics.

The method used is standard in the literature, involving a single semi-log regression covering the whole period, which was invented by Court (1939) and widely applied to other heterogeneous goods in different countries at different times. This choice of pooling the data and functional forms come after a Chow test and a Box-Cox transformation test are conducted and yield favorable result. Other methodological issues including multicollinearity, heteroskedasticity and omitted variable are given diagnostic tests and are under control.

Overall, the results show that customers do care about quality when purchasing cars, with most of the coefficients accompanying quality variables being statistically different from zero at 1% and 5% significance levels. That is, customers do value safety, performance, comfort, maneuverability, durability and practicality and are willing to pay for these qualities. However, number of airbags is found to not play a role in buyers’ consideration in terms of safety, possibly because it has become a norm in the automobile industry to have sufficiently 7 airbags regardless of body types and prices. In general, around 98% of the variations in prices have been explained for by the variations in characteristics between cars and between periods.

After forming crude, CPI-deflated and quality-corrected price indexes, it has been made clear that while nominal and real prices of automobiles were increasing in the US, controlling for quality improvements reveals that car buyers were actually effectively paying less. Specifically, nominal prices increase by 2.14% a year, real prices 1.97% a year, but quality-adjusted prices decrease by 1.47% a year. It is then found that automobile quality has been improved by manufacturers by an average of 3.44% a year. This is an appropriate pace and not too far away from previous work applied to other car markets.

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