Sylvain Prado
email: sylvain.prado@ge.com

A Family Hitch: Econometrics of the New and the Used Car Markets

Keywords: second-hand market, automotive market, prices, causality, cyclical correlations, VAR. JEL Classi…cation: C32, E31, E37

New cars of today are used cars of tomorrow and some people assume a competition between new and used markets. There are numerous, preconceived ideas and academic theories regarding the interactions between primary and secondary markets. To investigate the relations, we provide a macroeconomic analysis of the French, the British and the US car markets. We aim at answering the following questions. What are the interactions between the new and the second-hand car markets? Can we use the interactions to estimate the car prices of tomorrow? Our results indicate that the relations appear limited for France and the UK, whereas the US market faces a Scitovscky mechanism, de…ned by constant disequilibrium and multiple interactions between primary and secondary markets. Furthermore, they illustrate that the interrelations are not strong enough to fully explain and forecast market patterns.

Introduction

Apples are non-durable goods. Out of the new market, they have no value. On the contrary, cars are durable goods. They are usually bought with the intention to be used for a limited time and then re-sold. A car owner can choose for a duration, and then re-sell the vehicle on a well developed secondary market. Thanks to the durability of the car, drivers can re-sell cars to each other, and buy new or used vehicles. Durability creates speci…c dynamics of overlapping generations of durable goods that are not present in non-durable markets, and brings the question of the interaction between primary and secondary markets.

We aim to identify the relationship between new and used car markets in order to forecast car prices. For various industries the future car prices are of special interest. Indeed, among other things, used car market prices directly a¤ect leasing companies losses [START_REF] Caillaud | Pour comprendre l indice des Prix[END_REF] and bene…ts.

The paper is organized as follows. Section 2 reviews the literature related to the interdependence between primary and secondary markets, speci…cally in the automotive sector. Section 3 presents the data and our empirical setting. In Section 4, we empirically evaluate the interdependence between new and used cars for three major markets (France, the United Kingdom and the U.S.). Section 5 concludes.

2 Academic researches in the second-hand market are legion.

There has been a signi…cant amount of academic researches on the subject of durable goods in the secondhand market. The literature discusses why second-hand markets exist and highlights some mechanisms of interdependence between new and used markets, especially in the microeconomy area. It mainly focuses on three related axes of research: the Akerlof e¤ect, the optimal durability and the time inconsistency. Some researches, like Scitovsky (1994), also exist into a Keynesian system.

Why secondary markets exist?

Van Cayseel (1993) provides a framework: Second-hand markets are institutions dealing with transactions of durable goods [START_REF] Abdelaziz | Is Default Risk Related to In ‡ation?[END_REF] , and the durability constitutes their …rst condition of existence. As a second condition, the good utility needs su¢ cient volatility. For instance, an economic depreciation [START_REF] Sophronis | Gains from trade in used goods: Evidence from automobiles[END_REF] could appear if the consumer has no further need of the good or because the maintenance cost of the car increases [START_REF] Ronald | Durability and monopoly[END_REF] . Consequently, the second-hand market re-allocates goods from agents extracting a low utility to agents extracting a higher one. Mixing the condition of durability and a possible variance of utility, we can state that the longer the durability, the higher the probability for an asset to change of valuation. The longer the durability, the higher the probability for a consumer to drop the asset, and buy another one. The secondary market could also be a way for some users to drop goods with malfunctions and no functionality [START_REF]Policy Overview and Recent History[END_REF] . But dropping 'lemons' could only be an incentive for a minority of agents, otherwise the secondary market would collapse.

According to Van Cayseel (1993), the possibility of simultaneity of new and used markets constitutes the last condition, raising the question of bene…ts and constraints in the second-hand market for producers. In order to reduce the risk of competition with new products [START_REF] Fiorito | Stylized Facts of Business Cycles in the G7 from a Real Business Cycles Perspective[END_REF] , producers would try to prevent the existence of a secondary market (i.e. by only renting their equipment or reducing the substitutability between new and used markets). Fortunately, some incentives to tolerate and to even support a second-hand market, additionally exist for the producer. The …rst incentive would be the pressure created by other competitors with similar goods. Following researches on industrial regulation and anti-trust policies, a large amount of academic papers have studied durable goods in a monopolistic market [START_REF] Dennis | The Use of Hedonic Regressions to Handle Quality Change:The Experience in the[END_REF] . The incentive could be a law committing the monopoly to sell his products. The existence of asymmetric information could also restrain the opportunity of leasing, because users are less careful with goods they do not own. Anderson and Ginsburgh (1994), through a microeconomic analysis and under a monopolistic assumption, show a bene…cial e¤ect of secondary markets for the producers: consumer heterogeneous tastes result in a segmented secondary market allowing producers to establish a system of indirect price discrimination (by setting higher prices, a producer extracts higher surplus from consumers with higher willingness to pay). In the automotive industry, manufacturers are selling both new and used cars [START_REF] Drew | Upgrades, Trade-ins, and Buybacks[END_REF] . They also rent and provide services of maintenance in order to bene…t most of the needs related to their products (i.e. …nancing car ownership through their …nancial branch).

Manufacturers aim to collect various revenues from all available channels. De…ning the automotive industry as a monopoly would be a strong assumption. According to the ACEA [START_REF] Guillaume | The Convergence of Automobile Prices in the European Union: an Empirical Analysis for the Period 1993-1999[END_REF] in 2008, more than 15 manufacturers (through more than 43 brands) were sharing the market in Western Europe, and none of them had more than 21 percent of the market share. In the US, more than 15 automotive makers are competing and none of them had more than 15 percent of market share [START_REF] Bernard | Le marché automobile : un cycle spéci…que ? Économie et Statistique[END_REF] . Paredes (2006) argues that cars are 'durable experience goods'. Before buying a car, a consumer can't evaluate all of its characteristics. As a consequence, Paredes states that a link exists between consumer loyalty, satisfaction and retention value. The existence of consumer loyalty (and non loyalty) implies that consumers are able to choose di¤erent manufacturers and that car markets are not monopolistic. As a conclusion, an automotive company could only be de…ned as a monopoly during the introduction of new vehicles (i.e. minivans in the US market [START_REF] Pinelopi | The Evolution of Price Dispersion in the European Car Market[END_REF] ). Although we reject a monopolistic assumption, we take these studies into account by focusing on the highlighted mechanisms of interdependence. Scitovsky (1994) adopts a macroeconomic approach to explain the existence of secondary markets. He argues that durable goods are valued by the services they provide to the consumers. Because of time and obsolescence, the amount of services included decreases. Therefore the secondary market has two functions: …rst, it mitigates the inequalities by allowing poor customers to buy a cheaper bundle of services to richer ones. Second, it stimulates the economy by facilitating the replacement of obsolete durable goods. Scitovsky's theory explains why there are bigger proportions of second-hand markets (i.e. clothes, household appliances) in developing countries. But used car markets have a signi…cant size in countries with high standard of living. Indeed, automobiles are relatively expensive and, by increasing the price span, the second-hand market allows most of people to a¤ord a car. The empirical analysis of Clerides (1998) on the welfare e¤ects of trade liberalization [START_REF] John | Addressing misconceptions about the Consumer Price Index[END_REF] in 1993 (by permitting the importation of Japanese cars in Cyprius second-hand market) con…rms Scitovsky's opinion. Clerides concludes of signi…cant gains that bene…ted predominantly for low-income consumers because of an increase in product variety.

2.2

The Akerlof e¤ect and the car durability are linked.

The main area of research on durable goods comes from the most famous analysis on automotive second-hand market. Akerlof (1970) explained why used car valuation is so much lower than new car valuation. The automotive resale market is a¤ected by something called the 'lemon e¤ect'. A used car has a probability to be of a good quality or a bad one (i.e. lemon), and the uncertainty on quality implies a price adjustment.

In the resale market, there is an asymmetry of information; the car owner has a better knowledge of the probability of bad lemons. If second-hand vehicles were valued like as new vehicles, then it would attract lemons (sellers of lemons would have the opportunity to sale their vehicles and buy a new one on the new vehicle market) and it would create an arbitraging opportunity. Akerlof used the automotive market as a best illustration and extended his idea to other markets (the cost of dishonesty...). The Akerlof's article helps to understand why an adverse selection happens, as well as the large variance and the trends between new and second-hand prices. But some elements of the article have to be discussed.

First, the in ‡uence of new markets misses in the analysis. Hendel and Lizzeri (1999a) built a microeconomic model including a primary market and according to their conclusions, a su¢ cient level of trade could reduce the adverse selection. Moreover, buying new cars and selling used cars are complementary activities: even if they give higher valuation to their used units, owners …nd optimal to sell their good quality cars; once their used car has been sold, owners place a higher value on purchasing a new car. Finally, Hendel and Lizzeri argue that new market prices could be increased thanks to the adverse selection. The …rst explanation would be that a used good becomes a worse substitute than a new one (in case of an average quality reduction on the used market). The second reason would be that the buyer of new goods gets an option value and he or she can decide to keep the high quality realization of the used car.

Empirical analyses give a second perspective. Winand and George (2002) provided a large review of empirical tests on the Akerlof e¤ect and in various markets, as well as a speci…c analysis, in the second-hand car market of a Swiss canton. According to their conclusions, adverse selections are not always observed or could occur under a mitigated and non widespread form.

Car durability constitutes a third element. An increase of average durability, through the Akerlof analysis, could have either a negative or a positive e¤ect. A better durability implies a better quality of cars producing a lower probability of 'lemons'on the second-hand market. On the other hand, consumers would keep their car longer and it would increase the proportion of 'lemons'. Whatever the consequence (positive or negative for pro…ts), a manufacturer can impact the adverse selection e¤ect through guaranteed warranties, buyback or by improving information on the second-hand vehicles. Similarly, by the beginning of the 90's, Peach et al. (1996) noticed an improvement of the information availability on the US second-hand market and an increase of car durability. At the same time, the used car market experienced an increase of sales and a¤ordability.

All in all, it suggests a positive correlation between quality, durability, and non-adverse selection.

To conclude, the Akerlof e¤ect and the durability could explain the price trends through the structure of the market and the inner quality of cars. The questions of quality and optimal durability are developed in the next section.

Optimal durability and Time inconsistency are two areas of research.

Optimal durability constitutes another main area of research in the microeconomic analysis of durable goods. A non-competitive market might lead to a lower socially e¢ cient durability of goods in order to constraint consumers to increase purchase frequency. Sieper and Swan (1973), however, argue for an absence of durability distortion: monopoly market and competitive markets will always produce at minimum cost and then consider the durability as a minor problem. Some articles, like Hendel and Lizzeri (1999b), contest these outcomes: although used goods create competition for new goods, a manufacturer would bene…t from a well functioning used-goods market increasing the willingness of consumer to buy new goods easy to resale. At the same time, the producer could slightly reduce the durability (by under investing in durability, by directly reducing new units durability, by introducing frequent style changes and new products...): it alters the substitutability of new and used market and allows the …rm to increase the price of new units. The maintenance market could also interfere. Rust (1986) argues that, in case of a competitive maintenance market and a monopolistic new market, most of consumers would prefer over maintained used goods.

Durability could have a positive impact on prices for both new and used market by increasing the quality of cars and therefore the utility of the consumer. At the same time, it has a negative impact on prices in the new market by improving the competition with the second-hand market. In the US market, by the beginning of the nineties, Peach and al (1996) observed that cars reliability, survival rate, and warranties durations have been rising simultaneously with car prices. Acknowledging that durability has not been the only factor impacting the level of price, graphical analyses show similar trends, from 1990 to 2008, of the median age and the average sale price of new cars. But their conclusions have to be strongly quali…ed: for used cars and light truck markets, similar trends are less visible [START_REF] Simon | Price discrimination via second-hand markets[END_REF] . Furthermore the Consumer Prices Index for cars (new and used), that adjust prices through obsolescence and representative constant mixes of vehicles, has been decreasing since 1990 in the US [START_REF] Igal | a) Adverse Selection in Durable Goods Markets[END_REF] .

A third large area of research on durable goods discusses the Time inconsistency. Optimal durability and the Time inconsistency problem are embedded. According to Coase (1972) a monopolist has to manage the dilemma that the price of units sold in the future will be a¤ected by the characteristics of the units sold today. The Time inconsistency constitutes an issue for producers across planned obsolescence, R&D, and the introduction of new products on the market. Waldman (1996) argues that R&D could have a negative impact on new products because consumers expect a technological improvement in a later period. As a consequence, a monopolist should under invest in R&D and reduce the availability of the used goods (i.e. by reducing the durability of new unit, by repurchasing and scrapping the used units...) to maximize his pro…t.

On the other hand, Fudenberg and Tirole (1998) argue that new and used units could become imperfect substitutes after the improvement of new goods. They conclude that R&D could have a positive impact on new goods prices, as well as a negative impact on second-hand cars [START_REF] Igal | Interfering with Secondary Markets[END_REF] . As already mentioned, microeconomic studies usually make the strong assumption of a monopolistic market. But Schiraldi (2009) proposed a microeconomic model in an oligopolistic car market. She concluded on a possible collusion of manufacturers to increase prices on second-hand markets through leasing policy, warranty policy and buy-back policy in order to increase prices on new markets. By and large, microeconomic results lead to various conclusions, but they always bring the idea that new and used markets impact each other prices (and volumes) on a short and a long time perspective.

Scitovsky' s mechanisms are part of a Keynesian framework.

Most of mentioned articles assume a neoclassical economy driven by real factors and where money supply has no impact. Agents are optimizing their purchase and know the function to optimize. Scitovsky (1994) adopts a Keynesian approach that includes uncertainty and the impact of disposable incomes on the overall economy.

Scitovsky investigates the destabilizing impact of secondary markets on the overall economy. They strengthen both recessions and recoveries. He …rst focuses on speci…c movements of prices: consumers often react to a modi…cation of their income by shifting their demand between new markets and cheaper secondary ones. As a result, in case of a su¢ cient elasticity of goods substitution, new and second-hand markets become interdependent. A shock or a disequilibrium in each market impacts prices, demand and supply in the same direction. Additionally, both markets o¤set one another. The disturbed market excess demand (or supply) becomes equal to the other market excess supply (or demand) and prices are stabilized accordingly. Unfortunately, prices are stabilized only for a while.

A gap between demand and supply still exist in both markets and an opposite e¤ect soon appears because of a slow adjustment of stock in the second-hand market. In the automotive sector, for instance, owners of used vehicles are more or less willing to hold their vehicles according to increases and decreases of prices.

The slow variation of stock has the following consequences: the used market volume rises and reduces the level of price in the new market. So the interdependence disrupts the equilibrium in both markets.

To summarize, following disturbance disequilibrium in one market, a short-term e¤ect of arbitraging creates a temporary obstacle to price movement and a move on the other market on the same direction. Then, on a second period, the second-hand market's disequilibrium slowly liberates constraints of an equilibrating price movement.

Scitovsky extends the discussion to the impact on the overall US economy. The e¤ect depends of the size of the used market. It depends also on the length of time the secondary market is able to compensate the variation of the new market without impacting prices. Automobiles are exceptional durable goods because of the size of the second-hand market, but Scitovsky assumes that the in ‡uence of stocks would be limited to two months only [START_REF] Hodrick | Postwar U.S. Business Cycles: An Empirical Investigation[END_REF] (Car owners are rarely relinquish and dealers stocks are quite limited).

From an empirical perspective, Peach et al (1996) also conclude that used markets intensify economic cycles. But they have another explanation: there has been a long-term shift of the US consumer demand from new to used car markets [START_REF] François | On the In ‡uence of Oil Prices on Economic Activity and Other Macroeconomic and Financial Variables[END_REF] . Franchised new car dealers have captured much of the second-hand market growth. They are collecting most of their pro…ts from used cars and are less aggressive bidders on the demand side of auctions. Regarding the supply side, when demand for new cars increases, they accelerate the used car price reduction by sending more used cars to auctions. The mechanism become reversed when the demand for new cars decrease. At the end, car markets have more volatility. Pashigan (2001) observed that US used car prices index has much more volatility than the new car index. The supply curves are less elastic for used than for new cars and, as a consequence, contribute to a higher volatility.

There are implied mechanisms behind the academic theories.

Other mechanisms do not come from a speci…c literature and are implied in the previous contributions. We mention them for clari…cation purposes and to facilitate their identi…cations in the econometric analysis that will be implemented in the next section.

"The new market feeds the used market": as a result, volume and prices of today's used car market might be positively correlated with volume and prices of the past new market. The mechanism also interacts with renewals on the used and the new markets.

"Renewals": after some years, drivers have to renew their vehicles. Concentrations of renewals create cycles on both markets. Additionally, concentrations on the new market could create future concentrations on the used market.

"Volume e¤ ect": an increase of transaction volumes, if caused by a greater o¤er, could have a positive impact on the prices. An increase of transaction volumes, if caused by a greater demand, could have a negative impact on the prices. "Price e¤ ect": a price increase could have a positive impact on the volume of transactions by improving o¤er, or a negative impact by decreasing demand.

"Arbitration": a driver can buy a car on the used market or on the new market. A car bought from one market cannot be bought from another market at the same time. When most of drivers choose to buy used vehicles, volumes (and prices) improve in the used market and, as a consequence, decrease in the new market.

"Reallocation": when prices are too high in the new market, the buyers move to the second-hand market.

Consequently, used car prices increase. In other words, prices and volumes move in the same direction in both markets on a short term perspective. Scitovsky analyzed the reallocation mechanism by insisting on the threshold e¤ects (due to stocks) on volumes and the lags creating constant disequilibrium.

The "Income e¤ ect": a decrease of income (or consumption or con…dence) creates a decrease of demand, a decrease of transaction volumes, and a fall of prices in both markets [START_REF] Martin | Consumer Behavior in Markets of Durable Experience Goods[END_REF] . Alternatively, it could create a shift of consumption from the new market to the used market. As a consequence, volumes and prices go down in the new market while they are increasing in the used market.

3 The macroeconomic times series need clari…cations.

We aim to check the accuracy of the mechanisms mentioned in the previous sections using econometric tools.

The interactions of the consumer price indexes and the volume of transactions of new and second-hand cars are analyzed in three countries. Following an interpretation of the relations between the academic theories on durables goods and the time series behavior, we de…ne the limit of our macro-economic perspective.

Three countries are compared through four time series.

We study the automotive markets of France, the United Kingdom and the United States of America. We consider observations related to the Consumer Price Index (CPI) and the volume of registrations (or sales) for new and used cars [START_REF] Peter | The used car price index: A checkup and suggested repairs[END_REF] . The US volumes make the di¤erence: in 2007, used car sales volume was more than 41,4 millions for the US market. By comparison, it was 5.3 millions and 7 millions for France and the UK. Moreover, the passenger car populations in use for France, the UK, and the US were 30.7 millions, 30.1 millions, and 135.4 millions [START_REF] Richard | Core CPI: Excluding Food, Energy...And Used Cars?[END_REF] .

We aim to analyze the interdependence between primary and secondary markets on a macroeconomic perspective. The quality of the car (to account for the Akerlof e¤ect), informations regarding demand (i.e. consumer con…dence) and o¤er (i.e. business con…dence), the level of R&D (for the Time inconsistency), the mix of vehicles or the level of stocks constitute relevant explanatory variables. However, we only included four time series in our analysis (prices and volumes) because of the di¢ culty to collect standardized information and to allow a comparison from a country to another.

The National Statistical Institutes (INSEE for France, ONS for the UK, BLS for the US) provide the automotive Consumer Price Indexes. They re ‡ect the general movement of prices on the new and the used car markets. The statistical institutes do not communicate a precise list of the items included in the samples used to construct the indexes. And the precise locations, where the observations are collected, are neither provided. They communicate, however, a general setting of their methodologies [START_REF] Pierre | The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis[END_REF] . The frameworks are not always similar from a country to another, but share the same objectives. First, the CPI has to re ‡ect the cost of life and to give an overview of price variation of the general expenditure across the country. Then prices are collected from various areas and the selected samples of cars aim to be representative of what people buy in these areas. Second, although goods and services are changing through time in their characteristics, the statistical institutes intend to measure the e¤ects of price changes by keeping constant the other economic factors. The processes by which prices are adjusted to account for changes in product quality constitute an important subject of research and discussions in the automotive sector. The US applies the Grilitch methodology [START_REF] Amil | Quantifying the Bene…ts of New Products: The Case of the Minivan The[END_REF] for the quality adjustment of automotive observations: the Hedonic approach estimates the price of a good through the valuation of its attributes. France and the UK apply another methodology, the 'option costing', that can be used when a product changes in speci…cation and when it is possible to value separately the components that have changed.

We use the volumes of registrations (for France and the UK) and sales volumes (for the US) as proxies of the total amount of transactions. They do not allow a distinction between the variations of o¤ers and the variations of demands, and provide a slightly more ambiguous information than the CPI: an increase of sales could be either the consequence of an increase of demand, or an increase of o¤er, or a reduction of prices. The impacts of volumes on prices are also ambiguous. An increase of the volumes could cause either a reduction or an increase of prices. Following an improvement of the market size, for instance, the dealers could reduce their prices in order to increase their market share or to reduce …xed costs. They could also consider a high level of demand as an opportunity to improve their bene…ts by increasing prices.

How to connect the academic literature with a time series analysis?

We divide the economic literature, surveyed in Section 2, in three groups: the advanced mechanisms (Table 1), the Scitovsky theory (Table 2) and, the basic mechanisms (Table 3). Their consequences on the time series analyzed in our article are synthesized in the column 'Impact on Prices and Volumes'. The arrows ( =) () ) indicate that a parameter a¤ects or causes another one. In order to avoid any misunderstanding, we have to mention that we do not assume mechanical relations similar to a clockwork (or deterministic links), but we expect to identify probable interdependence between the new and the used markets (or stochastic links).

Mechanisms

Descriptions

Impact on Prices and Volumes Akerlo¤ e¤ect 1

An increase of quality or information in the Used Car Market creates an increase in price and demand on the used market.

Quality " or Information " =) Volumes Used " and/or Prices Used "

Akerlo¤ e¤ect 2

An increase of quality or information in the Used Car Market creates an increase in price and demand on the Used Car Market and the New Market.

Quality " or Information " =) Volumes Used " and/or Prices Used " and Volumes New " and/or Prices New "

Optimal durability

An increase of durability creates a decrease of demand of new cars; therefore, a decrease of prices in the New Car Market as well as a decrease of o¤ers in the Used Car Market and an increase of prices.

Durability " =) Volumes New # =) Prices New # and Volumes Used # =) Prices Used "

Time Inconsistency

An increase of durability creates a decrease of demand of new cars; therefore, a decrease of prices in the New Car Market as well as a decrease of o¤ers in the Used Car Market and an increase of prices.

R&D " =) Volumes Used " and/or Prices Used " and Volumes New # and/or Prices New # Table 1: Advanced Mechanisms.

Mechanisms Descriptions Impact on Prices and Volumes Scitovsky Theory

Interactions creating constant disequilibrium in the primary and secondary markets.

Volumes New # (insu¢ cient stocks) =) Prices New " =) Volumes Used " =) Prices Used " =) Volumes New ! =) Prices New ! =)
Volumes Used # (insu¢ cient stocks) =) Prices Used " =) Volumes New " =) Prices New " and again =) Volumes Used " =) Prices Used ". . . . As discussed in section 2.2, the new market could experience di¤erent consequences from the Akerlo¤ e¤ ect. Therefore we made a distinction between the Akerlo¤ e¤ ect 1 having only an impact on the used market and the Akerlo¤ e¤ ect 2 impacting both markets. There was a similar issue with the Income e¤ ect driving both markets in the same direction or in di¤erent ones. Another roadblock exists regarding the e¤ect of demand. As an example, for the Time inconsistency e¤ect, an increase of demand would create either an higher volume of transactions, or only an increase of prices, or both [START_REF] Sylvain | Hedging residual value risk using derivatives[END_REF] .

The Akerlo¤ , the Optimal durability and the Time inconsistency e¤ects are di¢ cult to investigate because they involve additional information (quality, durability, R&D...). They could be invalidated, however, when series move in di¤erent directions than the ones listed in the tables. For instance, the improvement of quality in the Akerlo¤ e¤ect would take some time to spread across the population of cars and therefore could be identi…ed by an increasing trend on volumes, or prices, or both. If the trends are decreasing, then the theory should be refuted.

Our attempt to translate the theoretical economic literature under an econometric analysis highlights a critical point: the timing. In most of academics papers, except the Scitovsky (1994)'s article, the period in which the mechanism has an e¤ect was never explicit and the lags are not precisely de…ned. For instance, are the adjustments simultaneous in the Arbitration e¤ ect ? Or are they lagged ? Do they last for the next six months ? Do they last for a year ? The econometrics of the next section will provide an insight on timing.

3.3

We work on macroeconomic time series, a limited information.

The macroeconomic perspective presents four limits: the cross border sales, the availability of the historical observations, the usual critics on Consumer Prices Indexes, and the heterogeneity of the markets.

As a …rst concern, the cross border sales might a¤ect the national prices and transactions of cars: the imported vehicles, for instance, could increase the competitiveness and reduce car prices. In the European market (including France) the existence of signi…cant cross bordering transactions should lead to a price convergence. Gaullier and Haller (2000), however, did not notice mechanisms creating an automobile price convergence in European countries. They argue that exchange rate ‡uctuations explain a large share of the price dispersion dynamics [START_REF] Sylvain | The European used-car market at a glance: Hedonic resale price valuation in automotive leasing industry[END_REF] . Parities between Euro-land countries were …xed in May 1998, so their study was too early to assess the long-term e¤ects implied by the implementation of the single currency. Prado (2009), through an Hedonic analysis on the 2005-2009 period, shows that even with the Euro implementation, distinct national markets still constitute the European second-hand car market. Thanks to the right wheel vehicles, we have few concerns for the UK market regarding a possible interaction, on prices and volumes, with the other countries. As a conclusion, the impact seems limited for France and the UK. The US car market has a size dramatically higher than the Mexican and the Canadian markets and we also expect a limited cross bordering impact.

As a second concern, we have to keep in mind that our results might be altered by the limited period of available observations. All in all, knowing that cars longevity can run up to 20 years, the study would hardly provide a long-term perspective. In France, the used car CPI is available since January 1998, while, in the UK, the used car Index is available since January 1996. In the US, the BLS has published the used car index since 1952 and, in order to re ‡ect the cost of living of a representative household, light truck vehicles have only been included in the CPI since 1998. To standardize the analyses (for the UK), for consistency purpose (for the US), and to allow a comparison of the three countries, we selected the CPI samples from January 1998. Regarding the times series of volumes (number of registrations, number of sales), we did not apply the same criteria for the selection of the period: we included as much information as possible, regarding the number of registrations and sales, maximizing the opportunity to identify a relation between prices and past volumes (i.e. correlation between used cars and previous …ve years used cars sales). Most of the time, the volume of transactions has been included according to the series provided by the statistical institutes and, as a result, series of volumes are longer than CPI series [START_REF] Marshall | A Review of Reviews: Ninety Years of Professional Thinking About the Consumer Price Index[END_REF] (except for the UK used car registrations). The time series for France, the UK and the US are presented in Appendix 3.

The relevance of the variables constitutes our third concern. Like any other statistical indicator, the Consumer Price Index has been the subject of several critics. In addition, because of the political and economical impacts on citizen (i.e. wage negotiations), there has always been a suspicion regarding the CPI accuracy. Two main critics show up: in the automotive area, people complain that Hedonic adjustments over de ‡ate the movement of prices and that CPI does not re ‡ect their 'feeling'of increasing prices. Greenlees and

McClelland (2008) discussed the limits of those critics. They demonstrated the limited impact of Hedonic adjustment on CPI results [START_REF] Rust | When Is It Optimal to Kill O¤ the Market for Used Durable Goods? Econometrica[END_REF] . And a well known psychological 'loss aversion'could increase the sensibility to increasing prices than to decreasing prices; because the CPI cannot re ‡ect the consumption of a particular group of customers, they are de…ned as an average of the in ‡ation rate. Consumers are always members of a speci…c group and they always have the feeling that the CPI is not in line with their speci…c consumption.

Fourth, speaking of di¤erent groups of customers, we have to clarify that, although we work at a country level, we do not assume heterogeneity of the markets: a national car market could be the sum of several sub markets involving very di¤erent populations of customers. A sub market might strongly impact the whole car market through a signi…cant size or a high level of volatility. But we aim to provide a macro-economic perspective and intra market interactions do not constitute the subject of our study.

What do the series look like?

The period of analysis has been standardized from January 1998 to June 2009. The French market seems rather stable, whereas the UK [START_REF] Pasquale | Second-Hand Markets and Collusion by Manufacturers of Semidurable Goods[END_REF] and the US prices follow a negative trend and display a high volatility [START_REF] Tibor | Towards a Theory of Second-Hand Markets[END_REF] .

For the last ten years the trends of the US series look negative and illustrate the crisis of the automotive sector in North America. All these characteristics remain through a growth rate perspective and after a seasonal adjustment [START_REF] Edward | Monopoly and Competition in the Market for Durable Goods[END_REF] .

At a glance, new car CPI are always more stable than used car CPI. Prices on the used market are the result of demands and o¤ers, while new car prices are set by the dealers and manufacturers according to constraints of production and maximization of pro…ts. If new car prices become too high, the number of sales decreases because of prices rigidity on the new market and the adjustment operates mainly by the volume of transaction 31 . As a result, registration (or sale) volumes are more volatile for new cars than second-hand cars, and new car prices are quite stable. The market readjustment through volumes explains why some economic institutions (i.e. OECD) use new car transactions as a short-term economic indicator. In contrast, quality adjustment methodologies applied on the French and the UK Consumer Price Index. 2 8 For UK, they are two big variances after 1999. There has been a change in the car registrations process after 1999. Prior to 1999, new plates were introduced in August. From 1999 onwards, there has been two plate changes, in March and September. 2 9 See graphs in Appendix 3. 3 0 Series are seasonally adjusted using X11 methodology. See graphs in Appendix 4.

3 1 These conclusions should be con…rmed by an analysis of the automotive production (does the manufacturers adjust the production according to prices ?) and stocks available (how the stocks impact the markets ?). prices in the second-hand market are set through o¤er and demand. As a result, used car prices display more volatility than new car prices.

By the beginning of 2008, the time series falled sharply. The subprime crisis, a global economical event, appears as an opportunity to compare the reaction on the di¤erent markets and to con…rm the previous statements. The new cars registrations (or sales for the US) are more impacted (by a stronger drop) than the used car registrations (or sales), and used car CPI is more impacted than new car CPI. As a …rst conclusion, it suggests that, in the case of an Income e¤ ect, the used car market has an higher probability to be impacted on a price perspective, whereas the new market would rather be impacted on a volume perspective because of a relative price rigidity from car manufacturers. The mechanisms mentioned as the Feeds e¤ ect, Arbitration, Prices e¤ ect and Volume e¤ ect might be similarly a¤ected.

All in all, new car markets in the UK and the US have been declining for the last 10 years, while France has been a stable market. 4 The econometric analysis shows di¤erent results by country.

The econometric tools identify trends, cycles and correlations through various durations (short-term, very short-term, the whole ten years period). At the same time, we evaluate if the outcomes are in line with the academic theories. At the end of the section, we estimate the VAR models to investigate the relations between the markets and the possible forecasts [START_REF] Van Cayseele | Lemons, peaches and creampu¤s: The economics of a second-hand market[END_REF] .

The unit root tests undermine the advanced mechanisms.

As previously stated, France appears as a stable market. To check this intuition, we apply the Augmented Dickey Fuller unit root test to the growth rate of the series. The results are reported in Table 4 and show that the French volumes and index prices have been stationary for the last ten years. On the contrary, the UK and the US have trends: new cars CPI in the UK, as well as the volume of new car and used car sales in the US, have a unit root (Di¤erence Stationnarity or DS). According to the econometric theory, it means that a macroeconomic shock would have an impact on the trend series forever. In contrast, a trend stationnarity (TS) has been identi…ed for the new car prices index in the US, implying that a macroeconomic shock would have a temporary e¤ect on the prices. Finally, the used car CPI has no trend in every country. The unit root test invalidates the assumption that, for the last ten years, prices and volumes have been moving in the same direction in the UK new car market (the new car CPI follows a DS process while the volume of used car sales was stable), and in the US new market (sale volumes and prices follow a di¤erent trend, a TS and a DS). Turning to the economic theories, it rejects the presence of mechanisms involving similar long-term trend on prices and volumes (like the Akerlo¤ e¤ ect, the Time inconsistency....). As an example, the decreasing trend in the US might be explained by the Optimal durability e¤ect: the demand for vehicles decreases because cars durability has improved. Drivers do not have to renew their vehicles as often as in the past. An improvement of cars quality should also lead to an expansion of the second-hand market, and in the same manner, an increase of used cars prices (and volumes). But the Optimal durability mechanism is invalidated by the stationnarity of the used car prices (and the decrease of used car volumes).

Focusing on car prices, the estimated trends refute several mechanisms and illustrate the absence of a long term relation between prices. The stability in France and the trends moving in the same direction in the UK invalidate the existence of a strong Akerlo¤ e¤ ect 2, or an Optimal durability e¤ ect.

Regarding the sale volumes, the trend analysis on the whole period illustrates the well known fact that the new cars of today are the used cars of tomorrow. In France and the UK, the new and the used car registrations share a similar stationnarity. In the US market, a cointegration test identi…es a common longterm trend between new car and used car sales [START_REF] Michael | Planned Obsolescence and the R&D Decision[END_REF] : for the last ten years, the new and used US sales have been declining. These results also weaken the mechanisms reported in Table 1. It is highly unlikely that the stability in France and the UK, as well as the decline in the US, would be due to a global decrease of cars quality [START_REF] Michael | Durable Goods Theory for Real World Markets[END_REF] (according to the Akerlo¤ e¤ ect, the Time inconsistency....).

The correlation analysis provides a one-month period perspective.

The correlation calculation provides a …rst insight on the simultaneity of market evolutions [START_REF] Emons | The Market for Used Cars: A New Test of the Lemons Model[END_REF] .

For France, a negative correlation between new CPI and used CPI suggests an arbitrage on prices (i.e. when prices decrease on the new market, they improve on the used market). The signi…cant correlation between new and used registrations has a positive sign that might be caused by an Income e¤ ect on the volume of transactions. In other words, when drivers incomes (and demand) improve, the volume of sales increases on both markets.

For the UK, there is a positive correlation between the new car registrations and the used car prices.

These results are in line with the graphical analysis: Market adjustments are made through new volumes and used prices whereas constraints exist on new car prices and on the volumes of used car transactions; following an economic crisis, new sales and second-hand prices fall sharply while new prices and second-hand volumes remain relatively stable.

For the US, a strong positive correlation exists between new and used prices (r = 0:54) as well as a negative correlation between new and used transactions. The US market dynamics are converse to the French ones; it suggests an Income e¤ ect on a price perspective and an Arbitraging e¤ ect on a volume perspective. These results evoke a Scitovsky's framework: in the new and the second-hand markets, prices move in the same direction but the variation of bid, o¤er and stocks in both markets lead to a constant disequilibrium.

The Granger causality tests elaborate the assessments of the correlation analysis.

To investigate the interdependence between new and used car markets, we …rst apply the Granger causality test 36 evaluating how much the previous six month information contained in a variable could improve the prediction of another variable. Results are given in Table 5. In the French market, new and used cars registrations are interrelated : the null hypothesis, that the volume of used car registrations does not Granger cause the volume of new car registrations, has not been rejected at the 5% signi…cante level. In addition, the volume of new car registrations Granger causes the volume of used car registrations 37 . It con…rms the Income e¤ ect mentioned in the correlation analysis.

Furthermore, the Granger test indicates that the used car CPI helps to predict used car registrations and new cars registrations: rising used car prices improve drivers willingness to resale their cars and to buy a 3 6 The Granger test has been set with six months lags. 3 7 See the detailed Granger test results in Appendix 5. new one, as a result, the number of registrations goes up.

For the UK, the used car CPI helps also to predict new cars registrations. The results corroborate the graphical and the correlation analyses and emphasize that the adjustments on the new market are more on volumes than on prices. Nevertheless, it seems that dealers and manufacturers try to adjust prices and volumes according to the state of the market, because new car registrations and new car prices also help to predict each other.

The causalities are more numerous in the US market: new car prices and used car prices help to predict each other; new car sales and new car prices help to predict used sales; at the same time, the new car sales help also to forecast new car prices. The test suggests the existence of multiple relations between new and second-hand cars and shows a strong interdependence in the US markets by comparison to France and the UK. To be speci…c, the Scitosky's theory, of constant disequilibrium from one market to another, constitutes a possible explanation.

The Hodrick-Prescott …lter reveals economic cycles.

In order to identify long-term trends of the series, we calculate Hodrick-Prescott …ltered series 38 . The …lter produces a smoothed non-linear representation of the time series that is more sensitive to long-term than to short-term ‡uctuations 39 .

For France, the graphs show larger cycles (of 2 years) for used car prices index by comparison to new car prices (6 months) and the volume of transactions. Similarly, second-hand price follows a longer and more visible cycles in the UK and the US car markets. The distinct pattern of the used car prices mitigates the validation of mechanisms involving prices and volumes moving in harmony (Akerlo¤ e¤ ect, Time inconsistency).

We evaluate the synchronizations of prices and volumes ‡uctuations. Following Fiorito and Kollintzas simultaneously. As a result, like the correlation analysis of Section 4.2, the Hodrick-Prescott …lter identi…es an Income e¤ ect on a volume perspective.

On the UK market, the …lter also con…rms the existence of a Feed e¤ ect: used car prices cycles are pro-cyclical to new car prices through lags of 3 to 12 and 36 months 43 . The absence of strong correlations on registrations cycles with other series reduces the probability of a Scitovsky mechanism.

For the US, markets cycles are well interrelated. There are several pro-cyclical and counter-cyclical relations between prices and volumes. First of all, we identify a positive correlation between new car CPI and the used car CPI. In addition, the used car CPI, with 9 months and 12 month lags, appears countercyclical to the volume of used sales. Finally, the used sales volumes have a cyclical relation with new car prices.

These results are in line with the Scitovsky theory.

Vector Autoregressive (VAR) models clarify the previous results.

A Vector Autoregressive model gives a straight perspective of the relation between prices and volumes in both markets. We selected the best model using the Akaike and the Schwarz criteria. The results are reported in Appendix 10 and show the usual greater interaction between the primary and the secondary markets for the US. Let us discuss the outcomes for each country.

For France, the used car prices mainly depend on their own lagged values 44 . The equation is in line with the Hodrick Prescott results displaying that used CPI cycles are di¤erent to other series cycles. For the new car prices equation, the model has a good …t to the data thanks to the relevant information from the previous month new prices and the constant. These results corroborate the graphical analysis revealing rigidity of new car prices by showing few ‡uctuations of the new car CPI.

Regarding the French volume equations, the new and the used cars registration models have a poor adjustment to the historical observations and none of the variables are statistically signi…cant. In other words, none of the variables from one market are relevant to model the other market, and the VAR methodology does not identify the suggested relations of the previous section (correlation and arbitraging). Gautier (1995) attempted to identify new car registration cycles, which would be a characteristic of durable goods in the French market since 1945. He concluded that registration cycles are more the result of the economic activity (with additional volatility and sectorial events) than to the internal dynamics of car markets. It means that, in order to forecast the registrations in France, a model including variables related to the economic activity would be more relevant.

For the UK, the used car CPI equation shows that, in a similar way to France having distinct cycles for used car CPI, the previous months used car prices information is statistically signi…cant. The new market variables are also crucial, but they have smaller coe¢ cients compared to used car prices lagged values. To be more speci…c, the coe¢ cients of the variables from the new market have a positive e¤ect and therefore reinforce the conclusions of the graphical and the correlation analyses (the new CPI coe¢ cient is less important because of the rigidity of new car prices created by production constraints), as well as the Granger causality test (in spite of the rigidity, dealers try to modify the prices according to the state of the economy). Regarding the new cars CPI equation, although the adjustment is poor, two variables appear signi…cant (the used car price index and the used car registrations). But even with a new car CPI series positively correlated to the used car market, the weakness of the relation suggests that any involved mechanism would be quite limited.

For the British used cars registrations equation, the model has also a poor adjustment and registrations seem slightly and positively impacted by the used car prices: when prices go up, dealers and privates get an opportunity and they increase the volumes of sales, but stocks are limited and the evolution remains limited as well. Into the new cars registrations equation, though the used cars CPI and the constant constitute the only relevant information, the model adjustment is quite good. Again, it strengthens the previous conclusions that economic readjustments are mainly made on the new market by volume (and on the used market by price): when the state of the economy improves, for instance, the volume of new cars and the prices of used cars react …rst and increase. The new car volumes are, however, limited by production constraints and consequently, the constant in the equations appears highly signi…cant. The positive coe¢ cient of the new car volume variable would only allow the existence of mechanisms with similar co-movements in both markets (Income e¤ ect, Akerlo¤ e¤ ect...) on a short period.

From the previous results in the US market, we know that the used CPI follows speci…c cycles and, at the same time, was positively correlated to new car prices. Accordingly, in the used CPI equation, the lagged used car prices and the new car CPI (with a positive sign) are statistically signi…cant. On the contrary to France and the UK, the new CPI equation is well …tted to the historical observations. New car prices are explained by the previous used car CPI and the previous new CPI. They are also positively impacted by the volume of transactions of the new market. Therefore the US car prices are connected in various ways with the new and the used market.

The explained variance of US volume equations are not as good: R 2 are equal to 20% and 47% for new and used sale equations. In the new sales equation the only important variables are the previous new sales; in the used sales equation the new and the used sales are signi…cant variables. Scitovsky (1994) mentioned that the market adjustments were altered by the limited variation of volumes. He argued that used car market volumes were limited by stocks. In addition, we argue that new car volumes are limited by production constraints, and that the VAR results on volumes are fully in line with his theory. 5 To conclude, what kind of interdependence exists between the new and the second-hand car markets?

The aim of this paper was to investigate the interdependences between the new and the second-hand car markets in three countries: France, the UK and the US. The analysis was limited to a ten year period; since cars are durable goods that can be used for more than 20 years, it might have restricted the results to interdependences shorter than a decade. The econometric tools, however, show consistent outcomes all along the study 45 .

Initially, we argue that in all countries the new market of the past is linked to the used market of today, through volumes and prices. Secondly, the interrelations appear limited for France and the UK, whereas the US market is characterized by a Scitovsky dynamics, de…ned by constant disequilibrium and multiple interactions between primary and secondary markets. Our contribution also highlighted that, depending of a short-term or a long-term perspective, interactions are di¤erent. Thirdly, theories implying volumes and prices moving in the same direction (Akerlo¤ e¤ ect, Optimal durability, Time Inconsistency) are di¢ cult to con…rm. Finally, for France, the UK, and the US the connections between primary and secondary car markets are not similar, but all markets experience a characteristic rarely mentioned in the literature: a rigidity of both the new car prices and the used car volumes of transactions. Another similar characteristic is that, for all countries, used car prices follow distinct cycles. All things considered, our results illustrate that the interrelations between the new and used car markets are not strong enough to fully explain and forecast the market patterns. The use of macroeconomic variables related to the disposable income of buyers or the general state of the economy might improve the forecast accuracy, and is left for future research.

France

  Used cars CPI =) Used cars Registrations Used cars CPI =) New cars Registrations Used cars Registrations () New cars Registrations UK Used cars CPI =) New cars Registrations New cars CPI () New cars Registrations US Used cars CPI () New cars CPI New cars CPI =) Used cars Sales New cars Sales =) New cars CPI New cars Sales =) Used cars Sales =) : Signi…cant Causality (): Signi…cant causality in both directions.

APPENDIX

S a m p l e ( a d j u s t e d ) : 1 9 . 5 3 4 5 S c h w a r z c r i t e r i o n -1 8 . 7 1 5 8 FranceI

 19588 l u d e d o b s e r v a t i o n s : 1 2 4 a f t e r a d j u s t m e n t s S t a n d a r d e r r o r s i n ( ) & t -s t a t i s t i c s i n [ ] U S E D _ C A R S _ C P I N E W _ C A R S _ C P I U S E D _ C A R S _ V O L N E W _ C A R S _ V O L U S E D _ C A R S _ C P I ( i k e i n f o r m a t i o n c r i t e r i o n -1 n c l u d e d o b s e r v a t i o n s : 8 8 a f t e r a d j u s t m e n t s S t a n d a r d e r r o r s i n ( ) & t -s t a t i s t i c s i n [ ] U S E D _ C A R S _ C P I D _ N E W _ C A R S _ C P I U S E D _ C A R S _ V O L N E W _ C A R S _ V O L U S E D _ C A R S _ C P I ( i k e i n f o r m a t i o n c r i t e r i o n -2 0 . 7 4 6 5 S c h w a r z c r i t e r i o n -1 9 . 7 3 3 0 UK S t a n d a r d e r r o r s i n ( ) & t -s t a t i s t i c s i n [ ] U S E D _ C A R S _ C P I T _ N E W _ C A R S _ C P I D _ U S E D _ C A R S _ V O L D _ N E W _ C A R S _ V O L U S E D _ C A R S _ C P I ( i k e i n f o r m a t i o n c r i t e r i o n -2 0 . 4 2 7 1 S c h w a r z c r i t e r i o n -1 9 . 6 0 8 3 US

Table 2 :

 2 Scitovsky Theory.

	Mechanisms	Descriptions	Impact on Prices and Volumes
	New market feeds used market	Past volumes of new sales transactions corre-lated positively with the current volumes of Used Sales transactions. Past prices of New	Positive Correlation: Past New Volumes () Current Used Volumes / Past New Prices () Current Used Prices
		Sales transactions correlated positively with
		current prices of Used Sales transactions
	Reallocation	Prices and volumes of New sales transactions correlated positively with prices and volumes of Used Sales transactions	Positive Correlation: New Volumes () Used Volumes / New Prices () Used Prices
	Arbitration Renewals	A car bought in one market can't be bought, at the same time, in another market. Concentrations of renewals create cycles in	Negative Correlation: New Volumes , Used Volumes / New Prices , Used Prices Cycles of Prices and volumes: Past New Vol-
		both markets. Concentrations in the new mar-ket could create future concentrations on the used market.	umes " =) Current Used Volumes " and Past New Prices " =) Current Used Prices "
	Price e¤ect	A price increase could have a positive impact on the volume of transactions by improving of-fers/sales, or a negative impact by decreasing	Prices " =) O¤er " =) Volume " or Demand # =) Volume #
		demand.
	Volume e¤ect	A volume increase could have a positive im-
		pact on the prices if caused by a greater o¤er
		or a negative impact, if caused by a greater
		demand.

Volume " =) Prices # or Prices " Income e¤ect 1 A decrease of consumers' income (or business activity or con…dence) reduces the demand for new cars and used cars decreasing in prices and volume in both markets. Income # =) Demand # =) Volumes # and/or Prices # Income e¤ect 2 A decrease of consumers income (or business activity or con…dence) reduces the demand for new cars and creates a shift to the used car market It's decreasing prices and volumes in the new market and an increase in the used market Income # =) Demand New # =) Volumes New # and/or Prices New # and Demand Used " =) Volumes Used " and/or Prices Used "

Table 3 :

 3 Basics Mechanisms.

Table 4 :

 4 Augmented Dickey Fuller Results.

Table 5 :

 5 Granger test Results.

  5: Granger Test

	Pairwise Granger Causality Tests Lags: 6 Null Hypothesis: NEW_CARS_CPI does not Granger Cause USED_CARS_CPI USED_CARS_CPI does not Granger Cause NEW_CARS_CPI USED_CARS_VOL does not Granger Cause USED_CARS_CPI USED_CARS_CPI does not Granger Cause USED_CARS_VOL NEW_CARS_VOL does not Granger Cause USED_CARS_CPI USED_CARS_CPI does not Granger Cause NEW_CARS_VOL USED_CARS_VOL does not Granger Cause NEW_CARS_CPI NEW_CARS_CPI does not Granger Cause USED_CARS_VOL NEW_CARS_VOL does not Granger Cause NEW_CARS_CPI NEW_CARS_CPI does not Granger Cause NEW_CARS_VOL NEW_CARS_VOL does not Granger Cause USED_CARS_VOL USED_CARS_VOL does not Granger Cause NEW_CARS_VOL France Pairwise Granger Causality Tests Lags: 6 Null Hypothesis: NEW_CARS_CPI does not Granger Cause USED_CARS_CPI USED_CARS_CPI does not Granger Cause NEW_CARS_CPI USED_CARS_VOL does not Granger Cause USED_CARS_CPI USED_CARS_CPI does not Granger Cause USED_CARS_VOL Appendix 6: Correlation Analysis USED_CARS_CPI NEW_CARS_CPI USED_CARS_CPI 1.00 -0.31 NEW_CARS_CPI -0.31 1.00 USED_CARS_VOL -0.03 -0.13 NEW_CARS_VOL 0.10 -0.17 France USED_CARS_CPI NEW_CARS_CPI USED_CARS_CPI 1.00 0.16 NEW_CARS_CPI 0.16 1.00 USED_CARS_VOL 0.05 -0.09 NEW_CARS_VOL 0.35 0.01 UK USED_CARS_CPI NEW_CARS_CPI USED_CARS_CPI 1.00 0.54 NEW_CARS_CPI 0.54 1.00 USED_CARS_VOL -0.01 0.02 NEW_CARS_VOL -0.01 NEW _CARS_CPI USED_CARS_VOL NEW _CARS_CPI 1.000 0.082 USED_CARS_VOL 0.082 1 NEW _CARS_VOL 0.058 0.421 USED_CARS_CPI 0.087 0.14 USED_CARS_CPI(36) 0.341 0.068 USED_CARS_CPI(24) -0.137 -0.068 USED_CARS_CPI(18) -0.107 -0.077 USED_CARS_CPI(12) -0.116 -0.085 USED_CARS_CPI(9) 0.298 -0.078 USED_CARS_CPI(6) 0.215 0.128 USED_CARS_CPI(3) 0.049 0.156 USED_CARS_CPI(-3) -0.119 0.101 USED_CARS_CPI(-6) -0.06 0.011 USED_CARS_CPI(-9) -0.012 0.066 USED_CARS_CPI(-12) 0.008 -0.001 NEW _CARS_CPI 1 -0.192 USED_CARS_VOL -0.192 1 NEW _CARS_VOL -0.042 0.026 USED_CARS_CPI 0.085 -0.132 USED_CARS_CPI(36) 0 -0.05 USED_CARS_CPI(24) 0.1 -0.209 USED_CARS_CPI(18) -0.043 -0.032 USED_CARS_CPI(12) -0.283 0.192 USED_CARS_CPI(9) -0.389 0.117 USED_CARS_CPI(6) -0.447 0.052 USED_CARS_CPI(3) -0.315 -0.143 USED_CARS_CPI(-3) 0.258 0.055 USED_CARS_CPI(-6) 0.339 -0.036 USED_CARS_CPI(-9) 0.347 0.071 USED_CARS_CPI(-12) 0.333 0.134 USED_CARS_CPI(-18) 0.137 0.141 USED_CARS_CPI(-24) -0.208 -0.067 NEW _CARS_CPI 1 0.299 USED_CARS_VOL 0.299 1 NEW _CARS_VOL 0.044 -0.048 USED_CARS_CPI(36) 0.097 0.139 USED_CARS_CPI(24) -0.134 -0.164 USED_CARS_CPI(18) 0.016 -0.02 USED_CARS_CPI(12) -0.105 0.023 USED_CARS_CPI(9) 0.146 0.054 USED_CARS_CPI(6) 0.369 0.123 USED_CARS_CPI(3) 0.445 0.048 USED_CARS_CPI 0.421 0.055 USED_CARS_CPI(-3) 0.206 0.024 USED_CARS_CPI(-6) -0.113 -0.034 USED_CARS_CPI(-9) -0.176 0.034 USED_CARS_CPI(-12) -0.178 0.027 USED_CARS_CPI(-18) -0.051 -0.082 USED_CARS_CPI(-24) -0.222 -0.006 0.04 Appendix 8: Cycles Correlations USED_CARS_VOL USED_CARS_VOL APPENDIX 10: Vector AutoRegressions	Obs 120 120 120 120 120 252 Obs 119 84 USED_CARS_VOL F-Statistic Probability 1.0125 0.4212 0.3615 0.9017 0.5774 0.7476 2.5318 0.0248 0.8105 0.5640 2.6519 0.0194 0.8364 0.5444 0.9842 0.4397 1.0053 0.4258 0.8752 0.5158 2.1592 0.0477 3.8416 0.0011 F-Statistic Probability 0.5688 0.7543 0.8581 0.5283 1.5144 0.1859 1.7610 0.1196 NEW_CARS_VOL -0.03 0.10 -0.13 -0.17 1.00 0.44 0.44 1.00 USED_CARS_VOL NEW_CARS_VOL 0.05 0.35 -0.09 0.01 1.00 0.16 0.16 1.00 USED_CARS_VOL NEW_CARS_VOL -0.01 -0.01 0.02 0.04 1.00 -0.28 NEW _CARS_VOL USED_CARS_CPI 0.058 0.087 0.421 0.14 1 0.179 0.179 1 0.206 -0.158 -0.005 -0.169 -0.065 -0.371 -0.223 -0.321 -0.145 -0.116 -0.094 0.101 0.101 0.513 0.018 0.513 -0.013 0.101 0.04 -0.116 0.058 -0.321 -0.042 0.085 0.026 -0.132 1 0.176 0.176 1 -0.018 -0.158 -0.005 -0.169 -0.047 -0.371 -0.059 -0.321 -0.053 -0.116 0 0.101 0.13 0.513 0.132 0.513 0.081 0.101 -0.015 -0.116 -0.131 -0.321 -0.177 -0.371 -0.139 -0.169 0.044 0.421 -0.048 0.055 1 0.136 0.196 0.19 -0.171 -0.087 0.025 -0.22 0.096 -0.522 0.068 -0.213 0.047 0.201 0.12 0.69 0.136 1 -0.027 0.69 -0.127 0.201 -0.238 -0.213 -0.287 -0.522 0.06 -0.22 0.266 -0.087 NEW _CARS_VOL USED_CARS_CPI NEW _CARS_VOL USED_CARS_CPI
	NEW_CARS_VOL does not Granger Cause USED_CARS_CPI USED_CARS_CPI(-18) -0.019 -0.181 USED_CARS_CPI(-36) 0.281 -0.024 USED_CARS_CPI(-36) 0.067 -0.15	120	0.7487 -0.107 -0.144 0.104	0.6117	-0.371 -0.158 0.19
	USED_CARS_CPI does not Granger Cause NEW_CARS_VOL USED_CARS_VOL does not Granger Cause NEW_CARS_CPI USED_CARS_CPI(-24) -0.07 -0.084 NEW _CARS_CPI(-6) 0.116 0.181 NEW _CARS_CPI(-6) -0.122 -0.09	84	3.5091 0.8961 0.019 -0.051 -0.033	0.0033 0.5027	-0.169 -0.447 0.369
	NEW_CARS_CPI does not Granger Cause USED_CARS_VOL USED_CARS_CPI(-36) 0.217 0.077 USED_CARS_VOL(-6) -0.058 -0.007 USED_CARS_VOL(-6) -0.108 -0.037		0.4179 -0.065 -0.037 0.038	0.8648	-0.158 0.052 0.123
	NEW_CARS_VOL does not Granger Cause NEW_CARS_CPI NEW_CARS_CPI does not Granger Cause NEW_CARS_VOL NEW _CARS_CPI(-6) -0.068 0.116 NEW _CARS_VOL(-6) -0.156 0.069 NEW _CARS_VOL(-6) -0.237 -0.137	119	10.6495 0.3673 0.195 0.152 0.066	0.0000 0.8982	0.215 0 0.047
	NEW_CARS_VOL does not Granger Cause USED_CARS_VOL USED_CARS_VOL does not Granger Cause NEW_CARS_VOL USED_CARS_VOL(-6) 0.041 0.152 NEW _CARS_CPI(-12) -0.333 0.146 NEW _CARS_CPI(-12) -0.159 0.079 UK NEW _CARS_VOL(-6) -0.079 -0.114 USED_CARS_VOL(-12) 0.125 -0.542 USED_CARS_VOL(-12) -0.137 -0.289	84	1.5057 0.7780 0.085 -0.18 -0.169 0.006 0.073 0.052	0.1888 0.5899	0.128 -0.283 -0.105 -0.094 0.192 0.023
	NEW _CARS_CPI(-12) NEW _CARS_VOL(-12) NEW _CARS_VOL(-12)	-0.392 0.078 0.144	-0.032 0.035 -0.05		0.035 -0.183 -0.407	-0.116 -0.059 0.096
	Pairwise Granger Causality Tests Lags: 6 USED_CARS_VOL(-12) NEW _CARS_CPI(-24) NEW _CARS_CPI(-24)	-0.038 -0.224 -0.472	-0.155 -0.094 -0.117		-0.012 0.039 0.27	-0.085 0.1 -0.134
	Null Hypothesis: NEW_CARS_CPI does not Granger Cause USED_CARS_CPI NEW _CARS_VOL(-12) -0.015 -0.16 USED_CARS_VOL(-24) 0.123 -0.161 USED_CARS_VOL(-24) -0.075 -0.174 USED_CARS_CPI does not Granger Cause NEW_CARS_CPI NEW _CARS_CPI(-24) -0.171 0.021 NEW _CARS_VOL(-24) -0.016 -0.132 NEW _CARS_VOL(-24) -0.054 0.139	Obs 120	F-Statistic 3.2097 -0.447 -0.179 0.113 2.3908 -0.235 -0.16 -0.256	Probability -0.223 -0.209 -0.164 0.0062 0.0331 -0.137 -0.005 -0.171
	USED_CARS_VOL does not Granger Cause USED_CARS_CPI USED_CARS_CPI does not Granger Cause USED_CARS_VOL USED_CARS_VOL(-24) -0.026 -0.299 NEW _CARS_CPI(-36) -0.066 -0.083 NEW _CARS_CPI(-36) -0.066 -0.215 NEW_CARS_VOL does not Granger Cause USED_CARS_CPI NEW _CARS_VOL(-24) 0.047 -0.102 USED_CARS_VOL(-36) -0.263 0.158 USED_CARS_VOL(-36) 0.098 -0.24	120 120	1.6204 1.7257 -0.064 0.15 0.08 0.7601 0.045 -0.011 -0.061	0.1485 0.1219 0.6028	-0.068 0 0.097 -0.005 -0.05 0.139
	USED_CARS_CPI does not Granger Cause NEW_CARS_VOL USED_CARS_VOL does not Granger Cause NEW_CARS_CPI NEW _CARS_CPI(-36) -0.07 -0.131 NEW _CARS_VOL(-36) 0.002 0.011 NEW _CARS_VOL(-36) -0.105 0.035 NEW_CARS_CPI does not Granger Cause USED_CARS_VOL USED_CARS_VOL(-36) 0.047 -0.258 Hodrick-Prescott correlations UK Hodrick-Prescott correlation US	120	0.4233 0.3855 0.117 -0.051 0.245 2.5894 -0.18	0.8621 0.8869 0.0221	0.341 -0.018 0.196 0.068
	NEW_CARS_VOL does not Granger Cause NEW_CARS_CPI NEW_CARS_CPI does not Granger Cause NEW_CARS_VOL NEW _CARS_VOL(-36) -0.072 -0.067 NEW_CARS_VOL does not Granger Cause USED_CARS_VOL Hodrick-Prescott Correlations France	120 134	2.0814 1.2774 -0.205 4.2343	0.0613 0.2738 0.0007	0.206
	USED_CARS_VOL does not Granger Cause NEW_CARS_VOL		1.7096	0.1244
	US

This article is part of a general study on resale market hedging[START_REF] Sylvain | Hedging residual value risk using derivatives[END_REF]. We aim to estimate the distribution of the resale price in order to include the depreciation behavior in a derivative product.

On a broader de…nition of Van Cayseel, the key concept should be not used goods but resales.

We are focusing on second-hand markets for automobiles. Most of the time there is a depreciation of the good over time. However, in some markets like art or …nancial product, the secondary market has a higher valuation than the primary market. Speci…c cars (luxury ones) could also gain value after some years because of collectors interests.

Regarding maintenance, the second hand market could be a way to reallocate used goods with high maintenance cost to users who have a better maintenance technology or skills.

It brings the problem of adverse selection discussed in the next section.

The problem of Time Inconsistency is discussed in section 2.2.

See Waldman (2003) for a large review in the microeconomy area.

usually through franchise dealer. 1 0 European Automobile Manufacturers'Association: www.acea.be/index.php/news/news_detail/new_vehicle_registrations_by_manufacturer/ 1 1 Source: CRS report for congress. 1 2 See Petrin (2002).

[START_REF] Abdelaziz | Is Default Risk Related to In ‡ation?[END_REF] In spite of the limitation of the study focusing on a country without a national automotive industry.

[START_REF] Sophronis | Gains from trade in used goods: Evidence from automobiles[END_REF] See graphs in Appendix

 1 5 See graphs in Appendix 2.

[START_REF]Policy Overview and Recent History[END_REF] Petrin(2002)'s empirical analysis on the impact of introduction of the minivan in the US market does not include the second-hand market, but the study con…rms the positive impact of innovation in a competitive market. When automotive …rms are introducing new products, they are cannibalizing each other pro…ts ignoring the externalities they create. In the end, new products can bring large pro…ts to the innovator and substantial gains for the consumer.

[START_REF] Fiorito | Stylized Facts of Business Cycles in the G7 from a Real Business Cycles Perspective[END_REF] According to Scitovsky, …nancial assets are the only exception. The destabilizing impact of …anacial secondary market would have no limit. Their sizes and shocks duration would signi…cantly impact the overall economy.

[START_REF] Dennis | The Use of Hedonic Regressions to Handle Quality Change:The Experience in the[END_REF] There has been a shift, as mentioned in the previous section, consequently to an increase of durability and a¤ordability of cars, as well as a higher level of available information for consumers.

[START_REF] Drew | Upgrades, Trade-ins, and Buybacks[END_REF] According to Scitovsky (1994), the Income e¤ ect causes cycles.

0 See Appendix 1 for data sources.

[START_REF] George | The Market for "Lemons": Quality Uncertainty and the Market Mechanism[END_REF] The number of new passenger car registrations in 2007 for France and UK was 2.0 millions and 2.4 millions. New vehicles sales in US were more than 13,6 millions. The average car age is 8.1 and 6.7 years for France and for UK. In US, the median age for automobiles is 9.2 years. See data sources in Appendix 1. 2 2 See Caillaud (98) for France See www.statistics.gov.uk/articles/nojournal/CPISQR.pdf for UK. See Reinsdorf & Triplett (2008) and also Pashigan(2001) who provides critical elements on the US CPI for used cars. 2

See Otha etGrilitch (1976) for additional details the Hedonic methodology in the automotive area and also Fixler et al(1999). See Prado (2009) for an application on the European used car market.

[START_REF] Sophronis | Gains from trade in used goods: Evidence from automobiles[END_REF] It is identi…ed every time there is an "and/or" in the table.

[START_REF] Ronald | Durability and monopoly[END_REF] They con…rm the conclusion of Goldberg and Verboven (1998) that prices follow exchange rates closely.

[START_REF]Policy Overview and Recent History[END_REF] France: New registrations and used car registrations since January 1987. UK: New registrations since January 1987/ Used car registrations since January 2001. US: New sales since January 1987/ Used car sales since January 1997.2 7 Although there is no European study that would corroborate these results, we also assume a limited impact regarding the

[START_REF] Caillaud | Pour comprendre l indice des Prix[END_REF] The econometrical analysis is inspired by Chazi (2007) and[START_REF] François | On the In ‡uence of Oil Prices on Economic Activity and Other Macroeconomic and Financial Variables[END_REF].

[START_REF] Abdelaziz | Is Default Risk Related to In ‡ation?[END_REF] See cointegration test details in Appendix 9. The construction of an Error Correction Model (ECM) including the US volumes series did not provide a good adjustment. As a result, the model did not constitute a useful tool to forecast the volumes and we did not keep it in the study. Moreover, the US market only has two identi…ed Di¤erentiated Stationnnarity (DS) time series. As a consequence, there is no possibility of a cointegration test and an ECM for France and the UK.3

We can't believe, as well, that it would be due to a decreasing quality of information available for buyers.[START_REF] Abdelaziz | Is Default Risk Related to In ‡ation?[END_REF]

Details are given in Appendix

The econometrics tools are applied on the seasonally adjusted growth rates and stationnary time series.

[START_REF] Dennis | The Use of Hedonic Regressions to Handle Quality Change:The Experience in the[END_REF] See HP …lter cycle and trend graphs in Appendix 7.3 9 The sensitivity of the trend to short-term ‡uctuations is adjusted through a multiplier . From an Empirical perspective the suggested is equal to 14,400 for monthly data. See[START_REF] Hodrick | Postwar U.S. Business Cycles: An Empirical Investigation[END_REF].

0 The complete results are reported in Appendix 8. 4 1 = 0:34 4 2 = 0:42

[START_REF] Abdelaziz | Is Default Risk Related to In ‡ation?[END_REF] At the same time, new car prices with a lag of 3 to 12 and 36 months are counter-cyclical to used car prices.4 4 Previous months of used CPI variables have a high statistical signi…cativity according to the student test.

[START_REF] Ronald | Durability and monopoly[END_REF] Results are synthesized in Appendix 9, Tables 7, 8, and 9.

[START_REF]Policy Overview and Recent History[END_REF] A special thanks to Tom Webb (Www.manheimconsulting.com/) for his support on US data.

(1994), we measure the degree of co-movement of the series' cyclical components through the correlation coe¢ cient . If the correlation between the cyclical components of two series is positive, null or negative the series cycles are identi…ed as procyclical, acyclical, or countercyclical. If 0:1 j j < 0:23 or 0:23 j j < 1:0 the cycles are classi…ed as weakly correlated or strongly correlated. We also calculate (j) with j 2 f 3; 6; 9; 12; 24; 36g in order to identify lagged correlations. We report the strong correlations 40 The …lter, applied to the French car prices series, allows the assumption of a Feed e¤ ect: there is a 36 month pro-cyclical movement of new prices with used prices 41 . The new prices of the past 36 months impact the second-hand prices of today. Furthermore, the …lter indicates a critical correlation between new cars and used cars registrations 42 : the cycles of new and second-hand transactions increase and decrease All these mechanisms might be altered by rigidity on the new car prices and constraints on the used car transaction volumes. However, we can't validate any of them: The main reasons are the stable prices and volumes in France, as well as the decrease of used car prices in UK and US.

Table 7: General Results on Advanced Mechanisms.

Scitovsky Theory

Links are too weak in the French and the UK markets to allow the possibility of a situation similar to the one described by Scitovsky article. In contrast, most of the statistical analyses identi…ed multiple and signi…cant relations between new and used cars in the US market and therefore, are in line with the assumption of a Scitovsky mechanism.

Table 8: General Results on Scitovsky Theory.

Mechanisms Results and Comments New market feeds used market

The trend analysis illustrates a feed e¤ect on a volume perspective in all markets. For the US market, new and used car sales time series are cointegrated. Additionally, the Hodrick-Prescott …lter suggests that used car prices of today are related to new car prices of yesterday.

Reallocation

Correlation calculations suggest an instantaneous Reallocation e¤ect, between the new and the used market, on volumes in France and on prices in the US Arbitration Correlation calculations suggest an instantaneous Arbitration e¤ect, between the new and the used market, on prices in France and on volumes in the US.

Renewals

The Hodrick-Prescott …lter did not allow a clear identi…cation of a renewal e¤ect in any of the three countries, neither in the new or the used market. It is may be due the limited sample (ten years) used in the study. Price e¤ect / Volume effect They are no signi…cant results for France and the UK. Regarding the US market, we noticed that in line with Scitovsky theory, prices impact volumes in both directions. Income e¤ect 1 / Income e¤ect 2

Although our results suggest some income e¤ects, it needs to be con…rmed through a proper analysis of the relations between disposables incomes and car market volatility.