The Environmental Effect of Green Taxation: the Case of the French Bonus/Malus

The Environmental Effect of Green Taxation: the Case of the French Bonus/Malus Xavier Boutin Xavier D Haultfoeuille Pauline Givord Preliminary, do not quote Usual disclaimers apply Abstract Green taxation of the purchase of new cars was established in France in late 2007. Between December 2007 and December 2009, the less polluting cars benefited from a price reduction of up to 1,000 euros, while the most polluting were subject to a taxation of 2,600 euros. This reform was largely unexpected and has no precedent in terms either of scope or magnitude in France. We first take advantage of this natural experiment and the exhaustive dataset of monthly car registrations to estimate a demand model for new vehicles. We then estimate, using data on car owners behavior, the impact of the reform on carbon dioxide emissions. We show that if the magnitude of the shift towards the classes benefiting from bonuses is very important, the short term ecological impact is far smaller. This can be explained by threshold effects and the fact that some individuals postpone their car replacement because of the reform. JEL : C25, L53, Q53. Keywords : environmental taxation, automobiles, carbon dioxide emissions, policy evaluation. We are grateful to Philippe Février and Stéphane Gauthier for their comments, and thank Julien Mollet and Marina Robin for providing us with the data. European Commission, Directorate General for Competition, Chief Economist Team and CREST- INSEE INSEE-CREST. E-mail address: xavier.dhaultfoeuille at insee.fr. INSEE-CREST. E-mail address: pauline.givord at insee.fr. 1

1 Introduction Public awareness on environmental issues have raised in the past decade and global warming is now a growing concern for rich and emerging nations. Policy initiatives are thus launched in many countries to reduce the human contribution to the emissions of global warming gas and, mainly, Carbon Dioxide (CO 2 ). As motor vehicles are responsible for a large part of the emissions of carbon dioxide (for a complete survey on the harmful effects of automobiles on environment, see, e.g., Parry et al., 2007), cutting automobile emissions is a necessary condition to control global warming. In this context, the French government introduced in late 2007 a tax scheme applying on new cars sales, the bonus/malus (bonus/penalty) scheme. This scheme gives financial reward (bonus) for purchasers of environmentally friendly new cars and a financial penalty (malus) for those buying cars emitting high levels of CO 2. The main objective of this law was to modify the consumers preferences in favor of greener cars. 1 This seems to have been achieved in a short period of time, as the share of smaller cars has doubled in few months. The impact of the system has actually exceeded the government expectations: calibrated to have a neutral influence on state resources, the system turned out to cost more than 200 millions euros in 2008. Such an economic cost calls for a precise evaluation of the environmental benefits of this policy. If public intervention is fully justified by the negative externalities of the vehicle use, one could indeed wonder whether this kind of policy is relevant. Generally speaking, the first best optimum can be recovered by implementing pigovian taxes only, i.e. indirect taxes on the polluting products. If the tax level is correctly set, individual choices remain optimal. For example, the fuel consumption could be reduced by a pigovian tax on the fuel, as the French TIPP (Taxe Intérieure sur les Produits Pétroliers) or the American taxes on Gasoline and Diesel for Transportation. In this framework, the use of the pigovian tax makes a policy such as the bonus/malus system irrelevant. To implement pigovian taxes, the regulator must however know the marginal costs of producers or preferences of consumers. In the example of fuel consumption, the state should observe the marginal utility to fuel of each consumer. This assumption is of course unrealistic and, in general, the state has to provide a taxation scheme which makes the consumers reveal their own marginal utility. Because of these asymmetries of information, the first-best optimum cannot be achieved in general, and it makes then sense to tax products which are complementary to the polluting 1 A similar scheme has been implemented in Belgium. Note that this scheme differs from the scrapping programs introduced in almost all developed countries as an economic stimulus during the global recession that began in 2008, with also the aim of removing high emissions vehicles from the road. See, e.g., the US Car Allowance Rebate System ( cash for clunkers ) implemented in July 2009. 2

one. 2 In order to reduce carbon dioxide, mainly due to fuel consumption, the promotion of more fuel efficient cars with a policy like the bonus/malus system may thus be useful. Three points should be emphasized however. First, the enhancement of fuel efficiency induced by the policy could be partially offset by a rebound effect (or take-back effect). This effect corresponds to the increase in total traveling due to the fact that, by the reform, the new vehicles bought have lower cost per kilometer. positive environmental effect of the tax. 3 This may reduce the Second, even if the policy lowers the average emissions of new vehicles, it may not be so on the whole stock of cars, at least in the short run. For example, people who prefer low MPG cars may postpone their purchase (or buy a second-hand car instead of a new one) because of the penalties on these cars. As new vehicles are less polluting than the older ones, this implies that some people may use more polluting cars because of the bonus/malus. 4 Third, if the total sales of new vehicles increase, then more emissions are generated by the manufacturing of new cars, and also possibly by the scrapping of older ones. In this paper, we estimate the short-run impact of the reform on CO 2 emissions using the exhaustive monthly dataset of car registration in France. 5 This dataset provides detailed information on both new vehicles and cars owners. We first take advantage of the natural experiment provided by the bonus/malus introduction to estimate a demand model for new vehicles. As the reform was largely unexpected three months before its introduction, firms were not able to modify immediately their supply of new vehicles in terms of fuel efficiency. The bonus/malus can then be considered as a valid instrument for price variations. We then relate choices of new vehicles with mileage, using a recent survey on car owner s behavior. These estimates allow us to compute the total CO 2 emissions under the bonus/malus scheme and without it. We show that if the magnitude of the shift towards the classes benefiting from a bonus is very important, the environmental impact is far smaller. This is mainly due to threshold effects and opportunism of buyers, who only marginally adjusted their demand in order to benefit from the bonus but did not buy much less polluting cars. 2 However if utilities only depend on the total amount of carbon dioxide emissions and satisfy a separability condition, a well-designed pigovian tax leads to a second best optimum (see Gauthier & Laroque, 2009, Remark 4), making the taxation of complementary goods useless. 3 In the short run, this effect is actually ambiguous because penalties may induce people who prefer low MPG cars to postpone their purchase, and thus use lower MPG cars with the reform than without it. The total traveling of these individuals is then lower under the bonus/malus system. 4 On the other hand, the policy is likely to have higher positive effects in the long run, as greener cars spread over the whole stock of cars. 5 Note that we do not address of long-run supply changes induced by the demand. This is beyond the scope of the paper, as it would require to observe the supply several years after the reform. 3

Furthermore, buyers of the less polluting cars are also those who travel the less. As a result, taking into account mileage lowers significantly the overall impact of the reform. The rebound effect mentioned above also lowers the efficiency of the policy, but only marginally. Finally, this low impact is robust to different specifications on the price model. The paper is organized as follows. The next section presents the reform. The third part presents the methodology, while the fourth is focused on the datasets at our disposal. The firth part presents the results, and the sixth concludes. 2 The bonus/malus system In December 2007, the French government introduces a new tax scheme on cars sales, the bonus/malus (bonus-penalty). This initiative rewards buyers of environmentally friendly cars and penalizes those who buy high pollution vehicles. More precisely, the purchasers of new cars emitting less than 130g of CO 2 per kilometer benefited from a direct price cut on their invoice. The amount of the bonus varied, depending on the class of the vehicle (see Table 1) with a maximum of 1,000 euros in practice. 6 Conversely, purchasers of cars emitting more than 160g of CO 2 per kilometer had to pay a tax of up to 2600 euros. The system was neutral for cars emitting between 130 and 160 g per kilometer. In practice, the bonus applied for new cars ordered on or after 5 December 2007, and the penalty applied for vehicles first registered in France on or after 1 January 2008. Note that at the same moment, the government introduced a scrapping subsidy of 300 euros for more than 15 year-old cars, provided that the new vehicle bought emitted less than 160g of CO 2. 7 It is worth emphasizing that the bonus/malus policy was largely unexpected three months before. It resulted indeed from a national environmental round table organized in Autumn 2007 by the newly elected president. The aim of this round table was to define the key points of government policy on ecological and sustainable development issues for the coming five years. 8 This process led to a number of policy projects, including the bonus/malus system, which were presented on 25 October 2007. This green taxation for the purchase of new cars by private owners has no precedent 6 These classes of vehicles based on average CO 2 emission were defined in 2006, following the introduction of a special tax on company cars. 7 This scrapping subsidy was extended to 1,000 euros and to cars between 10 an 14 years in 2009, in order to dampen the economic consequences of the 2009 crisis on car industry. 8 This round table was called Grenelle de l environnement" as an evocation of the Accord de Grenelle" concluded in May 68, see http://www.legrenelle-environnement.fr/spip.php?rubrique112. 4

Table 1: Amount of the bonus/malus as a function of CO 2 emissions Class CO 2 Emissions Average Price Market shares Bonus (g/km) (2007) (2007) A- 60 5000 Nd Nd A+ 100 1000 12,500 0.0% B 101-120 700 15,500 18.4% C- 121-130 200 19,000 10.2% C+ 131-140 0 19,000 18.8% D 141-160 0 23,000 26.6% E- 161-165 -200 23,500 3.2% E+ 166-200 -750 29,000 15.9% F 201-250 -1600 40,000 5.0% G >250-2600 60,500 1.9% in France, at least in magnitude and scope. Some measures intended to increase the population s awareness of the environmental costs of motor vehicles use were introduced in 2006. The most noticeable of them was a reform of company cars taxation. However, it mainly replaced a system based on fiscal power of cars, which was already unfavorable to the most polluting cars. For private users, the measures focused only on very specific and marginal segments of the market, by providing income tax reduction to the purchasers of hybrid vehicles for instance, or were larger in scope but marginal in magnitude, by imposing slightly the most polluting vehicles (around 100 euros for cars costing on average 35 000 euros). In contrast, the bonus/malus introduced at the end of 2007 applied to all cars, and the bonus could represent up to 8.8% of the list price of the corresponding cars, while the penalty could be as large as 14.1% of this price. The objective of the bonus/malus system was twofold. First, it intended to shift consumers demand towards greener cars. Secondly, it aims at encouraging manufacturers to develop greener vehicles. To better achieve this second purpose, it was mentioned from the beginning of the reform that the thresholds of eligibility for the bonus and imposition of the penalty were to be lowered, at a pace allowing manufacturers to adapt their production (5g of CO 2 /km every two years). As a result, the thresholds were decreased in January 2010. Less expectedly, the amount of the bonuses were also moved at the same date (from 1,000, 700 and 200 euros to 700, 500 and 100 euros, respectively), in order to make the bonus/malus system cost-neutral. Indeed, and although the initial values of the bonuses and penalties were already decided according to this criterion, the system turned out to cost around 285 million euros to the state in 2008 because of its overwhelming success in 5

favor of green cars. 3 Methodology 3.1 Delineation of the parameter of interest The aim of the paper is to measure the impact of the bonus/malus system on CO 2 emissions. As previously mentioned, we consider the short-run effects of the measure. This restriction allows us to greatly simplify the analysis. Indeed, and as shown below, it is likely that in such a short period, manufacturers were not able to modify the CO 2 emissions of their models. Besides, the policy effects on second-hand cars are probably negligible at this time. We come back to the issue of long-term effects in Subsection 5.3. CO 2 emissions depend both on the emissions per kilometer of cars which are chosen by the consumers, and on the mileage of the car. Let Y AB {0,..., J} denote the (new) car chosen by the consumer between March and May 2008 in the presence of the bonus system and Y SB his hypothetical choice in the absence of the policy. 9 If a consumer does not buy a new car during this period, we let Y AB = 0 (or Y SB = 0). This outside option represents either the non-replacement of an old car by a new one (or its replacement by a second-hand car), or the use of an alternative mean of transportation. T j,ab (resp. T j,sb ) is defined as vehicle j s average CO 2 emissions per kilometer for a use corresponding to 50 % of high road and 50% of urban area, in the presence (resp. absence) of the bonus system. N AB (resp. N SB ) is the corresponding mileage (in kilometers). The emissions of an individual in the presence of the system, CO 2,AB, are defined by: CO 2,AB = T YAB,ABN AB = j 1{Y AB = j}t j,ab N AB. CO 2,SB is defined similarly as the emissions of an individual in the absence of the system. We focus here on the effects of the system on the total emissions of CO 2, defined by = ne(co 2,SB CO 2,AB ), where n is the number of potential buyers. depends on the counterfactual variables Y SB, T j,sb and N SB. It is also related to the mileage of cars bought in 2008 N AB and 9 We exclude January and February from the analysis become of post-anticipation effects on the most polluting cars (see Section 4 for more details on this issue). 6

the average emissions corresponding to the outside option T 0,AB, which are not observed in the cars registration dataset. Thus, several assumptions are needed to identify. To recover parameters related to Y SB, we develop in the next subsection a demand model of new vehicles. We relate below the counterfactual variables T j,sb and N SB with T j,ab and N AB. Finally, we use a transportation survey conducted in 2007 by the INSEE to compute parameters depending on N AB and T 0,AB. Our first assumptions focus on the counterfactual variables T j,sb and N SB. A1. N AB = N SB. A2. For all j {0,..., J}, T j,sb = T j,ab. Assumption A1 supposes that the bonus/malus system has no consequence on mileage. This may not be the case since the reform lowers the average cost per kilometer. We come back to this assumption below. Two points are implicit in Assumption A2. First, manufacturers are supposed not to have modified the average emissions of their vehicles after the reform. As discussed above, this assumption, which is plausible in the short-run, is likely to fail in the long-run, as the modification of demand due to the reform provides the manufacturers with more incentives to improve the fuel efficiency of their models. Second, we suppose that the average emissions for people choosing the outside option is not affected by the policy in the short run, i.e. T 0,SB = T 0,AB (3.1) This requires that the relative share of other means of transportation is not modified by the reform, e.g. that people without a personal vehicle would buy (or conversely renounce to buy) a second-hand car because of the reform. Condition (3.1) also requires that the reform does not affect the average emissions of the whole stock of cars, apart from the new vehicles. Note that in the long-run, greener vehicles are sold in the second-hand market. Moreover, the composition of scrapped cars may be modified because of the reform. Indeed, the prices of high MPG cars is likely to decrease in the second-hand market because of the bonuses, making their scrapping more attractive. 10 However, these two effects are likely to be negligible in the short run. Less than one-year old resold automobiles represent less than 1% of the whole stock of cars. Similarly, because scrapped cars do not represent more than 5% of the whole stock of cars, and since prices on the second market are likely to 10 On the other hand, the scrapping of low MPG cars is less attractive because their price rises in the second-hand market, and the potential scrapping subsidies are independent of the CO 2 emissions of the scrapped cars. 7

adjust slowly, the effect of a change in the composition of scrapped cars is probably very small in the short run. Contrary to the average emissions of new cars T j,ab (j {1,..., J}), the average emissions of the outside option and the mileage are not observed in the cars registration dataset. Besides, they are probably dependent, and also related to the characteristics of the purchaser. People who travel much are more likely to be richer (see Table 5 in Section 4), and also to have chosen (or choose if they buy a second-hand car at the time we consider) a diesel car, for instance. Thus, imputing a constant value for T 0,AB and N AB would probably bias the estimate of. To tackle this issue, we use the INSEE 2007 transportation survey which provides information on cars owners as well as on the car itself, and we rely on Assumptions A3 and A4 below. In the following, D denotes individual characteristics, while Y 2007, N 2007 and T 0,2007 are defined as previously but applies to the period between March and May 2007. Finally, we let X 2007 denote characteristics of the vehicle bought in 2007 (or already owned if Y 2007 = 0). A3. (T 0,SB, N SB ) Y AB Y SB, D. A3. (T 0,2007, N 2007 ) Y 2007 X 2007, D. A4. For all j, the distribution of (T 0,SB, N SB ) conditional on (Y SB = j, D = d) is equal to the distribution of (T 0,2007, N 2007 ) conditional on (Y 2007 = j, D = d). Assumption A3 states that conditional on the vehicle choice without bonus/malus, the choice with the bonus/malus does not provide any information on the mileage and the average emissions corresponding to the outside option. The second condition is similar but somewhat stronger, since we assume independence between the choice of car and (T 0,2007, N 2007 ) conditional on some characteristics of the car. Such a condition is required here because we do not observe in the transportation survey the choice made by individuals Y 2007, but only the fact that the vehicle is new or not (1{Y 2007 = 0}) and some of its characteristics (X 2007 ). Assumption A4 is a stationarity condition on the period 2007-2008, as it states that the conditional distributions of fuel efficiency and mileage would have been identical in 2007 and 2008, absent the reform. Together with Assumption A3, this condition allows us to recover, using the transportation survey, the conditional distribution of (T 0,SB, N SB ). 11 11 Note that N 2007 is not directly observed in the Transportation Survey because it corresponds to the mileage in a mixed use (50% high road - 50% urban area) which leads to the same emissions as the true mileage done during this period. Details on the computation of N 2007 are given in appendix C. 8

Now, under Assumptions A1 to A4, we get (see Appendix C for a proof): E[CO 2,SB D = d] = s d0,sb E (T 0,2007 N 2007 Y 2007 = 0, D = d) J + s dj,sb T j,ab E (N 2007 X 2007 = x j, D = d), (3.2) j=1 E[CO 2,AB D = d] = s d00 E [T 0,2007 N 0,2007 Y 2007 = 0, D = d] J + s d0k E [T 0,2007 N 2007 Y 2007 = 0, X 2007 = x k, D = d] + + k=1 J s dj0 T j,ab E [N 2007 Y 2007 = 0, D = d] j=1 J j=1 k=0 J s djk T j,ab E (N 2007 X 2007 = x k, D = d), (3.3) where x k are the characteristics of vehicle k, s dj,sb = P (Y SB = j D = d) and s djk = P (Y AB = j, Y SB = k D = d). The transportation survey allows us to identify all terms above, except the counterfactual shares s dj,sb and the joint probabilities s djk. These two term are related to the choice Y SB consumers would have made absent the system. To identify them, we develop in the next subsection a demand model of new vehicles. Note that we should also take into account the fact that the offer of new vehicles might differ in the absence of the bonus/malus. However, and as already mentioned, we suppose that in the short-run, manufacturers were not able to modify the characteristics of their vehicles. As a result, only prices are supposed to be affected by the measure. The price model is developed in Subsection 3.3. Equations (3.2) and (3.3) are based on Assumption A1, which supposes that consumers do not modify their travels because of the bonus/malus. Yet, the cost per kilometer decreases for individuals who shift to less polluting cars, and thus their car s annual mileage should increase (for empirical evidence of this take-back effect, see,e.g., Small & Van Dender, 2007 or Brons et al., 2006). Theoretically, if the fuel price elasticities of the mileage ε N and of the average emissions ε T are constant, and under an additive separability of the agents utility, we have (see Appendix A for a proof) [ ] εn ln N AB ln N SB = (ln T YAB,AB ln T YSB,AB). (3.4) 1 + ε T The CO 2 emissions under a rebound effect of that kind are detailed in Appendix C. Note that this rebound effect could be partially offset by the fact that consumers do not choose the same (more fuel-efficiency) model, but a probably smaller vehicles and thus less suited to long distance drive. This comfort effect could at least partially offset the rebound effect. We thus consider below two somewhat extreme scenarios. 9 In the first, the two effects

exactly compensate, so that Assumption A1 holds. effect, and (N AB, N SB ) are related through (3.4). In the second, there is no comfort 3.2 The demand model We now turn to the demand model of new automobiles. The most popular way to model differentiated markets is to rely on the random coefficient utility model developed by Berry et al. (1995). A first advantage of these models is that they take into account observed and unobserved heterogeneity of both products and consumers, while remaining relatively parsimonious. Another advantage is that they only require market shares and aggregate data on demand (i.e., income distribution) for each market, but not characteristics of the purchasers. On the other hand, they require to define separated markets on which characteristics of the products vary. Such a delineation may be difficult to find. Moreover, difficulties with their numerical implementation have been raised recently. 12 We choose here to rely on another popular model, namely the nested logit model. Compared with the random coefficient one, this model has the advantage of requiring no different markets on which characteristics of the products should differ, and being straightforward to estimate. Moreover, less instruments are required to identify the model. In particular, we do not need here to rely on the usual assumption that the characteristics of the automobiles, apart from their price, are exogenous. On the other hand, the nested logit suffers from a limited ability to incorporate consumers heterogeneity on their valuation of products characteristics. Indeed, individuals may only differ according to variables observed on the purchasers. We believe however that this disadvantage is mitigated here by the fact that, contrary to usually, we do observe important determinants of new cars purchasers here (see Section 4 below). We thus consider groups of individuals, based on the variables we observe on the purchasers (see Section 5 for more details on the definition of these groups). The utility of consumer i belonging to group d for purchasing the car j is supposed to satisfy U ij = ln(p j )β d + X j γ d + ξ dj + ε ij = δ dj + ε ij, where p j is the price of car, X j its other observed characteristics (including the constant) and ξ dj its unobserved characteristics. The dependence in d of (β d, γ d, ξ dj ) accounts for 12 In particular, there is evidence that different choices on the tolerance criterion for the inner loop (see Dubé et al., 2008), or on the optimization algorithm (see Knittel & Metaxoglu, 2008), may lead to very different results. 10

the individual heterogeneity in preferences. Classically, we assume that the utility of the outside good is such that U i0 = ε i0 given that it is not possible to identify the average utility of the outside option and the parameter of γ d corresponding to the constant. The nested logit accounts for the fact that cars are generally classified in different segments, corresponding to very different use and sets of characteristics. 13 In other words, a customer whose preferred option is a compact car is more likely to switch to another compact car than to a large SUV for instance, in case of an increase in price of its preferred option. This substitution pattern is introduced by allowing for correlation between the idiosyncratic shocks (ε ij ) j {1,...,J} of cars belonging to the same segment g: ε ij = σ d ζ ig) + (1 σ d )η ij where the (η ij ) j {1,...,J} are independently distributed according to a Gompertz distribution and the (ζ ig ) g {1,...,G} are also independent, their distribution being implicitly defined by the fact that each (ε ij ) j {1,...,J} also follows a Gompertz distribution (even though they are not independent). 14 σ d [0, 1] models the proximity of individual unobserved preferences for cars of the same segment. If σ d = 0, then, preferences for each cars of a segment are independent and the demand corresponds to the simple logit model. Conversely, if σ d = 1, there is no difference in unobserved preferences between cars of a given segment. The previous assumptions lead to the following equation on the market shares of product j belonging to segment g, within the group of consumers d: ln(s dj ) ln(s d0 ) = ln(p j )β d + X j γ d + σ d ln(s dj/g ) + ξ dj, (3.5) where s dj/g = P (Y i = j Y i g) denotes the intra-segment share of product j among group d. Rather than estimating directly Equation (3.5), we can take advantage of the rich dataset at our disposal and of the nature of the bonus/malus system. First, because we observe the precise dates of all sales (or, rather, registrations), we are able to focus on a very short period around the policy change. We consider the period between September 2007 and May 2008, excluding the month of December 2007 and January and February 2008 due to anticipation phenomena just after the announcement of the system (see Section 4 below). During this very short period, it is reasonable to suppose that the observable 13 We choose to classify automobiles according to their main use. Details on the segmentation are provided in Appendix B. 14 Cardell (1997, theorem 2.1) showed that there exists indeed a unique distribution satisfying these assumptions for each value of σ d [0, 1]. 11

characteristics of the vehicles, apart from their price, remain stable. 15 We then have, with similar notations as previously, ln(s dj,ab /s d0,ab ) ln(s dj,2007 /s d0,2007 ) = α d + (ln p j,2007 ln p j,ab ) β d +σ d ln(s dj/g,ab /s dj/g,2007 ) + ε dj. (3.6) where ξ dj,ab ξ dj,2007 = α d + ε dj and E(ε dj ) = 0. α d captures potential modifications of demand irrespective of the bonus. It can for instance be linked to short term economic variations, which may affect the demand for new vehicles. Besides, the prices on the second-hand market could be affected by the bonus/malus system, changing the average value of the outside option. ε dj represents the evolution of the unobserved characteristics of the vehicle, such as a new design, engine, etc. The main advantage of the model in differences is that it only requires estimating (α d, β d ). The potential endogeneity of the other characteristics X j is not an issue anymore. However, the evolution of prices is still endogenous since car manufacturers are likely to adjust their prices to unobserved changes. The evolution of the share of model in its segment is also endogenous by construction. Both thus need to be instrumented. Our instrument of log prices is the value of the bonus/malus. In other terms, we suppose it to be correlated with variations in the log prices of cars, but uncorrelated with the residuals ε dj. The first condition is very weak because it is much unlikely that manufacturers perfectly offset price variations due to the policy, and is actually shown to hold in Section 5 below. The second condition holds if the evolution of unobserved characteristics is not correlated with the class of emissions, and if the classes of energy are not affected by changes in unobserved characteristics ε dj. If, of course, this assumption cannot be tested directly, we provide evidence below that in the short run, car manufacturers had no time to adjust observable characteristics to offset, for instance, a penalty. The instrument for intrasegment shares we choose is the difference between the bonus/malus of the vehicle and the average bonus/malus of other cars belonging to the same segment. Its exogeneity is based on the same argument as above, while the rank condition holds as soon as individuals have a nonzero price elasticity. In this case indeed, a given car is disadvantaged if the instrument is negative, since on average, other cars in the same segment will benefit from larger price reductions. 15 Fuel prices exhibit a dramatic increase during this period. This may have shifter consumers demand towards high MPG vehicles. We also estimate a model with difference in prices per kilometer. These parameters are never significant for all groups d. To remain parsimonious, we thus choose not to include them later on. 12

3.3 The price model If it is costly and time consuming for a firm to modify the technical characteristics of their models, prices can be adjusted more quickly and more easily. Car manufacturers could have modified their prices because of the reform. Even though the descriptive statistics show that this adaptation is likely to have been minor, this phenomenon cannot still totally be ignored. We consider two ways of estimating the counterfactual prices here. The first is to suppose that prices set by the manufacturers correspond to the Nash equilibrium of a Bertrand competition, following Berry et al. (1995). Let S f denote the set of products owned by firm f, Z j be the penalty of car j (which is negative if the car benefits from a bonus) and c j be the marginal cost of producing j. Let also and p j denote the prices set by the firm in 2008 before applying the bonus/malus, so that observed prices satisfy p j,ab = p j + Z j. Let p = (p 1,..., p J ) and Z = (Z 1,..., Z J ). The program of firm f in the presence of the bonus/malus system satisfies: max (p j c j )s j (p + Z) s.t. p k = p k, k S f, (p j ) j Sf j S f where s j (p+z) is the market share of j corresponding to (final) prices p+z. The first-order condition of the Nash equilibrium for product j owned by firm f is then s j (p AB ) + k S f (p k c k ) s k p j (p AB ) = 0, where p AB = (p 1,AB,..., p J,AB ). Let c = (c 1,..., c J ), S(p) = (s 1 (p),..., s J (p)) and (p) be the matrix whose (j, k) element is equal to zero when j and k are not produced by the same firm, s k / p j (p) otherwise. Then: c = (p AB ) 1 S(p AB ) + p AB Z. Once the demand model has been estimated, we can thus recover the marginal cost vector c. Then the price vector without the bonus/malus system p SB can be computed as the solution of (p SB )(p SB c) + S(p SB ) = 0. (3.7) A drawback of this approach is that it relies on strong assumptions on firm behaviors. There may be collusion between some manufacturers, for instance. Besides, the counterfactual prices depend on the choice of the demand model used in the estimation. If one does not rely on the true model, or if the structural parameters are not consistently estimated because instruments are invalid for instance, then the estimated counterfactual prices are 13

also inconsistent. We thus consider another more reduced form approach, based on the specificity of the bonus/malus. Generally speaking, car j price will depend on its own bonus/malus and also on the bonus/malus of the other cars. We also expect the dependence to be stronger on bonuses or penalties of the cars that are the most substitutable, that is to say those of its segment. Letting p j,z be the price of j in 2008 when the vector of penalties for all cars is z = (z 1,..., z J ), we then suppose: p j,z = p j,2007 + ζ + z j ξ 1 + 1 J g(j) 1 k g(j) k j z k ξ 2 + ν j, E(ν j ) = 0, cov(z, ν) = 0, (3.8) where J g is the number of cars in the segment g. In other terms, we assume that the change in prices between 2007 and 2008 is a linear function of the bonus/malus of the car and of the average bonus/malus of the cars of the same segment, and neglect any strategic interaction with cars belonging to other segments. Under these assumptions, parameters (ζ, ξ 1, ξ 2 ) as well as ν j are identified by the regression of p j,ab p j,2007 on Z j and ( k g(j) Z k)/(j g(j) 1). We then deduce the prices in the absence of the system, p j,sb, by p j,sb = p j,0 = p j,2007 + ζ + ν j. (3.9) Finally, once having estimated the demand for cars and prices without the bonus/malus, it is possible to come back to the quantities of interest s dj,sb and P (Y AB = j, Y SB = k D = d), which are necessary to the identification of. We have: s dj,sb = exp(δ dj,sb /(1 σ d )) [ ] [ k g exp(δ σd G [ ] dk,sb/(1 σ d )) g=1 k/g(k)=g exp(δ 1 σd ], dk,sb/(1 σ d )) with δ dj,sb = ln(p j,sb )β d + X j γ d + ξ dj,ab = (ln(p j,ab ) ln(p j,sb ))β d + δ dj,ab (3.10) = (ln(p j,ab ) ln(p j,sb ))β d + ln(s dj,ab ) ln(s d0,ab ) σ d ln(s dj/g,ab ). Equation (3.10) stems from our assumption that, apart from the price, neither the observed nor the unobserved characteristics are affected by the reform. Now, as for the joint probability s djk, no close form is available, and we estimate it by simulations. More precisely, we simulate within each group d a random set of N s individuals and, for each of them, the residuals (ε ij ) j {0,...,J} (see Appendix C for the simulation of the residuals). Using 14

(δ dj,sb, δ dj,ab ), we then compute their utilities and ultimately their choices (Y i,ab, Y i,sb ). We thus get an estimate of P (Y AB = j, Y SB = k D = d) by P s (Y AB = j, Y SB = k D = d) = 1 N s N s i=1 1{Y i,ab = j, Y i,ab = k}. 4 Data 4.1 Datasets The Association of French Automobile Manufacturers (CCFA, Comité des Constructeurs Français d Automobiles) has provided us with the exhaustive dataset on registration of new cars from January 2003 to January 2009. It includes all the information that is necessary for the registration of a new car, i.e. some characteristics of the car (brand, model, CO 2 emissions, etc) as well as a few information on the owner (professional activity, age and the city he lives in). The list price of the car is also included. As detailed above, we model the automobile market as a market of differentiated products. We define, as usually, a product by a set of characteristics. An important issue is then to choose which characteristics one should keep in this definition. On the one hand, if products are defined with few characteristics, very different items are mixed together, possibly leading to strong aggregation biases if the underlying model of demand is not linear, which is the case here. On the other hand, keeping many characteristics leads to smaller market shares for each product. Moreover, the observed market shares of these products in a given period are noisier measures of the probabilities of choice. Apart from the accuracy loss this entails, this may produce an important selection bias when the observed market shares of many products are null. Indeed, in most demand models on differentiated markets such as the nested logit or the random coefficient model considered by Berry et al. (1995), products with zero market shares cannot be taken into account in the estimation. 16 As a compromise, we select the brand, the model, the type of fuel, the type of car-body (urban, station wagon, convertible, etc), the number of doors and its class of CO 2 emissions. This selection leads to define 1027 different products (see Table 2) for the period between September and November 2007. Thus, we adopt a slightly more restrictive definition of a product than Berry et al. (1995). Even so, the dispersion of the 16 In the nested logit for instance, estimation consists of an instrumental regression of the logarithm of observed market shares, and thus one cannot include products with zero market shares. 15

remaining characteristics (such as price) within each product is not that small compared to the overall dispersion (see Table 3). A more restrictive definition of products (by including, e.g., horsepower) would reduce this dispersion but at the cost of increasing the proportion of null sales. Our definition allows us to keep this proportion of null sales is also relatively small on the whole population of buyers (15% of the models with positive sales between September and November 2007 have not been sold between March and May 2008). Table 2: Number of products and number of sales between September and November 2007 Models Number of sales Overall 1027 234173 By number of doors 3 204 47 178 5 530 165 030 Others 293 21 965 By type of car-body Station wagon 256 31 433 Convertible 85 4 303 Urban 680 198 420 Disabled 6 17 By type of fuel Gasoline 471 76 642 Diesel 556 157 531 Table 3: Dispersion of prices, CO 2 emissions and fiscal power of new cars registered between September and November 2007 Overall Within products Price (euros) 8,854.4 1,075.3 CO 2 (g/km) 27.4 2.6 Fiscal power 2.3 0.4 16

Table 4: Comparative statistics between characteristics of the buyer of new cars and the overall French population Variable Buyers of new cars Overall Rate of activity 68.9% 65.1% Age (years) 50.1 39.7 Type of area Rural 27.8% 23.8% Urban 60.9% 59.7 Paris 11.3% 16.5 Median income (euros) [0,22 000] 16.5% 22.1% [22 000, 32 000] 52.7% 57.6% [32 000,+] 30.8% 20.3% As mentioned above, we observe in the registration dataset the age, activity and city of the owners. However, income, which is likely to drive an important part of the heterogeneity of preferences, is not available. In order to proxy this income, we impute to each purchaser the median income of his age class in his city, using fiscal data. 17 Using data from the French national institute of statistics (INSEE), we also included in our final dataset the urban area to which the purchaser belongs. Table 4 displays the average characteristics of new car purchasers in terms of age, income, rate of activity and type of location. Not surprisingly, these individuals are on average older, richer and work more often than the rest of the population. Finally, we use the Transportation Survey conducted by INSEE in 2007 to estimate the dependence between mileage and choice of cars. This survey provides detailed information about the travel of individuals - in particular the annual mileage of their car - and on the characteristics of their vehicles, such as their type of fuel, their fiscal power and age. Table 5 summarizes the average number of kilometers covered by car for different ranges of characteristics of owners. These results highlight the heterogeneity of behaviors regarding car usage as well as the link between the characteristics of vehicles and their average usages. 17 This information is only available for towns of at least 2,000 inhabitants. For cities of more than 50 households but less than 2,000 inhabitants, only the median income is known. In this case, or if the age of the buyer is unknown, we impute the median income of the city. Sales to individuals living in less than 500 inhabitants cities have been dropped, as the median income is missing in this case. Note that such sales only represent 5% of the data. 17

Table 5: Yearly mileage in kilometers as a function of owner s or car s characteristics. Variable Yearly mileage (kms) Age of the car Less than one year 22,728 Between 1 and 3 years 15,836 Between 3 and 5 years 13,798 Between 5 and 10 years 11,973 More than 10 years 7,978 Type of fuel Gasoline 10,501 Diesel 18,450 Household income Less than 22,000 euros 7,892 Between 22,000 and 32,000 euros 13,212 More than 32,000 euros 14,818 Type of Area Rural 15,803 Urban 14,464 Paris 13,620 4.2 Variation of sales Because the implementation of the measure was almost immediate, neither consumers nor manufacturers could anticipate the reform before November 2007. Figure 1 that anticipation was spectacular on consumer side in December 2007, especially for the most polluting cars. Not surprisingly, this large increase for the last classes was followed by an undershooting in January and, to a lesser extent, in February. Note that we do not observe any noticeable change in November even though the reform was already announced then. This is probably due to the delivery time of new cars, as well as the small shift between reception and registration of new cars. Similarly, we observe a jump in the sales of the less polluting sales in January only, even though the measure was already in force for vehicles ordered after the 5th of December. This stems from the fact that owners of cars bought in December had to register it after the 1st of January 2008 to receive the bonus. Overall, the sales stabilize after February. As we do not seek to measure anticipations or undershooting effects, we exclude December 2007 as well as January and February 2008. 18

60% december 2007 25% december 2007 50% 20% 40% 30% 20% B C- C+ and D 15% 10% E- E+ F G 10% 5% 0% 0% 01-2003 07-2003 01-2004 07-2004 01-2005 07-2005 01-2006 07-2006 01-2007 07-2007 01-2008 07-2008 01-2009 01-2003 07-2003 01-2004 07-2004 01-2005 07-2005 01-2006 07-2006 01-2007 07-2007 01-2008 07-2008 01-2009 Vehicles benefitting from the bonus Vehicles affected by the malus Figure 1: Evolution of the market shares of the different classes of CO 2. 160 155 150 145 140 135 Average CO2 of new vehicles 130 Trend before december 2007 01-2005 07-2005 01-2006 07-2006 01-2007 07-2007 01-2008 07-2008 01-2009 Figure 2: Average CO 2 emissions of new cars. 19

0,05 0,045 0,04 0,035 0,03 0,025 0,02 0,015 0,01 0,005 2008 2007 0 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 Figure 3: Distribution of CO 2 emissions of new cars sold in 2007 and 2008. Figure 2 shows that the reform has had a real impact on average emissions. Compared to the trend between January 2005 and November 2007, the average decrease between March 2008 and January 2009 is 4.7%. This is, however, much smaller than the increase of market shares of A and B classes during the same period (namely, more than 200%). This mainly results from threshold effects: many buyers only marginally modified their purchasing decisions, choosing for instance a car emitting 120 g/km instead of one emitting 121 or 122. In this example, the shift is thus between the less polluting cars of class C- to the most polluting of class B. This fact is confirmed by the density of average emissions of new cars bought just before and just after the reform (see Figure 3): the shifts have mainly been towards the most polluting models of the lower class. Note that these threshold effects already existed before the measure. This is likely due to the pre-existing system for company cars, which has been based on these classes since 2006. Car manufacturers thus already had the possibility to partially adapt their offers to this classification. 4.3 Reaction of car manufacturers An explicit goal of the reform was to stimulate the reduction of CO 2, which should not only take place through shifts in demand, but also, in a second round, trigger innovation by manufacturers to produce greener cars. Focusing on the two quarters we select, we do not observe major changes between the end of 2007 and the beginning of 2008 (see Table 6). 20

Moreover, these changes are very similar to those observed on the same previous periods. Some shifts in supply can be seen, especially for classes C and G, at the end of 2008, but focusing on a very short time span after the reform for the estimation prevents us from capturing complex effects induced by the supply adaptation to the reform (see, however, Subsection 5.3 for an attempt to take into account these supply reactions in the impact of the reform). Table 6: Evolution of average CO 2 emissions before and after the reform. Variation (in %) Class end of 2005 / end of 2006 / end of 2007 / of CO 2 early 2006 early 2007 early 2008 B 0.61-0.09-0.17 C- 0.13-0.26-0.26 C+ -0.05-0.04-0.09 D -0.50-0.28-0.28 E- 0.48 0.00-0.80 E+ 0.00-0.07-0.22 F 0.00-0.61-0.31 G -0.06-0.28-0.72 The other potential impact on supply is related to price. In theory, manufacturers should try to compensate the effects of the measure and react by increasing the price of the cars with bonuses while decreasing these of the cars affected by penalties. Table 7 presents the evolution of average prices for each class of CO 2 between the months of September to November of one year over this of March to May of the following year. There does not seem to have been systematic differences, at least in the list prices, after the implementation of the measure. 21

Table 7: Evolution of average prices before and after the reform. Variation (in %) Class end of 2005 / end of 2006 / end of 2007 / of CO 2 early 2006 early 2007 early 2008 B 1.50 1.35 0.92 C- 1.30 0.78 0.72 C+ 0.83-0.75-0.65 D 1.00 0.56 0.27 E- 2.09 1.20 0.75 E+ 0.87 0.53 0.27 F 0.65 1.07 1.28 G 0.83 0.69 0.47 Reading note: The average price of models (defined by their brand, model, type of fuel, capacity, number of doors, power and weight) sold both between September and November 2005 and between March and Mai 2006 and that were in class G in the last quarter of 2005 has increased of 0.83% between the two periods. Data for class A from 2005 to 2007 were missing. 5 Results 5.1 Mileage and outside option emissions Before estimating the demand and price models, we use the Insee transportation survey to estimate a model between mileage or total CO 2 emissions and car and owner s characteristics. Such models are needed to recover E (N 2007 X 2007 = x j, D = d) and E [T 0,2007 N 0,2007 Y 2007 = 0, D = d], which appear in (3.2) and (3.3). We consider linear models where we include the type of fuel and the weight in the car characteristics. Results are displayed Table 8. We did not include income (nor the crossed variables between income and the type of fuel in the CO 2 emissions model) since none of the corresponding dummies is significant at a 10% level. 22

Table 8: Linear models on mileage and total CO 2 emissions Variables Mileage model Total CO 2 emissions Intercept 5, 051 13.7 10 4 (577) (14.0 10 4 ) Rural area Working Diesel Diesel second quintile 1, 665 (239) 3, 717 (234) 3, 842 (329) 1, 217 (413) Diesel third quintile 524 (416) Diesel fourth quintile Diesel fifth quintile Weight 1, 100 (459) 1, 643 (525) 3.39 (0.624) 39.0 10 4 (5.96 10 4 ) 84.5 10 4 (5.88 10 4 ) 60.7 10 4 (8.13 10 4 ) Not included - - - 1.784 (151) 0.248 (0.032) Square weight 1.35 10 4 (1.35 10 4 ) R 2 0.071 0.064 5.2 Demand parameters Given our estimation strategy in first differences (see Equation (3.6)), we are mainly interested by the characteristics of customers which explain heterogeneity of price elasticity. Driven by the data at our disposal, we choose to focus on three different dimensions, each buyer being affected to a cell of this three dimensional mapping. The first dimension captures to the need customers have for cars and is purely related to the typology of the area they live in. People leaving in rural area are likely to have a higher need for private mean of transport, given the general lack of public transportation in less densely populated areas. Conversely, people living in denser locations will face a higher offer of public transport and more traffic. Based on the location code, we thus differentiate rural from urban areas. Working people also have a very different use from not working people (unemployed, retired person...). Given the classification of the profession in the registration data, it is difficult to infer a classical mapping, corresponding for instance to education or tasks. We thus simply differentiate working people from the not working, which also has the by product to limit the final number of cells. This classification as occupied stems from the profession classification in the registration data when available. When it is not, we assume that buy- 23

ers beyond the legal age of retirement in France, 65, are unoccupied, while the other ones are assumed to be occupied. Finally, based on the age and the location, we attribute to each buyer the median income of the people of the location of its class of age, stemming from the 2007 fiscal dataset (when age is missing, we attributed the average income). The median earnings are then divided into 5 classes, corresponding to the five quintiles of the distribution of median earnings. Overall, each buyer of a new car is affiliated to one of the 20 cells. For each type of households, we estimate a price coefficient β d and a trend α d which reflects, among others, the sensitivity of these households to the macroeconomic activity. On the other hand, we suppose that the intra-segment share coefficient σ is independent of the households types, as the results with unconstrained σ d were noisy given the small number of observations. As mentioned before, we instrument the vehicle s price variation by its bonus or penalty, and its intra-segment share by the average bonus or penalty of the other vehicles in the same segment. Results are displayed in Table 9. First note that the instruments are highly correlated with the price variations, leading to Fisher statistics for the first step regressions around 80. This result is not surprising, as the price variations on a short period like the one we consider are mainly due to the bonus/malus. As expected, the intra-segment share depends less on the instruments. Still, the rank condition is easily satisfied, with a Fisher statistic around 16. The estimates of the constants α d are not significant. A plausible explanation is that in a short range as the one we consider, individuals preferences remain stable. We see this as a robustness check of our estimation procedure, as it reinforces the implicit assumption that β d and σ remain also constant between the two periods. The impact of prices is always negative and highly significant, as expected. It is large for all kinds of households, the estimated coefficients belonging in general to [ 7, 5]. 24