Car usage, CO₂ emissions and fuel taxes in Europe

Marrero, Gustavo A.; Rodríguez López, Jesús; González Marrero, Rosa M. Article Car usage, CO₂ emissions and fuel taxes in Europe SERIEs - Journal of the Spanish Economic Association Provided in Cooperation with: Spanish Economic Association Suggested Citation: Marrero, Gustavo A.; Rodríguez López, Jesús; González Marrero, Rosa M. (2020) : Car usage, CO₂ emissions and fuel taxes in Europe, SERIEs - Journal of the Spanish Economic Association, ISSN 1869-4195, Springer, Heidelberg, Vol. 11, Iss. 2, pp. 203-241, https://doi.org/10.1007/s13209-019-00210-3 This Version is available at: https://hdl.handle.net/10419/286516 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Marrero1·Jesús Rodríguez-López2·Rosa Marina González3 Received: 11 May 2018 / Accepted: 23 October 2019 / Published online: 12 November 2019 © The Author(s) 2019 Abstract The number of diesel cars in Europe has grown significantly over the last three decades, a process usually known as dieselization, and they now account for nearly 40% of the cars on the road. We build on a dynamic general equilibrium model that makes a distinction between diesel motor and gasoline motor vehicles and calibrate it for main European countries. Firstly, we find that the dieselization can be explained by a change in consumer preferences paired with the productivity gains from the specialization of the European automotive industry. Secondly, the lenient tax policies in favor of diesel fuel help to explain the rebound effect in road traffic. Finally, from a normative standpoint, the model suggests that a tax discrimination based on the carbon content of each fuel (higher for diesel relative to gasoline) would actually be more effective in curbing CO2emissions rather than a tax based on fuel efficiency. Based on the existing studies, we also document that other external costs of diesel are always higher than those of gasoline, and the Pigouvian tax rates should reflect this aspect. This recommendation is radically different to the existing fuel tax design in most European countries. Keywords Cars CO2emissions ·Dieselization ·Dynamic general equilibrium · Pigouvian fuel taxes ·Europe JEL Classification E13 ·H22 ·Q43 ·Q54 ·R40 1 Introduction The composition of the passenger car fleet has been transformed in Europe over the last few decades. Diesel cars accounted for a minor part of the fleet at the beginning BJesús Rodríguez-López [email protected] 1Universidad de La Laguna and CEDESOG, San Cristóbal de La Laguna, Spain 2Universidad Pablo de Olavide, Seville, Spain 3Universidad de La Laguna, San Cristóbal de La Laguna, Spain 123 204 SERIEs (2020) 11:203–241 of the 1980s and nowadays represent more than 40% of the total EU fleet, a process referred to as dieselization. The choice between a gasoline versus a diesel car is a key factor in a consumer’s decision when purchasing a new car. Nowadays, when comparing certain important vehicle attributes, such as speed, safety, size, design or horsepower, there are hardly any substantial differences between the two types of vehicles. But in terms of fuel efficiency, diesel cars consume, on average, about 17% less fuel per kilometer than gasoline cars (Verboven 2002). An additional aspect that is likely to be behind the popularity of diesel vehicles is related to the fuel tax policy implemented by most European Governments over the last decades. As early as in 1973, the European Economic Community adopted the European Fuel Tax Directive. Most European governments have been more lenient with diesel fuel, generating an extra incentive to use diesel motor cars.1European governments have usually put forward two arguments to defend this discriminating tax policy in favor of diesel: first, the gains in energy savings; second, because diesel is more efficient, a reduction in CO2emissions was expected (Schipper et al. 2002 or Sullivan et al. 2004, among others). However, the success of dieselization as a measure to control CO2emissions has been questioned by many authors in the literature surrounding Transport Economics, such as Schipper (2011), Schipper and Fulton (2013), González and Marrero (2012) or González et al. (2019). In this paper, we explore the conditions under which the dieselization holds and its consequences on road traffic and CO2emissions. We address these issues by building a dynamic general equilibrium (DGE) model taking into account the decisions surrounding the purchase and usage of a car (Wei 2013), together with the generation of CO2emissions and its external effects on climate change (Golosov et al. 2014). More precisely, we build on a neoclassical framework with a representative household, whose utility is determined by their amount of leisure, consumption of non-durable goods and the services provided by diesel motor and gasoline motor automobiles. Both automobiles are powered with their corresponding (non-substitutable) fuels. When households make vehicle purchase decisions, the price of new vehicles reflects fuel prices and fuel taxes. The choice between a gasoline car or a diesel car is made optimally. However, once this decision is made, the type of fuel cannot be changed, while taxation can be altered by fiscal authorities. As we show, this fact produces different short-run and long-run price elasticities of fuel use. Additionally, motor vehicle users do not perceive the effect of their own choices over climate change, as competitive prices fail to inform about the external costs of using vehicles. Moreover, the effects of CO2emissions are long lasting. Notice that this sort of issues cannot be addressed using a traditional discrete choice analysis.2 We calibrate the economy of 13 EU countries and find that the model produces demand elasticities similar to those reported by empirical studies. In a model validation exercise, we conclude that the bulk of the dieselization could be associated with 1See, among others, Verboven (2002), Rietveld and Van Woudenber (2005)orZervas(2010). Alternatively, Miravete et al. (2018) find that a non-tariff barrier against foreign imports is hidden behind such tax practices. 2Additionally, most economic decisions are dynamic and entail labor productivity changes, which in turn affect firms’ decisions to hire labor and capital and affect prices in other markets. For all that, we need for a DGE model for our analysis. 123 SERIEs (2020) 11:203–241 205 consumer preferences paired with the productivity gains from the specialization of the European automotive industry. Indeed, the popularity of diesel vehicles is a peculiar feature of the European auto market (Miravete et al. 2018). On the contrary, we find that, at the very best, policy decisions affecting fuel taxes and the sale price of new vehicles (such as VAT, registration fees or replacement subsidies) could account for around 8% of the increase in diesel vehicles between 1999 and 2015 in Europe. However, given the stock of diesel and gasoline cars, we show that fuel taxation can help to explain the higher mileage of diesel vehicles, fuel consumption and CO/2 vehicle emissions in Europe. The second aspect addressed in this paper is normative and deals with the optimality of the tax policy implemented in Europe. Parry et al. (2007) identify several vehicle externalities, such as noise, congestions, accidents, local pollutionand global warming. In this paper, we only focus on CO2emissions, which can justify a different tax treatment between diesel and gasoline cars. CO2emissions of fuel combusted depend on the carbon content per liter of fuel (US Environmental Protection Agency (EPA) 2011; Santos 2017). For European countries, Santos (2017) reports carbon contents that are always greater for diesel than for gasoline fuel, by factors ranging from 5 to 29%, depending on the country.3 We obtain that the Pigouvian taxation of each type of fuel must be proportional to the amount of carbon emissions of the fuel. When we consider CO2as the only externality, we estimate the Pigouvian tax rates to be 1.83 Euro cents per liter of diesel and 1.60 cents per liter of gasoline, which is equivalent to imposing a tax of about 25 Euros per ton of carbon. In addition, Pigouvian taxation would require a 0% sale tax on new purchases of cars to internalize the external costs of CO2emissions. Both results are at odds to the policy of dieselization implemented during the last decades in most OECD countries. We also solve numerically the model under two alternative tax regimes: the Pigouvian tax regime and one consistent with the dieselization in Europe. Based on our simulations, we show that the current tax design in Europe has caused an increase in traffic density by 2.7% and in CO2emissions by 2.4% in excess of those levels obtained under the Pigouvian scenario. To our knowledge, this is the first paper addressing all these issues related to dieselization using a DGE model. Wei (2013) is probably an exception in using a similar theoretical framework, analyzing the consequences of Corporate Average Fuel Economy (CAFE) standards on gasoline consumption and miles driven in the USA. By contrast, in our paper, we take fuel efficiency as given and focus on the diesel– gasoline decision taken by a representative household. Our model is linked to a broad range of topics. Given that we deal with the external impacts on global warming, we extend some ideas from Nordhaus and Boyer (2000), Nordhaus (2008), Golosov et al. (2014) and Hassler et al. (2016) concerning the carbon cycle and adapt them to CO2emissions from passenger cars. The articles by Fullerton and West (2002) 3Santos (2017) also estimates the external cost of gasoline and diesel vehicles accrued over all types of externalities. Road congestion and accidents account for the bulk of these costs per liter of both fuels (82% for diesel and 87% for gasoline), while CO2emissions have a minor role, about 4% in both cases. For local pollution, diesel is more than twice costlier than gasoline, both in terms of kilometer driven or per liter of fuel. In relative terms, a liter of diesel is on average 21% costlier than a liter of gasoline. 123 206 SERIEs (2020) 11:203–241 and Parry and Small (2005) share with ours a common interest of optimal (gasoline) taxation. By contrast, we incorporate dynamic aspects which help understand driving and purchasing decisions, fuel consumption and total kilometers driven. The paper is structured as follows. The second section presents evidences describing the evolution of the vehicle fleet, fuel consumption and CO2emissions of cars in our set of EU 13 countries. The DGE model is established in the third section. In the fourth section, the market equilibrium and the social planner problem are solved. In the fifth section, the model is calibrated for an aggregate economy of a set of representative European countries. Using this calibration, a model validation exercise is performed and the Pigouvian taxation is quantified. Next, the model is numerically solved and CO2emissions and welfare are evaluated from moving from a steadystate equilibrium consistent with the dieselization in Europe toward the Pigouvian allocation. Conclusions are summarized and presented in the last section. 2 The dieselization process in Europe We first report evidence of the sharp increase in the share of diesel-powered vehicles in Europe. Data on fuel consumption (equivalent million tons of oil), car stock and sales of new cars (millions), kilometers driven (km-travelled/car-year), fuel efficiency (l/100 km.) and CO2emissions (Mt. CO2) come from the Odyssee-Mure database.4Data are collected and aggregated from the following 13 western EU countries (henceforth, EU13) from 1998 and 2015: Austria, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Portugal, Spain, Sweden and the UK. These economies accounted for about three quarters of European GDP in 2015. Figure 1reflects the intensive dieselization process that took place in these European countries between 1998 and 2015. The percentage of diesel cars increased from 16.5% in 1998 to 42.4% in 2015. Similar patterns are observed when looking at the ratios of new cars registrations and fuel consumption of passenger cars. Except for Greece, these ratios rose in all EU countries during this period. For example, Austria, Belgium, France, Portugal, Spain or Italy, currently holding the highest proportion of diesel cars, have shifted from ratios of between 22 and 52% in 1998 to ratios between 64 and 71% in 2015. Figure 2represents the average number of liters of fuel needed per 100 km for diesel and gasoline cars (i.e., the inverse of fuel efficiency) from 1998 to 2015. As of 2015, while a diesel motor car burned about 6.40 l of fuel per 100 km, a gasoline motor car burned 7.5 l on average, i.e., 17% more. Fuel efficiency has improved in both types of cars. Hence, there is the advantage in fuel efficiency of diesel cars over gasoline cars. On the other hand, most European Governments have implemented a tax policy favoring diesel over gasoline. Figure 3shows the evolution of the average prices of gasoline and diesel in these countries (with and without taxes) from 1998 to 2015. While the price of both fuels (net of taxes) has evolved evenly during this 4http://www.indicators.odyssee-mure.eu/online-indicators.html. 123 SERIEs (2020) 11:203–241 207 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Diesel ratio, % Diesel cars (stock) ratio Diesel cars (new registration) ratio Diesel cars (fuel consumption) ratio Fig. 1 Dieselization in main Western EU countries diesel cars (stock), new registration and fuel consumption with respect to the total 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Liters/100 km. Gasoline cars Diesel cars Fig. 2 Fuel intensity of diesel and gasoline car fleet in main Western EU countries (liters per 100 kms) period, the price of gasoline is about 20% higher on average than that of diesel for the whole period when taxes are included.5 As already discussed in Introduction, regarding the impact of dieselization on the road transport sector, Transport Economics has been far from consensus. On the one hand, some authors, such as Sullivan et al. (2004), Rietveld and Van Woudenber (2005), Zervas (2010), Zachariadis (2006) and Jeong et al. (2009), have argued that the dieselization could be used for energy saving and to curb CO2emissions. On the other hand, the suitability of dieselization for these two roles has been called into question 5This taxation practice is common among OECD countries (Knittel 2012). Two exceptions are Switzerland and the USA, where the tax rate on gasoline is lower. In Australia and the UK, both fuels are equally taxed. 123 208 SERIEs (2020) 11:203–241 0 € 20 € 40 € 60 € 80 € 100 € 120 € 140 € 160 € 180 € 1998 2000 2002 2004 2006 2008 2010 2012 2014 €Cents/Liter Diesel (with taxes) Diesel (withouth taxes) Gasoline(with taxes) Gasoline (withouth taxes) Fig. 3 Diesel and gasoline prices in main Western EU countries (Euros per liter, with and without taxes) by other authors, such as Schipper et al. (2002), Mendiluce and Schipper (2011) and Schipper and Schipper and Fulton (2013). Marques et al. (2012) found that the reduction in CO2emissions from diesel vehicles (due to the higher fuel efficiency) was outweighed by the increase in kilometers driven (due to the rebound effect). Similarly, González and Marrero (2012), using a sample of 16 Spanish regions between 1998 and 2006, concluded that the (negative) impact of the rebound effect was greater than the (positive) effect of energy-efficiency gains. More recently, in the same vein, González et al. (2019), for a sample of 13 European countries from 1990 to 2015, provide evidence that CO2emissions have benefited from global technological progress and changes in average fuel efficiency, while increases of economic activity, motorization rate, and the dieselization process hold a positive and significant relationship with car CO2emissions. To understand why this second set of results can occur, a first factor to consider deals with the higher carbon content per liter of diesel (EPA 2011; Santos 2017). This partially offsets the fuel efficiency in diesel-powered cars. On average, the CO2 emissions generated per liter of diesel are 2.72 kg, which is 14.5% higher than the amount of CO2emissions generated when consuming 1 l of gasoline (2.35 kg of CO2 ). Thus, CO2emissions per kilometer driven in a diesel car are just 2.5% higher than those generated in gasoline cars. A second factor is that the dieselization process may imply an increase in total kilometers driven. Due to the fact that diesel cars are more efficient (in terms of liters per km driven) and its fuel is cheaper (in terms of euros per liter), diesel cars are driven more intensely than gasoline cars. Figure 4shows that the average number of kilometers driven by gasoline and diesel cars is about 11,500 and 19,000, respectively, and the ratio shows an upward trend with values well above one, between 1.75 and 1.85.6 6Due to a lack of available data, Fig. 4is constructed using data from a reduced number of countries: Austria, Denmark, France, Germany, Ireland, Netherlands, Portugal and Spain. Verboven (2002) reports similar figures for France, Belgium and Italy. See Small and Van Dender (2007) for a discussion about these data. 123 SERIEs (2020) 11:203–241 209 1.700 1.720 1.740 1.760 1.780 1.800 1.820 1.840 1.860 1.880 1.900 8000 10000 12000 14000 16000 18000 20000 22000 24000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Relave Kms diesel/gasoline kms/car (yearly) Avg. Km. traveled per gasoline car (left axis) Avg. Km. traveled per diesel car (left axis) Kms diesel car/kms gasoline car (right axis) Fig. 4 Kilometers travelled of vehicles in main Western EU countries (yearly average kms/vehicle) 10 11 12 13 14 15 16 17 18 19 20 80 85 90 95 100 105 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 CO2 Cars/total ratio, % CO2 emissions. MtCO2 CO2 Cars/CO2 final consumers CO2 final consumers CO2 cars Fig. 5 CO2emissions in main Western EU countries from cars and final consumers (Index: year 1998 = 100) Finally, Fig. 5shows the evolution of total CO2emissions coming from all final consumers (including electricity) as well as those CO2emissions only coming from passenger cars, which represents, on average, about 15% of total emissions. While both series have decreased for the entire period analyzed, the reduction has been significantly smaller for the passenger cars sector (2% for cars vs. 15% for total emissions). As commented above, however, the existing empirical papers lead to contradictory conclusions about this issue. In order to analyze the correlation between these variables and to characterize whether the fuel taxation is optimal, we rely on predictions from a dynamic general equilibrium (DGE) model, which puts together several of the most important aspects of the cars sector and makes the distinction between diesel motor and gasoline motor vehicles. 123 210 SERIEs (2020) 11:203–241 3 A dynamic model of car usage and carbon emissions We build on a neoclassical DGE model with a representative agent and durable goods (cars), distinguishing between diesel and gasoline motor cars. Special attention is given to the services provided by automobiles and the indirect effects that they generate through their use and the consequent CO2emissions. We assume the presence of a government that levies a variety of fiscal tools that affect the decisions to acquire a new car and the amount it is driven. The time subscript is omitted if unessential, with Vdenoting the one-period ahead value of the variable V. The diesel attribute is subindexed with j=1 and the gasoline attribute with j=2. The analysis of car usage (Wei 2013) together with the externality of climate change (Golosov et al. 2014) requires the use of a DGE model for three main reasons. First, climate change is a global externality that motivates the use of analytic general equilibrium tools. Second, CO2emissions linger in the atmosphere with a very high persistency, which damages human welfare in the short and long terms. Thus, we need tools that quantify the cost of current and future damage. Finally, cars are durable goods, and agents take their purchase and usage decisions in a dynamic way. 3.1 Preferences The economy is inhabited by an infinitely lived, representative household with timeseparable preferences in terms of consumption of a final non-durable good, C, direct services provided by cars (a final durable good), S, and hours worked, H. Preferences are represented by a strictly concave utility function, ∞  t=0 βtu(Ct,St,Ht),(1) where β∈[0,1)is the discount factor. The principal results of this paper only require quasi-concavity of the utility function, and thus, they are not affected by the form of the utility function, as in Golosov et al. (2014).7However, in order to conduct the simulations in Sect. 5, which illustrates (quantitatively) our model and results, we need to assume a specific utility function. We consider the following separable utility function, which is a standard functional form in the DGE literature (Greenwood et al. 1988), adapted to the case of the usage of a car: u(C,S,H)=ln (C)+ψsln (S)−ψh H1+1/ν 1+1/ν ,(2) where ψs>0 accounts for the willingness to drive a car; ψh>0 represents the (un-)willingness to work; and ν>0 is the Frisch elasticity of labor.8 7Appendixes A and B, which show the detailed solutions of the competitive equilibrium and the central planner problem, respectively, are formulated using a generic utility function. 8Indeed, this type of utility function is in response to Greenwood et al. (1988) preferences. It is Gorman type, so it possesses clear advantages for aggregation purposes. This type of utility function fairly describes the macroeconomic impact of technology that affects the productivity of new capital goods. 123 SERIEs (2020) 11:203–241 217 for n=1,2,3, noting that 0 =δ1<δ 2<δ 3<1, and with the first term −γYuC<0 denoting the instant marginal damage of an extra carbon molecule emitted in the atmosphere. Iterating forward in time on VZprovides an alternative manner to interpret this term, VZn,t=−γ ∞  i=0 βi(1−δn)iuC,t+iYt+i<0.(28) Thus, VZn,tcan be seen as the discounted value of future marginal damages from global warming, with (1−δn)β<1 being the discount factor for each component of carbon concentration, Zn,forn=1,2,3. The set of expressions in (28), combined with (26), provide the SCC (in present value and utility units) in the economy, which is given by: SCC =−βVZ uC .(29) 4.3 Pigouvian taxation Comparing the decision of driving in the market equilibrium with its social planner counterpart, (22)versus(25), the Pigouvian tax on fuel jcan be written as, τ+ Fj =−φj VZ uC >0,(30) for j=1,2.13 This proportion is given by the CO2content per liter of fuel jparameter, φj, regardless of the fuel efficiency of the motor car, fj. Thus, the relative Pigouvian tax rate (diesel vs. gasoline) is given by τ+ F1 τ+ F2 =φ1 φ2 ,(31) which is independent of the fuel efficiency ratio, f1/f2. Recall from the discussion in Introduction that the fact that the f1/f2ratio is less than one (i.e., diesel cars need fewer liters than gasoline cars to travel the same distance) has been used to argue the benefits of the dieselization policy. Our result points out that the correct policy is independent of this ratio. The fact that f1/f2is less than one is already internalized by the household in their decisions; thus, the government should not intervene at this point and further incentivize the use of diesel. However, households are not internalizing the amount of CO2they generate when they consume each type of fuel, which depends on φ1and φ2. 13 A more formal derivation of this result is provided in the technical “Appendix C.” Fullerton and West (2002), Parry and Small (2005), Nordhaus (2008) or Parry et al. (2014), do similar exercises for similar purposes, though they focus on other externalities, such as congestions, local pollution or accidents. 123 218 SERIEs (2020) 11:203–241 It is illustrative to derive an explicit expression for τ+ Fjfrom (30) in steady state, τ+ Fj =φjγβ ϕL 1−β+(1−ϕL)ϕ0 1−β(1−δ2)+(1−ϕL)( 1−ϕ0) 1−β(1−δ3)Y.(32) This condition implies that the Pigouvian tax rate increases with the scale of emissions from fossil fuel combustion by cars φj, with the residence time of CO2in the atmosphere (the closer to zero δ2and δ3are), with the damage parameter γ, and decreases with the discount rate (the closer to one the βis). Finally, whenever fuel taxes are fixed according to a Pigouvian criterion and in the absence of other distortions, it is straightforward to obtain that tax on the purchase of vehicles must be zero, i.e., τ+ X1=τ+ X2=0 (see the technical Appendix C for a formal proof). This result implies that sales taxes are not needed to internalize the costs from CO2emissions and that fuel taxes are sufficient to encompass the social damage generated from fuel combustion if they are set in a Pigouvian way. Note, however, that this result does not imply that car purchases should be VAT exempt. Rather, it claims only that a sales tax is inadequate to internalize the external cost of CO2emissions. 5 Quantitative analysis: car usage, dieselization and CO2emissions In this section, we first calibrate our DGE model for the set of EU countries. Second, we provide a model validation exercise to show whether our simulations are able to reproduce, among other things, key elasticities and dynamics in the car sector in Europe. Third, we quantify the Pigouvian taxation. Finally, we solve the model numerically to quantify the benefits of adopting the Pigouvian allocation (or, from another angle, the cost of being away from the optimal policy). 5.1 Calibration We summarize the most important aspects of the calibration. To simplify the presentation, we pay special attention to those parameters related to the stock of cars (Q1,Q2),kilometers driven ˜ N1,˜ N2, and to the carbon cycle. All parameters are given in Tables 1and 2.14 The model is calibrated for our sample of EU13 countries (Sect. 2). The year 1999 is chosen as the reference period for several reasons. Certain series that distinguish between diesel and gasoline in cars, such as kilometers driven or fuel efficiency, are only available from 1999 onward. Our set of EU13 economies were relatively close to their balanced growth path by this year.15 Overall, choosing 1999 as the reference 14 An extensive technical Appendix about the calibration is available at: https://www.upo.es/econ/ rodriguez/index_archivos/Diesel/Appendix_A.pdf. 15 The average GDP growth rate was 2.4% for 1995–2007 (just before the Great Depression), while it is 1.5% when one includes the years up to 2014, i.e., 1995–2014. The growth rate was 2.3% in 1999, which is in line with the average growth before the Great Depression. Moreover, at world wide level, Hassler et al. (2016) use 2000 as the reference year to set the initial level of carbon concentration. 123 SERIEs (2020) 11:203–241 219 year is a reasonable assumption and the main conclusions of the paper do not heavily depend on it. Parameters determined ex ante Table 1presents the list of parameters taken exogenously from the model, together with their data source or reference. This list of parameters include the Frisch elasticity, the labor income share for the final good sector, the fuel prices (plus taxes) and those parameters related to the carbon cycle. For average prices and taxes, we use pF1=0.330 euros per liter of diesel, pF2= 0.357 euros per liter of gasoline, and τF1=0.812 euros per liter of diesel versus τF2=1.111 euros per liter of gasoline (Weekly Oil Bulletin, European Commission). From the European Automobile Manufacturers Association (ACEA), we take a 20% sales tax for new cars which is same for both types of vehicles, τX1=τX2=0.20. We retrieve series of capital and value added from the EU KLEMS database for our EU sample to calculate an average capital-to-output ratio of 3.56 between 1993 and 2007 (an interval around 1999). This ratio is referenced to set a (yearly) real interest at 4.29%, which implies a subjective discount rate βof 0.990. The key parameters for measuring the SCC are the discount rate β, the damage factor γ, those related to the carbon cycle in (17 ), and to the CO2emissions from fuel, φj,fjj=1,2. From Sect. 2, we described that φ1=2.689 kg. CO2/l of diesel, and φ2=2.348 kg. CO2/l of gasoline, with φ1/φ2=1.1455. Although these parameters are estimated for the USA (EPA 2011), they are very similar to those reported by Santos (2017) for the EU countries. The global warming damage parameter γin the production function ( 6)isset to 2.379 (×10−5)(IPCC 2007), which means that a concentration of Z=802 Gt. in excess of the preindustrial level 581 Gt. produced a 0.52% increase in damage on the 1999–2000 global output, i.e., 1 −e−γ(802−581)=0.0052. The parameters related to the carbon cycle in (14)–(16) are borrowed from Golosov et al. (2014) and the references therein: ϕL=0.2 (20% of total emissions remain in the atmosphere forever), (1−δ2)4×200 =0.5 (carbon concentration Z2has an average life of 300 years), δ3=1 4×10 (Z3has a residence time of one decade following a geometric decay); finally, the percentage ϕ0is calibrated to ensure that total emissions have an average life of 200 years, 0.5=ϕL+(1−ϕL)ϕ0(1−δ2)4×200 +(1−ϕ0)( 1−δ3)4×200, which implies ϕ0=0.4557. Parameters that require solving the model Table 2presents the complete list of endogenous parameters and targets (i.e., statistical moments and other references). We use the steady-state first-order conditions and the state equations as a system of equations whose solution meets the targeted moments given in Table 2, given the parameters in Tables 1and 2. The main moments required in our calibration are the following: gross investment accounts for 20% of the EU13 GDP; the labor income share (Table 1,EU KLEMS) is 0.658; the diesel to gasoline of vehicle ratio, Q1/Q2,is0.188; the diesel to gasoline fuel consumption ratio, F1/F2,is0.331; the fuel efficiency ratio f1/f2is 0.877; and the relative mileage is ˜ N1/˜ N2=1.63 (i.e., diesel motor cars are driven 63% more than gasoline cars).16 16 As commented in Sect. 2, data for kilometers driven should be used cautiously. This ratio is rather low compared to that reported in Sect. 2for 1999, which was 1.73. However, ˜ N1/˜ N2=1.63 is a reasonable 123 220 SERIEs (2020) 11:203–241 Table 1 Targets and parameters Parameter Value Definition Source A. Parameters determined ex ante (17 parameters) Parameters associated to utility (1 parameter) ν0720 Frisch elasticity of labor supply Heathcote et al. (2010), Chetty et al. (2011) Parameters associated to technology (3 parameters) θ0658 Technology in final good sector Y Labor income share (EU KLEMS) α10021 Depreciation rate of diesel vehicles Avg. lifespan of vehicles = 12 years (48 quarters) α20021 Depreciation rate of gasoline vehicles Idem Stationary prices and taxes (6 parameters) pF10330 Price of diesel fuel (e/l, 1999) Weekly Oil Bulletin, European Commission pF20357 Price of gasoline fuel (e/l, 1999) Idem τF10812 Diesel fuel tax rate (e/l, 1999) Idem τF21111 Gasoline fuel tax rate (e/l, 1999) Idem τX10200 Sale tax on new diesel cars European Automobile Manufacturers Association (ACEA) τX20200 Sale tax on new gasoline cars Idem Carbon cycle: emissions, CO2concentration and damage (7 parameters) ϕL0200 Fraction of emissions that remain forever Golosov, Hassler, Krusell and Tsyvinski (2014) ϕ00595 Fraction of emissions that remain 300 years Idem δ2(×104)5,775 Persistency of (1−ϕL)ϕ0CO2emissions Idem (half life 300 years, Archer (2005)) δ30025 Persistency of (1−ϕL)(1−ϕ0)CO2emissions Idem (residence time 10 years, (IPCC 2007)) γ(×105)2379 Global warming damage parameter Idem φ12689 Carbon content per liter of diesel Environmental Protection Agency, EPA (2011); Santos (2017) φ22348 Carbon content per liter of gasoline Idem 123 SERIEs (2020) 11:203–241 221 Table 2 Parameters that require solving the model (15 parameters) Parameter Value Definition Target β0990 Time discount rate Capital/Total income, K/(WH+RK)=3.56 δ0014 Depreciation rate of capital asset Dynamic FOC, intertemporal equation A0829 Final good Yproduction function Share of gross investment over GNP, I=0.20 ψH12,133 Willingness to work Static FOC, trade-off consumption–leisure, and fraction of hours worked, H=0.31 ψS0081 Willingness to drive Share of new cars investment over GNP, pXj ·Xj=0.0438; and fraction of diesel cars in 1999, Q1=0.188 χ10355 Utility weight of diesel cars Share of fuel expenditure over GNP, pFj ·Fj=0.0302 ς0597 Substitutability diesel–gasoline km Relative dynamic FOC, new cars investment ρ0153 Substitution of services of both types of cars Share of car fixed costs over GNP, TI =0.0120 μ0810 Fischer complementarity hours-cars Relative fuel consumption, F1/F2=0.331 a10012 Diesel cars production function Relative fuel price, pF1/pF2=0.924 a20013 Gasoline cars production function Idem f10068 Gallons per mile (diesel cars) Relative static FOC for km driven ˜ N1/˜ N2=1.63 f20082 Gallons per mile (gasoline cars) Relative fuel efficiency f1/f2=0.877 m10018 Maintenance need (diesel cars) Share of maintenance and repairs over GNP, MR =0.0195 m20018 Maintenance need (gasoline cars) Assumption: m1=m2 123 222 SERIEs (2020) 11:203–241 Given the calibrated value of the parameter ς=0.6, we propose a value for ρ=0.15, which entails a certain degree of substitution between gasoline and diesel vehicles (when ρis in the interval (0; 1], diesel and gasoline cars are substitute). According to these parameters, the elasticity of substitution of the mileage with respect to the relative operating costs is −1/(1−ςρ)=−1.10. This elasticity is key to predict changes in Q1/Q2,˜ N1/˜ N2and TKD, according to equation (23). 5.2 Model elasticities We next provide a set of simulation exercises to validate model predictions. We focus on the average behavior of our set of EU13 countries between 1999 and 2015, as described in Sect. 2. Our benchmark calibration is taken to reproduce the situation at the beginning of the sample (1999 in our case). First, we show that the model produces elasticities similar to those estimated by the empirical literature. Table 3presents a summary of elasticities given by Goodwin et al. (2004). The short-run price elasticity of fuel demand is −0.25 (averaged over 46 studies), ranging between −0.57 and −0.01. For the long term, this elasticity is −0.64 (averaged over 51 studies), and ranges between −1.81 and 0. Kilometer driven (both total and individual per vehicle) is usually more inelastic than fuel demand by factor of 1.5–2.0.17 These estimates do not differentiate between diesel and gasoline. For our benchmark calibration, Table 4presents model elasticities of fuel demand. Given that the model does not produce isoelastic behaviors, we provide a range of values for several changes in both fuel prices and fuel efficiencies. To implement exogenous changes in fuel prices, we impose a permanent change in fuel taxation (ceteris paribus) and quantify the implied change in key endogenous variables: fuel demanded, kilometers driven and vehicle stock. We also analyze the effect of a permanent change for the relative fuel efficiency (diesel relative to gasoline, f1/f2in our notation). The first column in Table 4reports elasticities with respect to the diesel fuel price. The own-price elasticity of diesel demand ranges between −0.69 and −0.79, which meets the surveyed values of Goodwin et al. (2004). Analogously, the crossprice elasticity of gasoline demand (i.e., w.r.t. the price of diesel) is positive but low, due to a long-run substitution effect. Traffic elasticities are lower than fuel demand elasticities, though not by the factor of 1.5–2.0 highlighted by Goodwin et al. (2004). When we consider permanent changes in the relative fuel efficiency, the responses are always inelastic (i.e., their absolute values never exceed unity). In response to a one percent permanent increase in the relative fuel efficiency (lower diesel liters per km), kilometers driven by diesel vehicles increase between 0.78 and 0.92% (kilometers Footnote 16 continued assumption. For Belgium, France and Italy, Verboven (2002) reports ratios varying with the weight of the vehicle (1.65 on average). The Encuesta de Hogares y Medio Ambiente by the Spanish National Institute of Statistics (INE 2008) reports an estimate of mileage per diesel car that exceeds that of gasoline cars by 40%. When taking into account the family size, the ratio goes from 60% for single households to 32% for families with 4 or more members. 17 More recently, Brons et al. (2008) estimated similar values in a meta-analysis. They found long-run values for the price elasticities of (gasoline) fuel demand, kilometers driven and vehicle stock of −0.864, −0.493 and −0.08, respectively. 123 SERIEs (2020) 11:203–241 223 Table 3 Goodwin, Dargay and Hanly’s (2004, Table 4) summary of elasticities w.r.t fuel price Short term Long term Fuel demand (total) −0.25 −0.64 Range [−0.57, −0.01] [−1.81, 0] Fuel demand (per vehicle) −0.08 −1.1 Kilometer driven (total) −0.10 −0.29 Range [−0.17, −0.05] [−0.63, −0.10] Kilometer driven (per vehicle) −0.10 −0.30 Range [−0.14, −0.06] [−0.55, −0.11] Vehicle stock −0.08 −0.25 Range [−0.21, −0.02] [−0.63, −0.10] Table 4 Implied elasticities of various measures of demand Elasticities (long run, range of values) w.r.t Diesel fuel price Gasoline fuel price Relative fuel efficiency Fuel demand Diesel fuel [−0.79, −0.69] [0.19, 0.20] [−0.25, −0.21] Gasoline fuel [0.051, 0.054] [−0.70, −0.61] [−0.057, −0.061] Kilometer driven Per diesel vehicle [−0.77, −0.67] [0.06, 0.07] [0.78, 0.92] Per gasoline vehicle [0.017, 0.018] [−0.78, −0.67] [−0.038, −0.041] Vehicle stock Diesel vehicles [−0.018, −0.017] [0.12, 0.13] [0.017, 0.018] Gasoline vehicles [0.03, 0.04] [0.07, 0.08] [−0.027, −0.030] driven by gasoline vehicles change by −0.06%), the stock of diesel cars increases by 0.018% (the stock of gasoline motor vehicles change by −0.03%), and the demand of both types of fuel decreases (between 0.21 and 0.25% of diesel and about 0.06% of gasoline). Consistent with our simulations, Frondel and Vance (2018) report evidence for Germany that distance traveled is less elastic with respect to prices (−0.39) than to fuel efficiency (0.67). As a second numerical exercise, we simulate the market equilibrium taking the average fuel taxes for our set of EU13 countries between 2000 and 2015 as exogenous (those shown in Fig. 3), and assuming that all other parameters are constant (the state of productivity, preferences, other taxes, etc.).18 Figure 6represents the simulated trajectories for relative vehicle stock, kilometers driven and fuel consumption (diesel to gasoline). For comparative purposes, we also include the observed series of these three ratios between 2000 and 2015. 18 We eliminate 1998–1999 to avoid a drastic fall in fuel taxation occurred in European countries in these 2 years. 123 224 SERIEs (2020) 11:203–241 Fig. 6 Simulation The simulated series for the diesel to gasoline cars ratio and the relative fuel consumption (first and third subplots, respectively) widely differ from the reported observed series. Thus, we can conclude that the dieselization process (i.e., the replacement of gasoline vehicles by diesel vehicles) cannot be justified on the grounds of the existing fuel taxation policies favoring the use of diesel fuel. While the relative diesel to gasoline taxation has remained quite stable from 2000 to 2015, the share of diesel cars has increased from 19 to 42%. The small simulated elasticities (last row in Table 4), which are consistent with empirical estimates, already pointed out to this fact. The second subplot in Fig. 6represents the diesel to gasoline relative mileage. According with our simulations, the higher mileage of diesel vehicles is consistent with the existing fuel taxation differences between diesel and gasoline. In this case, taking fuel taxes for granted and holding constant the rest of structural elements, the diesel to gasoline mileage ratio is always higher than one and close to the observed levels (ranging between 1.6 and 1.7) in the 2000–2015 period. Moreover, the model reproduces part of the observed dynamics. Finally, by comparing the three subplots, we can also conclude that the increase in the relative fuel demand is associated with the steady increase in the relative stock of diesel cars rather than with the trajectory of the relative kilometers driven. 5.3 Model validation We next analyze whether our DGE model can reproduce the dieselization process which took place in Europe between 1999 and 2015 in response to changes in certain fundamentals. Results are shown in Table 5. More specifically, we try to explain the increase in the share of diesel vehicles from 18 to 42%, an increase in the relative fuel consumption (diesel/gasoline liters) from 0.33 to 1.10 and a relative mileage of 1.81. (These three targets are presented in the last column of Table 5.) 123 SERIEs (2020) 11:203–241 225 Table 5 Model validation Reference year 2000 (a) (b) (c ) (d) (e) Target year 2015 Exogenous Diesel fuel taxation τF1 0.49 0.71 0.71 0.71 0.71 0.71 Gasoline fuel taxation τF2 0.66 0.89 0.89 0.89 0.89 0.89 Relative fuel taxation τF1/τF2 0.74 0.79 0.79 0.79 0.79 0.79 Diesel sale tax τX1 0.20 0.20 0.00 0.00 0.00 0.00 – Gasoline sale tax τX2 0.20 0.20 0.20 0.20 0.20 0.20 – Relative sale tax τX1 /τX2 1.00 1.00 0.00 0.00 0.00 0.00 – Relative fuel efficiency f1/f20.88 0.88 0.88 0.85 0.85 0.85 – Relative preferences χ1/χ20.36 0.36 0.36 0.36 1.00 1.00 – Relative productivity a1/a20.50 0.50 0.50 0.50 0.50 0.62 – Endogenous Relative fuel demand F1/F20.33 0.33 0.33 0.33 1.10 1.12 1.10 Diesel cars share Q1/(Q1+Q2)0.19 0.19 0.21 0.21 0.37 0.42 0.42 Relative km driven ˜ N1/˜ N21.63 1.61 1.45 1.48 2.20 1.82 1.81 The endogenous values given in the lower panel of this table represent steady-state equilibrium solutions under the (exogenous) parameters reported in the upper panel. The first column presents figures of 2000, year of reference. Column (a) calculates equilibrium when fuel taxes are those of 2015 (average tax rate over countries, Weekly Oil Bulletin of the European Commission, https://ec.europa.eu/energy/en/statistics/weekly-oil-bulletin). Column (b) adds to (a) a change in the diesel sale tax. Column (c) adds to (b) a change in the fuel efficiency of gasoline and diesel vehicles (liters per km., average rate, Odyssee-Mure database, http://www.indicators.odyssee-mure.eu/onlineindicators.html). Column (d) adds to (c) a change in preferences χ1/χ2to target the relative fuel consumption observed in 2015, F1/F2=1.1. Column (e) adds to (d) a change in the productivity parameters a1/a2to target the share of the diesel stock observed in 2015, Q1/(Q1+Q2)=0.42 123 226 SERIEs (2020) 11:203–241 To this purpose, we consider the following five structural forces of change: fuel taxes, new vehicle sale taxes, fuel efficiency, preferences and productivity. We calculate the equilibrium values by incorporating these five sources of change sequentially. Columns (a)–(c) incorporate changes of fuel taxes, sale taxes and fuel efficiency, respectively. These factors are exogenously determined. Fuel taxes are changed from the average observed levels in 2000 (τF1=0.49 and τF2=0.66) to the average observed levels in 2015 (τF1=0.71 and τF2=0.89). Notice that diesel taxation is more lenient than gasoline in all years (recall from Fig. 3). As the second source, we consider a permanent reduction in the tax rate levying the purchase price of diesel cars from τX1=0.2 (benchmark case) to τX1=0. To justify this case, apart from the arguments provided in Miravete et al. (2018),19 we consider all possible circumstances that have incentivized the purchase of diesel cars in Europe during the last decades, such as a VAT rate reduction, tax rebates to diesel car buyers, lower registration fees or the benefits in ownership cost per year (once the vehicle has been purchased).20 As the third channel, we assume fuel efficiency changes between 2000 and 2015 as measure in the data (Fig. 2): f1/f2changes from 0.88 to 0.85. We first notice that these exogenous factors (columns a, b, c) add little to explain the dieselization of the vehicle fleet. These three changes together (accrued in column c) would predict a 2 p.p. in the variation of the diesel car share from 0.19 to 0.21, and a decrease in the relative mileage from 1.63 to 1.48. Thus, the remaining fraction should be accounted by other factors. In our exercise, we consider in columns (d) and (e) changes in relative preferences and productivity, χ1/χ2and a1/a2, respectively. Since we cannot observe these changes in the data, we choose values in χ1/χ2and a1/a2in order to target the following observed ratios in 2015: F1/F2=1.10 (relative fuel), Q1/(Q1+Q2)=0.42 (relative cars stock) and ˜ N1/˜ N2=1.81 (relative mileage). Thus, our fourth driver is related to a change in preferences, where consumer preferred vehicles with greater fuel economy and other diesel vehicle improvements, such as design or speed. In this sense, Miravete et al. (2018) provide evidence of European policies that “served to protect domestic European manufacturers by fostering a preference for diesel cars mainly produced by European automakers.” In terms of our model, this change can be motivated by increasing the ratio χ1/χ2in the household utility function (3) to target the increase in the relative fuel consumption from F1/F2=0.33 to 1.10 (under the benchmark case, the ratio of these parameters is χ1/χ2=0.36). Under this case (column d), which adds to the scenario in column (c), the share of diesel cars increases to 37% (a 18 p.p. increase), although the relative 19 Miravete et al. (2018) emphasize that the more lenient NOxemissions standards adopted by European regulators have reduced the sale prices of diesel vehicles and hence have incentive their purchase. A stricter NOxemissions policy would have entailed higher marginal cost for the European auto makers, which were specialized in the production of diesel cars. These costs would have implied higher sale prices and led some consumers to substitute diesel cars by gasoline cars. 20 In this sense, despite most EU countries are using similar instruments, they apply them differently. Mandell (2009) discusses several Swedish policies, mostly reducing the purchase price of new cars, aimed at achieving a more efficient vehicle fleet. For instance, the purchase of an “environment-friendly” car is subsidized by 1000 Euros (10.000 SEK). In most countries, scrapping vehicles that fulfilled certain requirements (related to car age, CO2emissions or pollutants), entitled the owner of the vehicle to a grant to buy a brand new one. 123 SERIEs (2020) 11:203–241 233 TR ≡ j=1,2τfj fj˜ NjQj+τxj pXjXj, mcj≡pF,j+τF,jfj+pMRmj,  H≡HμS1−μ.(34) and the accumulation of capital and vehicles: K=(1−δ)K+I,(35) q j=1−αjqj+xj,j=1,2.(36) The wage W, the rental price of capital R, the government transfer TR, the dividend from the automotive industry , all remaining prices pXj,pFjj=1,2,pMR and taxes τFj,τXjj=1,2, are given to the household. We require concavity on the instantaneous utility function u(C,S,H), where vehicle services Sare given by the following CES specification: u(C,S,H)=ln (C)+ψsln (S)−ψh H1+1/ν 1+1/ν , S=χ1Sρ 1+χ2Sρ 21/ρ , sj=˜ Nς jQj,j=1,2. In a recursive manner, the first-order conditions are uC=βV K,(37) VK=RuC+(1−δ)βV K,(38) 0=WμS1−μ H1−μuC+uH,(39) and βV Qj =1+τx,jpXjuC,(40) VQj =χjsρ−1 j˜ Nς jS1−ρuS−mcj˜ Nj−(1−μ)WH Sμ χj˜ Nς juC(41) +1−αjβV Qj, 0=S1−ρuSςχ j˜ Nςρ−1 jQρ−1 j+(1−μ)WHμ Sμςχ j˜ Nςρ−1 jQρ−1 j−mcjuC. (42) Expressions (37) through (42) represent the derivative of the Bellman equation with respect to C,K,H,Xj,Qjand ˜ Nj, respectively. 123 234 SERIEs (2020) 11:203–241 Combining previous conditions, we reach the following: uC=βu CR+1−δ,(43) −uH=WμS1−μ H1−μuC,(44) 1+τx,jpXjuC=βχj˜ N jςρ Q jρ−1 −mc j˜ N ju C +1−αj1+τ Xjp Xju C.(45) ςχj˜ Nςρ−1 jQρ−1 j=mcjuC.(46) where ≡S1−ρuS+(1−μ)W(Hμ/Sμ)uC. Using a general form for the utility function, expressions (45) and (46) are equivalent to Euler equations (21) and (22). A.2 Firms Firms maximize their profits within each time period by taking prices and technology as given and do not consider carbon concentration Zwhen they make decisions. The representative firm in the final goods sector solves max ( H,K)Y−W· H−R·K, Y=e−γ(Z−581)A· HθK1−θ Y,  H=HμS1−μ,(47) given (W,R)and S. First-order conditions are: W=MPH =θY/ H,(48) R=MPKY=(1−θ)Y/KY.(49) The representative firm in the automotive industry solves max (kX1,kX2)pX1Aa1K1−θX X1+pX2Aa2K1−θX X2−R(KX1+KX1), where Rand (pX1,pX2)are given. First-order conditions are: R=pX1MPKX1=pX2MPKX2.(50) MPKXj denotes the marginal product of capital in the production of vehicles with engine j=1,2. 123 SERIEs (2020) 11:203–241 235 The third sector, the refinery, employs crude oil and capital in order to maximize profits: max (o1,o2,kF1,kF2)pF1Ab1oθF 1K1−θF F1+pF2Ab2oθF 2K1−θF F2 −po(o1+o2)−R(KF1+KF2)], given the price of oil, po, the rental price of capital, R, and the prices of fuels (pF1,pF2). First-order conditions are: po=pF1MPOF1=pF2MPOF1,(51) R=pF1MPKF1=pF2MPKF2.(52) MPKFj,MPOFjdenote the marginal products of capital and crude oil in the production of fuel j=1,2. A.3 General equilibrium Given a government policy, τX,1,τX,2,τF,1,τF,2,TR , the competitive equilibrium is a set of rules for making decisions, C(ζ),Xj(ζ),˜ Nj(ζ)j=1,2,H(ζ),K(ζ), prices for fuel and new vehicles, pXj (ζ),pFj (ζ)j=1,2, and factor prices W(ζ), R(ζ),po, such that: 1. Given the government policy and factor prices, households decide according to (33), subject to the budget constraint (34), the state equations for capital (35), vehicle accumulation (36), and the nonnegative constraints. 2. All factors (hours, capital and crude oil) are employed at their marginal productivity, (48) through (52). 3. The government satisfies its budget constraint every period. 4. Markets clear: labor demand is equal to labor supply; the same condition holds for physical capital; for j=1,2, Xj=Xjfor cars and Fj=Fjfor fuel; and, consequently, condition (34) for the final consumption goods sector also holds. B The solution of the social planner This part of Appendix is analogous to the previous for the market equilibrium. The only difference is that the social planner considers the damaging effect of the output of CO2concentration Z, when deciding the optimal allocation. Thus, the vector of aggregate state variables for the social planner ζSP now includes the stock of CO2=Z concentration into the atmosphere, Z: ζSP =(K,Q1,Q2,A,po,Z). 123 236 SERIEs (2020) 11:203–241 The social planner maximizes the present value function VζSP=max u(C,S,H)+βVζSP,(53) with respect to C,H,K,KY, and ˜ Nj,KXj,KFj,ojj=1,2, subject to the following constraints: e−γ(Z−581)A· HθK1−θ Y=C+I+ j=1,2pooj+mj˜ NjQj,(54)  H≡HμS1−μ, fj˜ NjQj=AbjoθF jK1−θF Fj ,for j=1,2,(55) Q j=1−αjQj+AajK1−θX Xj ,for j=1,2,(56) K=(1−δ)K+I,(57) K=KY+ j=1,2KXj +KFj,(58) and Z=Z1+Z2+Z3,(59) Z 1=Z1+ϕLE,(60) Z 2=(1−δ2)Z2+(1−ϕL)ϕ0E,(61) Z 3=(1−δ3)Z3+(1−ϕL)( 1−ϕ0)E,(62) E=ERW +Eother +Ecars,(63) Ecars =φ1f1˜ N1Q1+φ2f2˜ N2Q2.(64) Equation (54) represents the feasibility constraint in the final goods sector; expressions (55)–(58) define feasibility constraints, and expressions (59)–(64) represent the state equations which describe the stock of CO2,Z(Golosov et al. 2014, and references therein). Edenotes the world flow of CO2emissions, Ecars denotes the emissions due to passengers vehicles in Europe, Eother is the flow of European emissions other than those emitted by European cars, and ERW denotes emissions from the rest of the world. In the above, φjis the amount of CO2per liter of fuel j=1,2. The optimal intertemporal allocations are summarized by the following expressions: uC=βu C1−δ+MPK Y,(65) uH=−μθ Y HuC,(66) uC MPKY MPKXj =βχj˜ N jςρ Q jρ−1uSS1−ρ+u C(1−μ)θY S 123 SERIEs (2020) 11:203–241 237 −u CMPK Y MPK Fj fj+p MRmj˜ N j+p TI −1−αjMPK Y MPK Xj  +φjfj˜ N jV Z(67) φjfjVZ=MPKY MPKFj fj+pMRmjuC −ςχj˜ Nςρ−1 jQρ−1 juS Sρ−1+(1−μ)θY SuC,(68) where MPKdenotes the marginal product of capital in the production of product =Y,X1,F1,X2,F2. We assume that certain real prices are exogenously given, such as (pMR,po). Finally, the last condition sets an expression for the marginal social cost of CO2 concentration, VZ: VZ≡ϕLVZ1+(1−ϕL)ϕ0VZ2+(1−ϕL)( 1−ϕ0)VZ3,(69) with, VZn=−γuCY+(1−δn)βV Zn,(70) for n=1,2,3 with 0 =δ1<δ 2<δ 3<1. C Pigouvian taxation In this part of Appendix, we present the details to determine the tax scheme for τF1,τF2,τX1,τX2that must be set in a market economy in order to implement the social planner allocations: (65), (66), (67) and (68). For this scheme to be implemented, two circumstances are called for: •As stated in the competitive equilibrium condition, aggregate choices need to meet individual ones when the household is representative. •Market equilibrium prices are equal to the marginal rates of transformation: pXj =MPKY MPKXj ,(71) pFj =MPKY MPKFj ,(72) W=θY  H=θY HμS1−μ,(73) for j=1,2, where MPK denotes the marginal product of capital. Wage meets the marginal product of labor. The two prices (pMR,po)are exogenous in any case. 123 238 SERIEs (2020) 11:203–241 In view of these conditions, we derive two normative propositions. The first one is related to fuel taxes. Proposition 1 The Pigouvian tax on fuel j that internalizes the cost of global warming is given by τ+ Fj=−φj VZ uC >0,(74) where VZis the social marginal costs of CO2, defined by (69). Proof #1Consider the condition for optimal vehicle utilization (68), the decision of driving undertaken by a representative household in a decentralized economy (46), and exploiting the previous pricing relations: ςχj˜ Nςρ−1 jQρ−1 jS1−ρuS+(1−μ)θY SuC =pF,jfj+pMRmjuC−φjfjVZ,(75) ςχj˜ Nςρ−1 jQρ−1 jS1−ρuS+(1−μ)WHμ SμuC =pF,j+τF,jfj+pMRmjuC.(76) When we impose that individual choices meet aggregate choices in equilibrium, expressions (75) and (76) must coincide if the fuel tax is set to τFjuC=−φjVZ> 0.  The second proposition sets the Pigouvian sales tax on the purchase of new vehicles: Proposition 2 If the fuel tax is set according to the rule (74), τFj=τ+ Fj,the Pigouvian sales tax on the purchase of new vehicles for all periods t is nil: τ+ Xj,t=0.(77) Proof 2 Rewrite the optimal acquisition of new vehicles (67 ), the decision of purchasing a brand new car of type j(45), the pricing rules (71)-(73), and the Pigouvian fuel tax rule (74): pXjuC=βχj˜ Nςρ jQρ−1 jS1−ρuS+(1−μ)θY Su C −u Cp Fj fj+p MRmj˜ N j+p TI −1−αjpXj+fj˜ N jτ+ Fju C, (78) 1+τx,jpXjuC=βχj˜ Nςρ jQρ−1 jS1−ρu S+(1−μ)WHμ Sμu C −u Cp F,j+τ+ F,jfj+p MRmj˜ N j−1−αj1+τ Xjp Xj, 123 SERIEs (2020) 11:203–241 239 (79) When we impose that individual choices meet aggregate choices in equilibrium, subtracting expressions (78) and (79) yields τX,j,tpXj,tuC,t=β1−αjτX,j,t+1pX,j,t+1uC,t+1. For any initial period t0, iterating forward on this expression we reach τX,j,t0pX,j,t0uC,t0=lim t→∞ βt1−αjtτX,j,tpXj,tuC,t=0. For this expression to be true, the Pigouvian sales tax must be nil as in (77)whenever the fuel taxes are fixed according to a Pigouvian criterion (74) DCO 2vehicle emission decomposition Let Ecars denote vehicle emissions in (12)as Ecars =φ1F1+φ2F2 =[−(φ2f2−φ1f1)1+φ2f2]·TKD,(80) where φ2f2>φ 1f1for the benchmark calibration, and let 1≡˜ N1Q1/TKDdenote the share of diesel driven kilometers. An increase in 1, i.e., 1>0 (the share of kilometers driven by diesel cars), can be seen as a consequence of dieselization. Differentiating over (80), we reach the following decomposition: Ecars Ecars =−(φ2f2−φ1f1) Ecars/TKD 1   Efficiency effect +TKD TKD   Intensive margin .(81) When 1>0, the efficiency effect is negative because (φ2f2−φ1f1)>0. 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