The effectiveness of policy on consumer choices for private road passenger transport emissions reductions in six major economies

The effectiveness of fiscal policy for emissions reductions in private passenger road transport depends on its ability to incentivise consumers to make choices oriented towards lower emissions vehicles. However, car purchase choices are known to be strongly socially determined, and this sector is highly diverse due to significant socio-economic differences between consumer groups. Here, we present a comprehensive dataset and analysis of the structure of the 2012 private passenger vehicle fleet-years in six major economies across the World (UK, USA, China, India, Japan and Brazil) in terms of price, engine size and emissions distributions. We argue that aggregate choices and corresponding elasticities of substitution under changes of fiscal policy can be estimated, with uncertainty, using this data. This enables to evaluate the likely effectiveness of potential fiscal and technological change policies on fleet-year emissions reductions. We provide tools to do so based on the distributive structure of prices and emissions in segments of a diverse market, both for conventional as well as unconventional engine technologies. We find that markets differ significantly between nations, and that correlations between engine sizes, emissions and prices exist strongly in some markets and not strongly in others. We furthermore find that markets for unconventional engine technologies have patchy coverages of varying levels. These findings are interpreted in terms of policy strategy.


Introduction
Transport generates an important fraction of global fuel combustion greenhouse gas (GHG) emissions contributing to climate change. It produces 5.3 Gt out of a total of 32.7 Gt of CO 2 , making historically over 30% of total emissions annual growth (IEA, 2013). The current trend of increase in global emissions is currently leading the world towards global warming exceeding 4 • C, with the most important component emitted by the electricity sector. 2 However, as was shown by Mercure et al. (2014), reducing global electricity sector emissions by as much as 90% is still insufficient to avoid warming beyond 2 • C, which would require large emissions reductions from all other sectors, notably in road transport.
The fuel efficiency of the car fleet depends directly on its composition of engine types and sizes. In contrast to the electricity and other industrial sectors, where technologies of the same type (e.g. coal boilers, blast furnaces) differ modestly from one another due to technology vintage, 3 the transport sector features a very wide continuous array of possible fuel efficiencies (spanning a factor of 3-4, see data below), that do not depend as strongly on vintage as it does on socio-economic characteristics of owners. As shown by McShane et al. (2012), vehicle choices strongly relate to social groups, and thus existing socio-economic differences are reflected in the types of vehicles that consumers purchase. As we note below, the effectiveness of policy to influence consumer choices is a controversial subject. Policies for emissions reductions are often chosen and applied without a clear quantitative understanding of their likely impact. Therefore we ask two questions here. Do different markets respond differently to policy instruments? If so, is it possible to obtain quantitative insight on the effectiveness of proposed policies from data on the market structure itself?
Cars typically survive in the fleet for around 12 years. 4 Each time a vehicle is replaced, an opportunity arises to reduce fleet emissions, which are gradually changed according to choices of consumers, and this constrains the timescale over which emissions reductions can be achieved (fleet turnover, e.g. see Mercure, 2013). Emissions can be reduced in two different ways: by improving the fuel economy of new models with conventional engine technology, or by radical changes in engine technology of new vehicles such as hybrid and electric power trains. This means that two types of policies can be considered for this purpose: policies targeting the fuel economy and policies supporting the diffusion of alternative engine technologies. The carbon intensity of new vehicles fleet-years can be transformed using two policy-making approaches, from the supply or from the demand side. On the supply side, manufacturers can be bound to reach efficiency targets using schemes such as the Japanese 'top runner' program, while on the demand side, measures can be used to alter consumer choices. Although in an ideal case both approaches would be used simultaneously, in this work we focus on consumer policies such as emissions based taxes. Car purchases are strongly socially determined (Mc-Shane et al., 2012). The substitution of different types of vehicles has elasticities that depend strongly on the distribution of socio-economic characteristics of consumers, which vary across the world. 5 Effective policy making for emissions reductions must take full account of this diversity. If the technical characteristics of private passenger car fleets are highly distributed due to the diversity of owners, then the individual effectiveness of transport policies on consumer choices is also highly distributed, and their aggregate effectiveness is not immediately obvious to predict. A broad understanding of the impacts of emissions reductions policies in transport thus requires a careful assessment of the diversity of market agents in the geographical areas in which they apply.
In this paper, we explore the emissions, technical and economical characteristics of car markets in six major representative economies of the World: the United Kingdom, the United States, China, India, Japan and Brazil. These markets possess very different characteristics that are the result of different histories of policy and regulations, but also different socio-economic characteristics of their populations as well as different cultures. We show that, even with highly globalised car manufacturers, meaning that all technologies can in principle be made available essentially everywhere, the distribution of car purchases and their fuel efficiencies have radically different characteristics in different markets. This leads to two considerations: firstly, different car markets may require different policies for effec-tive emissions reductions. Secondly, differences in characteristics between countries show comparatively what may be realistically achievable elsewhere.
In the Methods section, we first review the literature on the policy effectiveness in the private passenger transport sector. We then introduce concepts for evaluating the effectiveness of transport emissions reduction policies. In the Results section, we present current distributions of new car emissions, engine sizes and prices in each of the six representative countries, for different technologies. This is followed by calculations of correlations between these characteristics (or lack of), from which insight on the effectiveness of policy is derived. In the discussion, we analyse the meaning and implications of the varying vehicle market structures across countries. Finally, in the Policy Implications section we discuss and summarise, based on the evidence presented and supported by calculations presented in the supplementary information (SI), the current likely effectiveness of policies for influencing consumer choices. In Appendix A, we present a calculation method to evaluate more accurately the effectiveness of policy based on datasets such as ours, and in Appendix B we provide country specific policy analyses.

Review of the policy literature
There exists a large amount of literature on the potentials for emissions reductions in the transport sector, originating mostly from the engineering community (as reviewed, for example, in the IPCC, 2014). However, this type of work does not address how such potentials can be achieved with policy, and why little progress is made with existing policies beyond stating the presence of 'behavioural' barriers. For example, authors of WEC (2009) claim that the power of vehicles is a critical parameter for fleet emissions and should be a target for policy, but they do not analyse how consumer choices relate to vehicle power, making their recommendations difficult to interpret in real policy-making terms. Meanwhile, the body of literature concerning the effectiveness of transport policy for emissions reductions is much thinner. Here we review some of the highlights of existing work.
The IEA (2012b) discusses briefly the costs of reducing emissions in the transport sector, which includes Light Duty Vehicles (LDVs). There, cost values appear based on differences between fleet-wide averages, ambiguous for policy-making since one doesn't know a priori which particular vehicles people would purchase in different policy contexts, and the range of prices for new vehicles is extremely wide. The approach is the same in the costoptimisation energy modelling community (e.g. McCollum et al., 2014, Takeshita, 2012, van der Zwaan et al., 2013 where, for instance, without policy the chosen 'representative' electric vehicle models emerge as more expensive than the 'representative' internal combustion engine (ICE) models. This leads modellers to expect low or zero uptake of low emissions vehicles by identical cost-minimising agents unless the average cost difference is bridged by a fiscal policy, a difference between averages over values that, as we show here, span two orders of magnitude. Making abstraction of the distributed nature of prices is most likely not sophisticated enough for modelling the effectiveness of policy on the diffusion of alternative technology or lower emissions vehicles. Considering that many internal combustion engine ICE vehicles recently purchased were more expensive than common electric and hybrid vehicle models (section 3) makes this clear.
Some policy analysis work focuses on evaluating the willingness to pay for higher fuel efficiency (Anderson et al., 2011, Gallagher and Muehlegger, 2011, Greene, 2010, which could be used to project diffusion rates in different policy contexts. However, recent studies do not agree with one another on the average value given by consumers to the fuel economy (25 studies reviewed by Greene, 2010). This may be explained by the fact that some of these only analyse subsets of the market such as the hybrid vehicle market in North America (Gallagher and Muehlegger, 2011). This, as we show below, covers only a restricted range and type of consumers, and thus not representative of the whole market. It is also possible that the influence of the fuel economy in the broader sum of considerations affecting consumer choices, in their respective contexts, may be minor, in other words 'lost in the noise' and difficult to measure. In any case, in the light of the present study, it is most likely the case that the distribution of values that consumers may give to the fuel economy is very broad.
Studies exist that assess the impact of past vehicle emissions reduction policies. Gallachoir et al. (2009) review the impact of recent policies in Ireland on the composition of subsequent fleet-years, explaining the origin of recent of trends in fuel efficiency. They find that recent gains in fuel efficiencies were offset by gradually more frequent choices towards more powerful engines. Zachariadis (2013) finds a similar trend in Germany, where petrol cars were replaced by more powerful diesel cars, leading to compensated fuel efficiencies and emissions. These studies show how important it is to understand the effectiveness of future transport emissions policy in terms of fleet dynamics and distributions of emissions factors.
The most relevant work in this respect was made by He and Bandivadekar (2011), who review current fiscal policies for private passenger transport emissions reduction in eight major economies. It explores their effectiveness in terms of their potential for transforming the fleets, showing the impacts of existing fiscal policies, such as taxes on engine size or emissions or subsidies for low emissions vehicles, on the prices of available models in existing markets. When markets have structures such that the resulting fiscal policy values become an increasing function of emissions, it is explained that an effective incentive emerges, while if the structure is such that no clear function exists, the incentive is ambiguous. The authors thus argue that fiscal policies that do not directly target emissions, such as taxes based on brackets of engine sizes, are not always likely to generate the expected incentive for emissions reductions. This work is very insightful for policy-making, as it directly shows which policies are effective in which context and why, based on a broad view of the market as it is. However as we show here, the study is not as well supported by its data as it could be, which, we argue, is not comprehensive enough. In particular, in order to correctly determine the effectiveness of policy, observations of the actual fleet-years (numbers of vehicles bought by modelyear), rather than enumerations of models available on the market, are necessary. Building on their work, we present here a comprehensive dataset for the 2012 fleet-years in six countries of the world, providing the first empirical analysis of this kind covering all market segments. Figure 1 presents historical data from Euromonitor International (2012) for the registration of new private vehicles (a) and for the size of their fleets (b) in our six representative countries. While the USA has possessed throughout recent history the largest vehicle fleet, with around 0.39 vehicles per capita, registrations have gradually decreased during the last two decades. China, however, sees the largest growth of its car fleet worldwide (20% per year), and will rapidly reach and overtake that of the USA. 6 Note that if China had the current level of per capita car ownership as the USA or the UK, it would have a fleet of over half a billion cars. The second and third fastest growing fleets are the Indian and the Brazilian. The Japanese vehicle fleet is the second largest, and as in the USA, it is roughly constant with decreasing purchases.

Theory for car purchases and behaviour
These vehicle purchases are socially determined. Mc-Shane et al. (2012) makes a remarkable demonstration using correlations spatially resolved using postcode data, showing how vehicle purchases in the USA are visually influenced by previous purchases of similar vehicles locally, but not by purchases that happen at distances where visual influence is weak. This takes place within geographical areas, social identity groups, and within vehicle types and price tiers. The work provides very strong evidence of how vehicle choices are determined by and within social groups, where buyers make decisions within a restricted subset the vehicle market, and that this subset is determined by the social group they belong to. In particular, vehicle purchases of particular types have similar price tags and are strongly influenced by previous purchases of vehicles of similar types and price tags. It emerges from this that any vehicle choice model assumptions where agents seek to minimise their vehicle costs are untenable: agents apparently instead seek to follow their social group and keep their vehicle costs more or less constant. The diversity of social groups in our six major economies is moreover quite different. This is further supported by data in fig. 2, which shows the distribution of income for the whole UK population (extracted from UKDWP, 2013), along with the UK distribution of car purchase prices (this work) multiplied by average car ownership, in 2012. Both datasets are well described by lognormal distributions and a close similarity is observed between their scaling, 7 suggesting a possible proportional relationship, of which the simplest explanation is that particular socio-economic groups purchase vehicles of similar prices. For instance, one may expect that the distribution of car purchases may widen if the income distribution widens, or the reverse, and that spending on vehicles makes a somewhat well-defined fraction of personal or household income. However, the strength of this correlation and its scaling is found to vary across the world, where in some countries, the importance of vehicle purchases relative to other expenditures may differ. 8 6 At the current rate, before 2020, obtained by extrapolating the data of fig. 1 using various methods.
7 The ratio between their mean and their standard deviation or median is nearly the same. 8 E.g. in Japan, the car is losing its significance as an identity symbol and expenditure, and the relationship between income and vehi- In attempts to preserve social identity and status, we may perhaps infer from this that car buyers seek to display their identity, and thus social group characteristics, when purchasing a vehicle (and other goods, an assertion that stems from the anthropology of consumption, seminal work by Douglas and Isherwood, 1979), principles well understood in marketing research. Many stereotypical examples are intuitively understood: it may be unwise to design policies targeting incentivising wealthy middle-aged professionals living in affluent suburbs to purchase low cost economical vehicles designed for families of modest income or for students; meanwhile the access to luxury vehicles to modest income households is most likely barred by either or both cultural and budgetary constraints. While all vehicles possess common features such as wheels, brakes, an engine and a steering mechanism built for the purpose of transporting persons from point A to point B, they also possess characteristics that determine their desirability for particular social groups, and lack of interest in others, aspects reflected in their price tags. The price one is able to pay for a vehicle may be a particularly important channel for the communication of one's social identity (Douglas and Isherwood, 1979), or at the very least it appears from fig. 2 to be an indicator of one's disposable income and social status. If these decisional aspects are important for technology choice, then the diversity of social groups within a nation crucially determines the evolution of the technology composition within any sector that is consumer-based, in particular in transport. Formally, the breadth of consumer diversity determines the elasticities of technology substitution, an assertion that can best be understood using discrete choice theory (for instance in Ben-Akiva and Lerman, 1985). This can be further understood through the lens of diffusion theory (Rogers, 2010), in which the diversity of consumers determine the scaling of the typical S-shaped profile of diffusion.

Theory for evaluating the effectiveness of policy
Emissions reduction policies for private vehicles have an effectiveness that depend on the structure of local vehicle markets. 9 Intuitively, one expects that the fuel efficiency decreases with increasing levels of luxury. For example, fast expensive cars can have comparatively large engine displacement, high power and therefore high emissions. As we find here, however, the price does not always scale with emissions, and we describe below the consequences for the response to consumer policy-making.
Vehicles with large engine displacements have in general higher torque and power (for a review of data see WEC, 2009). For this enhanced power, more fuel (energy) is used and therefore, for any carbon-based fuel (i.e. excluding electricity), higher power means higher emissions per kilometre travelled. 10 We explore this relationship below; even though significant amounts of energy may be used in vehicles for other purposes than movement (e.g. air conditioning, electronics), we find that a relationship between emissions and engine size is always measurable, and it is linear.
Vehicles with larger engine displacements are generally thought more luxurious and expensive than vehicles with small economical engines. This, however, is not always true and, as we find below, depends on particular vehicle markets. As we show below, when it exists, it loglinear. 11 Therefore, whether emissions, or the fuel economy, are functionally related in any particular way with vehicle price depends on these two relationships: between emissions and engine size, and between engine size and price. 12 When it exists, it is also of the log-linear type.
The effectiveness of taxes or subsidies applied on vehicle properties such as engine size or emissions 13 corresponds to their ability to generate substitution between available vehicle models in order to achieve reductions in the emissions of new vehicles. We show here that at the aggregate level, the effectiveness depends on the structure of the market and on whether a relationship between emissions and price exists. If a relationship exists, the effectiveness is closely related to its correlation parameters. If no relationship exists, the aggregate outcome of fiscal policies may not turn out to match what was expected in their design, and high levels of uncertainty remains. Furthermore, given the loglinear structure of the market, an emissions reduction tax 9 By this we mean markets for new vehicles, since the sale of second hand vehicles does not change fleet emissions.
10 Two aspects of driving behaviour predominantly underlie a demand for higher power. For the same travel itinerary, (1) higher constant speeds (wind resistance increases faster than linearly with speed, which thus requires more energy per kilometre the faster the vehicle is driven). (2) higher acceleration (requires more energy since energy losses are proportionally higher at higher engine revolutions required for higher acceleration).
11 The log of the price is a linear function of engine size. 12 There is obviously no particular reason why emissions should be related directly with vehicle price other than through paying for higher power.
13 By this we consider mainly registration taxes at the time of purchase, but road taxes (e.g. UK) or fuel taxes over the life of the vehicle can also be considered. In the latter case, a discount rate would need to be used, reflecting the time preference of the consumer. that produces a significant incentive across the spectrum of vehicles requires a fee that increases with the emissions rating.
This is demonstrated schematically in fig. 3 a and b, in which two fictitious vehicle markets are illustrated using one circle per model, of which the area scales with the number of sales. In a., we have a market where more expensive vehicles have on average proportionally higher fuel consumption, thus a correlation exists. Applying a fiscal policy on engine size or emissions is likely to lead to some emissions reductions if consumers, when replacing a vehicle, attempt to remain within a particular price bracket. By seeking a price reduction to compensate for the tax, they will be forced by the market structure to choose in almost every case lower emissions vehicles. In this case the policy effectiveness is well defined, and is determined by the slope of the relationship. In Appendix A, we derive a mathematical method to determine the most likely choices of consumers given a tax using market data, and demonstrate that the resulting policy effectiveness is equivalent to the slope of regressions in the data, with supporting example calculations in the SI.
In b., we have a situation where no correlation exists between emissions and price. In this case, the aggregate impact of a fiscal policy on emissions is ambiguous and could lead to uncertain changes in emissions. This is because there is a wide range of possible fuel economy values that consumers can access while attempting to choose lower price vehicles to compensate for the tax. In this case the policy effectiveness is potentially ambiguous. We argue here, with supporting numerical evidence given in Appendix A and the SI, that insight on the effectiveness of policy can be obtained from a combination of the strength of the correlation between prices and emissions (the level of confidence that a response to the policy would arise), and the slope of the relationship itself (the strength of the response), which we calculate for our six vehicle markets in section 4. Where the response to fiscal policies is ambiguous, alternative strategies may be considered, including supply side policies.
Meanwhile, emissions can also be influenced using policies supporting changes in engine technologies, such hybrid or electric. The effectiveness of policies for technological change may sometimes be more effective than fiscal policies if the technology targeted has significantly lower or zero emissions, such as support for hybrid or electric vehicles. Currently, however, as we show below with data, most markets do not offer a very wide range of models, which may not have the ability to capture the whole breadth of existing consumer diversity, which thus influences the effectiveness of such policies. This is depicted schematically in panel c., where hypothetical price distributed sales for an alternative technology are shown (in red) along with a typical sales distribution of conventional vehicles. It is very likely that the range of the market that can be expected to be affected by a policy and incentivised for choosing this alternative technology is a restricted segment of the whole market. This can be explained candidly by stating that these vehicle models are too expensive for less wealthy households, while not luxurious enough for very wealthy households. This situation restricts the effectiveness of technological change policy, but may be altered if manufacturers open up a wider choice by producing models and marketing that target all segments of the market.
Vehicle markets, policy and consumer choices clearly coevolve with time (e.g. Geels, 2006). For example, the emergence of sports-utility vehicles (SUVs) in the USA is likely related to the structure of the gas guzzler tax and the CAFE 14 standards, which do not include light duty and pick-up trucks, which has incentivised manufacturers to invent a new vehicle type to circumvent the policies. It is thus clear that the analysis presented is a present day picture which will evolve in the future in this co-evolution manner. While the market structure will likely change, the analysis approach given here however should remain valid.

Results
Sales for new private passenger vehicle were obtained from Marklines (2012) for all six countries except the UK, for which a more detailed dataset was used for new vehicle registrations from the registration agency DVLA (2012a). Entries were matched, model by model, to various data sources, all commercial websites, for vehicle price, engine size and rated emissions: (Car Pages, 2012) (UK), AutoUSA.com (2013) (USA), SohuAuto (2012) and Au-toHome (2013) (China), Zigwheels (2013) and CarWale (2013) (India), and individual car maker websites. For almost all models matched, we thus obtained their price, rated emissions, engine size and the number sold from the combination of only two data sources by model, enabling to look for correlations. We matched in this way over 4200 models across the world. 15 On the commercial websites, prices were given in local currency which were converted to US dollars using current exchange rates from www.XE.com (June 2014). Rated emissions and engine sizes are those provided by the manufacturers. Marklines (2012) numbers were checked for reliability against total sales given by a number of official data sources, and proved to be reliable. We stress that Marklines data are total sales in these countries, not samples. Variations of prices for particular models related to 14 Corporate Average Fuel Economy 15 2212 in the UK, 470 in the USA, 630 in China, 188 in India, 455 in Japan, 335 in Brazil. All data sets cover all types of private passenger vehicles with 4 wheels (i.e. we excluded buses and motorcycles). Where numbers of models are higher, such as in the UK, more variants of similar models were included. In the UK, the DVLA (2012a) database for new registrations has over 29 000 entries, featuring large numbers of entry variants of similar or identical models. In the UK the matching was restricted to entries with sales of more than 100 units, however for other countries, all Marklines data was used. optional features were found to remain most of the time within about 5-10% of the basic model prices. Figure 4 shows distributions of private passenger vehicle prices on linear price axes for 2012 registrations in our six chosen countries. Sales of alternative technologies, hybrid and electric cars, are shown in pink and red respectively. Distributions of sales of alternative technologies were scaled up by different amounts given in the legends for legibility. All graphs have identical abscissa scaling for comparison. All distributions can be parameterised by log-normal distributions. 16 However we considered more appropriate to simply provide average and median prices with their standard deviations ( Table 1).
The distributions of emissions and engine sizes for the same data are shown in figure 4, where engine sizes are given in the insets. Sales of alternative technologies are shown in pink scaled by numbers indicated in the legends for clarity (hybrid only here since electric cars do not have engine displacement volume or emissions). All graphs have identical abscissa scaling for comparability. Average and median emissions and engine sizes, with their standard deviations, are given in Table 1.
Linear univariate correlations between engine sizes and the logarithm of vehicle prices were calculated, shown in the left hand panels of figures 5 and 6. The same was calculated between emissions and engine sizes, middle panels, and between emissions and the logarithm of vehicle prices, in the right hand panels. In these bubble graphs, one circle is shown per model, of which the area is scaled with the root of the number of sales, 17 with associated legends given. The same circle size scaling was used in all graphs. Lines are population weighted linear fits of two variables only, with coefficients of determination R 2 indicated. We did not assume that emissions were correlated with engine sizes and prices simultaneously (the regressions are not multivariate); instead we considered that emissions depend on vehicle prices exclusively through the relationship between emissions and engine sizes. Table .3 gives the parameters of all calculated population weighted correlations, with uncertainty and correlation parameters. Missing values for particular technologies in particular countries (e.g. hybrids in India) indicate low quality or lack of data leading to spurious results (e.g. anticorrelations). Uncertainty values for correlation parameters were obtained using a Monte-Carlo method described in the SI. The last column of Table .3 gives average tax effectiveness per unit of tax paid calculated using the equations of Appendix A, where we determine the most likely choices and substitutions by consumers, given a particular emissions tax, using the same data.

Distributions
Results of this study are remarkable. Firstly, the structures of vehicle markets are completely different across countries. Price distributions ( fig. 5), compared using a common currency, are very different, and not necessarily in a way that would be expected intuitively. For instance, while the price distribution in the UK is roughly similar to that of the USA although reaches higher prices more frequenly, for a relatively similar average level of income and economic development, the distribution in Japan is lower and much narrower. This means that cars in japan are concentrated in more similar and low price brackets, while in the UK and the USA they are distributed over a broader range, and many more expensive cars are bought there. Meanwhile, for the emerging nations, in India and Brazil the distributions are narrow and similar to that of Japan, while the distribution in China is broad, reaches high prices and closer to that in the UK. This is very   likely related to income distribution, culture and social dynamics within those societies, as discussed in section 2.2. However this does not have any clear relationship to GINI coefficients for these countries or other measures of inequality. While a relationship with income distribution apparently exists (as suggested by figure 2), the relationship with inequality is probably more complex, depending also on different histories of taxation, which is not the focus of the present analysis. It is nevertheless remarkable that such disparities exist in different markets that have the same objective, providing means for generating essentially the same transport services.
Significant disparities also exist between distributions of engine sizes across nations, seemingly unrelated to any particular physical or geographical features or constraints. These are also unrelated to differences in price distributions. For example, despite similar price distributions in the UK and the USA, the distribution of engine sizes in the USA covers 1000 to 6000cc, while that of the UK is concentrated between 1000 and 3000cc.
Emissions and engine sizes are correlated in all six nations (see below), and thus the same disparities exist between distributions of emissions across nations. Again, these differences do not completely correlate with those of the price distributions. Cars in the USA have the broadest emissions distribution, while those of Brazil and India are the narrowest, followed by the UK and Japan. The USA has the highest average and median emissions, while Brazil and Japan have the lowest. The comparison between the USA and Japan or the UK is particularly interesting, since levels of wealth are similar and many of the same manufacturers operate in these countries, nevertheless allowing for completely different fleet-year characteristics. The upper end of the emissions distribution in the USA has a value of almost twice that in the UK, Japan or Brazil.
Price distributions of alternative technologies are also very different in these countries. The UK is the nation with the most apparent choice for hybrid cars while it is the USA for electric cars. Japan sees the highest market penetration in absolute numbers for both, however these cover only about the upper half of the market in terms of price. The availability and penetration of alternative technologies in emerging nations is very low, and in India and Brazil the price of hybrid vehicles is prohibitively higher than what people spend on vehicles. This means that in the USA and the UK, most people can access an alternative vehicle technology in price ranges near what they are willing to pay for a vehicle. Meanwhile this is not the case in emerging countries where the market coverage of these technologies is very patchy. Japan is in an intermediate situation.
The emissions distributions of hybrid vehicles have lower averages than those of ICE vehicles, as one would expect.
However their emissions are not always lower than the fleet-year averages, where for example in the USA, many hybrid vehicles have higher emissions than most petrol cars. A similar observation can be made about Japan and the UK. As the availability of technologies in these countries is fairly good, this feature correlates with the fact that emissions of hybrid vehicles sold to consumers purchasing in large engine size brackets (which in some cases, but not always, correlates with high price brackets) are higher than emissions of any vehicles in lower engine power brackets; however emissions of high power hybrids are still lower than those of the vehicles they most likely replace in the same price or engine size brackets. In other words, low emissions large engine size (and often luxury) vehicles in general have higher emissions than the economic vehicles with highest emissions; however we know from McShane et al. (2012) that there is very little sub-stitution between engine size/price brackets that are very different, and therefore one cannot expect vehicles in high engine size or price brackets to ever reach as low emissions as economic vehicles, unless they have zero emissions (i.e. electric).

Correlations
Correlations between emissions and engine sizes exist clearly in all countries, and this is due to this relationship being mostly an engineering one (figures 5 and 6, middle panels, and Table .3, middle columns), where larger engines are more powerful, use more energy (fuel) and therefore produce higher emissions per distance driven. The parameters of these correlations are similar but differ across countries, and this may be related to either or both: (1) additional features coming with higher power vehicles that also use energy, of which the purchase differ between countries, or (2) different levels of technology sophistication in the construction of economy vehicles leading to varying levels of fuel efficiency at similar engine sizes.
However, correlations do not always exist between prices and engine size (or power, left panels). Their strength (the R 2 parameters), when they exist, vary considerably between countries. In particular, while a very clear log-linear relationship exists in the UK, India, Japan and Brazil, the relationships are much weaker in the USA and China. This indicates a clear hierarchy between engine size and prices in vehicle markets in the UK, India, Japan and Brazil, but less so in the USA or China. It thus emerges that in China and the USA, the size of the engine is not a major determinant of the price in manufacturer marketing decisions, while it is elsewhere.
Depending whether relationships exist between prices and engine sizes, the existing relationships between emissions and engine sizes bridges to possible relationships between emissions and prices. Thus, wherever relationships exist between engine sizes and prices, they exist between emissions and prices, and conversely where they don't exist. Thus weak relationship exists between emissions and prices in the USA, and a weak one in China, while it exists in all other countries.
The scaling parameters in these relationships (Table .3) give an indication of what could be the consumer response to fiscal policy in these countries. However, for higher accuracy, it is likely better to use the average effectiveness of policy per average unit tax paid given in the same table, determined using the equations of Appendix A. 18 From there, one expects a higher response to policy in the USA, however with higher uncertainty as well, while in several other countries including the UK, the fleet-year-average effectiveness lies in the area of 0.3-0.4 gCO 2 /km per percent of tax (30-40 gCO 2 /km for 100% tax). This of course has clear implications for fiscal transport policy.
18 Detailed calculation of the numbers in Table .3 are given in the SI.

Conclusion and policy implications
The data and analysis presented in this paper has clear policy implications, which differ by country analysed. Here, we are interested in policies for promoting effective emissions reductions in vehicle fleets through incentivising vehicle choices in six major economies. For this, we have provided tools that can help understand and determine the likely outcome of chosen policies for emissions reductions.
We stress here the distributed nature of the problem in terms of socio-economic variations, which itself partly determines the elasticities of substitution and thus the likely market response to fiscal or technological change policies. Based on previous sociological and anthropological work, we have attempted to provide an understanding of how and why the market response may be determined by microdynamics occurring within social identity groups that are subsets of each society. From this, we have built a theory for the market response to emissions reductions policy in the private passenger vehicle sector, in which the structure of the market itself determines the aggregate outcome of emissions reduction policies. Since vehicle markets are very different across the world, policies likely to be effective will be different in each case.
We have showed that insight on the market response to a fiscal policy (e.g. an emissions-based registration tax) can be obtained using population weighted regressions on vehicle population data by model between their emissions and their prices. If a correlation exists, a market response will likely emerge where emissions decrease, by a magnitude dictated approximately by the slope of the relationship. If no correlation exists, the effectiveness of the policy is potentially ambiguous, and other types of policies, such as complementary technological change or supply side policies, may generate more reliable results. A more accurate method for evaluating the expected market response was given in Appendix A, with detailed calculations provided in the SI.
Re-iterating the conclusion of He and Bandivadekar (2011), both the stringency and the structure of policies are important. Different segments of vehicle markets will respond differently to fiscal policies, due to a simple scaling of the relative value of various cost components of vehicle ownership (e.g. price, fuel, maintenance compared to taxes). But also, different segments may or may not see opportunities for changing type of engine technology (e.g. hybrid or electric) or vehicle efficiency depending whether models exist within the reach of each segment, and whether they are popular. This varies significantly, and Appendix B presents country specific policy analyses. Therefore, technological change policies also face effectiveness challenges that depend on market structures. Where choice is restricted, as is currently the case in most countries, even high magnitude support policies for vehicle types such as electric or hybrid may foster their uptake only in restricted segments, which once again points towards complementary supply side policies to alter the   figure 5 and 6. Units are in (a 1 ) (cc = cubic centimetres, L = litres) cc / log P, (b 2 ) cc, (a 3 ) gCO 2 /km/L, (b 4 ) gCO 2 /km, (a 5 ) gCO 2 /km/log P and (b 6 ) gCO 2 /km. R 2 indicates coefficients of determination expressing the strengths of the correlations. P indicates parameters while ∆P indicates uncertainty on parameters. The last column, ∆E/ ln T , is the effectiveness of fiscal policy, i.e. emissions reductions expected for 100% tax applied, was calculated using the equations of Appendix A, with details given in the SI. Uncertainty values for correlation parameters were obtained using Monte-Carlo analysis, described in the SI.
market structure.

Acknowledgements
The authors wish to thank H. Pollitt, P. Summerton and Miyoshi Hiroaki for highly insightful comments. We thank the Energy Systems Seminar participants for lively discussions on the subject. We acknowledge our respective funders, the Three Guineas Trust (A. Lam) and the UK Engineering and Physical Sciences Research Council (EPSRC), fellowship no EP/K007254/1 (J.-F. Mercure).

Appendix A. Calculating the effectiveness of a fiscal policy
Given knowledge of a market structure, the likely effectiveness of a fiscal policy can be calculated if one assumes the conclusion of McShane et al. (2012) and Douglas and Isherwood (1979), where consumption habits by social groups indicate that consumers are likely to remain in approximately constant price brackets 19 when choosing among vehicles. Thus we assume that when imposing a new tax on the purchase of vehicles based on emissions, the response of consumers will be to choose in an approximate range corresponding, on average, to what their social group would typically purchase, minus the value of the policy tax. We define a symmetric probability distribution (in log scale) f (ln P i − ln P j + ln T j , σ), that determines the approximate region in the (E, ln P ) plane where they will be considering their options. P i is the price of vehicles i considered before the tax comes into force, i.e. current sales. P j is the price of vehicles j that consumers decide to purchase instead once the tax comes into force, however without the tax included. r j = T j − 1 is the vehicle dependent tax rate 20 applied on models j based on their rated emissions E j . In this model therefore, ln P j + ln T j is approximately equal to ln P i , within a range of ±σ, which is the tolerance of consumers for price differences from what they were initially hoping to spend, taken constant in log scale. 21 For consumers who would, before the tax, have purchased vehicle model i, their probability of choosing model j instead will be proportional to the relative popularity of model j, (it's number of sales N j ): In order to normalise this expression correctly, the probability must sum to one, i.e. k P i→k = 1, and thus .

(A.2)
Before the tax was applied, N i consumers per unit time purchased model i. After the tax is applied, these consumers will most likely purchase other models instead (although some may decide to keep the same plan), while other consumers from another price tier will purchase model i. Since there were N i consumers initially considering model i, the number of consumers changing their choice from i to j is thus Consumers who would have purchased model j also have a non-zero probability of purchasing model i (especially if the tax was negative, i.e. a subsidy; this equation must be symmetric under changes of sign of ln T i ), ∆N j→i . We denote The number of changes of choices between model i and j is A new set of vehicle sales when the tax applies can thus be calculated using j ∆N ij + N i . Here, we are interested in calculating the average emissions change related to these change of choices. We therefore add up each choice change's impact on emissions: It is possible to calculate in a similar way the average price difference (before tax) accepted by consumers due to the tax, The cumulative amount of tax applied and paid associated to new choices is calculated differently since the tax value is zero before the tax is applied: This value is approximately equal to an average tax rate r between zero and one. In Table .3, we find values of the ratio ∆E/ln T around 30-40 gCO 2 /km per unit of tax applied, the emissions reductions expected for a 100% tax rate. This means that for example, if the tax paid averaged over the fleet is 10%, then emissions reductions averaged over the fleet-year can be expected to be of about 3-4gCO 2 /km. The emissions change averaged over the whole fleet per unit of tax applied is the ratio of the total emissions change arising as a result of the tax, ∆E, and the total value of tax applied, ln T , the ratio of equations A.6 and A.8. This can be calculated using the data for E, P and N from our dataset, assuming a tolerance of consumers for price deviations σ (the approximate width of their price bracket) and an emissions dependent tax rate T i . A tax based on emissions is normally not function of the vehicle price (as opposed to, for instance, value-added tax VAT), which is in parts what provides a differential incentive to all consumers across the range to choose lower emissions vehicles. However the tax can have any possible structure.
In a hypothetical case where the data displayed a prefect correlation between E and ln P , the value of the ratio ∆E/ln T would be equal to the slope of the E, ln P relationship. 22 However, where the correlation is not perfect, this calculation method is more accurate. In the SI, we show that both the regression and this method agree quantitatively for a large range of possible tax schemes and values of σ.

UK
In the UK vehicle market, a clear hierarchy exists between emissions and vehicle prices. This indicates that a clear measurable response will exist to fiscal policies targeting low emissions vehicles. Either taxing high emissions vehicles or subsidising lower emissions vehicles will effectively incentivise vehicle buyers to alter their choice to lower emissions vehicles within what is available in their own price brackets. In the UK, luxury vehicles can have up to twice higher emissions than low price vehicles, and these prices range between about 15kUSD to 100kUSD. 23 Fiscal policies currently exist since 2001, when reporting of emissions appeared on registration documents, but they are of moderate stringency: (the yearly UK road tax and the first year registration tax He and Bandivadekar, 2011). Nevertheless, average fleet emissions have increased slightly over the last five years, where gradually increasing fuel efficiencies have been counterbalanced by a trend towards purchasing higher power vehicles, pointing at the insufficient stringency of these policies. 24 22 This can be easily shown from equations A.6 and A.8 as follows. In a perfect correlation, points in the (E,ln P ) plane lie exactly on a straight line. For any pair of vehicles, the value of E i − E j , weighted by N i N j (g ij − g ji ), divided by the tax difference (before and after), ln T i , itself equal to the price difference ln P i − ln P j , also weighted by the same factor N i N j (g ij − g ji ), is always equal to the slope of the relationship. If it is true for every possible pair of vehicles, each term ln P i − ln P j can be replaced by its corresponding E i − E j pair times the slope, the equality demonstrated.
23 Roughly £10k to £60k, the highest in our database being a Lamborghini at about £300k) 24 Authors' own statistics using DVLA (2012b), not included here.
Meanwhile, a fairly broad choice exists for alternative vehicle technologies in most market segments. This offers an opportunity to reduce vehicle emissions more radically without requiring very large fiscal policies, as it enables consumers to jump to much lower emissions brackets in a discontinuous manner. For example, both luxury car owners can access low emissions hybrids and economic vehicle owners can access economic hybrid vehicles. However this is not quite the case yet for electric vehicles, a market that yet needs to expand across all market segments. In the case of electric cars, mostly mid-range vehicle owners would respond to technological change support policies such as feebates.

USA
In the USA, no clear relationship exists between emissions and vehicle prices. This is most likely the result of the structure of the CAFE (Corporate Average Fuel Efficiency) standards and the 'gas guzzler tax'. The latter applies a tax on emissions larger than 300 gCO 2 /km but does not cover large engine size light duty trucks such as pick-up trucks and SUVs (He and Bandivadekar, 2011). Meanwhile the first requires manufacturers to meet standards over the averaged fuel efficiency of their fleet-years. The lack of clear fiscal policies for fuel efficiency applied to all vehicles individually have likely shaped the market in terms of manufacturer strategies attempting to avoid the existing regulations (Miyoshi and Kii, 2011).
The lack of relationship between prices and emissions means that the outcome of fiscal policies, although likely very high, is uncertain, possibly indeterminate and ambiguous. Taxing high emissions vehicles may incentivise consumers towards lower emissions, but consumers can also choose lower price vehicles with higher emissions, of which the price difference compensates for the tax, in order to remain in the same price brackets; the lack of market hierarchy concerning fuel efficiency does not force consumers towards lower emissions vehicles as they choose lower price vehicles. This then means that an emissions tax becomes just an ordinary tax without a clear outcome other than increased income for the government, unlikely to be popular. Such a tax, however, if maintained for a long time and applied across the whole range of vehicles, could gradually re-shape the market towards what is found in the UK or elsewhere by structuring consumer and manufacturer choices.
Technological change policy has a higher likelihood of delivering emissions reductions, by targeting lower emissions technologies. Taxes or subsidies that apply only differentially between engine technologies are likely to have a response given that low emissions technologies exist in many market segments, and therefore most consumers can access low emissions models within their price ranges. This already exists of course, with federal tax credits applied to hybrid and alternative fuel vehicles (He and Bandivadekar, 2011). Our conclusion implies that the further develop-ment of markets for low emissions vehicles will likely promote this change.

China
Vehicle ownership on a per capita basis in China is much lower than most developed countries and the world average, and the potential for vehicle population growth is high (Davis et al., 2008, IEA, 2012a. The growth of vehicle ownership in China is extremely fast, and is currently leading to important increases in GHG emissions and pollution from fuel combustion (see fig. 1). Given the existing levels of particulate matter concentrations in Chinese urban settings (for instance see Speed, 2014), change in mobility trends may be required in order to limit or mitigation the health impacts of particulate matter emissions.
Compared to most developed countries, vehicle emissions policies are relatively new for China. China's first fuel consumption standards for passenger vehicles were adopted in 2004. The standard requires that each individual vehicle model comply with fuel consumption regulations such as corporate-average fuel consumption (CAFC) prior to entering the market. Instead of relying on direct charges, China uses specific fuel consumption limits by weight class (see http://Transportpolicy.net). Excise tax is established with the percentage tax rates indexed to engine size. There is a temporary reduction in acquisition tax for vehicles with ≤1.6 L engines (He and Bandivadekar, 2011). If engine sizes or weight classes were highly correlated with prices, taxation on these attributes could effectively cut emissions. However, as shown in figure 5, the diversity of the car market in China produces a weak relationship between vehicle prices and engine sizes or emissions.
Although Chinese fleets have seen deployment of advanced engine technologies, such as boosted gasoline direct injection and variable valve timing, the average fleet technology development level lags those of the EU and US fleets (He and Bandivadekar, 2011). For instance, alternative power train technologies are more widely present in the current market than in recent years, but their penetration occurs at a much slower pace than that in the US (see fig. 4). The market for alternative technologies is patchy, with low overall market penetration. Thus here also the market response to technological change support policies is likely to be patchy in the short run. Technological change policies however could send a signal to manufacturers, which could help better shape the market.

India
The vehicle market in India is highly concentrated towards low cost vehicles, which itself is quite large in absolute numbers. This is related to the income distribution of Indians in comparison to vehicle prices globally and only a subset of the population has access to enough funds or finance to purchase a passenger vehicle. In this context, the vehicle manufacturer Tata released in 2008 its Nano model, the 'World's cheapest car', targeting lower income classes, at a price of 2500USD (Lim et al., 2013). The Tata Nano turned out significantly less popular than the firm expected even given the gigantic size of the targeted market, likely due to a low-cost social stigma in the context of an aspiring lower middle class (Mclain, 2013). It has recently been redesigned with more options, targeting a more expensive class, indicating that even in a very low income context, vehicle ownership of any particular kind may be an expression of a corresponding social status, and no-one apparently wants to be the owner of the 'World's cheapest car'. He and Bandivadekar (2011) review current policies in India. We find from our data that engine sizes are in general quite low in India (especially in comparison to the USA). The relationship between engine size and price is also fairly clear and structured. This means that a policies targeting engine sizes is likely to have some effectiveness. However, given the current situation with the Nano, which features an engine smaller than 700cc, it may be unlikely that the distribution of engine sizes could be shifted to lower values.
Meanwhile, the relationship between emissions and engine sizes is less well determined, likely due to variations in fuel efficiency related to manufacturing quality variations for models of similar engine sizes in low cost vehicles. This produces a relationship between emissions and vehicle prices that is not very well structured. Since access to personal mobility is already comparatively restricted in India, 25 taxing emissions is a policy that is unlikely to gain political momentum.
Therefore technological change policies are probably more likely to gain traction, which could take the form of subsidies for low carbon technologies rather than a tax on emissions. However, this requires availability of low cost low emissions technologies, and this not yet available for most market segments. Low cost electric vehicles could likely transform mobility in India if it can reach middle to low income households, and this would avoid exacerbating significant pollution problems in high density urban areas. 26

Japan
The Japanese car market is extremely well developed, Japanese cars currently making 11% of global production, figure exceeded only by China (25%) and the USA (13%) (Marklines, 2012). Japanese car manufacturers operate 25 1 vehicle per 56 persons, in comparison to 1 per 2.6 in the USA, 1 per 2 in the UK, the highest in our six countries, using data in fig. 1 and population data.
26 Note that two-and three-wheelers are very popular in India, which are not covered by our analysis. Two-and three-wheelers have comparatively low emissions in general due to low body mass, however they have high particulate matter emissions, leading to smog and related health problems (e.g. in Guttikunda and Kopakka, 2014). truly globally and have adapted to most major local vehicle markets, including the USA and Europe. They have led for many years most innovations for road safety and fuel efficiency, which can be partly ascribed to their 'top runner' program (Miyoshi and Kii, 2011). Effectively, in this system, national transport regulations were determined according to the best innovations, promoting significant R&D activity by manufacturers. These innovations subsequently diffused to other nations (such as the USA) where Japanese cars have important market shares, driving competition at that end as well, and promoting technological change world-wide (Miyoshi and Kii, 2011).
The Japanese car market is quite structured with engine sizes scaling with the logarithm of vehicle prices. With a well-defined relationship between emissions and engine sizes, perhaps indicating that most vehicles are near the efficiency limit of their design, and energy use is a function of power use. This is also the case for hybrids, even when calculated separately. Thus emissions scale with the logarithm of the price. This indicates that fiscal policies are likely to have a good degree of effectiveness, and indeed, as emphasised by Miyoshi and Kii (2011), this market has evolved around its own fiscal system of emissions taxes. Its history dates from 1968 (CO emissions), followed by amendments: 1973 (some pollutants not including CO 2 ), 1979 (fuel economy), 1998 (top-runner program for fuel economy) and many further subsequent changes (Miyoshi and Kii, 2011). It currently includes a vehicle acquisition tax differentiated by vehicle segment and tax breaks for alternative technologies (He and Bandivadekar, 2011).
While Japanese brands provide many of the alternative technologies sold worldwide (e.g. the Toyota Prius), the Japanese market for alternative technologies itself does not quite reach all of its own market segments, and thus is not completely developed. There is thus an opportunity for expanding the market for alternative technologies. The penetration, however, of hybrid cars in the upper half of the price distribution is very important. Many electric vehicles can also be found. In such an advanced diffusion state, alternative technologies are in a good position to diffuse further, potentially massively. This indicates that with relatively moderately stringent policies of support for technological change the balance could be tipped very rapidly. It is to be noted that, as it has been the case for decades, the diffusion in Japan of developments made in Japan for alternative vehicle technologies is likely to bring costs down, with learning-by-doing (e.g. Weiss et al., 2012), making these technologies increasingly affordable to the rest of the world.

Brazil
Brazil has a mixture of passenger vehicles that can use petrol, biofuels (ethanol) or both, and diesel. Brazilian sugar cane ethanol offers the advantage, from the environmental viewpoint, to be nearly carbon neutral (von Blot-tnitz and Curran, 2007). 27 Depending on relative prices, many consumers will switch between fuels. Environmental policy for passenger vehicles is not highly sophisticated or particularly oriented towards reducing emissions, featuring only three brackets of engine sizes (He and Bandivadekar, 2011).
The relationships between engine size and vehicle prices, and between emissions and price are clearly structured, with ethanol vehicles emitting clearly less CO 2 but with a similar slope. This offers an opportunity decrease emissions further with fiscal policies on emissions. The penetration of alternative technologies is however only restricted to the high price end, inaccessible to less wealthy households. The development of markets for lower cost alternative engine technology vehicles could bring transport emissions to near zero with high efficiency, through either or both electric car fleets, running on an already low emissions electricity system (e.g. Mercure et al., 2014) or using hybrid vehicles using biofuels. households-below-average-income-1994-1995.pdf van der Zwaan, B., Keppo, I., Johnsson, F., 2013 A. Lam is a PhD student in the Department of Land Economy, University of Cambridge. Her interests concerns modelling the diffusion of new vehicle technologies in global vehicle fleets, and their interaction with the climate and economic systems. (P j < P i ) lead to new emissions higher than old emissions (E j > E i ), although this might not be the majority of cases. This means that there are instances where consumers are able to save money (i.e compensate the tax) with their choice while increasing emissions.
To explore this in more detail, we display similar bubble plots of choices in terms of emissions before and after the tax is enforced, given in the bottom six panels of fig. S.1. Here again, bubbles lying below the solid line indicate emissions reductions, while those above the line indicate emissions increases. We observe that in many instances, emissions do increase; this occurs more frequently the lower the correlation coefficient is. For example, this is prominently the case in the USA, while for the UK, points lie much more closely along the solid line, with a majority lying below.
All the the bubble plots shown are representations of the flows of vehicle choices from categories i towards categories j, denoted ∆N ij in Appendix A. Since each of these movements are associated to both price and emissions values, it is straightforward to display them according to either variables. However noise in the correlations between these variables lead to differences in the position of the circles; the points are shuffled around the graph. In order to determine the average fleet-year emissions reductions that results from a particular tax scheme, one only needs to carry out a weighted average of these movements, i.e. eq. A.6. One can also calculate the weighted average tax rate paid using eq. A.8. The ratio of these two numbers should relate to the scaling of the correlations when the correlations are good, but possibly less so when they are poor. However this may also depend on the choice of consumer tolerance σ.
Resulting Without noise in the correlations and with perfect market coverage in the dataset, we expect in principle (from the argument of section 2.2 and Appendix A) that this quantity should be a constant equal to the slope of the E, ln P relationship, the effectiveness of the fiscal policy.
We observe different behaviour of this quantity in different countries, and changes that relate to the value of the tolerance. When using a low tolerance value, results appear noisy in countries where the data is more aggregated. For example, our dataset features a choice between 2200 vehicle models in the UK, therefore a near to continuous price distribution of choices, which enables to use a low tolerance (consumers more often find models available near the to the amount they were hoping to spend). In this case, the effectiveness of the tax (emissions reductions per unit tax) is nearly constant for any tax value, except at low values, where the calculation approaches a value of zero divided by zero and small amplitude noise leads to a divergence instead of the expected null effectiveness at zero tax. We stress that the UK dataset is formed by an ensemble of vehicle models each available in a good number of variants at slightly different prices. While the DVLA dataset (see main paper) featured around 30k model variants, while our price data featured over 8000 model variants, our data matching between these was limited to 2200 evenly distributed models due to lack of information over their exact correspondence.
Cases of lower quality datasets, as it is the case for India, the data forces a concentration of choices to a small granular set of popular vehicle models, and this choice is not entirely constant as function of the value of the tax (lumpy jumps occur at particular tax values). We observe however that increasing the tolerance damps this effect, as one intuitively expects. Since we know that in reality, most vehicle models are available at a wide number of possible price values depending on particular choices of vehicle options (as with the UK dataset), with better data the calculation would most likely reach a stable value in every case. Table .3 presents values of the average effectiveness of policy per unit tax paid, as obtained from correlations calculations of the main paper, and from the calculation carried out here, in this case for three values of σ of 0.05, 0.1 and 0.2. As σ increases, it is observed that the uncertainty generally tends to decrease. However the boundary values of 0.2 and 0.05 can perhaps be considered unlikely themselves, and therefore values for σ = 0.1 are reported in the main text. All values are roughly consistent with the slopes of the correlations, however these do not always fall within the uncertainty bounds. We consider that the results of the calculation given here are more accurate than the values of the correlations. We thus observe that on average, the effectiveness of policy per average percentage point of tax applied on emissions is of around 40 ± 8 gCO 2 /km per unit tax across countries. This means that at a tax of 100%, a reduction of emissions of 40 gCO 2 /km is expected to take place. However the USA has a much higher response value that the other countries. Excluding america, the value becomes 32 ± 8 gCO 2 /km. These values can be compared to those of the correlations calculated in the main paper. Correlations generate scaling parameters which may be sensitive to the choice of data points within the dataset. In particular, correlations calculated using the whole dataset may not always generate the same values as correlations carried out using subsets of the data. In order to test this, simple Monte Carlo techniques can be used. Here, we calculated the correlation parameters 10 000 times using each time half the number of data existing points chosen randomly. From the outcomes, we carried out statistics in order to determine the uncertainty over the scaling parameters. The frequency count of the outcomes are given in figure S.4 for the case of the E, ln P relationship, from which we derived means and standard deviations. The resulting uncertainty is given in table .3 and in table 2 of the main text. The same was carried out for the other two relationships, with results indicated in table 2 of the main text.   Table .3: Table of parameters and averages of calculation results for the effectiveness of policy. The correlation parameters (in units of emissions reductions per unit tax, gCO 2 /km) and R 2 parameters are the same as those given in the main paper (table 2). The numbers of models correspond to subsets of the data for which values were available for the number of sales, their price, emissions ratings and engine size simultaneously. The last three columns are values of the effectiveness of policy, averaged over all tax scenarios above $5k at 300gCO 2 /km, in units of average emissions reductions per unit of average tax paid, calculated as described above using three values of the tolerance parameter σ. Uncertainty values correspond to two standard deviations.