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

McShane et al 2012 makes a remarkable demonstration, using correlations spatially resolved using postcode data, that 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. This work provides strong evidence of how vehicle choices, determined within social groups, take place within restricted subsets the vehicle market in specific price segments.

This can be directly observed using socio-economic distribution data. Figure 1 shows the 2012 distribution of income for the whole UK population (from UKDWP 2013), along with the 2012 UK distribution of car purchase prices (this work, see below) multiplied by average car ownership. Both datasets are well described by lognormal distributions and a close relationship is observed between their scaling parameters⁵ , suggesting a likely proportional relationship. This indicates that particular socio-economic groups, on average, purchase vehicles of similar prices⁶ .

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Based on this evidence, here we infer that car buyers seek to display their social identity, and thus social group characteristics, when purchasing a vehicle, an assertion supported by socio-anthropological theory (the anthropology of consumption, seminal work by Douglas and Isherwood 1979), principles generally accepted in marketing research. Following the reasoning of Douglas and Isherwood 1979, while all passenger vehicles are built for the purpose of transporting persons, they are marketed for particular social groups at particular prices that match their willingness to pay, and these prices also restrict access to other social groups. The price one is able to pay for a vehicle may be a particularly important channel for the communication of one's social identity, and, as emerges from figure 1, appears to be a good indicator of one's disposable income.

The diversity of social groups within a nation therefore strongly influences the diffusion of innovations in the private transport fleet. Formally, the breadth of consumer diversity determines the elasticities of technology substitution, an assertion that is best understood using discrete choice theory (for instance inBen-Akiva and Lerman 1985). This assertion is consistent with classical diffusion theory (Rogers 2010), in which the diversity of consumers determine the scaling of the typical S-shaped profile of diffusion. It also follows from evolutionary economics, where technology diversity continually increases to ever better match evolving consumer tastes.

Emissions reduction policies targeting private vehicle choices have an effectiveness that depends on the structure of local vehicle markets⁷ . Intuitively, one expects that fuel efficiencies decrease with increasing levels of luxury. As we find here, however, prices do not always scale with emissions, and we describe below the implications to the response of consumers to 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, higher power means higher emissions per kilometre travelled⁸ . 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 is log-linear⁹ . 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. 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 corresponds to their ability to generate substitutions 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 or may not turn out to match what was expected in their design, and high levels of uncertainty remains. Given the log-linear structure of the market, an emissions reduction tax on the purchase price that produces a non-negligible incentive across the spectrum of vehicles requires a fee that increases at least proportionally to the emissions rating. When proportional, it is consistent with the 'polluter pays' principle. Note, however, that with fiscal policies based on the polluter pays principle, according to our data, the incentive comparatively decreases with increasing car price¹⁰ . The effect of taxes on the price of fuels to the choice of vehicles is technically very similar to that of taxes on rated emissions, since the consumer, at purchase time, can only at best estimate future fuel cost using manufacturer rated emissions. Thus we treat them in the same way here. Estimating their effectiveness however requires extra knowledge, or assumptions, on the extent to which consumers evaluate and take consideration of fuel costs over the vehicle's lifetime in their purchasing decisions.

The effectiveness of policy in a diverse market is explained schematically in figures 2(a) and (b), in which two fictitious vehicle markets are illustrated using one circle per vehicle model, of which the area scales with its number of sales. In a., we have a market where exponentially more expensive vehicles have on average proportionally higher fuel consumption. Applying a fiscal policy based on engine sizes or rated emissions is likely to lead to some emissions reductions if consumers, when replacing a vehicle, attempt to remain within a particular price bracket, as the work of McShane et al 2012 suggests they would. By seeking a price reduction to compensate for the tax, consumers are forced by available choice to pick in almost every case lower emissions vehicles. In this case the policy effectiveness is well defined, and is equal to the slope of the relationship. Note that this effect also works in reverse: if their income increases, consumers may seek higher price vehicles, which in turn would have higher emissions. Note also that the effectiveness value is independent of the shape of the chosen relation between the tax value and rated emissions (i.e. proportional or not)¹¹ .

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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 itself ambiguous. Insight on the effectiveness of policy can thus 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).

Meanwhile, emissions can also be influenced using policies supporting changes in engine technologies, such hybrid or electric. Technological change could effectively reduce emissions if alternative engine vehicle models have very low emissions and if they are accessible to most consumers. Currently, however, (see below) 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, restricting their diffusion. The effectiveness of subsidies will be determined by whether they help better match new technologies to consumer tastes in market segments where they can be made attractive. 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. The range of the market that can be expected to be affected by a policy, according to McShane et al 2012, is a restricted segment of the whole market. A subsidy policy changes the market segment in which the technology is being marketed. This restricted effectiveness can be altered in the future if manufacturers succeed in broadening market choice in order to cover more social identity groups.

Finally, we may ask, is the analysis of the impact of a tax on the price of fuels conceptually any different to that for a tax on the price of vehicles proportional to emissions? There is considerable controversy on how buyers of new vehicles take consideration of fuel costs when taking a decision (e.g. Busse et al 2013, OECD 2010). In the consumer's perspective, a fuel tax applies later in time than a tax on vehicle prices. There is no clear evidence to support a claim that high emissions vehicles are scrapped more quickly in situations of a high tax on fuels; it mostly changes their trading value in second hand markets, but they likely remain in the fleet (Busse et al 2013). There is evidence that fuel taxes lead to reductions of car use and associated emissions (Busse et al 2013), which originates from changes in lifestyles, transport modes, load factors and economic impacts, but this subject is outside of the scope of the present paper, which focuses on consumer choices for new vehicles. Thus for our purposes, for a similar tax value, a fuel tax influences the choice of new vehicles in a similar way as a registration tax proportional to emissions.

The extent to which consumers consider fuel costs when choosing a vehicle can be expressed by how much they discount future fuel costs, and the discount rate expresses their time preference. The literature reports values from around 5–10% (Busse et al 2013) to 20, even 40% (OECD 2010), depending how the measurement is done. We show in the SI that fleet averaged lifetime fuel costs are most of the time much lower than fleet averaged car prices. The effectiveness of a tax on fuels, per percent of tax applied, is proportionally lower than a tax on car prices proportional to emissions, by the proportion that fuel costs make in the total cost, which partly depends on the discount rate chosen. Calculations using various rates are given in the SI.

Vehicle markets, policy and consumer choices co-evolve with time (e.g. Geels 2006). It is thus understood that the analysis presented is a present day picture which will evolve as manufacturers, consumers and policies co-evolve. While the market structure will likely change, the short term analysis approach proposed here should remain valid.

Given comprehensive market data, the likely effectiveness of a fiscal policy given above can be calculated using a regression. However, more detailed insight may be obtained with a model of distributed choice dynamics. We assume, as in the above, that when imposing a new tax on the purchase of vehicles based on emissions, the response of consumers will be to compensate the tax with a lower vehicle cost. We define a symmetric probability distribution (in log scale) $f(\mathrm{ln}{P}_{i}-\mathrm{ln}{P}_{j}+\mathrm{ln}{T}_{j},\sigma )$, that determines the approximate region in the $(E,\mathrm{ln}P)$ plane where they search the market. P_i is the price of vehicles i considered before the tax comes into force, 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, and ${r}_{j}={T}_{j}-1$ is the vehicle dependent tax rate applied on models j based on their rated emissions E_j. σ is the tolerance of consumers to price differences, as a fraction of price, that we assume within 5–20%. Following McShane et al 2012, 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):

$$\begin{eqnarray}&&{\mathcal{P}}_{i\to j}={\displaystyle \frac{{N}_{j}f(\mathrm{ln}{P}_{i}-\mathrm{ln}{P}_{j}+\mathrm{ln}{T}_{j})}{{{\displaystyle \sum }}_{k}{N}_{k}f(\mathrm{ln}{P}_{i}-\mathrm{ln}{P}_{k}+\mathrm{ln}{T}_{k})}}.\end{eqnarray} \tag{ 1 }$$

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, 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

$$\begin{eqnarray}&&\Delta {N}_{i\to j}={N}_{i}{N}_{j}{\displaystyle \frac{f(\mathrm{ln}{P}_{i}-\mathrm{ln}{P}_{k}+\mathrm{ln}{T}_{k})}{{{\displaystyle \sum }}_{k}{N}_{k}f(\mathrm{ln}{P}_{i}-\mathrm{ln}{P}_{k}+\mathrm{ln}{T}_{k})}}\Delta t.\end{eqnarray} \tag{ 2 }$$

Consumers who would have purchased model j also have a non-zero probability of purchasing model i ¹² , $\Delta {N}_{j\to i}$. The number of changes of choices between model i and j is

$$\begin{eqnarray}\begin{array}{ccc}\Delta {N}_{{ij}} & = & \Delta {N}_{i\to j}-\Delta {N}_{j\to i},\\ & = & {N}_{i}{N}_{j}\left[{g}_{{ij}}(\mathrm{ln}{T}_{i})-{g}_{{ji}}(\mathrm{ln}{T}_{i})\right]\Delta t,\end{array}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{g}_{{ij}}(\mathrm{ln}{T}_{i})={\displaystyle \frac{f(\mathrm{ln}{P}_{i}-\mathrm{ln}{P}_{k}+\mathrm{ln}{T}_{k})}{{{\displaystyle \sum }}_{k}{N}_{k}f(\mathrm{ln}{P}_{i}-\mathrm{ln}{P}_{k}+\mathrm{ln}{T}_{k})}}.\end{eqnarray} \tag{ 4 }$$

A new set of vehicle sales when the tax applies can be calculated using ${{\displaystyle \sum }}_{j}\Delta {N}_{{ij}}+{N}_{i}$. 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 total fleet-year emissions:

$$\begin{eqnarray}&&\bar{\Delta E}={\displaystyle \frac{1}{{N}_{\mathrm{tot}}}}{\displaystyle \sum }_{{ij}}{E}_{j}\Delta {N}_{{ij}},\quad {N}_{\mathrm{tot}}={\displaystyle \sum }_{i}{N}_{i},\end{eqnarray} \tag{ 5 }$$

The cumulative amount of registration tax applied and paid associated to new choices is calculated differently since the tax value is zero before the tax is applied:

$$\begin{eqnarray}&&\bar{\mathrm{ln}T}={\displaystyle \frac{1}{{N}_{\mathrm{tot}}}}{\displaystyle \sum }_{{ij}}\left(\Delta {N}_{{ij}}+{N}_{i}\right)\mathrm{ln}{T}_{j}.\end{eqnarray} \tag{ 6 }$$

$\bar{\mathrm{ln}T}$ is approximately equal to an average tax rate $\bar{r}$ between zero and one. The value obtained from the ratio $\bar{\Delta E}/\bar{\mathrm{ln}T}$ gives the weighted average emissions reductions per unit of average tax paid that result from consumer choice¹³ .

The breadth of the variations between individual choices and the average $\bar{\Delta E}/\bar{\mathrm{ln}T}$ is obtained using $\delta \bar{\Delta E}=\sqrt{\langle \Delta {E}^{2}\rangle -{\langle \Delta E\rangle }^{2}}$, where $\langle \rangle$ indicates a population weighted average¹⁴ . This may be interpreted as an uncertainty range; however note that it actually corresponds to the standard deviation of a known distribution of individual behaviour, while $\bar{\Delta E}$ is its mean, with significant amounts of variations cancelling in the aggregate. The same calculation is done for engine sizes $\bar{\Delta S}$.

We observe that the structures of vehicle markets are widely different across countries. Within developed nations, while the price distribution in the UK is comparable to that of the USA, the distribution in Japan is lower and narrower. 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, comparable to that in the UK. This is likely related to income distribution, culture and social dynamics within those societies. These variations do not have any clear relationship to GINI coefficients for these countries or other measures of inequality¹⁹ .

We also find disparities between distributions of engine sizes across nations, seemingly unrelated to any particular physical or geographical features or constraints. These are 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 1000–6000cc, while that of the UK is concentrated between 1000 and 3000cc.

We find similar disparities across countries in the distributions of rated emissions. Cars in the USA have the broadest emissions distribution, while Brazil and India have 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 upper end of the emissions distribution in the USA has a value of almost twice that in Brazil or India, and 50% higher than the UK and Japan. These market structure differences are identified as tied to cultural and behavioural characteristics of consumers, but also tied to their regulatory and tax history (including fuel taxes, which are markedly lower in the USA).

Price distributions of alternative technologies are also very different across countries. The UK is the nation with the widest 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 price range. 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 consumers 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. This limits highly the effectiveness of alternative technology support policies such as subsidies.

The emissions distributions of hybrid vehicles have lower averages than those of ICE vehicles. 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 comparatively high, this feature correlates with the fact that emissions of hybrid vehicles sold to consumers purchasing in large engine size 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. It suggests that subsidising hybrid vehicles can lead to increased emissions.

Correlations between emissions and engine sizes exist in all countries, and this is due to this relationship being mostly an engineering one (figures 4 and 5, middle panels, and table 2, 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 vehicles leading to varying levels of fuel efficiency at similar engine sizes.

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However, correlations do not always exist between prices and engine sizes (or power, left panels). Their strength (the R² 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 very weak 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 none 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, although with weaker correlations than with engine sizes. Thus, wherever relationships exist between engine sizes and prices, they exist between emissions and prices, and conversely where they don't exist. Thus very weak relationships exist between emissions and prices in the USA and China, while they are stronger in other countries.

The scaling parameters of these relationships (table 2) indicate the likely consumer response to fiscal policy in these countries, with a confidence measure given by R². However, we consider that more reliable values, along with measures of variations in consumer behaviour, are given by using the average effectiveness of policy per average unit tax paid determined using equations 5 and 6. According to these, one expects a high response to policy of 0.6–0.9 gCO₂ km⁻¹ per percent of average tax in the USA (60–90 gCO₂ km⁻¹ for 100% tax), indicating a very high abatement potential with moderate tax values. Meanwhile in all other countries, the fleet-year-average effectiveness lies in the area of 0.3–0.4 gCO₂ km⁻¹ per percent of average tax. These values agree with those obtained with regressions. It has been suggested that indirect emissions taxes based on engine sizes are less efficient at reducing emissions than direct taxes (He and Bandivadekar 2011). From the consumer choice perspective, this is not supported by our data, where little difference is observed in aggregate between the two tax schemes. Therefore, this assertion is likely to be only true from the supplier perspective, where manufacturers are likely to attempt to circumvent engine size-based taxes by designing vehicles with smaller engines for the same amount of power (e.g. with turbo-chargers).

Negative tax values also lead to increases in emissions by the same factors, suggesting that relative consumer income increases lead to increasing emissions. This can explain current trends of increase in engine sizes in the UK²⁰ , Ireland (Gallachoir et al 2009) and Germany (Zachariadis 2013). Finally, the effectiveness of taxes are orders of magnitude higher in the short term than those obtained when policy only supports the diffusion of alternative engine technologies with subsidies.