TY - JOUR
AU - Zachariadis,, Theodoros
AB - Abstract Vehicle taxation based on CO2 emissions is increasingly being adopted worldwide to shift consumer purchases to low‐carbon cars, yet evidence on its effectiveness and economic impact is limited. We focus on feebate schemes, which impose a fee on high‐carbon vehicles and give a rebate to low‐carbon cars. We estimate demand for passenger cars in Germany and simulate the impact of alternative feebate schemes on emissions, consumer welfare, public revenues and firm profits. We find that revenue‐neutral feebate schemes are welfare decreasing; welfare can only increase with schemes that increase tax revenues at the expense of consumer and producer surplus. Transport is globally the largest final energy consuming sector, accounting for about 19% of worldwide energy consumption and 23% of energy‐related CO2 emissions. These shares are growing; current projections put the sector's carbon emissions at 50% of the total in 2030 and over 80% in 2050 (International Energy Agency, 2009). This increase essentially cancels out any progress towards limiting carbon emissions in other sectors of the global economy. A wide consensus is now emerging that carbon emissions from the transport sector need to be curbed substantially to successfully address the risks associated with global warming. The most widely discussed policy instruments for limiting motor vehicle fuel consumption and CO2 emissions are fuel economy standards, which aim to induce technological progress in vehicle manufacturers; and fuel taxes, which intend to encourage consumers to purchase fuel‐efficient cars (and to limit their use). A third policy option that has been receiving increased attention in Europe and the US is the design of a motor vehicle taxation system that will induce consumers to purchase vehicles with low CO2 emissions. The idea is to use the tax system to change the relative prices of vehicles of different carbon emission levels, thus leading to substitution from high‐emission to low‐emission vehicles. This is the rationale behind recently introduced feebate schemes, which pay a rebate to consumers purchasing a fuel‐efficient vehicle and impose a penalty on those purchasing ‘gas guzzlers’. The feebate system may be a promising policy option because it involves a market‐based instrument that can affect consumer behaviour, in contrast to command‐and‐control regulations that may be economically inefficient. Consumers may adjust their behaviour more easily than car producers, as the latter have to find a difficult (and costly) compromise between regulatory mandates for high fuel economy and consumer willingness to purchase bigger and more powerful (and hence less fuel efficient) cars. If the tax levied per unit of carbon emitted is fixed (i.e. if the tax is a linear function of a vehicle's carbon emissions) this equates marginal compliance costs across car models and manufacturers, thus leading to an efficient outcome (Anderson et al., 2011). In countries that already have significant car taxes in place, the shift to CO2‐based taxation can be designed to be revenue neutral by adjusting existing taxes and is therefore politically more palatable than unpopular fuel taxes. It should be noted, however, that fuel taxes may be more effective because they apply to all cars and because they penalise usage rather than ownership. Feebates apply to newly sold cars only and – like fuel economy standards and unlike fuel taxes – may give rise to rebound effects.1 Most European Union countries currently have in place a CO2‐based component in their calculation of vehicle taxes – either as a part of registration taxes (paid once upon purchase) or of circulation taxes (paid annually).2 Despite the increased use of such schemes, there is little research regarding their appropriate design and impact, especially at the European level. The few existing studies focus on the US, yet the impact of feebate schemes may be different in Europe with its high fuel taxes and relatively more efficient vehicle fleet. The aim of this study is to contribute to the debate by analysing the environmental and economic effects from the hypothetical adoption of a feebate system in Germany. Germany is an important case study because it is the largest European economy and its regulatory initiatives can have a wider impact across the continent. We estimate demand for cars during 2002–8 using three different variants of the widely used nested logit model. We use the estimated demand systems to simulate feebate policies of varying stringency and compute the impact of the various policies on consumer welfare, profits, public revenues and CO2 emissions. With the aid of this model we experiment with different parameters of a potential feebate programme. We introduce a tax for new car purchases that is positive for cars with CO2 emissions over a given emission level (the so‐called pivot point) and negative for cars with emissions lower than this threshold. The tax can be symmetric – meaning equal rates for the positive and negative parts – or asymmetric. We then explore trade‐offs between environmental effectiveness and economic impact. We initially focus on revenue‐neutral schemes that are more likely to be implemented for political reasons. We find that revenue neutrality can be achieved with a low tax rate and a pivot point that is somewhat lower than the current average CO2 emission level of newly sold cars. However, the environmental benefit – when evaluated using conventional measures of the damage caused by emissions – is not enough to make‐up for the loss in consumer and producer surplus induced by the scheme. Hence, a key finding that emerges from our analysis is that revenue‐neutral schemes cannot be welfare improving. We then extend our investigation to identify welfare‐improving schemes. We find that welfare can increase if the pivot point is set at a level that is considerably lower than the current average emission level and the marginal tax rate is not too high, i.e. corresponds to a price of less than 100 euro per tonne of CO2 ⁠. Such a combination increases overall welfare through the combined effect of improved public finances and lower environmental damage through reduced CO2 emissions, despite a decline in consumer and producer surplus. Essentially, for welfare to increase, the feebate must look a lot more like a fee than a rebate; only a small fraction of vehicles should receive rebates. Alternatively, we find that sales and consumer welfare can increase with asymmetric schemes where the tax levied on high‐emitting vehicles is lower than the rebate offered to low‐carbon cars. Our work adds to only a handful of studies of the impact of carbon‐based vehicle taxation. Most work in the area has analysed the US case (Greene et al., 2005; Fischer, 2008). A small number of studies for Europe that have been carried out on behalf of the European Commission, the EU's executive body, have dealt with this issue in an aggregate manner and with simple statistical/econometric methods (European Commission, 2002). A few other studies have made ex post assessments of taxation schemes implemented in specific countries. Some are mostly descriptive (Rogan et al. (2011) for Ireland or Bastard (2010) for France), whereas others use econometric frameworks similar to ours (D'Haultfoeuille et al. (2014) for France and Huse and Lucinda (2014) for Sweden). To our knowledge, ours is the first ex ante econometric analysis of the possible impact of carbon‐based vehicle taxation that conducts a detailed welfare analysis and focuses on the design of schemes that can deliver the desired outcomes.3 At a time when national governments increasingly adopt a CO2‐based element in the calculation of their vehicle taxes, it is important to ensure that policies are properly designed to achieve their stated objectives. Current vehicle taxation policies seem to have been designed with rough approaches and have typically underestimated consumer response. As a result, these policies have proven more successful than initially thought, which in turn has led to a significant loss of public revenues in the Dutch, Irish and French experiences. Our study highlights the trade‐offs between environmental quality, government revenues and consumer and producer surplus that factor into the design of effective policies. 1. Existing Literature The feebate option currently implemented nationwide in Canada and France and to some extent in other European countries4 has been a subject of debate in North America for several years (Greene et al., 2005; Fischer, 2008). Recently, Peters et al. (2008) have discussed issues regarding the design of a feebate system in Europe on the basis of stated preference data from consumer surveys in Switzerland. Moreover, de Haan et al. (2009) have applied an agent‐based microsimulation model of car purchasing consumer behaviour that attempts to account for both direct monetary effects of such a system on consumer behaviour and indirect effects because of gradual changes in consumer preferences. In a recent development, Bunch et al. (2011) have explored the effectiveness of alternative feebate programmes in California with the aid of a dynamic multi‐period optimisation model that simulates car manufacturers' behaviour and consumer response. Liu et al. (2011) have extended this assessment by evaluating the effectiveness of these programmes if implemented across the whole US. Other recent work that is close to ours includes: D'Haultfoeuille et al. (2014), on the impact of the ‘bonus/malus’ feebate system in France; Huse and Lucinda (2014), on the impact of Sweden's green car rebate programme; and Beresteanu and Li (2011), which focuses on federal income tax incentives in the US. Environmental reforms of vehicle taxation schemes are often required to be revenue neutral to make them politically viable. Depending on vehicle tax systems currently in place in each country, revenue neutrality can be achieved in two ways: (i) In countries with registration taxes on all new car purchases (such as numerous European countries), registration taxes can be calculated on the basis of CO2 emissions in a way that equates total revenues of the new tax scheme to that of the previous scheme. This calculation would have to take into account the estimated shifts in market shares of car models because of the response of consumers to tax incentives. (ii) Countries without a registration tax (such as the US, Japan, Canada as well as the car‐producing countries in Europe) implement a feebate system in which consumers receive a rebate when purchasing low‐ CO2 cars or incur an additional fee when purchasing a high‐ CO2 car.5 If the system is properly designed, then total revenues from fees may be approximately equal to governmental payments for rebates. In general, a feebate system is almost equivalent to a fuel economy regulation with flexibility mechanisms, i.e. allowing trading of fuel economy credits across vehicle types and manufacturers (Fischer, 2008). In our econometric analysis we specify and estimate a discrete choice model of demand for differentiated products. We chose to use the nested multi‐nomial logit model (NML) as in Berry (1994) and Verboven (1996) over the random coefficients model developed by Berry et al. (1995) (widely referred to as BLP). The random coefficients model is more flexible but also more computationally demanding. Both models have been used widely to estimate demand and market equilibrium in markets for differentiated products, particularly car markets. The random coefficients model was first used to estimate the impact of policy and environmental changes on market shares by the BLP authors in Pakes et al. (1993). Fershtman et al. (1999) estimated a nested logit model with a single nest and simulated the impact of tax reform in the Israel car market. We opted for the nested logit model because it is easier to estimate and it has been successfully used in many applications. We used a flexible specification that allows for more consumer heterogeneity by specifying two levels of nests, as in Verboven (1996). We estimated several variants of the model that lead to the same qualitative conclusions with regard to the questions we are interested in, even though the estimated demand systems have different characteristics. This is important because – unlike most previous work – our analysis does not seek to evaluate a specific programme but rather to explore a wider range of options. Experimenting with several model variants allows us to be confident that our conclusions do not depend on a particular specification but have more general applicability. 2. Demand Estimation 2.1. Model We employ the widely used multi‐nomial nested logit model to estimate demand for cars. As the model is well‐known we present just a summary here. In each period, consumers face the problem of purchasing one of many available car models or of making no purchase. Each car model j is described by a set of characteristics xj and a price pj ⁠. Consumers have preferences over the characteristics and select the option that delivers the highest level of utility. Products (models) are divided into groups on the basis of some criterion of similarity. This might seem arbitrary but in practice one can often adopt already existing conventions or industry classifications. In the case of cars, different models can be classified as compact, economy, medium, luxury, SUV, MPV, estate and so on. In the two‐level nested logit model employed here, products are divided into groups, indexed by g, and each group g is further divided into subgroups, indexed by h. Most studies employing the NML model to estimate demand for cars use vehicle class (compact, midsize, etc.) as the main criterion for dividing products into groups. In addition, one can specify additional groupings based on product characteristics that are critical in consumer decision making. One such characteristic is engine (and, by extension, fuel) type. Diesel engines are widely used in Europe (unlike the US) and the choice between a petrol and a diesel engine is one of the most important criteria in vehicle choice (Verboven, 2002). We therefore allow for correlation across models using the same engine type. More details are provided in the estimation subsection below. From this choice framework one can derive the following regression equation to be taken to the data:6 ln(sjt)−ln(s0t)=xjt′β−αpjt+σ1ln(sj/h,t)+σ2ln(sh/g,t)+ξjt.(1) Variable sjt is the market share (units sold divided by Mt consumers) of product j in period t; s0t is the share of the outside good; sj/h,t is the share of product j in subgroup h and sh/g,t is the share of all subgroup‐h products in group g. Parameter α represents the marginal utility of income, whereas parameters σ1 and σ2 capture the degree of substitutability among products in the same group/subgroup. McFadden (1978) has shown that the nested logit model with two nests is consistent with random utility maximisation if 0≤σ2≤σ1≤1 ⁠. If σ1=σ2=0 ⁠, an individual's preferences are uncorrelated across all available models and the model reduces to the simple NML. If σ1>0 and σ2=0 are zero, preferences are correlated across cars from the same subgroup. If σ1>0 and σ2>0 ⁠, individual preferences are also correlated across cars from different subgroups within the same group. If σ2→σ1 ⁠, preferences are equally correlated across all cars belonging to the same group, meaning that the second grouping is not needed. If σ1→1 ⁠, cars in the same subgroup become perfect substitutes. If in addition σ2→1 ⁠, all cars in the same group become perfect substitutes. On the supply side, multi‐product firms are assumed to choose prices to maximise total profits from all their products. The first‐order condition under the assumption of Bertrand–Nash equilibrium in prices is given by the following relationship: pjt1+vt=mcjt+α(1+vt)11−σ1−11−σ1−11−σ2sf/h,t−σ21−σ2sf/g,t−sft−1.(2) The first‐order condition implies that price net of value added tax (denoted by vt ⁠) is equal to marginal cost (⁠ mcjt ⁠) plus a markup term. Parameters α, σ1 and σ2 come from the demand equation (1). The term sf/h,t=∑fsj|h,t denotes the share of firm f's products within subgroup h; sf/g,t=∑fsj/g,t denotes the share of firm f's products within group g and sft=∑fsjt represents the share of firm f's products in the potential market. One can proceed by either estimating (1) in isolation or by jointly estimating (1) and (2).7 Joint estimation increases efficiency at the cost of imposing the assumption of Bertrand–Nash pricing. As we have enough data, we opted for simplicity and fewer assumptions and estimated only the demand equation. The estimates of α, σ1 and σ2 from the demand equation are substituted into (2) to recover estimates of marginal cost for each product. To obtain consistent estimates of the demand equation, it is necessary to address the endogeneity of prices and ‘within’ shares. If firms observe unobserved quality ξjt they will take it into account when they set prices. This will induce a positive correlation between price and the error term in an OLS regression, leading to an upwards bias (lower α in absolute terms) in the estimated coefficient. The other endogenous variables are also positively correlated with unobserved quality and the coefficients σ1 and σ2 will also be biased upwards in the OLS case. For this reason, general method of moments or instrumental variable (IV) methods should be used. Further details are provided in subsection 2.3. 2.2. Data Data for the period 2002–8 were obtained from JATO Dynamics, a company specialising in the collection of automotive data worldwide. For every type of car on the market in each year we observe 17 attributes such as vehicle weight, engine displacement, sales volume and sales price. The data are highly disaggregated; two model variants that differ in only one of the 17 attributes (e.g. whether they have climate control or not) are recorded separately. As a result there is a very large number of observations (157,047 in total), some of which correspond to a very small number of units sold. Estimation of the model at this level of disaggregation is not advisable as observations with very low sales are susceptible to measurement or recording errors. Typically in studies of car markets the product is at the level of the model (nameplate), e.g. Ford Focus or Renault Scenic. Given that this choice is somewhat arbitrary but potentially important, we constructed two data sets, each at a different level of aggregation. In the ‘aggregated’ data set a product is defined by the model and engine type (petrol or diesel); this results in 729 unique products or 3,139 observations.8 In the ‘disaggregated’ data set, models were split into separate products on the basis of engine displacement. The rule was to split models based on 100cc increments (1150–1250cc, 1250–1350cc etc.). This roughly doubles the data set to 1,571 products or 6,061 observations. Of the 729 unique products in the aggregated data set, 289 remain a single product in the disaggregated data set, 228 are split into two products and the remaining 212 are split into three products or more. In the aggregated data set, a product is defined by model name and engine type (e.g. ‘Ford Focus, diesel’); in the disaggregated data set engine displacement is added to the description (‘Ford Focus, diesel, 1.6 litres’). Sales assigned to each observation are the total sales of all model variants corresponding to the observation. Price and vehicle characteristics are from the best‐selling variant. Observations with a sales volume of under 50 units in a year, or with a sales price of over € 100,000 or with engine capacity over 5 litres were removed from the data set as they can be considered to be market niches. Non‐passenger cars such as pickups and large vans were also excluded. Summary statistics of key variables for the disaggregated data are provided in Table 1. Table 1 Means of Key Variables Statistics . Engine size (l) . CO2 emission (kg/km) . Power (HP/1000) . Frame (⁠ m2 ⁠) . Sales (units) . Prices (2005€) . Min 0.6 0.081 0.041 3.79 51 6,745 5% 1.2 0.126 0.068 6.05 82 11,998 25% 1.6 0.157 0.102 7.13 319 17,727 50% 2.0 0.187 0.136 7.89 1,030 24,700 75% 2.5 0.227 0.177 8.54 3,321 34,981 95% 4.0 0.293 0.286 9.38 16,184 64,108 Max 5.0 0.440 0.530 10.18 115,451 101,312 Mean 2.14 0.196 0.149 7.79 3,619 28,886 SD 0.80 0.053 0.068 1.03 7,539 15,949 Statistics . Engine size (l) . CO2 emission (kg/km) . Power (HP/1000) . Frame (⁠ m2 ⁠) . Sales (units) . Prices (2005€) . Min 0.6 0.081 0.041 3.79 51 6,745 5% 1.2 0.126 0.068 6.05 82 11,998 25% 1.6 0.157 0.102 7.13 319 17,727 50% 2.0 0.187 0.136 7.89 1,030 24,700 75% 2.5 0.227 0.177 8.54 3,321 34,981 95% 4.0 0.293 0.286 9.38 16,184 64,108 Max 5.0 0.440 0.530 10.18 115,451 101,312 Mean 2.14 0.196 0.149 7.79 3,619 28,886 SD 0.80 0.053 0.068 1.03 7,539 15,949 Sources. JATO Dynamics. These are means over the 6,061 observations of the disaggregated data. Prices are deflated (that is why the upper bound of € 100,000 is exceeded). Frame (often called ‘footprint’ by car regulators) is length × width. Open in new tab Table 1 Means of Key Variables Statistics . Engine size (l) . CO2 emission (kg/km) . Power (HP/1000) . Frame (⁠ m2 ⁠) . Sales (units) . Prices (2005€) . Min 0.6 0.081 0.041 3.79 51 6,745 5% 1.2 0.126 0.068 6.05 82 11,998 25% 1.6 0.157 0.102 7.13 319 17,727 50% 2.0 0.187 0.136 7.89 1,030 24,700 75% 2.5 0.227 0.177 8.54 3,321 34,981 95% 4.0 0.293 0.286 9.38 16,184 64,108 Max 5.0 0.440 0.530 10.18 115,451 101,312 Mean 2.14 0.196 0.149 7.79 3,619 28,886 SD 0.80 0.053 0.068 1.03 7,539 15,949 Statistics . Engine size (l) . CO2 emission (kg/km) . Power (HP/1000) . Frame (⁠ m2 ⁠) . Sales (units) . Prices (2005€) . Min 0.6 0.081 0.041 3.79 51 6,745 5% 1.2 0.126 0.068 6.05 82 11,998 25% 1.6 0.157 0.102 7.13 319 17,727 50% 2.0 0.187 0.136 7.89 1,030 24,700 75% 2.5 0.227 0.177 8.54 3,321 34,981 95% 4.0 0.293 0.286 9.38 16,184 64,108 Max 5.0 0.440 0.530 10.18 115,451 101,312 Mean 2.14 0.196 0.149 7.79 3,619 28,886 SD 0.80 0.053 0.068 1.03 7,539 15,949 Sources. JATO Dynamics. These are means over the 6,061 observations of the disaggregated data. Prices are deflated (that is why the upper bound of € 100,000 is exceeded). Frame (often called ‘footprint’ by car regulators) is length × width. Open in new tab Each vehicle model in our data is assigned to one of 24 market segments. This classification was too detailed for our purposes, so we aggregated up to seven broader segments (small, medium, large, luxury, sport, MPV and SUV). Table 2 shows the average prices, sales, engine capacity and CO2 emissions by vehicle class and engine type. As expected, larger cars have higher CO2 emissions on average. In general, diesel cars have lower CO2 emissions compared to their petrol counterparts due to the higher fuel economy of diesel engines. This car classification (two fuel types and seven segment classes for each fuel type) is the one we use in the demand estimation below. Note also that we have taken into account that the value added tax rate in Germany (variable vt in (2)) was 16% until 31 December 2006 and increased to 19% thereafter. Table 2 Means of Key Variables by Vehicle Class Class . Observations . Engine displacement . CO2 emissions . Sales . Price . Petrol engine Small 705 1.33 0.149 6,466 13.358 Medium 649 1.76 0.182 4,660 19.884 Large 749 2.25 0.212 2,497 29.496 Luxury 412 3.23 0.258 1,179 53.155 SUV 421 2.90 0.268 987 37.229 Sport 408 2.63 0.229 1,444 42.667 MPV 669 1.87 0.198 2,662 22.654 Diesel engine Small 273 1.47 0.122 2,227 15.037 Medium 280 1.84 0.143 7,139 21.376 Large 378 2.13 0.167 7,201 29.315 Luxury 230 2.81 0.213 4,757 50.002 SUV 325 2.68 0.244 2,849 40.343 Sport 49 2.16 0.164 1,211 35.245 MPV 513 1.96 0.172 3,508 25.378 Class . Observations . Engine displacement . CO2 emissions . Sales . Price . Petrol engine Small 705 1.33 0.149 6,466 13.358 Medium 649 1.76 0.182 4,660 19.884 Large 749 2.25 0.212 2,497 29.496 Luxury 412 3.23 0.258 1,179 53.155 SUV 421 2.90 0.268 987 37.229 Sport 408 2.63 0.229 1,444 42.667 MPV 669 1.87 0.198 2,662 22.654 Diesel engine Small 273 1.47 0.122 2,227 15.037 Medium 280 1.84 0.143 7,139 21.376 Large 378 2.13 0.167 7,201 29.315 Luxury 230 2.81 0.213 4,757 50.002 SUV 325 2.68 0.244 2,849 40.343 Sport 49 2.16 0.164 1,211 35.245 MPV 513 1.96 0.172 3,508 25.378 Source. JATO Dynamics. Open in new tab Table 2 Means of Key Variables by Vehicle Class Class . Observations . Engine displacement . CO2 emissions . Sales . Price . Petrol engine Small 705 1.33 0.149 6,466 13.358 Medium 649 1.76 0.182 4,660 19.884 Large 749 2.25 0.212 2,497 29.496 Luxury 412 3.23 0.258 1,179 53.155 SUV 421 2.90 0.268 987 37.229 Sport 408 2.63 0.229 1,444 42.667 MPV 669 1.87 0.198 2,662 22.654 Diesel engine Small 273 1.47 0.122 2,227 15.037 Medium 280 1.84 0.143 7,139 21.376 Large 378 2.13 0.167 7,201 29.315 Luxury 230 2.81 0.213 4,757 50.002 SUV 325 2.68 0.244 2,849 40.343 Sport 49 2.16 0.164 1,211 35.245 MPV 513 1.96 0.172 3,508 25.378 Class . Observations . Engine displacement . CO2 emissions . Sales . Price . Petrol engine Small 705 1.33 0.149 6,466 13.358 Medium 649 1.76 0.182 4,660 19.884 Large 749 2.25 0.212 2,497 29.496 Luxury 412 3.23 0.258 1,179 53.155 SUV 421 2.90 0.268 987 37.229 Sport 408 2.63 0.229 1,444 42.667 MPV 669 1.87 0.198 2,662 22.654 Diesel engine Small 273 1.47 0.122 2,227 15.037 Medium 280 1.84 0.143 7,139 21.376 Large 378 2.13 0.167 7,201 29.315 Luxury 230 2.81 0.213 4,757 50.002 SUV 325 2.68 0.244 2,849 40.343 Sport 49 2.16 0.164 1,211 35.245 MPV 513 1.96 0.172 3,508 25.378 Source. JATO Dynamics. Open in new tab The averages reported in Table 2 mask substantial variability in CO2 emissions of relatively similar cars. Even within the same market segment, CO2 emissions vary by up to a factor of 2. This suggests that appropriate incentives such as vehicle taxation can induce consumers to switch to a low‐ CO2 vehicle in their preferred segment without much utility loss. In the UK it has been assessed that choosing the lowest CO2 emitters in any car market segment can make a difference of about 25% to fuel efficiency and CO2 emissions (King, 2007). The calculation of market shares requires an assumption on potential market size. As is common in the literature, we use the total number of private households in each year, obtained from the UNECE Statistical Database.9 The measure varies from 38,720 thousand (2002) to 40,076 thousand (2008). 2.3. Estimation We experimented extensively to identify the appropriate nesting structure for each data set. For the disaggregated data, engine type and market segment emerged as the most appropriate classifications. We estimated the model using each variable as the group variable and the other as the subgroup variable. Estimation using market segment as the group and engine type as the subgroup produced the relationship σ1<σ2 ⁠, meaning that the particular nesting structure is not consistent with random utility maximisation (McFadden, 1978). The reverse nesting structure (with engine type as the group and market segment as the subgroup) produced σ1>σ2 ⁠, as required for consistency with random utility maximisation. The analysis that follows is based on estimates from this nesting structure. With the aggregated data, the best fitting nesting structure is a single level with engine type as the key variable. As a further test, we experimented with the way price enters the demand equation. Typically price enters linearly because this is consistent with utility maximisation in a discrete choice framework but some studies have also used a logarithmic specification. A logarithmic specification implies constant expenditure and does not seem appropriate for cars, a classic example of discrete choice. On the other hand, if cars are purchased with a loan that is paid back over time, then the constant expenditure implication might not be unreasonable. From an empirical standpoint, the two specifications differ in one important dimension. Elasticities in the linear case are typically much more dispersed than in the logarithmic case and, conversely, implied markups are more dispersed in the logarithmic specification. This is simply because price enters directly in the expression for elasticity in the linear case but not in the logarithmic case. The linear model's implication that elasticities are a linear function of price is recognised to be somewhat problematic.10 Despite the questionable theoretical justification of the logarithmic specification, it provides an opportunity to test whether a tighter range of elasticities has different implications from the other models. We therefore estimated the logarithmic specification using the disaggregated data. In selecting instruments, we followed the standard approach in the literature.11 Specifically, we used the sum of each continuous product characteristic (engine capacity, CO2 emissions, horsepower and frame) and of the constant term over all competing products belonging to the same subgroup. Note that the sum of the constant term is a count of the number of competing products in the subgroup.12 The Anderson canonical correlation LM statistic – a test of the null hypothesis that the model is underidentified – was rejected for all the three models. The Sargan statistic – a test of the null hypothesis that the instruments are valid – is rejected in all three cases; this is common when all instruments are used. As a robustness test, we experimented extensively with subsets of the potential instruments but were unable to obtain alternative estimates that differ qualitatively from the ones we present below. We are thus confident that the results are robust to the choice of instruments. In Table 3 we report estimates of three models: a model using the aggregated data and linear price; and two models using the disaggregated data, one with linear and one with logarithmic price. The aggregate data set did not support a theoretically consistent two‐level nesting structure. We therefore estimated a single‐level model with engine type as the sole nesting variable. With the disaggregate data, the two‐level nesting structure worked well. A Wald test rejects the null hypothesis σ1=σ2 and therefore the single‐level NML. In comparing OLS and IV estimates for both one‐level and two‐level NML models, recall that the OLS estimate of the price coefficient will be biased towards zero if the endogeneity problem exists. This is because price is positively correlated with the error term, which represents unobserved quality. This is clearly the case in all three cases: the coefficient on price drops substantially when we instrument for price. Similarly, the coefficient on the other endogenous variables, the within shares, are positively correlated with unobserved quality and they also drop once we instrument for them. Table 3 Estimates of Demand Equation Variables . Aggregate . Disaggregate linear . Disaggregate ln . OLS . IV . OLS . IV . OLS . IV . α (price) −0.0094* −0.054* −0.0048* −0.038* −0.36* −2.02* (0.00041) (0.0058) (0.00029) (0.0022) (0.011) (0.091) σ1 (group) 0.999* 0.530* 0.99* 0.95* 0.99* 0.84* (0.0015) (0.170) (0.012) (0.016) (0.0011) (0.020) σ2 (subgroup) 0.99* 0.91* 0.98* 0.71* (0.0025) (0.014) (0.0024) (0.020) Engine capacity 0.045* 0.316* −0.17* 0.062* −0.17* 0.046* (0.0052) (0.089) (0.0061) (0.017) (0.0056) (0.019) CO2 emissions 1.86* −3.52 2.53* 1.57* 2.62* 0.37 (0.082) (2.26) (0.066) (0.24) (0.062) (0.33) Horsepower 1.25* 4.62* 1.88* 4.69* 2.35* 5.79* (0.091) (1.32) (0.068) (0.27) (0.065) (0.30) Frame −0.062* 0.058*** −0.047* 0.025* −0.0025 0.28* (0.0033) (0.032) (0.0024) (0.0057) (0.0028) (0.015) Manual gearbox 0.011 −0.15** −0.015* −0.16* −0.020* −0.14* (0.0076) (0.062) (0.0053) (0.013) (0.0049) (0.016) Climate control 0.0043 0.020 0.0028 0.051* 0.027* 0.15* (0.0056) (0.039) (0.0041) (0.0098) (0.0040) (0.015) Constant −3.04* −5.82* −3.00* −3.59* −0.0027 12.90* (0.025) (0.98) (0.019) (0.083) (0.091) (0.77) F‐test 24,727* 262.4* 36,826* 3,134* 41,527* 1,429* Wald test, H0 ⁠: σ1=σ2 29.71* 137.86* Underidentification test 8.70** 102.07* 164.11* Overidentification test 7.84** 821.47* 6.16** Variables . Aggregate . Disaggregate linear . Disaggregate ln . OLS . IV . OLS . IV . OLS . IV . α (price) −0.0094* −0.054* −0.0048* −0.038* −0.36* −2.02* (0.00041) (0.0058) (0.00029) (0.0022) (0.011) (0.091) σ1 (group) 0.999* 0.530* 0.99* 0.95* 0.99* 0.84* (0.0015) (0.170) (0.012) (0.016) (0.0011) (0.020) σ2 (subgroup) 0.99* 0.91* 0.98* 0.71* (0.0025) (0.014) (0.0024) (0.020) Engine capacity 0.045* 0.316* −0.17* 0.062* −0.17* 0.046* (0.0052) (0.089) (0.0061) (0.017) (0.0056) (0.019) CO2 emissions 1.86* −3.52 2.53* 1.57* 2.62* 0.37 (0.082) (2.26) (0.066) (0.24) (0.062) (0.33) Horsepower 1.25* 4.62* 1.88* 4.69* 2.35* 5.79* (0.091) (1.32) (0.068) (0.27) (0.065) (0.30) Frame −0.062* 0.058*** −0.047* 0.025* −0.0025 0.28* (0.0033) (0.032) (0.0024) (0.0057) (0.0028) (0.015) Manual gearbox 0.011 −0.15** −0.015* −0.16* −0.020* −0.14* (0.0076) (0.062) (0.0053) (0.013) (0.0049) (0.016) Climate control 0.0043 0.020 0.0028 0.051* 0.027* 0.15* (0.0056) (0.039) (0.0041) (0.0098) (0.0040) (0.015) Constant −3.04* −5.82* −3.00* −3.59* −0.0027 12.90* (0.025) (0.98) (0.019) (0.083) (0.091) (0.77) F‐test 24,727* 262.4* 36,826* 3,134* 41,527* 1,429* Wald test, H0 ⁠: σ1=σ2 29.71* 137.86* Underidentification test 8.70** 102.07* 164.11* Overidentification test 7.84** 821.47* 6.16** Notes Significance levels *1%, **5%, ***10%. N = 3,139 for the aggregate model and N = 6,061 for the disaggregate. Standard errors are reported in parentheses. Time and country dummies are included but not reported for brevity. Open in new tab Table 3 Estimates of Demand Equation Variables . Aggregate . Disaggregate linear . Disaggregate ln . OLS . IV . OLS . IV . OLS . IV . α (price) −0.0094* −0.054* −0.0048* −0.038* −0.36* −2.02* (0.00041) (0.0058) (0.00029) (0.0022) (0.011) (0.091) σ1 (group) 0.999* 0.530* 0.99* 0.95* 0.99* 0.84* (0.0015) (0.170) (0.012) (0.016) (0.0011) (0.020) σ2 (subgroup) 0.99* 0.91* 0.98* 0.71* (0.0025) (0.014) (0.0024) (0.020) Engine capacity 0.045* 0.316* −0.17* 0.062* −0.17* 0.046* (0.0052) (0.089) (0.0061) (0.017) (0.0056) (0.019) CO2 emissions 1.86* −3.52 2.53* 1.57* 2.62* 0.37 (0.082) (2.26) (0.066) (0.24) (0.062) (0.33) Horsepower 1.25* 4.62* 1.88* 4.69* 2.35* 5.79* (0.091) (1.32) (0.068) (0.27) (0.065) (0.30) Frame −0.062* 0.058*** −0.047* 0.025* −0.0025 0.28* (0.0033) (0.032) (0.0024) (0.0057) (0.0028) (0.015) Manual gearbox 0.011 −0.15** −0.015* −0.16* −0.020* −0.14* (0.0076) (0.062) (0.0053) (0.013) (0.0049) (0.016) Climate control 0.0043 0.020 0.0028 0.051* 0.027* 0.15* (0.0056) (0.039) (0.0041) (0.0098) (0.0040) (0.015) Constant −3.04* −5.82* −3.00* −3.59* −0.0027 12.90* (0.025) (0.98) (0.019) (0.083) (0.091) (0.77) F‐test 24,727* 262.4* 36,826* 3,134* 41,527* 1,429* Wald test, H0 ⁠: σ1=σ2 29.71* 137.86* Underidentification test 8.70** 102.07* 164.11* Overidentification test 7.84** 821.47* 6.16** Variables . Aggregate . Disaggregate linear . Disaggregate ln . OLS . IV . OLS . IV . OLS . IV . α (price) −0.0094* −0.054* −0.0048* −0.038* −0.36* −2.02* (0.00041) (0.0058) (0.00029) (0.0022) (0.011) (0.091) σ1 (group) 0.999* 0.530* 0.99* 0.95* 0.99* 0.84* (0.0015) (0.170) (0.012) (0.016) (0.0011) (0.020) σ2 (subgroup) 0.99* 0.91* 0.98* 0.71* (0.0025) (0.014) (0.0024) (0.020) Engine capacity 0.045* 0.316* −0.17* 0.062* −0.17* 0.046* (0.0052) (0.089) (0.0061) (0.017) (0.0056) (0.019) CO2 emissions 1.86* −3.52 2.53* 1.57* 2.62* 0.37 (0.082) (2.26) (0.066) (0.24) (0.062) (0.33) Horsepower 1.25* 4.62* 1.88* 4.69* 2.35* 5.79* (0.091) (1.32) (0.068) (0.27) (0.065) (0.30) Frame −0.062* 0.058*** −0.047* 0.025* −0.0025 0.28* (0.0033) (0.032) (0.0024) (0.0057) (0.0028) (0.015) Manual gearbox 0.011 −0.15** −0.015* −0.16* −0.020* −0.14* (0.0076) (0.062) (0.0053) (0.013) (0.0049) (0.016) Climate control 0.0043 0.020 0.0028 0.051* 0.027* 0.15* (0.0056) (0.039) (0.0041) (0.0098) (0.0040) (0.015) Constant −3.04* −5.82* −3.00* −3.59* −0.0027 12.90* (0.025) (0.98) (0.019) (0.083) (0.091) (0.77) F‐test 24,727* 262.4* 36,826* 3,134* 41,527* 1,429* Wald test, H0 ⁠: σ1=σ2 29.71* 137.86* Underidentification test 8.70** 102.07* 164.11* Overidentification test 7.84** 821.47* 6.16** Notes Significance levels *1%, **5%, ***10%. N = 3,139 for the aggregate model and N = 6,061 for the disaggregate. Standard errors are reported in parentheses. Time and country dummies are included but not reported for brevity. Open in new tab Engine capacity, horsepower, frame, automatic transmission and climate control are important car attributes and have the expected signs. The coefficient on CO2 emissions was only statistically significant in the disaggregate linear case and is positive, implying that consumers like high emissions vehicles. But the coefficient is also small in magnitude and therefore its economic significance limited. We found the same result when we replaced the CO2 variable with a variable expressing fuel costs per kilometre. This may seem odd but is consistent with our experience with other data sets; the coefficient on emissions (or, equivalently, fuel consumption) is hard to pin down.13 The signs on country dummies (not shown) are also what might be expected; e.g. German cars are more highly regarded than Chinese cars. Public revenue (due to VAT receipts) from sales of the models included in our estimation in the year 2008 was 11.1 billion euro (at 2005 prices) or 3,847 euro per vehicle. Average CO2 emissions are 164 g per km per car. Manufacturer profits are estimated at 12.3 billion euros and consumer welfare (without the constant of integration) is 3.9 billion euro. 2.4. Implications of Estimated Models As the estimated models are going to be used to simulate the impact of price changes, it is important to get a sense of the implied substitution patterns. Table 4 provides the distribution of own price elasticities from each of the three models. We observe that the median elasticity from the aggregate model is 2.7, and 90% of elasticities are in the range 1.5–5.3. These estimates are comparable with existing work. Elasticities from the disaggregate model are substantially higher. This is to be expected because the choice unit is defined at a finer level and therefore some of the choices are very close substitutes to each other. With the linear specification, the median elasticity is 19.5 and a substantial fraction are above 30. The difference with the logarithmic specification is quite striking; here, elasticities are lower overall (although still higher than the aggregate model, as they should be) but they are very tightly packed around the median of 12.5. Both the relative magnitudes and the degree of dispersion of these elasticities are similar to those obtained by Björnerstedt and Verboven (2013), who estimate both a linear and a logarithmic specification and find that elasticities from the linear specification are substantially higher and much more dispersed.14 Table 4 Distribution of Own Price Elasticities from the Three Models . 1% . 10% . 25% . 50% . 75% . 90% . 99% . Aggregate 9.6 5.3 3.8 2.7 1.9 1.5 1.0 Disaggregate linear 67.5 38.3 27.7 19.5 14.1 11.1 7.3 Disaggregate logarithmic 12.6 12.6 12.5 12.5 12.5 12.3 11.6 . 1% . 10% . 25% . 50% . 75% . 90% . 99% . Aggregate 9.6 5.3 3.8 2.7 1.9 1.5 1.0 Disaggregate linear 67.5 38.3 27.7 19.5 14.1 11.1 7.3 Disaggregate logarithmic 12.6 12.6 12.5 12.5 12.5 12.3 11.6 Open in new tab Table 4 Distribution of Own Price Elasticities from the Three Models . 1% . 10% . 25% . 50% . 75% . 90% . 99% . Aggregate 9.6 5.3 3.8 2.7 1.9 1.5 1.0 Disaggregate linear 67.5 38.3 27.7 19.5 14.1 11.1 7.3 Disaggregate logarithmic 12.6 12.6 12.5 12.5 12.5 12.3 11.6 . 1% . 10% . 25% . 50% . 75% . 90% . 99% . Aggregate 9.6 5.3 3.8 2.7 1.9 1.5 1.0 Disaggregate linear 67.5 38.3 27.7 19.5 14.1 11.1 7.3 Disaggregate logarithmic 12.6 12.6 12.5 12.5 12.5 12.3 11.6 Open in new tab To get a sense of cross‐price elasticities, we calculated the absolute changes in sales following a hypothetical 10% increase in the price of Nissan Micra, a model in the small diesel subgroup. The disaggregate linear estimates imply that as a result of this increase, Micra sales will drop by 93 units (rounding off to the nearest integer). This loss of 93 sales will be distributed as follows: 41 to vehicles in the same subgroup, 47 to other diesel categories and 5 to the outside good (no purchase). Substitution to models outside the group (petrol models) amounted to a small fraction of a vehicle. With the disaggregate logarithmic model, sales dropped by 101, with 44 going to the same subgroup, 40 to other diesel, 1 to petrol and 17 to the outside good. With the aggregate model, sales dropped by 20, with 11 going to the same group and 9 to the outside good. To summarise, we estimated three variants of the nested logit model by choosing different levels of data aggregation and different econometric specifications. The models deliver substantially different implications for demand elasticities. This serves as a reminder that every econometric model imposes restrictions that need to be well understood. For our purposes, the variation in outcomes is useful because it allows us to perform our analysis with three different demand systems. If the conclusions from the three cases are similar, then we can state them with greater confidence than if we had a single model. In the next Section we present in detail the counterfactual analysis using the estimates from the disaggregate linear model. At the end of the section we discuss the outcome of the same analysis with each of our other two specifications. 3. Policy Simulations 3.1. Implementation Using the estimated model parameters, we can simulate the implementation of a feebate in the German car market and assess the effects on car sales, prices, public revenues, firm profits, consumer welfare and CO2 emissions. All results presented in this Section show the effect of a hypothetical feebate scheme in the year 2008, the last year covered by our data. This provides a reasonably good indication about eventual changes in car sales in the near future (e.g. in year 2011 or 2012).15 A simple way to proceed would be to assume that the amount of the feebate will be completely passed through to the final price. That is, the final price will change by the amount of the feebate and the producer's markup will remain the same. With this assumption, all one has to do is to plug the new final prices (old price plus feebate) into the demand system to compute counterfactual shares and all other desired quantities. This may provide a good first approximation but a proper analysis should take manufacturers' pricing responses into account. Doing so requires solving for equilibrium prices in the hypothetical scenario where a feebate scheme is introduced. The supply model outlined in subsection 2.1 produces a set of pricing equations: one equation like (2) for each car model. Our counterfactual exercise involves simulating the equilibrium in year 2008, in which there were 912 car models for the disaggregate data set (and 492 for the aggregate one). We therefore have a system of 912 (492) non‐linear equations that need to be solved to produce the 912 (492) prices. The technical details of how this was implemented are described in Appendix A. One point worth mentioning is that the results from the analysis using optimal prices are very similar to those obtained under the assumption of 100% feebate pass‐through. We assume that a feebate Aj is introduced. The VAT rate remains the same as before. The simplest case is that of a symmetric linear tax that is positive for cars with CO2 emissions over a given emission level (the so‐called pivot point) and negative for cars with emissions lower than this threshold: Aj=t(Ej−PP),(3) where Ej is the CO2 emissions level of model j and PP is the pivot point. Both Ej and PP are expressed in grammes of CO2 per kilometre (g/km), t is the tax rate in euro per g/km and Aj is the total tax in euro per car of model j. The rate t is independent of the total amount emitted by the vehicle (linearity) and is the same regardless of whether it is a tax or a subsidy (symmetry). The symmetric linear feebate is theoretically appealing because it imposes equal marginal abatement costs for all manufacturers, thus leading to an economically efficient solution. In practice, asymmetric schemes have been implemented in several countries (Bunch et al. 2011). For this reason, we also consider several asymmetric schemes that have different values for the ‘fee’ and the ‘rebate’ part. It is also possible to simulate schemes with a non‐linear feebate function, but we did not pursue this possibility. It is important to keep in mind the correspondence between a feebate system and an equivalent carbon tax. Assuming that a car travels 200,000 km throughout its lifetime, a rate t = 10 corresponds to a tax of 50 euro per tonne of CO2 ⁠, whereas a rate t = 40 corresponds to a tax of 200 euro per tonne of CO2 ⁠. Although the latter is higher than the usual value used to assess marginal CO2 damage costs (approximately 15–30 euro per tonne CO2 according to Aldy et al. (2010) and Interagency Working Group on Social Cost of Carbon 2010, henceforth IWG), it is comparable to the implied marginal carbon tax rates of some CO2‐based vehicle tax systems currently implemented in European countries.16 3.2. Impact of Feebate Schemes on Prices and Sales To get a better understanding of the demand system, we selected two feebate schemes and calculated their effect on prices, sales and per car revenues by car segment and CO2 emissions class (recall that we are using the estimates from the disaggregated linear model). Results are presented in Table 5 for two revenue‐neutral schemes: a ‘lenient’ one with t = 10 and a ‘stringent’ one with t = 40 (the pivot points are set at 135.2 and 127.7 g/km respectively). We report only the small, medium and large segments that are the most important in terms of sales, as well as the figures for the overall market (labelled ‘All’). We report the median percentage price change among products in each group. In the lenient feebate case price changes are relatively small, from −1.2% for small low‐carbon cars up to +3.0% for medium high‐carbon cars. In the stringent feebate case, the median price change ranges from −2.7% (for small cars with low carbon emissions) to +13.0% (for the highest emissions class of medium cars). Table 5 Change in Prices, Sales and Revenues/Car by Size and Co2 Emission Class . Prices . Sales . Revenues per car . . S . M . L . All . S . M . L . All . S . M . L . All . Lenient scheme (t = 10, PP = 135.2) <130 −1.2 −0.4 −0.3 −1.0 25.1 19.1 24.1 22.9 −11.5 −4.2 −1.9 −8.4 130–160 0.7 0.7 0.7 0.7 3.5 4.6 8.1 5.8 3.7 4.7 3.0 4.5 160–180 2.1 1.8 1.3 1.6 −14.3 −6.9 −10.1 −6.7 14.4 12.4 8.3 9.7 180–200 2.7 2.5 2.0 2.2 −28.9 −21.0 −17.0 −16.2 19.0 16.3 13.1 14.3 >200 3.0 2.8 2.6 −37.1 −39.3 −36.4 20.3 12.4 12.3 All 0.2 1.3 1.8 1.6 10.6 2.9 −3.0 −0.8 −2.3 4.8 4.9 0.8 Stringent scheme (t = 40, PP = 127.7) <130 −2.7 0.04 0.2 −2.0 118.8 72.6 98.0 101.9 −35.1 −7.1 1.6 −24.3 130–160 5.3 4.3 4.0 4.3 1.0 6.1 18.6 9.4 28.8 27.5 17.2 26.6 160‐180 10.2 8.6 6.5 7.8 −53.0 −33.4 −44.4 −34.8 70.5 60.1 39.3 45.7 180–200 12.2 11.2 9.3 10.0 −77.7 −65.7 −60.3 −59.1 85.8 73.8 59.3 63.4 >200 13.0 11.8 11.3 −85.6 −87.0 −84.2 85.9 56.0 50.5 All 3.0 6.6 8.6 7.7 41.0 5.4 −15.9 −3.3 −6.3 21.6 21.1 3.4 . Prices . Sales . Revenues per car . . S . M . L . All . S . M . L . All . S . M . L . All . Lenient scheme (t = 10, PP = 135.2) <130 −1.2 −0.4 −0.3 −1.0 25.1 19.1 24.1 22.9 −11.5 −4.2 −1.9 −8.4 130–160 0.7 0.7 0.7 0.7 3.5 4.6 8.1 5.8 3.7 4.7 3.0 4.5 160–180 2.1 1.8 1.3 1.6 −14.3 −6.9 −10.1 −6.7 14.4 12.4 8.3 9.7 180–200 2.7 2.5 2.0 2.2 −28.9 −21.0 −17.0 −16.2 19.0 16.3 13.1 14.3 >200 3.0 2.8 2.6 −37.1 −39.3 −36.4 20.3 12.4 12.3 All 0.2 1.3 1.8 1.6 10.6 2.9 −3.0 −0.8 −2.3 4.8 4.9 0.8 Stringent scheme (t = 40, PP = 127.7) <130 −2.7 0.04 0.2 −2.0 118.8 72.6 98.0 101.9 −35.1 −7.1 1.6 −24.3 130–160 5.3 4.3 4.0 4.3 1.0 6.1 18.6 9.4 28.8 27.5 17.2 26.6 160‐180 10.2 8.6 6.5 7.8 −53.0 −33.4 −44.4 −34.8 70.5 60.1 39.3 45.7 180–200 12.2 11.2 9.3 10.0 −77.7 −65.7 −60.3 −59.1 85.8 73.8 59.3 63.4 >200 13.0 11.8 11.3 −85.6 −87.0 −84.2 85.9 56.0 50.5 All 3.0 6.6 8.6 7.7 41.0 5.4 −15.9 −3.3 −6.3 21.6 21.1 3.4 Notes Both schemes are revenue neutral. Reported numbers are percentage changes. S, small; M, medium; L, large. Open in new tab Table 5 Change in Prices, Sales and Revenues/Car by Size and Co2 Emission Class . Prices . Sales . Revenues per car . . S . M . L . All . S . M . L . All . S . M . L . All . Lenient scheme (t = 10, PP = 135.2) <130 −1.2 −0.4 −0.3 −1.0 25.1 19.1 24.1 22.9 −11.5 −4.2 −1.9 −8.4 130–160 0.7 0.7 0.7 0.7 3.5 4.6 8.1 5.8 3.7 4.7 3.0 4.5 160–180 2.1 1.8 1.3 1.6 −14.3 −6.9 −10.1 −6.7 14.4 12.4 8.3 9.7 180–200 2.7 2.5 2.0 2.2 −28.9 −21.0 −17.0 −16.2 19.0 16.3 13.1 14.3 >200 3.0 2.8 2.6 −37.1 −39.3 −36.4 20.3 12.4 12.3 All 0.2 1.3 1.8 1.6 10.6 2.9 −3.0 −0.8 −2.3 4.8 4.9 0.8 Stringent scheme (t = 40, PP = 127.7) <130 −2.7 0.04 0.2 −2.0 118.8 72.6 98.0 101.9 −35.1 −7.1 1.6 −24.3 130–160 5.3 4.3 4.0 4.3 1.0 6.1 18.6 9.4 28.8 27.5 17.2 26.6 160‐180 10.2 8.6 6.5 7.8 −53.0 −33.4 −44.4 −34.8 70.5 60.1 39.3 45.7 180–200 12.2 11.2 9.3 10.0 −77.7 −65.7 −60.3 −59.1 85.8 73.8 59.3 63.4 >200 13.0 11.8 11.3 −85.6 −87.0 −84.2 85.9 56.0 50.5 All 3.0 6.6 8.6 7.7 41.0 5.4 −15.9 −3.3 −6.3 21.6 21.1 3.4 . Prices . Sales . Revenues per car . . S . M . L . All . S . M . L . All . S . M . L . All . Lenient scheme (t = 10, PP = 135.2) <130 −1.2 −0.4 −0.3 −1.0 25.1 19.1 24.1 22.9 −11.5 −4.2 −1.9 −8.4 130–160 0.7 0.7 0.7 0.7 3.5 4.6 8.1 5.8 3.7 4.7 3.0 4.5 160–180 2.1 1.8 1.3 1.6 −14.3 −6.9 −10.1 −6.7 14.4 12.4 8.3 9.7 180–200 2.7 2.5 2.0 2.2 −28.9 −21.0 −17.0 −16.2 19.0 16.3 13.1 14.3 >200 3.0 2.8 2.6 −37.1 −39.3 −36.4 20.3 12.4 12.3 All 0.2 1.3 1.8 1.6 10.6 2.9 −3.0 −0.8 −2.3 4.8 4.9 0.8 Stringent scheme (t = 40, PP = 127.7) <130 −2.7 0.04 0.2 −2.0 118.8 72.6 98.0 101.9 −35.1 −7.1 1.6 −24.3 130–160 5.3 4.3 4.0 4.3 1.0 6.1 18.6 9.4 28.8 27.5 17.2 26.6 160‐180 10.2 8.6 6.5 7.8 −53.0 −33.4 −44.4 −34.8 70.5 60.1 39.3 45.7 180–200 12.2 11.2 9.3 10.0 −77.7 −65.7 −60.3 −59.1 85.8 73.8 59.3 63.4 >200 13.0 11.8 11.3 −85.6 −87.0 −84.2 85.9 56.0 50.5 All 3.0 6.6 8.6 7.7 41.0 5.4 −15.9 −3.3 −6.3 21.6 21.1 3.4 Notes Both schemes are revenue neutral. Reported numbers are percentage changes. S, small; M, medium; L, large. Open in new tab The middle columns of Table 5 report the percentage change in total category sales compared to actual sales in year 2008. In each segment, cars belonging to the lowest CO2 emission class (<130 g/km) gain significantly in sales. There is also a sales increase for cars belonging to the second lowest CO2 emission class (130–160 g/km) for the ‘lenient’ case. Total sales of new cars, which amounted to about 2.9 million cars in year 2008, decrease by 0.8% in the lenient feebate case and by 3.3% in the stringent feebate case. This is the primary reason for reduced profits and consumer welfare as will be demonstrated in the next subsection. Substitution across categories is very high, reflecting the high elasticities implied by our estimates. The last set of columns reports changes in total revenue per vehicle. They are negative for the low‐carbon cars with the lenient feebate and for small and medium‐size low‐carbon cars with the stringent feebate. This happens because in the lenient case the pivot point is set to 135.2 and all the low‐carbon cars get a rebate. Similarly for the stringent case almost all small cars have lower emissions than 127.7. Although the overall change in revenues per vehicle is positive, the overall reduction in sales leads to revenue neutrality for both scenarios. 3.3. Welfare Impact of Feebate Schemes In Table 5 we reported results from simulating two revenue‐neutral feebate schemes. Revenue neutrality is an objective that is typically associated with the introduction of feebates, therefore we continue focusing on revenue‐neutral schemes in this subsection. The top part of Table 6 displays the impact of several schemes of this type on consumers, producers and the level of emissions. We first note that the range of values that the pivot point PP can take is relatively limited. This is due to the requirements that the scheme be symmetric and revenue neutral. To understand why, consider a hypothetical world with a continuum of emissions levels and a distribution of sales that is symmetric with respect to emissions levels. Suppose further that market shares are fixed; they cannot change after prices change. For a symmetric linear feebate scheme to be revenue neutral in this world, the pivot point must be exactly equal to the mean level of emissions. This is true for any value of t. Table 6 Simulated Impact of Selected Feebate Schemes Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 135.2 −23.8 −96 −30 −60 −66 (−0.8) (−1.7) (−0.8) (−4.2) (−0.3) 20 132.7 −47.6 −191 −58 −110 −139 (−1.6) (−3.3) (−1.5) (−7.7) (−0.7) 30 130.2 −71.9 −288 −84 −155 −217 (−2.5) (−4.9) (−2.1) (−10.7) (−1.0) 40 127.7 −97.3 −388 −109 −196 −300 (−3.3) (−6.7) (−2.8) (−13.4) (−1.4) 30.7 130 −73.7 −295 −86 −158 −223 (−2.5) (−5.1) (−2.2) (−10.9) (−1.1) 71.6 120 −186.7 −732 −175 −315 −593 (−6.4) (−12.6) (−4.4) (−20.8) (−2.8) Revenue‐neutral asymmetric schemes −10/+20 130.6 −26.3 −106 −34 −66 −74 (−0.9) (−1.8) (−0.8) (−4.6) (−0.3) −20/+10 136.7 −43.5 −175 −52 −101 −127 (−1.5) (−3.0) (−1.3) (−7.0) (−0.6) −5/+20 127.2 −14.4 −58 −19 −38 −39 (−0.5) (−1.0) (−0.5) (−2.7) (−0.2) −20/+5 139.4 −41.0 −165 −49 −95 −119 (−1.4) (−2.8) (−1.2) (−6.6) (−0.6) −10/+30 127.3 −28.2 −114 −36 −70 −80 (−1.0) (−2.0) (−0.9) (−4.9) (−0.4) −30/+10 136.6 −61.8 −248 −72 −134 −185 (−2.1) (−4.3) (−1.8) (−9.3) (−0.9) −5/+30 123.8 −15.4 −62 −21 −41 −43 (−0.5) (−1.1) (−0.5) (−2.9) (−0.2) −30/+5 138.8 −58.8 −236 −67 −127 −176 (−2.0) (−4.1) (−1.7) (−8.8) (−0.8) Welfare‐improving schemes 10 130 −29.1 −118 −37 −62 61 (−1.0) (−2.0) (−0.9) (−4.4) (0.3) 20 120 −73.2 −293 −92 −122 473 (−2.5) (−5.0) (−2.3) (−8.4) (2.2) −2/+3 130.6 −6.0 −24 −8 −14 13 (−0.2) (−0.4) (−0.2) (−1.0) (0.06) −10/+20 123.8 −34.2 −138 −44 −68 141 (−1.2) (−2.4) (−1.1) (−4.7) (0.7) Sales‐increasing schemes 0/+10 120 0.6 3 0.3 −1.5 −31 (0.02) (0.04) (0.01) (−0.1) (−0.15) 0/+10 140 3.8 15 4 −6 −167 (0.1) (0.3) (0.1) (−0.4) (−0.8) 0/+10 160 12.7 52 15 −13 −508 (0.4) (0.9) (0.4) (−0.9) (−2.4) Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 135.2 −23.8 −96 −30 −60 −66 (−0.8) (−1.7) (−0.8) (−4.2) (−0.3) 20 132.7 −47.6 −191 −58 −110 −139 (−1.6) (−3.3) (−1.5) (−7.7) (−0.7) 30 130.2 −71.9 −288 −84 −155 −217 (−2.5) (−4.9) (−2.1) (−10.7) (−1.0) 40 127.7 −97.3 −388 −109 −196 −300 (−3.3) (−6.7) (−2.8) (−13.4) (−1.4) 30.7 130 −73.7 −295 −86 −158 −223 (−2.5) (−5.1) (−2.2) (−10.9) (−1.1) 71.6 120 −186.7 −732 −175 −315 −593 (−6.4) (−12.6) (−4.4) (−20.8) (−2.8) Revenue‐neutral asymmetric schemes −10/+20 130.6 −26.3 −106 −34 −66 −74 (−0.9) (−1.8) (−0.8) (−4.6) (−0.3) −20/+10 136.7 −43.5 −175 −52 −101 −127 (−1.5) (−3.0) (−1.3) (−7.0) (−0.6) −5/+20 127.2 −14.4 −58 −19 −38 −39 (−0.5) (−1.0) (−0.5) (−2.7) (−0.2) −20/+5 139.4 −41.0 −165 −49 −95 −119 (−1.4) (−2.8) (−1.2) (−6.6) (−0.6) −10/+30 127.3 −28.2 −114 −36 −70 −80 (−1.0) (−2.0) (−0.9) (−4.9) (−0.4) −30/+10 136.6 −61.8 −248 −72 −134 −185 (−2.1) (−4.3) (−1.8) (−9.3) (−0.9) −5/+30 123.8 −15.4 −62 −21 −41 −43 (−0.5) (−1.1) (−0.5) (−2.9) (−0.2) −30/+5 138.8 −58.8 −236 −67 −127 −176 (−2.0) (−4.1) (−1.7) (−8.8) (−0.8) Welfare‐improving schemes 10 130 −29.1 −118 −37 −62 61 (−1.0) (−2.0) (−0.9) (−4.4) (0.3) 20 120 −73.2 −293 −92 −122 473 (−2.5) (−5.0) (−2.3) (−8.4) (2.2) −2/+3 130.6 −6.0 −24 −8 −14 13 (−0.2) (−0.4) (−0.2) (−1.0) (0.06) −10/+20 123.8 −34.2 −138 −44 −68 141 (−1.2) (−2.4) (−1.1) (−4.7) (0.7) Sales‐increasing schemes 0/+10 120 0.6 3 0.3 −1.5 −31 (0.02) (0.04) (0.01) (−0.1) (−0.15) 0/+10 140 3.8 15 4 −6 −167 (0.1) (0.3) (0.1) (−0.4) (−0.8) 0/+10 160 12.7 52 15 −13 −508 (0.4) (0.9) (0.4) (−0.9) (−2.4) Notes Reported changes are in levels; percentage changes are in parentheses. Total sales are expressed in thousands. Consumer and producer surplus and emissions costs are expressed in million euro. Government revenues for the welfare‐improving schemes are 154 (+1.4%), 736 (+6.5%), 31(+0.3%) and 255(+2.3%) million euro respectively. Government revenues for the total sales‐improving schemes are −36 (−0.3%), −193 (−1.7%) and −587 (−5.2%) million euro respectively. For the asymmetric schemes, the first number is the fee part and the second number the rebate part. Open in new tab Table 6 Simulated Impact of Selected Feebate Schemes Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 135.2 −23.8 −96 −30 −60 −66 (−0.8) (−1.7) (−0.8) (−4.2) (−0.3) 20 132.7 −47.6 −191 −58 −110 −139 (−1.6) (−3.3) (−1.5) (−7.7) (−0.7) 30 130.2 −71.9 −288 −84 −155 −217 (−2.5) (−4.9) (−2.1) (−10.7) (−1.0) 40 127.7 −97.3 −388 −109 −196 −300 (−3.3) (−6.7) (−2.8) (−13.4) (−1.4) 30.7 130 −73.7 −295 −86 −158 −223 (−2.5) (−5.1) (−2.2) (−10.9) (−1.1) 71.6 120 −186.7 −732 −175 −315 −593 (−6.4) (−12.6) (−4.4) (−20.8) (−2.8) Revenue‐neutral asymmetric schemes −10/+20 130.6 −26.3 −106 −34 −66 −74 (−0.9) (−1.8) (−0.8) (−4.6) (−0.3) −20/+10 136.7 −43.5 −175 −52 −101 −127 (−1.5) (−3.0) (−1.3) (−7.0) (−0.6) −5/+20 127.2 −14.4 −58 −19 −38 −39 (−0.5) (−1.0) (−0.5) (−2.7) (−0.2) −20/+5 139.4 −41.0 −165 −49 −95 −119 (−1.4) (−2.8) (−1.2) (−6.6) (−0.6) −10/+30 127.3 −28.2 −114 −36 −70 −80 (−1.0) (−2.0) (−0.9) (−4.9) (−0.4) −30/+10 136.6 −61.8 −248 −72 −134 −185 (−2.1) (−4.3) (−1.8) (−9.3) (−0.9) −5/+30 123.8 −15.4 −62 −21 −41 −43 (−0.5) (−1.1) (−0.5) (−2.9) (−0.2) −30/+5 138.8 −58.8 −236 −67 −127 −176 (−2.0) (−4.1) (−1.7) (−8.8) (−0.8) Welfare‐improving schemes 10 130 −29.1 −118 −37 −62 61 (−1.0) (−2.0) (−0.9) (−4.4) (0.3) 20 120 −73.2 −293 −92 −122 473 (−2.5) (−5.0) (−2.3) (−8.4) (2.2) −2/+3 130.6 −6.0 −24 −8 −14 13 (−0.2) (−0.4) (−0.2) (−1.0) (0.06) −10/+20 123.8 −34.2 −138 −44 −68 141 (−1.2) (−2.4) (−1.1) (−4.7) (0.7) Sales‐increasing schemes 0/+10 120 0.6 3 0.3 −1.5 −31 (0.02) (0.04) (0.01) (−0.1) (−0.15) 0/+10 140 3.8 15 4 −6 −167 (0.1) (0.3) (0.1) (−0.4) (−0.8) 0/+10 160 12.7 52 15 −13 −508 (0.4) (0.9) (0.4) (−0.9) (−2.4) Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 135.2 −23.8 −96 −30 −60 −66 (−0.8) (−1.7) (−0.8) (−4.2) (−0.3) 20 132.7 −47.6 −191 −58 −110 −139 (−1.6) (−3.3) (−1.5) (−7.7) (−0.7) 30 130.2 −71.9 −288 −84 −155 −217 (−2.5) (−4.9) (−2.1) (−10.7) (−1.0) 40 127.7 −97.3 −388 −109 −196 −300 (−3.3) (−6.7) (−2.8) (−13.4) (−1.4) 30.7 130 −73.7 −295 −86 −158 −223 (−2.5) (−5.1) (−2.2) (−10.9) (−1.1) 71.6 120 −186.7 −732 −175 −315 −593 (−6.4) (−12.6) (−4.4) (−20.8) (−2.8) Revenue‐neutral asymmetric schemes −10/+20 130.6 −26.3 −106 −34 −66 −74 (−0.9) (−1.8) (−0.8) (−4.6) (−0.3) −20/+10 136.7 −43.5 −175 −52 −101 −127 (−1.5) (−3.0) (−1.3) (−7.0) (−0.6) −5/+20 127.2 −14.4 −58 −19 −38 −39 (−0.5) (−1.0) (−0.5) (−2.7) (−0.2) −20/+5 139.4 −41.0 −165 −49 −95 −119 (−1.4) (−2.8) (−1.2) (−6.6) (−0.6) −10/+30 127.3 −28.2 −114 −36 −70 −80 (−1.0) (−2.0) (−0.9) (−4.9) (−0.4) −30/+10 136.6 −61.8 −248 −72 −134 −185 (−2.1) (−4.3) (−1.8) (−9.3) (−0.9) −5/+30 123.8 −15.4 −62 −21 −41 −43 (−0.5) (−1.1) (−0.5) (−2.9) (−0.2) −30/+5 138.8 −58.8 −236 −67 −127 −176 (−2.0) (−4.1) (−1.7) (−8.8) (−0.8) Welfare‐improving schemes 10 130 −29.1 −118 −37 −62 61 (−1.0) (−2.0) (−0.9) (−4.4) (0.3) 20 120 −73.2 −293 −92 −122 473 (−2.5) (−5.0) (−2.3) (−8.4) (2.2) −2/+3 130.6 −6.0 −24 −8 −14 13 (−0.2) (−0.4) (−0.2) (−1.0) (0.06) −10/+20 123.8 −34.2 −138 −44 −68 141 (−1.2) (−2.4) (−1.1) (−4.7) (0.7) Sales‐increasing schemes 0/+10 120 0.6 3 0.3 −1.5 −31 (0.02) (0.04) (0.01) (−0.1) (−0.15) 0/+10 140 3.8 15 4 −6 −167 (0.1) (0.3) (0.1) (−0.4) (−0.8) 0/+10 160 12.7 52 15 −13 −508 (0.4) (0.9) (0.4) (−0.9) (−2.4) Notes Reported changes are in levels; percentage changes are in parentheses. Total sales are expressed in thousands. Consumer and producer surplus and emissions costs are expressed in million euro. Government revenues for the welfare‐improving schemes are 154 (+1.4%), 736 (+6.5%), 31(+0.3%) and 255(+2.3%) million euro respectively. Government revenues for the total sales‐improving schemes are −36 (−0.3%), −193 (−1.7%) and −587 (−5.2%) million euro respectively. For the asymmetric schemes, the first number is the fee part and the second number the rebate part. Open in new tab In reality, the sales distribution is not symmetric; depending on its shape, the pivot point might be higher or lower than the mean. But more importantly, market shares are not fixed. Once a feebate is introduced, sales will shift from high‐emission to low‐emission vehicles. The pivot point would thus have to shift down in order for revenue neutrality to be restored. The higher the tax rate, the lower the pivot point would have to be because there will be greater substitution from high‐emission to low‐emission vehicles. Generally then, the pivot point of a revenue‐neutral linear symmetric scheme would have to be smaller than the mean emissions level and decline slowly with increasing tax rate t. This is indeed what we observe in Table 6. How much lower than the mean emissions level must the pivot point be? This will depend on the elasticities. The more elastic the demand, the greater the substitution due to the feebate, and the lower the pivot has to be to achieve neutrality. Changing relative prices through taxation is distortionary and would be expected to lead to lower consumer and producer surplus relative to the efficient outcome. This is clearly apparent in Table 6. As the tax rate increases and the scheme becomes more distortionary, losses in consumer and producer surplus increase. This is because – as already shown in Table 5 – such a scheme substantially increases the price of most large and medium‐sized cars, thereby reducing car sales in general (displayed in the column headed ‘Total sales’) and leading to a drop in both producer prices (due to lower demand) and consumer welfare (as some consumers avoid purchasing a new car at these prices). Feebate policies can nonetheless be welfare improving if their environmental benefit exceeds the loss in consumer and producer surplus. To quantify this benefit we first need to calculate the reduction in emissions caused by each scheme. We assume that each vehicle will travel 200,000 km during its lifetime and its CO2 emission level will remain constant (at the initial registered level) throughout.17 With these assumptions we can calculate total emissions pre and post‐feebate and compare the two. This, however, is likely to overestimate the reduction in emissions. To see why, note that total emissions from new vehicles are reduced for two reasons: substitution from high‐emission to low‐emission vehicles and, to a lesser extent, reduced sales. The benefit from substitution is obvious. As an example, suppose that the feebate induces a consumer who would have bought a vehicle emitting 180 g/km to purchase instead a vehicle emitting 160 g/km. This switch reduces emissions by four tonnes during the vehicle's lifetime (200,000×(180 − 160)÷1,000). The impact of reduced sales on emissions is not as clear cut. Lower sales will certainly lead to lower emissions from new vehicles. But a consumer who switches out of the market because of the feebate might already own an older, possibly more polluting vehicle that he will continue to use. The calculation above essentially assumes that all consumers who opt out of the market will ride bicycles instead. To avoid this assumption, we adjusted pre‐feebate emissions downwards by a percentage equal to the ratio of post‐feebate to pre‐feebate sales. In other words, if post‐feebate sales were 98% of pre‐feebate sales, then we multiply total pre‐feebate emissions by 98%. This is a more reasonable assumption than the switch‐to‐bicycles assumption described above.18 To compare this benefit to the loss in consumer and producer surplus, we have to express emission reductions in monetary terms. We use the central estimate of a social cost of carbon (SCC) equal to 15 euro (at 2005 prices) per tonne of CO2 provided by expert groups for policy makers.19 According to a standard definition, the SCC is an estimate of the monetised damages associated with an incremental increase in carbon emissions in a given year, to account for adverse economic impacts of climate change to agricultural productivity, human health, natural disasters, so on (see IWG). Multiplying the reduction in emissions by €15 gives the value of the environmental benefit in million euro. The resulting figure, reported in the columns headed ‘Emissions cost’ in Table 6, is clearly less than the sum of consumer and producer surplus lost. For the environmental benefit to make‐up for lost consumer surplus we would require the SSC to be roughly 1.5–2 times bigger than €15/tonne; to make up for the loss in both consumer and producer surplus we would need it to be 2–2.5 times bigger.20 In the second panel of Table 6 we explore several revenue‐neutral asymmetric schemes, all of which also turned out to be welfare decreasing. We were unable to come up with linear schemes that are welfare improving. This is not definitive proof, but our results are highly suggestive that the distortionary cost of revenue‐neutral schemes far exceeds conventional estimates of the environmental benefits achieved. Revenue‐neutral schemes might seem attractive to consumers worried about the government extracting tax revenue from them but they may be oblivious to a much greater distortionary cost imposed by the schemes. This raises an important question: Is it possible to design welfare‐improving feebate schemes? The answer is affirmative. The outcomes of several such schemes are reported in the lower part of Table 6. They differ from the revenue‐neutral schemes examined above in featuring a lower pivot point and a low tax rate. The combination of a low pivot and a low tax rate means that more taxes are paid than rebates are collected, resulting in a net revenue gain for the government that – together with the environmental benefit due to reduced emissions costs – is substantial enough to outweigh the consumer and producer surplus loss. A high tax rate would be counterproductive because it would lead to large shifts from high‐emission to low‐emission vehicles that would generate revenue losses for the government. In other simulations (not reported here) we found that lowering further the pivot point (e.g. to 120 g/km) seems to be welfare improving as well but leads to very large reductions in consumer and producer surplus that may give rise to undesirable general equilibrium effects on the whole economy. Finally, we note that the reduction in emissions attained by the welfare‐improving schemes is relatively modest. The above hold for symmetric schemes; Table 6 shows that asymmetric schemes can also turn out to be welfare improving if the tax levied on high‐emitting vehicles is lower than the rebate offered to low‐carbon cars, thus ensuring a net gain in public tax revenues. Table 6 highlights the key trade‐off involved in carbon taxation: higher taxes reduce emissions but also lower consumer and producer welfare. Environmental effectiveness comes at the detriment of consumer and producer surplus. Nonetheless, it is possible to design a feebate system that can be reasonably effective in terms of reducing CO2 emissions of new cars without being detrimental to overall economic welfare. 3.4. Alternative Demand Specifications We repeated the simulation analysis for the our other demand specifications. The main qualitative conclusions from the disaggregate linear model carry through to the other two cases as well. That is, revenue‐neutral schemes decrease overall welfare; and welfare can only increase by feebates that reduce consumer and producer surplus and substantially raise government revenue. To avoid repetition we will not discuss the other two cases in detail; for the interested reader, full results (equivalent to 6) are provided in Tables Table B1. and Table B2. in Appendix B. Here, we will discuss differences between the three cases that are of interest. Different outcomes in the simulations arise because of differences in elasticities, which are high and dispersed in the main model, somewhat lower and very tight in the logarithmic model, and significantly lower in the aggregate model. As discussed in the beginning of subsection 3.3, this should lead to higher pivot points for the logarithmic model than the main model and even higher for the aggregate model. This is indeed what we observe. In terms of consumer surplus, low elasticities in the aggregate model translate to a smaller impact on total sales and thus also to consumer surplus. Producer surplus is relatively small in the main model (high elasticities mean small markups) and therefore absolute changes are also small. The impact on producer surplus is much greater in the aggregate model (because lower elasticities imply higher markups and greater producer surplus) and even more so in the logarithmic model. Interestingly, producer surplus changes are greater in the logarithmic model than in the aggregate model, even though elasticities are larger; this is because markups are much more dispersed in the logarithmic model. 4. Summary and Conclusions The effectiveness of different policy instruments in reducing the transport sector's carbon emissions is a subject of much interest in academic and policy circles. This study aims to contribute to this debate by providing a rigorous analysis of the impact of feebates, a combination of a tax for high‐carbon vehicles and a rebate for low‐carbon vehicles. Using data from Germany for the period 2002–8, we estimated demand for cars using three variants of the widely used nested logit model. The three demand systems have quite different implications for the level and dispersion of price elasticities; this is a useful reminder of the restrictions imposed by our modelling and data construction choices. Nonetheless, all three demand systems have the same implications with regard to the main questions we are interested in. We can thus be confident that our findings have general applicability. We use our estimates to simulate the impact of various feebate schemes. We first focus on revenue‐neutral schemes that are less likely to face resistance from voters. The analysis shows that the environmental benefit from such schemes is not substantial enough to counterbalance the distortionary effects of taxation, meaning that the schemes are welfare decreasing overall. We find that it is possible to design welfare‐improving schemes by setting a low pivot point and a low tax rate – essentially the ‘fee’ part dominating the ‘rebate’ part. These schemes generate enough government revenue to outweigh the loss in consumer and producer surplus, whereas the environmental benefit remains modest. There are several caveats to the analysis. Perhaps the most important one is that it can only address the short term. It analyses the impact of a policy change in the first year that it is implemented, focusing on consumer response and keeping the supply side fixed. In the longer term manufacturers might respond to this policy by producing more fuel‐efficient vehicles. If this is the case, then our estimates will understate the policy's true impact. Dynamics might also be important on the demand side. If the feebate is temporary – or is perceived to be so by consumers – then the consumer response might be substantially greater than what the model predicts. Consumers who were perhaps considering buying a new fuel‐efficient car in the next couple of years might bring their purchase forward to take advantage of the feebate. Similarly, consumers who were planning on buying a gas guzzler in the year of the rebate might put off their purchase to avoid paying the fee. This will result in a large but temporary shift from high‐emission to low‐emission vehicles. This may be at least part of the explanation behind the strikingly large consumer response in some countries, such as France. Our findings are based on linear schemes. There is clearly vast room for experimentation with non‐linear schemes, but it is hard to see intuitively why non‐linearity could produce different outcomes. An additional consideration is that the impact of feebate‐like schemes takes many years to materialise because they exclusively target new cars. It will take several years (the average life of a vehicle) for the entire car stock to be replaced with vehicles with lower emissions. This is an important disadvantage of feebate schemes relative to fuel taxation, which is levied on the entire car stock. Another caveat is that used vehicles were not included in the demand system because of lack of data. Hence, our model does not capture any substitution from new vehicles to used vehicles due to the introduction of a new tax scheme. Finally, it is always possible to estimate more general models that generate richer substitution patterns. Caveats aside, the analysis is a useful exercise because it highlights and quantifies the trade‐offs involved in the design of an appropriate emissions‐based taxation scheme for new cars. It shows that – if revenue neutrality is a requirement – a car feebate system will probably reduce total economic welfare in the short term. This should not be interpreted, however, as a recommendation against such schemes. A feebate programme, which is a flexible market‐based alternative to fuel economy or CO2 standards, may have a small immediate impact because it addresses only new cars sold in the market. Nonetheless, it can provide a long‐term price signal to both car manufacturers and consumers and hence can induce low‐carbon investments in the car industry. This signal will be even stronger if the system's pivot point decreases over the years, which is equivalent to an increasingly stringent CO2 standard and provides incentives for continuous technological improvements. Appendix: A Simulation Details We need to solve a system of 912 non‐linear equations of the form (2). Matlab's built‐in non‐linear equation solver failed to produce a solution. To circumvent this problem we resorted to contraction mapping techniques. Consider a slightly simplified form of (2) in vector form: P=MC+MU(P).(A.1) The vector of prices P is equal to marginal cost MC plus a markup term MU, which is itself a function of P. We know MC and the functional form MU(P) and we are interested in the unique vector P* that solves (A.1). Define T as the mapping: T(P)=MC+MU(P).(A.2) Suppose we start from an initial vector of prices P0 and repeatedly apply T: Pn=MC+MU(Pn−1)(A.3) Then, if T is a contraction mapping with modulus less than one (more on that below), limn→∞Pn=P* ⁠. In other words, starting from P0 and repeatedly applying T will converge to the unique solution P* ⁠. We conjectured that T is indeed a contraction and applied this procedure to our problem. The method converged to a solution in both the one‐level and the two‐level nested logit. Verifying that the convergence point is a solution to (A.1) is straightforward; one just has to substitute it into (A.1) and verify that the equation holds. Showing that the solution is unique is more difficult. Ideally one would like to establish uniqueness by showing that T is a contraction mapping with modulus less than one. A contraction mapping, or contraction, on a metric space (M,d) is a function T, with the property that there is some non‐negative real number k ∈ (0,1) such that for all P in M, d[T(P),T2(P)]≤kd[P,T(P)] ⁠. We were not able to show that T is a contraction. To ensure that our solution was unique we experimented with different starting points P0 ⁠. The procedure converged to the same solution no matter where we started from, even from out‐of‐the‐way points such as identical prices. This does not constitute formal proof that the solution is unique, yet it is hard to see what another possible solution could lie. We therefore use the solution obtained from this method to conduct the analysis in Section 3. Appendix: B Simulation Results With Different Demand Estimates Table B1 Simulated Impact of Feebate Schemes with Linear Price and Aggregated Data Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 153.5 −6.4 −18 −60 −12 −66 (−0.2) (−0.5) (−0.2) (−0.9) (−0.2) 20 152.6 −14.2 −39 −132 −24 −148 (−0.5) (−1.0) (−0.5) (−1.8) (−0.4) 30 151.6 −23.2 −64 −216 −36 −244 (−0.8) (−1.7) (−0.8) (−2.7) (−0.6) 40 150.7 −33.3 −92 −311 −49 −354 (−1.2) (−2.4) (−1.2) (−3.6) (−0.9) 47.8 150 −41.9 −116 −391 −59 −449 (−1.5) (−3.0) (−1.5) (−4.3) (−1.1) 110 145 −129.8 −353 −1213 −140 −1426 (−4.6) (−9.1) (−4.6) (−9.9) (−3.5) Revenue‐neutral asymmetric schemes −10/+20 146.6 −7.9 −22 −76 −15 −84 (−0.3) (−0.6) (−0.3) (−1.1) (−0.2) −20/+10 159.7 −11.5 −32 −103 −19 −116 (−0.4) (−0.8) (−0.4) (−1.4) (−0.3) −5/+20 140.6 −4.4 −12 −45 −9 −48 (−0.2) (−0.3) (−0.2) (−0.6) (−0.1) −20/+5 167.6 −9.2 −26 −81 −15 −92 (−0.3) (−0.7) (−0.3) (−1.1) (−0.2) −10/+30 142.6 −9.0 −25 −89 −16 −97 (−0.3) (−0.6) (−0.3) (−1.2) (−0.2) −30/+10 163.3 −16.2 −45 −144 −26 −163 (−0.6) (−1.2) (−0.6) (−1.9) (−0.4) −5/+30 136.7 −5.0 −14 −52 −10 −56 (−0.2) (−0.4) (−0.2) (−0.7) (−0.1) −30/+5 171.6 −12.8 −36 −113 −20 −128 (−0.5) (−0.9) (−0.4) (−1.5) (−0.3) Welfare‐improving schemes 5 148 −7.3 −20 −68 −8 3 (−0.3) (−0.5) (−0.3) (−0.6) (0.008) 20 145 −35.5 −98 −329 −34 19 (−1.2) (−2.5) (−1.3) (−2.5) (0.05) −2/+3 145 −3.1 −9 −29 −3 2 (−0.1) (−0.2) (−0.1) (−0.3) (0.004) −10/+20 136.7 −26.1 −72 −243 −22 72 (−0.9) (−1.9) (−0.9) (−1.6) (0.2) Sales‐increasing schemes 0/+10 145 7.2 20 64 −2 −77 (0.3) (0.5) (0.2) (−0.1) (−0.2) 0/+10 155 13.1 37 117 −3 −137 (0.5) (0.9) (0.4) (−0.3) (−0.3) 0/+10 165 21.8 61 197 −6 −220 (0.8) (1.6) (0.8) (−0.5) (−0.5) Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 153.5 −6.4 −18 −60 −12 −66 (−0.2) (−0.5) (−0.2) (−0.9) (−0.2) 20 152.6 −14.2 −39 −132 −24 −148 (−0.5) (−1.0) (−0.5) (−1.8) (−0.4) 30 151.6 −23.2 −64 −216 −36 −244 (−0.8) (−1.7) (−0.8) (−2.7) (−0.6) 40 150.7 −33.3 −92 −311 −49 −354 (−1.2) (−2.4) (−1.2) (−3.6) (−0.9) 47.8 150 −41.9 −116 −391 −59 −449 (−1.5) (−3.0) (−1.5) (−4.3) (−1.1) 110 145 −129.8 −353 −1213 −140 −1426 (−4.6) (−9.1) (−4.6) (−9.9) (−3.5) Revenue‐neutral asymmetric schemes −10/+20 146.6 −7.9 −22 −76 −15 −84 (−0.3) (−0.6) (−0.3) (−1.1) (−0.2) −20/+10 159.7 −11.5 −32 −103 −19 −116 (−0.4) (−0.8) (−0.4) (−1.4) (−0.3) −5/+20 140.6 −4.4 −12 −45 −9 −48 (−0.2) (−0.3) (−0.2) (−0.6) (−0.1) −20/+5 167.6 −9.2 −26 −81 −15 −92 (−0.3) (−0.7) (−0.3) (−1.1) (−0.2) −10/+30 142.6 −9.0 −25 −89 −16 −97 (−0.3) (−0.6) (−0.3) (−1.2) (−0.2) −30/+10 163.3 −16.2 −45 −144 −26 −163 (−0.6) (−1.2) (−0.6) (−1.9) (−0.4) −5/+30 136.7 −5.0 −14 −52 −10 −56 (−0.2) (−0.4) (−0.2) (−0.7) (−0.1) −30/+5 171.6 −12.8 −36 −113 −20 −128 (−0.5) (−0.9) (−0.4) (−1.5) (−0.3) Welfare‐improving schemes 5 148 −7.3 −20 −68 −8 3 (−0.3) (−0.5) (−0.3) (−0.6) (0.008) 20 145 −35.5 −98 −329 −34 19 (−1.2) (−2.5) (−1.3) (−2.5) (0.05) −2/+3 145 −3.1 −9 −29 −3 2 (−0.1) (−0.2) (−0.1) (−0.3) (0.004) −10/+20 136.7 −26.1 −72 −243 −22 72 (−0.9) (−1.9) (−0.9) (−1.6) (0.2) Sales‐increasing schemes 0/+10 145 7.2 20 64 −2 −77 (0.3) (0.5) (0.2) (−0.1) (−0.2) 0/+10 155 13.1 37 117 −3 −137 (0.5) (0.9) (0.4) (−0.3) (−0.3) 0/+10 165 21.8 61 197 −6 −220 (0.8) (1.6) (0.8) (−0.5) (−0.5) Notes Government revenues for the welfare‐improving schemes are 83 (+0.8%), 412 (+3.9%), 36 (+0.3%) and 364(+3.4%) million euro respectively. Government revenues for the total sales‐improving schemes are −160 (−1.5%), −287 (−2.7%) and −472 (−4.5%) million euro respectively. Open in new tab Table B1 Simulated Impact of Feebate Schemes with Linear Price and Aggregated Data Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 153.5 −6.4 −18 −60 −12 −66 (−0.2) (−0.5) (−0.2) (−0.9) (−0.2) 20 152.6 −14.2 −39 −132 −24 −148 (−0.5) (−1.0) (−0.5) (−1.8) (−0.4) 30 151.6 −23.2 −64 −216 −36 −244 (−0.8) (−1.7) (−0.8) (−2.7) (−0.6) 40 150.7 −33.3 −92 −311 −49 −354 (−1.2) (−2.4) (−1.2) (−3.6) (−0.9) 47.8 150 −41.9 −116 −391 −59 −449 (−1.5) (−3.0) (−1.5) (−4.3) (−1.1) 110 145 −129.8 −353 −1213 −140 −1426 (−4.6) (−9.1) (−4.6) (−9.9) (−3.5) Revenue‐neutral asymmetric schemes −10/+20 146.6 −7.9 −22 −76 −15 −84 (−0.3) (−0.6) (−0.3) (−1.1) (−0.2) −20/+10 159.7 −11.5 −32 −103 −19 −116 (−0.4) (−0.8) (−0.4) (−1.4) (−0.3) −5/+20 140.6 −4.4 −12 −45 −9 −48 (−0.2) (−0.3) (−0.2) (−0.6) (−0.1) −20/+5 167.6 −9.2 −26 −81 −15 −92 (−0.3) (−0.7) (−0.3) (−1.1) (−0.2) −10/+30 142.6 −9.0 −25 −89 −16 −97 (−0.3) (−0.6) (−0.3) (−1.2) (−0.2) −30/+10 163.3 −16.2 −45 −144 −26 −163 (−0.6) (−1.2) (−0.6) (−1.9) (−0.4) −5/+30 136.7 −5.0 −14 −52 −10 −56 (−0.2) (−0.4) (−0.2) (−0.7) (−0.1) −30/+5 171.6 −12.8 −36 −113 −20 −128 (−0.5) (−0.9) (−0.4) (−1.5) (−0.3) Welfare‐improving schemes 5 148 −7.3 −20 −68 −8 3 (−0.3) (−0.5) (−0.3) (−0.6) (0.008) 20 145 −35.5 −98 −329 −34 19 (−1.2) (−2.5) (−1.3) (−2.5) (0.05) −2/+3 145 −3.1 −9 −29 −3 2 (−0.1) (−0.2) (−0.1) (−0.3) (0.004) −10/+20 136.7 −26.1 −72 −243 −22 72 (−0.9) (−1.9) (−0.9) (−1.6) (0.2) Sales‐increasing schemes 0/+10 145 7.2 20 64 −2 −77 (0.3) (0.5) (0.2) (−0.1) (−0.2) 0/+10 155 13.1 37 117 −3 −137 (0.5) (0.9) (0.4) (−0.3) (−0.3) 0/+10 165 21.8 61 197 −6 −220 (0.8) (1.6) (0.8) (−0.5) (−0.5) Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 153.5 −6.4 −18 −60 −12 −66 (−0.2) (−0.5) (−0.2) (−0.9) (−0.2) 20 152.6 −14.2 −39 −132 −24 −148 (−0.5) (−1.0) (−0.5) (−1.8) (−0.4) 30 151.6 −23.2 −64 −216 −36 −244 (−0.8) (−1.7) (−0.8) (−2.7) (−0.6) 40 150.7 −33.3 −92 −311 −49 −354 (−1.2) (−2.4) (−1.2) (−3.6) (−0.9) 47.8 150 −41.9 −116 −391 −59 −449 (−1.5) (−3.0) (−1.5) (−4.3) (−1.1) 110 145 −129.8 −353 −1213 −140 −1426 (−4.6) (−9.1) (−4.6) (−9.9) (−3.5) Revenue‐neutral asymmetric schemes −10/+20 146.6 −7.9 −22 −76 −15 −84 (−0.3) (−0.6) (−0.3) (−1.1) (−0.2) −20/+10 159.7 −11.5 −32 −103 −19 −116 (−0.4) (−0.8) (−0.4) (−1.4) (−0.3) −5/+20 140.6 −4.4 −12 −45 −9 −48 (−0.2) (−0.3) (−0.2) (−0.6) (−0.1) −20/+5 167.6 −9.2 −26 −81 −15 −92 (−0.3) (−0.7) (−0.3) (−1.1) (−0.2) −10/+30 142.6 −9.0 −25 −89 −16 −97 (−0.3) (−0.6) (−0.3) (−1.2) (−0.2) −30/+10 163.3 −16.2 −45 −144 −26 −163 (−0.6) (−1.2) (−0.6) (−1.9) (−0.4) −5/+30 136.7 −5.0 −14 −52 −10 −56 (−0.2) (−0.4) (−0.2) (−0.7) (−0.1) −30/+5 171.6 −12.8 −36 −113 −20 −128 (−0.5) (−0.9) (−0.4) (−1.5) (−0.3) Welfare‐improving schemes 5 148 −7.3 −20 −68 −8 3 (−0.3) (−0.5) (−0.3) (−0.6) (0.008) 20 145 −35.5 −98 −329 −34 19 (−1.2) (−2.5) (−1.3) (−2.5) (0.05) −2/+3 145 −3.1 −9 −29 −3 2 (−0.1) (−0.2) (−0.1) (−0.3) (0.004) −10/+20 136.7 −26.1 −72 −243 −22 72 (−0.9) (−1.9) (−0.9) (−1.6) (0.2) Sales‐increasing schemes 0/+10 145 7.2 20 64 −2 −77 (0.3) (0.5) (0.2) (−0.1) (−0.2) 0/+10 155 13.1 37 117 −3 −137 (0.5) (0.9) (0.4) (−0.3) (−0.3) 0/+10 165 21.8 61 197 −6 −220 (0.8) (1.6) (0.8) (−0.5) (−0.5) Notes Government revenues for the welfare‐improving schemes are 83 (+0.8%), 412 (+3.9%), 36 (+0.3%) and 364(+3.4%) million euro respectively. Government revenues for the total sales‐improving schemes are −160 (−1.5%), −287 (−2.7%) and −472 (−4.5%) million euro respectively. Open in new tab Table B2 Simulated Impact of Feebate Schemes with Logarithmic Price and Disaggregated Data Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 148.0 −7.1 −72 −174 −34 −213 (−0.2) (−2.7) (−2.8) (−2.4) (−1.1) 20 144.4 −24.0 −156 −355 −71 −440 (−0.8) (−5.9) (−5.8) (−5.0) (−2.2) 30 140.8 −50.7 −250 −540 −112 −678 (−1.7) (−9.4) (−8.8) (−7.8) (−3.4) 40 137.3 −86.9 −352 −727 −156 −923 (−3.0) (−13.3) (−11.9) (−10.7) (−4.6) 62.6 130 −197.4 −598 −1133 −259 −1472 (−6.7) (−22.6) (−18.5) (−17.1) (−7.3) 103.8 120 −450.2 −1023 −1750 −434 −2338 (−15.4) (−38.6) (−28.6) (−26.0) (−11.7) Revenue‐neutral asymmetric schemes −10/+20 139.6 −11.9 −93 −218 −45 −266 (−0.4) (−3.5) (−3.6) (−3.2) (−1.3) −20/+10 153.3 −15.3 −119 −279 −52 −346 (−0.5) (−4.5) (−4.6) (−3.7) (−1.7) −5/+20 134.1 −6.3 −55 −132 −28 −159 (−0.2) (−2.1) (−2.2) (−2.0) (−0.8) −20/+5 161.5 −11.0 −94 −220 −39 −274 (−0.4) (−3.5) (−3.6) (−2.8) (−1.4) −10/+30 134.1 −16.7 −109 −248 −54 −304 (−0.6) (−4.1) (−4.1) (−3.8) (−1.5) −30/+10 155.6 −25.0 −161 −365 −68 −459 (−0.9) (−6.1) (−6.0) (−4.8) (−2.3) −5/+30 129.1 −8.8 −64 −149 −33 −180 (−0.3) (−2.4) (−2.4) (−2.3) (−0.9) −30/+5 163.8 −18.3 −127 −289 −52 −365 (−0.6) (−4.8) (−4.7) (−3.6) (−1.8) Welfare‐improving schemes 10 130 −57.5 −114 −207 −52 279 (−2.0) (−4.3) (−3.4) (−3.6) (1.4) 20 120 −159.3 −264 −440 −117 901 (−5.4) (−10.0) (−7.2) (−7.8) (4.5) −2/+3 139.6 −5.6 −19 −41 −9 2 (−0.2) (−0.7) (−0.7) (−0.6) (0.01) −10/+20 129.1 −51.3 −118 −226 −55 164 (−1.8) (−4.5) (−3.7) (−3.8) (0.8) Sales‐increasing schemes 0/+10 120 2.9 −0.72 −7 −1 −41 (0.1) (−0.027) (−0.1) (−0.1) (−0.2) 0/+10 140 14.9 0.16 −23 −2 −199 (0.5) (0.006) (−0.4) (−0.2) (−1.0) 0/+10 160 46.3 10.6 −46 0.6 −569 (1.6) (0.4) (−0.7) (0.04) (−2.8) Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 148.0 −7.1 −72 −174 −34 −213 (−0.2) (−2.7) (−2.8) (−2.4) (−1.1) 20 144.4 −24.0 −156 −355 −71 −440 (−0.8) (−5.9) (−5.8) (−5.0) (−2.2) 30 140.8 −50.7 −250 −540 −112 −678 (−1.7) (−9.4) (−8.8) (−7.8) (−3.4) 40 137.3 −86.9 −352 −727 −156 −923 (−3.0) (−13.3) (−11.9) (−10.7) (−4.6) 62.6 130 −197.4 −598 −1133 −259 −1472 (−6.7) (−22.6) (−18.5) (−17.1) (−7.3) 103.8 120 −450.2 −1023 −1750 −434 −2338 (−15.4) (−38.6) (−28.6) (−26.0) (−11.7) Revenue‐neutral asymmetric schemes −10/+20 139.6 −11.9 −93 −218 −45 −266 (−0.4) (−3.5) (−3.6) (−3.2) (−1.3) −20/+10 153.3 −15.3 −119 −279 −52 −346 (−0.5) (−4.5) (−4.6) (−3.7) (−1.7) −5/+20 134.1 −6.3 −55 −132 −28 −159 (−0.2) (−2.1) (−2.2) (−2.0) (−0.8) −20/+5 161.5 −11.0 −94 −220 −39 −274 (−0.4) (−3.5) (−3.6) (−2.8) (−1.4) −10/+30 134.1 −16.7 −109 −248 −54 −304 (−0.6) (−4.1) (−4.1) (−3.8) (−1.5) −30/+10 155.6 −25.0 −161 −365 −68 −459 (−0.9) (−6.1) (−6.0) (−4.8) (−2.3) −5/+30 129.1 −8.8 −64 −149 −33 −180 (−0.3) (−2.4) (−2.4) (−2.3) (−0.9) −30/+5 163.8 −18.3 −127 −289 −52 −365 (−0.6) (−4.8) (−4.7) (−3.6) (−1.8) Welfare‐improving schemes 10 130 −57.5 −114 −207 −52 279 (−2.0) (−4.3) (−3.4) (−3.6) (1.4) 20 120 −159.3 −264 −440 −117 901 (−5.4) (−10.0) (−7.2) (−7.8) (4.5) −2/+3 139.6 −5.6 −19 −41 −9 2 (−0.2) (−0.7) (−0.7) (−0.6) (0.01) −10/+20 129.1 −51.3 −118 −226 −55 164 (−1.8) (−4.5) (−3.7) (−3.8) (0.8) Sales‐increasing schemes 0/+10 120 2.9 −0.72 −7 −1 −41 (0.1) (−0.027) (−0.1) (−0.1) (−0.2) 0/+10 140 14.9 0.16 −23 −2 −199 (0.5) (0.006) (−0.4) (−0.2) (−1.0) 0/+10 160 46.3 10.6 −46 0.6 −569 (1.6) (0.4) (−0.7) (0.04) (−2.8) Notes Government revenues for the welfare‐improving schemes are 549 (+4.9%), 1488 (+13.2%), 53 (+0.5%) and 453 (+4.0%) million euro respectively. Government revenues for the total sales‐improving schemes are −34 (−0.3%), −178 (−1.6%) and −533 (−4.7%) million euro respectively. Open in new tab Table B2 Simulated Impact of Feebate Schemes with Logarithmic Price and Disaggregated Data Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 148.0 −7.1 −72 −174 −34 −213 (−0.2) (−2.7) (−2.8) (−2.4) (−1.1) 20 144.4 −24.0 −156 −355 −71 −440 (−0.8) (−5.9) (−5.8) (−5.0) (−2.2) 30 140.8 −50.7 −250 −540 −112 −678 (−1.7) (−9.4) (−8.8) (−7.8) (−3.4) 40 137.3 −86.9 −352 −727 −156 −923 (−3.0) (−13.3) (−11.9) (−10.7) (−4.6) 62.6 130 −197.4 −598 −1133 −259 −1472 (−6.7) (−22.6) (−18.5) (−17.1) (−7.3) 103.8 120 −450.2 −1023 −1750 −434 −2338 (−15.4) (−38.6) (−28.6) (−26.0) (−11.7) Revenue‐neutral asymmetric schemes −10/+20 139.6 −11.9 −93 −218 −45 −266 (−0.4) (−3.5) (−3.6) (−3.2) (−1.3) −20/+10 153.3 −15.3 −119 −279 −52 −346 (−0.5) (−4.5) (−4.6) (−3.7) (−1.7) −5/+20 134.1 −6.3 −55 −132 −28 −159 (−0.2) (−2.1) (−2.2) (−2.0) (−0.8) −20/+5 161.5 −11.0 −94 −220 −39 −274 (−0.4) (−3.5) (−3.6) (−2.8) (−1.4) −10/+30 134.1 −16.7 −109 −248 −54 −304 (−0.6) (−4.1) (−4.1) (−3.8) (−1.5) −30/+10 155.6 −25.0 −161 −365 −68 −459 (−0.9) (−6.1) (−6.0) (−4.8) (−2.3) −5/+30 129.1 −8.8 −64 −149 −33 −180 (−0.3) (−2.4) (−2.4) (−2.3) (−0.9) −30/+5 163.8 −18.3 −127 −289 −52 −365 (−0.6) (−4.8) (−4.7) (−3.6) (−1.8) Welfare‐improving schemes 10 130 −57.5 −114 −207 −52 279 (−2.0) (−4.3) (−3.4) (−3.6) (1.4) 20 120 −159.3 −264 −440 −117 901 (−5.4) (−10.0) (−7.2) (−7.8) (4.5) −2/+3 139.6 −5.6 −19 −41 −9 2 (−0.2) (−0.7) (−0.7) (−0.6) (0.01) −10/+20 129.1 −51.3 −118 −226 −55 164 (−1.8) (−4.5) (−3.7) (−3.8) (0.8) Sales‐increasing schemes 0/+10 120 2.9 −0.72 −7 −1 −41 (0.1) (−0.027) (−0.1) (−0.1) (−0.2) 0/+10 140 14.9 0.16 −23 −2 −199 (0.5) (0.006) (−0.4) (−0.2) (−1.0) 0/+10 160 46.3 10.6 −46 0.6 −569 (1.6) (0.4) (−0.7) (0.04) (−2.8) Scheme . Change in . t . PP . Total sales . Consumer surplus . Producer surplus . Emissions cost . Total welfare . Revenue‐neutral symmetric schemes 10 148.0 −7.1 −72 −174 −34 −213 (−0.2) (−2.7) (−2.8) (−2.4) (−1.1) 20 144.4 −24.0 −156 −355 −71 −440 (−0.8) (−5.9) (−5.8) (−5.0) (−2.2) 30 140.8 −50.7 −250 −540 −112 −678 (−1.7) (−9.4) (−8.8) (−7.8) (−3.4) 40 137.3 −86.9 −352 −727 −156 −923 (−3.0) (−13.3) (−11.9) (−10.7) (−4.6) 62.6 130 −197.4 −598 −1133 −259 −1472 (−6.7) (−22.6) (−18.5) (−17.1) (−7.3) 103.8 120 −450.2 −1023 −1750 −434 −2338 (−15.4) (−38.6) (−28.6) (−26.0) (−11.7) Revenue‐neutral asymmetric schemes −10/+20 139.6 −11.9 −93 −218 −45 −266 (−0.4) (−3.5) (−3.6) (−3.2) (−1.3) −20/+10 153.3 −15.3 −119 −279 −52 −346 (−0.5) (−4.5) (−4.6) (−3.7) (−1.7) −5/+20 134.1 −6.3 −55 −132 −28 −159 (−0.2) (−2.1) (−2.2) (−2.0) (−0.8) −20/+5 161.5 −11.0 −94 −220 −39 −274 (−0.4) (−3.5) (−3.6) (−2.8) (−1.4) −10/+30 134.1 −16.7 −109 −248 −54 −304 (−0.6) (−4.1) (−4.1) (−3.8) (−1.5) −30/+10 155.6 −25.0 −161 −365 −68 −459 (−0.9) (−6.1) (−6.0) (−4.8) (−2.3) −5/+30 129.1 −8.8 −64 −149 −33 −180 (−0.3) (−2.4) (−2.4) (−2.3) (−0.9) −30/+5 163.8 −18.3 −127 −289 −52 −365 (−0.6) (−4.8) (−4.7) (−3.6) (−1.8) Welfare‐improving schemes 10 130 −57.5 −114 −207 −52 279 (−2.0) (−4.3) (−3.4) (−3.6) (1.4) 20 120 −159.3 −264 −440 −117 901 (−5.4) (−10.0) (−7.2) (−7.8) (4.5) −2/+3 139.6 −5.6 −19 −41 −9 2 (−0.2) (−0.7) (−0.7) (−0.6) (0.01) −10/+20 129.1 −51.3 −118 −226 −55 164 (−1.8) (−4.5) (−3.7) (−3.8) (0.8) Sales‐increasing schemes 0/+10 120 2.9 −0.72 −7 −1 −41 (0.1) (−0.027) (−0.1) (−0.1) (−0.2) 0/+10 140 14.9 0.16 −23 −2 −199 (0.5) (0.006) (−0.4) (−0.2) (−1.0) 0/+10 160 46.3 10.6 −46 0.6 −569 (1.6) (0.4) (−0.7) (0.04) (−2.8) Notes Government revenues for the welfare‐improving schemes are 549 (+4.9%), 1488 (+13.2%), 53 (+0.5%) and 453 (+4.0%) million euro respectively. Government revenues for the total sales‐improving schemes are −34 (−0.3%), −178 (−1.6%) and −533 (−4.7%) million euro respectively. Open in new tab Footnotes 1 " The term ‘rebound effect’ refers to the tendency for vehicle use to increase when fuel efficiency increases (as the cost per unit distance decreases). 2 " See European Automobile Manufacturers Association (2009) and OECD (2009) for overviews of the CO2‐based taxation schemes implemented before the end of year 2009 by individual countries. 3 " In a parallel work (Adamou et al., 2012) we performed an ex ante analysis of feebate policies for Greece. That study was much more limited in scope than this study as it only examined the impact of specific symmetric schemes on market shares; it did not consider welfare implications or explore the design of schemes that are consistent with different objectives. 4 " See the review by Bunch et al. (2011); countries such as Denmark, the Netherlands and Norway have implemented some type of feebate programme but have combined it with wider reforms in their car registration tax systems. 5 " It is also possible to apply the feebate on the supply side, i.e. on car manufacturers or dealers. In theory, the effect would be the same regardless of where the tax is levied; in practice, however, it seems that price incentives are more effective if levied at the consumer rather than the producer level (Sallee, 2010). 6 " The rest of this subsection is based on Verboven (1996). 7 " The latter would require an assumption on the marginal cost function. 8 " There are other engine/fuel types (electric, CNG, LPG, E85, hydrogen, methanol) but they only make up 0.8% of observations and they were removed from the data set. 9 " UNECE is the United Nations Economic Commission for Europe; its database is available at http://w3.unece.org/pxweb/. 10 " This feature of the model was discussed in Verboven (1996), who tried to circumvent it by using a Box‐Cox specification that has the linear and logarithmic specifications as special cases. Note that this implication of linearity extends to the random coefficient case. For a recent lucid exposition of the difference between the linear and logarithmic specifications see Björnerstedt and Verboven (2013). 11 " See discussions in Berry et al. (1995) and Bresnahan et al. (1997), among others. 12 " In the aggregate linear model, this instrument was excluded because it had no explanatory power in the first‐stage regression. 13 " See Adamou et al. (2012) for an example with Greek data. 14 " Björnerstedt and Verboven (2013) use a slightly modified version of the logarithmic specification that they show to be consistent with utility maximisation. 15 " In fact, using data of more recent years 2009 and 2010 might have been misleading: car demand and supply patterns may have been temporarily altered during those two years due to the implementation of accelerated car scrappage schemes as part of fiscal stimulus measures. 16 " Braathen (2012, p. 2012 estimates implied tax rates as high as €200 per tonne of CO2 for countries such as Ireland, Finland, the Netherlands and Norway. 17 " We arrived at the 200,000 figure after consulting with several European transport policy analysts; it is considered a good approximation of the lifetime mileage of an average car in Europe. In the US, official data indicate a higher mileage of about 240,000 km (150,000 miles); Davis et al. (2012). 18 " This calculation is mathematically equivalent to measuring the change in emissions as the difference between pre and post‐feebate weighted mean emissions multiplied by post‐feebate sales. The details are somewhat tedious but available from the authors upon request. 19 " Aldy et al. (2010) and Interagency Working Group on Social Cost of Carbon (2010). The €15 figure corresponds to the value of 21 US dollars at 2007 prices per tonne of CO2 suggested by IWG, deflated to prices of year 2005 that we use throughout the article, and assuming an exchange rate of 1.4 US dollars per euro. 20 " Some of the loss in producer surplus is likely to be absorbed by foreign manufacturers and should not be included in a national calculation. Calculating the German portion of producer surplus is complicated for several reasons such as cross‐ownership and the distribution of profits between manufacturers and retailers. For this reason we chose to report the entire producer surplus. 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Clerides thanks Northwestern University's Center for the Study of Industrial Organisation for its hospitality and the European Commission for financial support through the Marie Curie programme. © 2013 Royal Economic Society
TI - Welfare Implications of Car Feebates: A Simulation Analysis
JO - The Economic Journal
DO - 10.1111/ecoj.12094
DA - 2014-08-01
UR - https://www.deepdyve.com/lp/oxford-university-press/welfare-implications-of-car-feebates-a-simulation-analysis-1ox0kAJyU4
SP - F420
VL - 124
IS - 578
DP - DeepDyve
ER -