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A generic discrete choice model of automobile purchase



The introduction of novel fuel and propulsion technologies, such as battery, (plug-in) hybrid and fuel cell electric vehicles, and the need to combat the exhaust emission of local and global pollutants from the passenger car fleet have enhanced the political interest in the vehicle purchase choices made by private households and firms, and in how these choices can be influenced through fiscal and regulatory penalties and incentives.


As a tool to understand and analyse such questions, we have developed a generic nested logit model of automobile choice, based on complete disaggregate vehicle sales data for Norway for the period ranging from January 1996 until July 2011. The data set contains 1.6 million vehicle transactions.


Being sensitive to changes in the vehicle purchase tax and the fuel tax, the model discriminates well between various fiscal policy scenarios. In using the model for such purposes, one is greatly helped by the fact that the model distinguishes between price changes due to taxation and those originating from the manufacturing or marketing side.


The strongly CO2 graduated vehicle purchase tax, with exemptions granted for battery electric vehicles, is shown to have a major impact on the average type approval rate of CO2 emissions from new passenger cars registered in Norway. The fuel tax also helps induce car customers to buy low emission vehicles.

1 Introduction

Since the seminal papers by Lave and Train [24] and Manski and Sherman [25], automobile demand and vehicle choice have been the subjects of multiple studies by transport researchers. Most studies (e. g., [3, 4, 8, 10, 21, 34]) are based on disaggregate discrete choice modelling of household behaviour. But some are also based on aggregate sales data, whereby one estimates total demand or market shares held by various vehicle models (e.g., [1, 5, 14, 20, 22]). Common to most of these studies is that their data sets and methodology are too crude or too incomplete to allow for reliable predictions of the car fleet composition under varying fiscal and regulatory policy options. Some recent studies have, however, come a long way towards modelling the complex, joint decision processes of vehicle choice and usage [6, 9, 18, 19, 28].

The introduction of novel fuel and propulsion technologies, such as battery, (plug-in) hybrid and fuel cell electric vehicles, and the need to combat the exhaust emission of local and global pollutants from the passenger car fleet have enhanced the political interest in the vehicle purchase choices made by private households and firms, and in how these choices can be influenced through fiscal and regulatory penalties and incentives. In Norway, a large number of incentives have been implemented over the last 10–12 years, most importantly a steeply CO2-graduated vehicle purchase tax. These incite a growing number of car buyers to prefer low and zero emission vehicles [13, 16]. In 2015, no less than 17% of all new automobiles registered in Norway were zero emission cars, almost all of them battery electric vehicles (BEVs).

The Norwegian Parliament has adopted a non-binding target for the average type approval CO2 exhaust emission rate of new passenger cars to be registered in Norway in 2020. The target has been set at 85 gCO2/km, i. e. 10 gCO2/km lower than the EU mandated target, which commits car manufacturers not to exceed 95 gCO2/km as averaged over all cars sold in 2020/2021.

How can the continued use of fiscal incentives ensure that this and subsequent – possibly sharpened – targets are reached? Is it possible to fine-tune the vehicle purchase tax so as to obtain desired market shares for certain, more environmentally friendly vehicle types? If and when the fiscal privileges currently enjoyed by BEVs are abolished, how much will their market share drop? What kind of tax incentives are needed in order for plug-in hybrid vehicles (PHEVs) to obtain a certain share? How will the environmental attributes of petrol and diesel driven cars develop under the present tax regime, or under some stiffer or laxer alternative? Will the environmentally oriented taxes eventually erode their own basis, as consumers respond to the incentives by buying cars with steadily lower exhaust emission rates and lower tax? How can the government maintain the level of revenue from vehicle purchase taxes?

In order to answer these questions, a detailed and comprehensive behavioural model of demand for new passenger cars is needed.

2 Approach and method

We have developed a nested logit model of automobile choice, based on complete vehicle sales data for Norway for the period ranging from January 1996 until July 2011.

For each year, more than 2000 different vehicle model variants have been identified and their annual sales recorded. Obviously, few – if any – of these model variants are available on the market throughout the period. Only a certain subset of variants enters the choice set in a given year.

In the nested logit model every single car sale is regarded as a discrete choice where, in principle, every model variant available in the market at that time is included in the buyers’ choice set. There are a total of approximately 1.6 million transactions, or choice situations, registered in the new car sales database. For each vehicle model variant, the database includes information such as the vehicle’s make, list price, purchase tax amount, type of fuel, calculated kilometre cost of fuel, curb weight, engine power, drivetrain, and number of seats and doors. The nested logit model uses these individual vehicle characteristics as explanatory variables in the indirect utility function.

Since the model is supposed to predict the market share of potential new car model variants with known or assumed attributes, care was taken to specify the model as a generic one. There are no alternative specific coefficients, other than the dummies capturing the vehicle’s make.

Extensive testing was done in order to find the appropriate nest structure. At first, we tried a structure in which the upper nests were defined by such segments as ‘mini’, ‘small’, ‘compact’, ‘medium’, ‘fullsize’, ‘luxury’, ‘minivan’, ‘off-road’ or ‘sport-utility vehicle’ (SUV). Secondly, we examined structures based on more objective size categories, such as kilogram curb weight intervals. Nesting based on fuel or propulsion technology was also tried. We found, however, that the only nest structure compatible with a priori assumptions under the utility maximization paradigm (scale parameters larger than unity) was one in which each vehicle make forms one nest. Thus, there are 21 such nests in the model, the last one being a residual nest assembling ‘all other makes’. Fig. 1 illustrates the model’s nest structure.

Fig. 1
figure 1

Nest structure in automobile purchase model

According to this structure, the probability of choosing a given vehicle model variant i of make j is the product of the probability of choosing make j and the conditional probability of choosing model variant i given the set available within make j. The mathematical formula for calculating the choice probability in year t can be stated as:

$$ {P}_t\left( variant= i\right)={P}_t\left( variant= i| make= j\right)\cdotp {P}_t\left( make= j\right) $$

If we denote by M tj the set of model variants of make j available in year t, the two factors in Eq. (1) can be specified as

$$ {P}_t\left( variant= i| make= j\right)=\frac{ \exp \left({\mu}_j{V}_{ij}\right)}{\sum_{h\in {M}_{t j}} \exp \left({\mu}_j{V}_{h j}\right)},\kern0.5em \left( t=1996,1997,\dots, 2011\right) $$
$$ \begin{array}{cc}\kern1em {P}_t\left(\mathrm{make}= j\right)=\frac{{ \exp}^{\frac{1}{\mu_j} \ln \left[{\sum}_{i\in {M}_{t j}} \exp \left({\mu}_j{V}_{i j}\right)\right]}}{\sum_{k=1}^{21}{ \exp}^{\frac{1}{\mu_k} \ln \left[{\sum}_{i\in {M}_{t k}} \exp \left({\mu}_k{V}_{i k}\right)\right]}}\kern1em & \kern1em \left( t=1996,1997,\dots, 2011\right).\kern1em \end{array} $$

In these two expressions μ j denotes the estimated scale parameter for each make in the lower nest. When normalizing the upper scale parameter to unity, these lower scale parameters are restricted to be larger than unity. The indirect utility function specified for each individual vehicle model variant i of make j, denoted V ij , is specified as a linear combination of coefficients and explanatory variables:

$$ {V}_{ij}=\sum_k{\beta}_k{x}_{ij k}+{\gamma}_j. $$

Here, the explanatory variables x ijk are vehicle attributes. The γ j are make-specific constants, estimated as the coefficients of a set of dummy variables – z ij , say – equal to one if and only if model variant i belongs to make j (see Table 1 below for details). Note that the β k coefficients are not indexed by i or j – they are generic, i. e. identical across vehicle model variants and makes.

Table 1 Estimation results from generic automobile choice model. Norway 1996–2011

As analysts, we do not have full information about the indirect utility generated by each vehicle model variant. Following common practice [2], we assume that the observable utility U ij (say) consists of the systematic term V ij and some random disturbance term e ij , i. e.

$$ {U}_{ij}={V}_{ij}+{e}_{ij}, $$

where the e ij are independent and identically Gumbel distributed random variables with scale parameters μ j .

3 Estimation results

3.1 Model coefficients

Maximum likelihood estimates were derived using the Biogeme Python software [7]. All coefficient estimates are shown in Table 1.

Most coefficients are significantly different from zero at the 1% level. They also have the anticipated sign, whenever a priori expectations apply.

The Price coefficient is negative, as expected. Other things being equal, a higher price reduces a vehicle’s market share.

The Resourcecostshare variable, being constrained between zero and one, is defined as the share of the vehicle’s retail price that is not made up by purchase tax or value added tax (VAT), i. e. as the price net of tax divided by the price including tax. As expected, its coefficient comes out positive, suggesting that, other things (including the price) being equal, buyers are more reluctant to choose a heavily taxed car than one that is subject to zero or little tax. The Resourcecostshare variable allows us to distinguish the effect of a tax increase from that of a higher manufacturing or marketing cost.

The variable Fuelcost, defined as the relevant per litre real fuel price (in NOK 2010) times the type approval rate of fuel consumption per 10 km, captures the expected fuel cost per unit of driving distance. Its coefficient is negative, as expected. For BEVs, zero fuel cost is assumed.

Bigger is better. The Size variable, defined by the log-transformed product of the vehicle’s length and width, as measured in square metres, comes out with a positive coefficient.

The Acceleration variable, defined by the amount of engine power in relation the vehicle’s weight, comes out with a positive sign, but the coefficient is not statistically significant. To reflect the decreasing marginal utility of acceleration, the variable is not entered linearly, but specified as the negative of the inverse, squared ratio of engine power to weight, corresponding to a Box-Cox transformation with parameter minus two.

Load measures the log-transformed, maximum utility load of the vehicle (passengers and luggage, not including 75 kg driver) relative to its size in square metres. It has the expected positive sign, and is statistically significant at the 5% level.

The Dieseltrend variable captures the gradual improvement of diesel vehicle technology as compared to petrol driven cars. It is specified as a diesel vehicle dummy multiplied by the natural logarithm of years passed since 1996. The starting point of the diesel trend effect is determined by the dummy C_Diesel, estimated at −0.803, which translates into a significant disadvantage as compared to petrol cars in 1996.

Dummy variables C_Electric and C_Hybrid capture the effect of propulsion systems other than the petrol engine, which acts as our reference category. The hybrid class includes plug-ins as well as ordinary hybrids. These coefficients are both positive, but not highly significant.

Another set of dummy variables – C_Fourwheeldrive and C_Frontwheeldrive – capture the quality differences with respect to the standard rear-wheel drivetrain. 4-wheel drive is highly valued by Norwegian consumers, but front-wheel drive does not stand out as preferable to rear-wheel drive.

The dummy C_Fiveormoredoors typically captures station wagons and multi-purpose vehicles (MPV) as opposed to ordinary sedans, while the variables C_Fiveseats and C_Sixormoreseats measure differences with respect to cars with four seats or less.

The dummies capturing vehicle make are all positive and, with one exception, significantly different from zero, suggesting a higher choice probability than the reference category ‘all other makes’. These dummy variables are, however, hard to interpret. On the one hand, they reflect the popularity of each make as measured by their market share. On the other hand, they are also affected, and negatively so, by the number of different model variants offered by each manufacturer. The larger the number of similar vehicles the consumer can choose from, the smaller will be the market share of each particular model variant – confer the famous ‘red bus – blue bus’ example ([2]: 51–55). This explains why the prestigious Mercedes-Benz (MB) make comes out with the smallest coefficient of all makes. While, in our data set, the average number of model variants offered annually by each manufacturer is 45 (disregarding ‘all other makes’), MB have split their sales among, on average, 206 different model variants, with a mean sale of only 15 cars per model variant per year. While their aggregate market share is only 3.1%, they represent 8.6% of all the model variants entering the market (Table 2).

Table 2 Aggregate number of new automobiles sold, mean number of model variants offered per year, and average number of vehicles sold annually per model variant, by make. Norway January 1996–July 2011

3.2 Model predictions vs. observed outcomes

In Fig. 2 we show observed and predicted annual market shares, at the most disaggregate level.

Fig. 2
figure 2

Observed and fitted annual market shares of individual vehicle model variants 1996–2011. Logarithmic scale

As can be expected in a data set where all choice probabilities are quite small, the fit is rather poor, as measured by the adjusted likelihood ratio index \( {\overline{\rho}}^2 \)= 0.054. One notes that for model variants with a very low market share, some of the predicted values are widely off the mark. Certain variants sell only one or two units in a given year, corresponding to an observed market share between 0.0008 and 0.003%. On account, however, precisely of these variants’ infinitesimal market shares, their weak fit is of little consequence to the model’s predictive power. For variants with a higher market share, the correspondence between observed and fitted values is stronger.

The differences between the various vehicle model variants making up our data set are, in many cases, miniscule. To fix ideas we show, in the Appendix, data lines pertaining to the 2010 assortment of Volkswagen Golf model variants. There are 73 such variants in the market, no two of them being exactly equal in terms of the attributes entering the discrete choice model: engine power, curb weight, utility load, cylinder volume, fuel, no. of seats, no. of doors, length, width, body style, or traction.

Obviously, the prediction of market share for each of these individual variants is of limited commercial or political relevance. Comparing observed and fitted market shares at the somewhat more aggregate levels carries more interest. In Fig. 3 we have grouped observations into segments defined by energy carrier and/or curb weight.

Fig. 3
figure 3

Observed and fitted annual market shares 1996–2011, by energy carrier and/or curb weight. Linear scale

Again, the predictive power is comparatively weak for segments with very low market shares. Within the more popular vehicle segments, however, the fit seems quite satisfactory. A case in point is the 1000–1199 kg class of petrol driven cars, exhibiting a 40% observed and predicted market share in 1996, declining to a 7% observed and predicted market share in 2011.

The model is somewhat less accurate in predicting the respective market shares of different vehicle makes (Fig. 4), but fairly precise in terms of the distribution between CO2 emission intervals (Fig. 5).

Fig. 4
figure 4

Observed and fitted annual market shares 1996–2011, by vehicle make. Linear scale

Fig. 5
figure 5

Observed and fitted annual market shares 1996–2011, by type approval CO2 exhaust emission bracket (gCO2/km). Linear scale

In Fig. 6, we show how well the model explains the trend towards lower average type approval exhaust emission rates during 1996–2011. The model picks up the trend reasonably well.

Fig. 6
figure 6

Mean observed and predicted type approval CO2 exhaust emission rates of new Norwegian registered automobiles 1996–2011

3.3 Willingness-to-pay for vehicle attributes

Following common practice in hedonic demand modelling [30], we derive the willingness-to-pay for a certain attribute by taking the ratio of its coefficient estimate to the price coefficient. Table 3 summarizes the calculated willingness-to-pay for selected vehicle attributes.

Table 3 Willingness-to-pay for selected vehicle attributes

Our nested logit model implies a value of NOK 8600 for a one percentage point increase in the non-tax share of the vehicle retail price. By extrapolation, the willingness-to-pay for a non-taxed vehicle is NOK 430000 higher than for a vehicle whose price consists of 50% tax.

The willingness-to-pay for a reduction in petrol or diesel consumption by one litre per 100 km is estimated at NOK 41,400. For a vehicle running 240,000 km during its lifetimeFootnote 1, the energy saving is 2400 l, at a cost of roughly NOK 30,000–35,000 (= appr. € 4000). Hence, when car buyers make their choice, they may seem to take more than full account of future energy costs, while also not applying a discount rate much higher than zero. The estimate may be affected by the fact that the type approval rates of fuel consumption entering our data set are typically 10 to 30% lower than the actual consumption on-the-road [27]. It may seem as if consumers are well aware of this. Also, the estimate may reflect concern about future energy prices and a desire to minimize such risk.

Norwegians love four-wheel drive, which provides superior traction on snow and ice as well as enhanced accessibility on the rough road to their mountain or seaside cottage. The willingness-to-pay for four-wheel relative to rear-wheel drive is calculated at NOK 230,000, while front-wheel drive is valued at NOK 15,900.

A vehicle model variant with five seats rather than four or less seats has an added value to the consumer of NOK 46,500. A station wagon or 5-door multi-purpose vehicle (MPV) is valued at NOK 149,000 more than the otherwise similar sedan.

The willingness-to-pay for a hybrid vehicle rather than a petrol car is approximately NOK 87,000 (2010 prices) (Fig. 7). This indicates that consumers assign an extra value to this type of vehicle compared to petrol driven ones, ceteris paribus.

Fig. 7
figure 7

Willingness-to-pay for hybrid, electric and diesel powered vehicles relative to petrol driven model variants

The estimated willingness-to-pay for diesel vehicles, rather than petrol cars, shifts from negative to positive in 2008, amounting to approximately NOK 35,000 in 2011.

The added willingness-to-pay for battery electric vehicles comes out at no less than NOK 431,000 = € 51,000. At first sight, this may seem exaggerated. However, the estimate must be interpreted in light of the fact that the Fuelcost variable is set to zero for BEVs. The estimate includes, in other words, the perceived advantage of having zero fuel cost throughout a vehicle’s lifetime. When we adjust for this, applying an average Fuelcost value of NOK 8.91 per 10 km, the BEVs’ market advantage is reduced to around NOK 66,000 = € 7800. This estimate reflects the fact that, in Norway, BEVs enjoy a large number of privileges, such as access to the bus lane, exemption from road tolls and public parking charges, strongly reduced ferry fares, and free recharging in many public parking lots. Among BEV owners in Norway as of March 2016, the median value of these benefits has been estimated at NOK 10,000 = € 1200 per year [13]. In certain parts of the country, the value of the toll exemption alone can exceed € 4000 per year for a motorist using a long bridge or subsea tunnel on his daily commute.

4 Policy analysis

There are several ways in which our nested logit model can be used as a policy support tool.

By simulating hypothetical changes in certain vehicle attributes, we can calculate policy or marketing relevant response surfaces at more or less aggregate levels. Thanks to the generic character of the model, we can predict the market shares of these hypothetical vehicles as well as the change in demand for every other passenger car in the market. Fridstrøm et al. [15] show how, by integrating the discrete choice model into a dynamic stock-flow model of the car fleet, one can assess the long-term consequences of changes in vehicle technology or in the fiscal incentives.

In this paper, we report on three other policy relevant applications of the model. In Section 4.1, we present a short-term analysis of potential changes in the Norwegian vehicle purchase tax. In Section 4.2, we present model simulations of changes in the fuel cost. In Section 4.3, we present the results of a counterfactual back-casting exercise, in which one simulates the market development during 2007–2014 under the hypothetical assumption that the strongly CO2-graduated purchase tax and/or the tax exemptions for BEVs had never been introduced.

4.1 Simulated changes to the vehicle purchase tax

The Norwegian automobile purchase tax, payable upon first registration of a vehicle, is a sum of four independent components, calculated on the basis of curb weight, ICE power, and type approval CO2 and NOX exhaust emission rates, respectively (Fig. 8). All but the NOX component are convex, exhibiting increasing marginal tax rates. The CO2 component is negative (as of 2014) for vehicles emitting less than 105 gCO2/km by the type approval test. That is, for these cars there is a deduction applicable to the sum of the weight, power and NOX components. The total purchase tax cannot, however, become negative, as in a feebate system.

Fig. 8
figure 8

Vehicle purchase tax as a function of curb weight, engine power, and type approval CO2 and NOX exhaust emission rates, in Norway 2014

Source: Fridstrøm et al. [17]

For PHEVs, the electric motor does not count towards the tax on engine power, only the combustion engine does, and the weight component is reduced by a benchmark 15% (as of 2014), so as to leave the weight of the battery pack out of the tax base. As noted above, BEVs and FCEVs are altogether exempt of purchase tax, as well as of the standard 25% value added tax (VAT).

Relying on the discrete choice model shown in Table 1, we have simulated six different policy options bearing on the automobile purchase tax:

  1. 1.

    A 10% increase in all purchase tax components.

  2. 2.

    A 10% increase in the CO2 component

  3. 3.

    A 10% increase in the curb weight component

  4. 4.

    A 10% increase in the engine power component

  5. 5.

    Introduction of purchase tax on BEVs, according to same rules as for PHEVs.

  6. 6.

    Introduction of VAT and purchase tax on BEVs, according to same rules as for PHEVs.

Simulations were made on the basis of a benchmark calculated for 2014. As seen from Fig. 9, more than half the passenger cars sold in 2014 had type approval CO2 exhaust emission rates between 100 and 149 gCO2/km. BEVs had a market share of 12.5% in Norway 2014.

Fig. 9
figure 9

Calculated automobile market shares for 2014, by type approval CO2 exhaust emission bracket

By adjusting the constant terms, we calibrated the model as of 2014 so as to yield correct aggregate market shares for battery electric, hybrid electric, petrol and diesel driven cars, as well as for the Tesla make of BEVs. Since the Teslas stand out as rather more expensive than other BEVs, it was considered necessary to account for these most expensive BEVs as accurately as possible. In all of the simulations, it has been assumed that tax changes are passed on 100% to the buyers, through corresponding changes in the retail price.

Figure 10 shows changes in the market shares of vehicles within different CO2 emission brackets. As shown by the left-most cluster of bars (alt. 1), a 10% increase in every purchase tax component would, when passed on entirely to the buyers, translate into a 24% lower market share for the most extreme ‘fuel guzzlers’, but an almost 10% increase in the sales of zero emission vehicles, i. e. BEVs.

Fig. 10
figure 10

Relative changes in market shares under six fiscal policy scenarios as of 2014, by CO2 exhaust emission interval, assuming that tax increases are passed on 100% to buyers

Obviously, when only one tax component changes (alt. 2 through 4), the resulting impact is smaller. If only the CO2 component is increased, low emission cars (emitting 1–99 gCO2/km) will gain market shares. Even the weight and power components are seen to have some effect on the market shares of low vs. high emission vehicles. An increased weight component will benefit zero emission vehicles only.

The introduction of purchase tax on BEVs (alt. 5) will have rather moderate effects, assuming BEVs would then be subject to the same tax rules as PHEVs. For most BEVs, the negative CO2 component would in such a case more than outweigh the positive weight component, resulting in zero purchase tax.

But if both exemptions – from VAT and purchase tax – were to be revoked (alt. 6), the BEV market share would drop by an estimated 24%, while the fuel guzzlers would see their market grow by around 10%.

The overall changes in average type approval CO2 exhaust emissions from new passenger cars, under the six different policy scenarios, are shown in Fig. 11.

Fig. 11
figure 11

Absolute changes in mean type approval CO2 exhaust emission rates of new passenger cars, compared to reference case, under six fiscal policy scenarios as of 2014

A uniformly 10% higher purchase tax will reduce the mean exhaust emission level by 2.4 gCO2/km, or about 2.2% compared to the reference level of 113 gCO2/km. Increasing the CO2 or weight component leads to a 1.1 gCO2/km decrease in average exhaust emissions, while an increase in the power component will have very little effect on the CO2 level.

Introducing a purchase tax for BEVs, identical to the one in effect for PHEVs, will lead to a moderate, 0.56 gCO2/km increase in the average exhaust emission level of new cars.

If, however, both the VAT and the purchase tax exemptions are lifted, the result will be an estimated 3.85 gCO2/km higher level of exhaust emissions. The VAT effect alone can be calculated as 3.85–0.56 = 3.3 gCO2/km by the type approval test.

Since, for the 2014 cohort of passenger cars in Europe, exhaust emissions on the road are roughly 40% higher than according to the NEDC laboratory testing cycle [33], the 3.85 gCO2/km type approval differential corresponds to 5.4 gCO2/km in real traffic. For a car running 240,000 km before scrapping, accumulated CO2 savings over the car’s lifetime amount to 1300 kgCO2. For the whole 2014 cohort of Norwegian registered cars (144,202 vehicles), lifetime CO2 savings amount to around 190,000 t.

The fiscal revenue impact of the six policy options is also calculable from the model (Fig. 12).

Fig. 12
figure 12

Differential annual VAT and purchase tax revenue under six fiscal policy scenarios as of 2014

Increasing all purchase tax components by 10% generates an extra NOK 742 million per annum for the public treasury, according to the model. Note, however, that the possible rebound effect in the form of lower aggregate car sales is not taken into account here, nor in any of the other scenarios studied.

Increasing the CO2 component by 10% will have comparatively small effects on the purchase tax revenue. The same is true of the engine power component. The weight component, however, is a potent one. Most of the revenue increase obtained by a uniform 10% increase in all tax components is due to the weight component.

Interestingly, the purchase tax exemption for BEVs reduces public revenue by only NOK 200 million – a small amount compared to the large numbers featured in multiple media announcements on the ‘cost’ of the electric vehicle incentives. Note, however, that our point of reference is a tax regime in which low and zero emission vehicles in general and PHEVs in particular enjoy very much lower tax rates than do fuel guzzlers.

A much larger increase in public revenue would take place if the VAT exemption were lifted as well. In such a case, some car buyers would shift from BEVs to ICE vehicles, whereby the purchase tax revenue would increase, not by NOK 200 million, but by more than NOK 500 million. A more than twice as large revenue increase would come from the VAT systemFootnote 2.

In the long run, reduced exhaust emissions from cars will go along with a proportional decrease in fossil fuel consumption and hence in fuel tax revenue. This effect is not included in our revenue calculations. For a car running 240,000 km before scrapping, a 3.85 gCO2/km difference in type approval exhaust emissions corresponds to fuel savings of roughly 500 l over the vehicle’s lifetime, with a NOK 2500–3000 (= € 300–350) reduced fuel tax bill. As applied to the entire 2014 cohort of new cars, the lifetime fuel tax revenue differential is around NOK 350–400 million.

There is thus an inherent contradiction between the fiscal and environmental policy goals. An effective environmental tax may erode its own base. The consequences could be wide-reaching, since fuel taxes are probably the most important market correction mechanism currently in place in Europe. According to Thune-Larsen et al. [32], the Norwegian petrol tax is just about high enough to balance the vehicles’ average marginal external cost. The per litre diesel tax, however, falls around NOK 3 (= appr. € 0.35) short of the associated external cost. BEVs are subject to only a small electricity tax, despite giving rising to an external cost that is only 30% lower than for petrol cars.

If and when BEVs make up a major share of the car fleet, the need for an alternative market correction mechanism, such as generalised marginal cost road pricing, will come to the fore. Satellite based road pricing was studied extensively in the Netherlands [26], but not implemented. Interestingly, the proposed Dutch scheme appears to have solved the privacy problem, in that the detailed information on the vehicle’s movements would be stored nowhere but in the vehicle owner’s own on-board unit.

4.2 Simulated changes to the fuel cost

To assess the impact on car purchases of changes in the price of fuel, as brought about e. g. by a higher fuel tax, we have simulated 10 and 50% increases in the Fuelcost variable. A generally increased fuel price would lead to proportional changes in the fuel cost of every car model in the sample. Response in terms of fuel consumption would translate into proportional changes in CO2 emissions. The results are shown in Fig. 13.

Fig. 13
figure 13

Mean type approval CO2 exhaust emissions from new automobiles, as simulated for 2010

In the hypothetical event of a 10% higher fuel price in 2010, the mean type approval CO2 exhaust emission rate is predicted to fall from 138.91 to 138.22 gCO2/km, i. e. by 0.5%, implying an elasticity of −0.05. In the case of a 50% price rise, the predicted effect is just about five times stronger: 2.43%, suggesting an almost constant elasticity.

By comparison, estimates of the price elasticity of demand for fuel, as measured in terms of short term car travel and fuel demand responses, generally range between −0.25 and −0.1 [12]. The indirect effect channelled through vehicle choice adds, in other words, an extra 20 to 50% on top of the direct fuel demand response, when assessed in a long-term perspective. The indirect effect works only in the long run, i. e. over the vehicle’s lifetime.

Underlying the indirect vehicle choice response to fuel price increases is, of course, a reallocation from higher to lower emission car models. This is shown explicitly in Figs. 14 and 15. As in Fig. 13, simulations are done as of 2010 – our last full year of sales data.

Fig. 14
figure 14

Predicted vehicle market shares, by type approval CO2 exhaust emission bracket, under actual 2010 and simulated 50% higher fuel cost

Fig. 15
figure 15

Predicted vehicle market shares, by energy carrier and/or curb weight, under actual 2010 and simulated 50% higher fuel cost

A higher fuel cost would induce car customers to buy fewer large cars and more small ones (Fig. 15). Also, since the diesel engine is generally more energy efficient than the petrol engine, a higher fuel price would, in general, boost demand for diesel cars at the expense of petrol cars.

4.3 A counterfactual back-casting

The CO2 component of the vehicle purchase tax was first introduced in 2007 and has since become gradually steeper. In Fig. 16 we show the outcome of a back-casting exercise with five alternatives. The reference scenario (A) mirrors more or less the actual history of the purchase and value added taxes applicable to passenger cars since 2007. In scenario B, we imagine that the CO2 component of the purchase tax was never introduced, but the remaining tax components apply as in the reference path. One notes that already in 2007, there is a marked difference between the two developments, as car buyers in the reference scenario are induced to choose more energy efficient cars with lower CO2 emissions. This shift has also been observed in reality [16].

Fig. 16
figure 16

Counterfactual back-casting simulating the non-introduction of CO2-graduated purchase tax and/or tax exemptions for battery electric cars

Note, however, that since our model does not predict aggregate automobile sales, only how it is distributed among model variants, the rebound effect due to generally cheaper cars in scenario B is not taken into account. D’Haultfoeuille et al. [11] show that such rebound effects are potentially important.

Under alternative C, the removal of the CO2 component is compensated by a 15.5% increase in the weight and power components, sufficient to uphold the government’s total purchase tax revenue during 2007–2014. This scenario is, in other words, fiscal revenue neutral compared to the reference path.

In scenario D, the tax exemptions for BEVs are abolished. Since there are few BEVs on the market in 2007, this policy measure does not take much effect until the last couple of years.

In the most radical scenario E, where neither the CO2 component nor the tax exemptions for BEVs are assumed to come true, the predicted mean type approval rate of CO2 exhaust emissions from new cars in 2014 is 136 gCO2/km, versus 113 gCO2/km under the reference pathFootnote 3. Apparently, the fiscal policy pursued by the Norwegian government since 2007 has been successful in lowering the average CO2 emissions from new cars registered. As of 2014, the CO2 component and the purchase tax and VAT exemptions for BEVs together account for an estimated 23 gCO2/km reduction in the type approval emission rate of new cars.

Note, however, that this estimate does not include the effects of numerous other incentives benefiting zero and low emission cars in Norway, such as the 15% ‘rebate’ in the weight tax component of PHEVs, the zero purchase tax on electric motor power, the BEVs’ access to the bus lane, their strongly reduced ferry fares and annual circulation tax, their exemption from road tolls and public parking charges, and their free recharging in many public parking lots.

Scenario E is not fiscal revenue neutral. A certain rebound effect, of uncertain direction, would have to be expected if this scenario had come true. The removal of the CO2 component would tend to increase aggregate automobile demand, while the imposition of VAT on BEVs would work in the opposite direction.

5 Discussion

Although the issue of GHG abatement through vehicle fleet renewal and electrification receives considerable attention from scientists [23, 29, 31], extensive literature reviews have shown no example of another approach to automobile market forecasting equivalent to ours. It appears to be unique in combining the following three features: (i) Nested logit modelling is applied to a disaggregate set of complete nationwide new vehicle sales data over an extended period. (ii) We specify and estimate an entirely generic model, which can be used to predict the market shares of hitherto non-existent vehicle model variants with certain characteristics. (iii) The model relies exclusively on objective vehicle registration data, requiring no input on household characteristics or preferences. Since our model keeps track of a five-digit number of different passenger car model variants sold in Norway during 16 years, with an average annual sale of about 40 vehicles per model variant, it is as detailed as any disaggregate approach, capturing differences between all the vehicles available in the market.

The generic character of the model does, however, come at a price. The model does not predict automobile sales at the level of the individual vehicle model variant with any degree of precision. Nor is this the intention. Some vehicle model variants are very similar – indeed, in some cases deciding whether two cars represent two different model variants or two versions of the same model variant may seem like a matter of fine judgment. Hence the prediction of demand at the level of the individual vehicle model variant carries less political interest than forecasting at the somewhat more aggregate level, whereby cars are grouped according to, e. g., their make, size, fuel economy or exhaust emissions. At this level, the model appears to discriminate well between various policy scenarios, as demonstrated by the simulation exercise described in Section 4 above. When fed into a dynamic stock-flow cohort model of the car fleet, it becomes a powerful policy support tool [15, 16].

There is at least one big advantage to this kind of disaggregate specification. Precisely because it does not involve averaging across type approved model variants, except that vehicles belonging to the same variant may be differently equipped and styled, aggregation bias is minimized.

But since the model contains no information on the human decision makers, it cannot predict trends rooted in changes occurring to these individuals – such as their income, education, family structure, residence pattern, employment, or travel demand.

The logic of forecasting by means of our model may appear intriguing. The future demand for automobiles will depend, in the aggregate as well as by make and model variant, on what car model variants manufacturers bring to the market. The suppliers determine the assortment of automobiles available. Obviously, our model cannot predict these changes in the choice set. Instead, future choice sets must be formed by assuming that (most) model variants available in our last year(s) of observation continue to be offered in the market, albeit possibly with certain alterations and improvements, such as a steadily improved fuel efficiency. When it is known – or assumed – that new vehicle technology will enter the market, the model user can specify any number of such model variants and include them in the choice set for future years. For the most part, however, forecasts must be based on the concrete model variants already observed in the past or present. In the forecast, these model variants play the role of abstract representatives of the future vehicle assortment.

In econometric models of demand for heterogeneous products, such as ours, an important source of omitted variable bias may be present if the product quality is positively related to its manufacturing cost and hence to its price. Unless the regression model succeeds in capturing all the quality aspects of the product through the inclusion of appropriate independent variables, the numerical value of the price coefficient will be underestimated, since the price embodies certain quality factors not otherwise accounted for. Such a pitfall could apply even to our model. Although our model does include several important quality attributes such as make, size, utility load, engine power, drivetrain, energy carrier, fuel mileage, seat capacity, and number of doors, the attributes not explicitly accounted for are even more numerous – suffice it to mention automatic shift, automatic cruise control, electronic stability control, anti-lock braking systems, airbags, power steering, power windows, leather upholstery, metallic paint, or the innumerable design features which distinguish model variants visibly from one another.

We may, however, have avoided – and perhaps even reversed – this type of bias through the inclusion of the Resourcecostshare variable, defined as the share of the retail price that is not made up by tax. Since it is positively related to the manufacturing and marketing cost of the vehicle, one possible interpretation of the Resourcecostshare variable could be as a residual measure of quality, over and above the quality attributes already included in the regression. It could, on the other hand, also reflect circumstances such as the manufacturer’s market power, profitability or production inefficiency, or simply the vehicle customers’ psychological aversion against taxpaying. Being inversely related to the amount of purchase tax payable, it tends to decrease with the vehicle’s weight, engine power and rate of CO2 emissions. It must, in other words, be interpreted with some caution.

One possible way of acquiring independent information on vehicle quality could be to exploit the many Internet surveys published on how owners perceive the properties of their car. Further research would be needed to ascertain the validity and practicality of such an approach.

6 Summary and conclusions

We have estimated a nested discrete choice model for new passenger cars registered in Norway. The model is based on exhaustive, disaggregate vehicle sales data covering almost 16 years. More than 1.6 million individual vehicle transactions make up the data set.

Since the model was intended to predict the market share of potential future car model variants with known or assumed attributes, care was taken to specify the model as a generic one. Model coefficients have the expected sign, almost all of them being highly significant by the robust t-test. The per kilometre fuel cost coefficient is compatible with car buyers taking full account of future energy cost savings, while also not applying a discount rate much higher than zero.

It was found that the only permissible nest structure is one that assigns all cars of a given make to one nest. There are 21 such nests in the model, the last one being a residual nest assembling ‘all other makes’.

At the disaggregate – i. e., single vehicle model variant – level, estimated response surfaces must be interpreted with great caution. At the more aggregate level, however, the model appears to discriminate well between various policy scenarios, differentiated, e. g., by the size and structure of fiscal penalties and incentives. In using the model for such purposes, one is greatly helped by the fact the model distinguishes between price changes due to taxation and those originating from the manufacturing or marketing side.

Our vehicle choice model differs from most models reported in the literature in that it contains no information on the vehicle owners or their households. Hence the model cannot predict the effect of changes occurring to the car owners rather than to the vehicles themselves. The benefit of this approach is one of considerable simplification, leaving room for a maximally detailed, exhaustive and disaggregate representation of the passenger car market. Also, it means that no input is required on such variables as household structure, population and income growth, or on transport infrastructure and prices, in order for the model to produce a policy dependent forecast.

Automobile choice models are important climate policy decision support tools, since the acquisition of a new car affects GHG emissions for the coming 15–20 years, regardless of whether the new vehicle remains at the hands of its first owner, or is traded second hand.


  1. Travelling, on average, 14,000 km annually, Norwegian registered automobiles have a life expectancy of 17 years [15].

  2. In Norway 2014, 47.4% of new cars were registered to commercial businesses (source: Most of these firms are VAT registered. With the exception of taxi companies, however, corporate buyers are not allowed to deduct input VAT on automobiles in their VAT account. We have therefore included the full amount of VAT on automobiles in our revenue calculations.

  3. The real, observed rates in 2007 and 2014 were 159 and 110 gCO2/km, respectively. Being a stylized instrument, the model does not produce perfectly accurate predictions.


  1. Allcott H, Wozny N (2014) Gasoline prices, fuel economy, and the energy paradox. Rev Econ Stat 96(5):779–795

  2. Ben-Akiva M, Lerman SR (1985) Discrete choice analysis. Theory and application to travel demand. MIT Press, Cambridge, Mass

    Google Scholar 

  3. Berkovec J (1985) Forecasting automobile demand using disaggregate choice models. Transp Res B Methodol 19:315–329

    Article  Google Scholar 

  4. Berkovec J, Rust J (1985) A nested logit model of automobile holdings for one vehicle households. Transp Res B Methodol 19:275–285

    Article  Google Scholar 

  5. Berry S, Levinsohn J, Pakes A (1995) Automobile prices in market equilibrium. Econometrica 63(4):841–940

    Article  MATH  Google Scholar 

  6. Beser Hugosson M, Algers S, Habibi S, Sundbergh P (2016) Evaluation of the Swedish car fleet model using recent applications. Transp Policy 49:30–40

    Article  Google Scholar 

  7. Bierlaire M (2010) Estimating hybrid choice models with the new version of Biogeme. École Polytechnique Fédérale de Lausanne, Switzerland

    Google Scholar 

  8. Brownstone D, Bunch D, Train K (2000) Joint mixed logit models of stated and revealed preferences for alternative-fuel vehicles. Transp Res B Methodol 34:315–338

    Article  Google Scholar 

  9. Cernicchiaro G, de Lapparent M (2015) A dynamic discrete/continuous choice model for forward-looking agents owning one or more vehicles. Comput Econ 46(1):15–34

    Article  Google Scholar 

  10. Choo S, Mokhtarian PL (2004) What type of vehicle do people drive? The role of attitude and lifestyle in influencing vehicle type choice. Transp Res A Policy Pract 38:201–222

    Article  Google Scholar 

  11. D’Haultfoeuille X, Givord P, Boutin X (2013) The environmental effect of green taxation: the case of the French bonus/malus. Econ J 124:F444–F480

    Article  Google Scholar 

  12. Fearnley N, Bekken J-T (2005) Etterspørselseffekter på kort og lang sikt: en litteraturstudie i etterspørselsdynamikk. TØI report 802, Institute of Transport Economics, Oslo

  13. Figenbaum E, Kolbenstvedt M (2016) Learning from Norwegian battery electric and plug-in hybrid vehicle users. TØI report 1492, Institute of Transport Economics, Oslo

  14. Fridstrøm L (1999) Econometric models of road use, accidents, and road investment decisions. Volume II. TØI report 457. Institute of Transport Economics, Oslo

  15. Fridstrøm L, Østli V, Johansen KW (2016) A stock-flow cohort model of the national car fleet. Eur Transp Res Rev 8:22

    Article  Google Scholar 

  16. Fridstrøm L, Østli V (2017) The vehicle purchase tax as a climate policy instrument. Transp Res A 96:168–189

    Google Scholar 

  17. Fridstrøm L, Steinsland C, Østli V (2014) Engangsavgift på personbiler. In: Fridstrøm L, Alfsen KH (eds) Vegen mot klimavennlig transport. TØI report 1321. Institute of Transport Economics, Oslo, pp 92–106

  18. Gillingham K, Iskhakov F, Munk-Nielsen A, Rust J, Schjerning B (2016) Nonstationary equilibrium in the auto market: structural estimation using Danish register data. Unpublished manuscript

  19. Glerum A E, Frejinger E, Karlström A, Hugosson MB, Bierlaire M (2014) A dynamic discrete-continuous choice model of car ownership and usage. STRC 14th Swiss transport research conference; Monte Verità/Ascona, Switzerland

  20. Gramlich J (2010) Gas prices, fuel efficiency, and endogenous product choice in the US automobile industry. Unpublished paper

  21. Kitamura R, Golob TF, Yamamoto T, Wu G (2000) Accessibility and auto use in a motorized metropolis. TRB ID number 00-2273. Paper presented at the 79th Transportation Research Board annual meeting, Washington, DC

  22. Klier T, Linn J (2010) The price of gasoline and new vehicle fuel economy: evidence from monthly sales data. Am Econ J Econ Pol 2(3):134–153

    Article  Google Scholar 

  23. Kloess M, Müller A (2011) Simulating the impact of policy, energy prices and technological progress on the passenger car fleet in Austria – a model based analysis 2010-2050. Energy Policy 39:5045–5062

    Article  Google Scholar 

  24. Lave CA, Train K (1979) A disaggregate model of auto-type choice. Transp Res A Policy Pract 13:1–9

  25. Manski CF, Sherman L (1980) An empirical analysis of household choice among motor vehicles. Transp Res A Policy Pract 14:349–366

    Google Scholar 

  26. Meurs H, Haaijer R, Geurs KT (2013) Modeling the effects of environmentally differentiated distance-based car-use charges in the Netherlands. Transp Res D 22:1–9

    Article  Google Scholar 

  27. Mock P, German J, Bandivadekar A, Riemersma I, Ligterink N, Lambrecht U (2013) From laboratory to road. A comparison of official and ‘real-world’ fuel consumption and CO2 values for cars in Europe and the United States. ICCT, Berlin

  28. Munk-Nielsen A (2015) Diesel cars and environmental policy. University of Copenhagen, Dept. of Economics

    Google Scholar 

  29. Pasaoglu G, Honselaar M, Thiel C (2012) Potential vehicle fleet CO2 reductions and cost implications for various vehicle technology deployment scenarios in Europe. Energy Policy 40:404–421

    Article  Google Scholar 

  30. Rosen S (1974) Hedonic prices and implicit markets: product differentiation in pure competition. J Polit Econ 92:34–55

    Article  Google Scholar 

  31. Thiel C, Perujo A, Mercier A (2010) Cost and CO2 aspects of future vehicle options in Europe under new energy policy scenarios. Energy Policy 38:7142–7151

    Article  Google Scholar 

  32. Thune-Larsen H, Veisten K, Rødseth KL, Klæboe R (2016) Marginale eksterne kostnader ved vegtrafikk – med korrigerte ulykkeskostnader. TØI report 1307, Institute of Transport Economics, Oslo

  33. Tietge U, Zacharof N, Mock P, Franco V, German J, Bandivadekar A, Ligterink N, Lambrecht U (2015) From laboratory to road: a 2015 update of official and 'real-world' fuel consumption and CO2 values for passenger cars in Europe. ICCT, Berlin

    Google Scholar 

  34. Train K, Winston C (2007) Vehicle choice behavior and the declining market share of U.S. automakers. Int Econ Rev 48:1469–1496

    Article  MathSciNet  Google Scholar 

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The basic research underlying this study was made possible through the TEMPO project funded by the Research Council of Norway (grant number 195191) and supported by 12 stakeholder partners, viz. the Norwegian Public Roads Administration, the Ministry of the Environment, the National Rail Administration, the Norwegian State Railways (NSB), Akershus County Council, Ruter AS, the Norwegian Automobile Association (NAF), NHO Transport, NOR-WAY Bussekspress, DB Schenker, Norsk Scania AS, and Vestregionen. Some of the policy analyses reported here were made possible through a grant from the Swedish-Norwegian BISEK programme. The last mile funding for the analysis presented herein came from the Institute of Transport Economics (TØI). The analysis relies on data provided by the Norwegian Road Federation (OFV). The authors are indebted to the editor and to two anonymous referees for their constructive comments, which helped improve the paper. All contributions are gratefully acknowledged.

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Correspondence to Lasse Fridstrøm.

Appendix: Example data file excerpt

Appendix: Example data file excerpt

Table 4 Example model variants entering data set in 2010: VW Golf

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Østli, V., Fridstrøm, L., Johansen, K.W. et al. A generic discrete choice model of automobile purchase. Eur. Transp. Res. Rev. 9, 16 (2017).

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