A generic discrete choice model of automobile purchase

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 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 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).

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

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.

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).

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.

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.

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 lifetime¹, 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.

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.

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 NO_X exhaust emission rates, respectively (Fig. 8). All but the NO_X 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 NO_X components. The total purchase tax cannot, however, become negative, as in a feebate system.

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:

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.

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.

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.

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).

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 system².

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.

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.

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.

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.

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].

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 path³. 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.