Chapter 4. Consumers’ Vehicle Preference Survey
B. Conditional Logit Model
In order to estimate the probability of consumers’ choice of vehicles, we first found the consumers’ utility function regarding the vehicles. This utility function was divided between the observable indirect utility function ( ) and the unobservable probability ( ). The consumer utility function can be expressed as follows:54
1).
In the equation above, xj represents the level of importance of the attribute, j, that consumers consider before selecting the given product. S represents the idiosyncrasies of consumers, and i represents the respondent. This model allows us to
52 Aside from the retail price, fuel type is the most important attribute influencing consumers’ choice of vehicle. The importance of fuel type, in fact, is so great that it could easily outweigh all the remaining attributes under consideration. Accordingly, we deliberately omitted fuel type from our analysis in order to determine the relative importance of all the other attributes.
53 The average mileage of an EV is estimated to be over 50 kilometers per liter (further details provided in the next section), but this mileage (50 km/l) was not included in our analysis because it was too high and had the potential to distort analysis results.
54 See Choi and Lee (2011), p. 107.
find the indirect utility function.
We used a conditional logit model, based upon the 16,576 selectable vehicle sample units, to estimate consumers’ indirect utility. The basic model can be expressed as follows:
2).
In the equation above, Xeff stands for mileage; Xprice, the retail price; Xtime charging time; Xdis, driving distance; and Xco2, carbon dioxide emissions. The indirect utility function V equals one if the given vehicle is chosen by consumers, and zero if the vehicle is not chosen.
Table 4-4. Indirect Utility Function Estimates
Variable Est. coefficient S.E. z P>∣z∣ Odds ratio 95% confidence interval
eff .07264** .00291 24.96 0.000 1.07534 .06694 .07834
price -.00067** .00003 -
26.47 0.000 .99932 -.00072 -.00062
time -.01670** .00189 -8.86 0.000 .98344 -.02040 -.01301
dist .00189** .00011 17.10 0.000 1.00189 .00167 .00211
co2 -.00163** .00046 -3.56 0.000 .99838 -.00252 -.00073
LRχ2(5) 1825.65**
Prob>χ2 0.0000
log L -7462.5227
Pseudo R2 0.1090
Note: **: Statistically significant at a one-percent level.
Table 4-4 lists our estimates of the indirect utility function. First, the hypothesis that the estimated coefficients of mileage (eff), retail price (price), charging time (time), driving distance (dis), and carbon dioxide emissions (co2) equals zero is null at a significance level of one percent, given the likelihood ratio values. Our indirect utility function estimates, therefore, are statistically significant. The signs attached to the estimated coefficients of each variable appear to be appropriate.
Mileage and vehicle choice, for example, bear a positive correlation. The retail price, charging time, and carbon dioxide emissions bear negative correlations, while the driving distance bears a positive correlation. The estimates of all the subcategories of the five attributes are statistically significant at one percent.
Table 4-4 lists the odds-ratio estimates of our analysis. An odds-ratio represents the marginal change, i.e., the margin by which the choice or the utility increases for every unit increase in a given variable. The odds-ratio of mileage, for example, is 1.075. This means that, assuming that all the other variables remain constant, consumers’ likelihood of choosing the given vehicle increases by 7.5 percent for every one-kilometer-per-liter increase in the vehicle’s mileage. Conversely, when the price of a given vehicle rises by KRW 1 million, the odds of consumers choosing that vehicle decreases by 6.7 percent ([1 – 0.99932] * 100). For every minute increase in charging time, the odds of consumers selecting the given vehicle drop by 1.6 percent. For every 100-kilometer increase in the driving distance, the odds of consumers selecting that vehicle increase by 18.9 percent, while every 100-gram-per-kilometer increase in carbon dioxide emissions decreases the odds by 16.2 percent. However, if a given vehicle’s driving distance increases by 100 kilometer, it would most likely be due to a larger battery with a greater capacity. Enlarging the battery ultimately decreases the odds of consumers choosing the vehicle because of other factors such as: a rise in the vehicle price, a drop in mileage (due to the heavier vehicle weight), and an increase in charging time. Caution is thus needed in interpreting the results of the odds-ratio analysis.
Table 4-5. Indirect Utility Function Estimates (Late Adopters)
Variable Est. coefficient S.E. z P>∣z∣ Odds ratio 95% confidence interval
eff .06576** .01212 5.43 0.000 1.06780 .04200 .08951
price -.00076** .00011 -7.02 0.000 .99924 -.00097 -.00055
time -.02465** .00798 -3.09 0.002 .97565 -.04028 -.00901
dist .00118* .00046 2.56 0.011 1.00118 .00027 .00208
co2 -.00168 .00190 -0.89 0.376 .99832 -.00540 .00204
LRχ2(5) 106.68**
Prob>χ2 0.0000
log L -431.72121
Pseudo R2 0.1100
Note: **: Statistically significant at a one-percent level. * Statistically significant at a five-percent level.
Table 4-5 lists the results of our indirect utility function analysis for late adopters (refer to Figure 4-7). The null hypothesis that all the coefficients involved in the model equal zero simultaneously can be dismissed at a significance level of one percent, given the likelihood ratio values. The signs of the coefficients also confirm the prevailing commonsense assumptions. Mileage, price, and charging time are statistically significant at a one-percent level, while driving distance is statistically significant at a five-percent level. Carbon dioxide emissions, on the other hand, fail to show a statistically significant coefficient.
Table 4-6. Indirect Utility Function Estimates (Slow Majority)
Variable Est. coefficient S.E. Z P>∣z∣ Odds ratio 95% confidence interval
eff .07125** .00524 13.60 0.000 1.07384 .06098 .0815141
price -.00076** .00005 -
16.30 0.000 .99923 -.00086 -.0006715
time -.02543** .00346 -7.34 0.000 .97489 -.03222 -.0186394
dist .00186** .00020 9.34 0.000 1.00186 .00147 .0022464
co2 -.00130** .00082 -1.58 0.113 .99870 -.00291 .0003092
LRχ2(5) 656.89**
Prob>χ2 0.0000
log L -2307.0394
Pseudo R2 0.1246
Note: **: Statistically significant at a one-percent level. *Statistically significant at a five-percent level.
Table 4-6 lists the results of our indirect utility function analysis for the slow majority, as shown in Figure 4-7. The null hypothesis that all the coefficients involved in the model would equal zero simultaneously is again dismissed at a significance level of one percent. The signs of the coefficients also confirm the prevailing commonsense assumptions.
Mileage, price, charging time, and driving distance coefficients are statistically significant at a one-percent level. In the
meantime, carbon dioxide emissions fail to show a statistically significant coefficient even at a 10-percent level.
Table 4-7. Indirect Utility Function Estimates (Early Majority)
Variable Est. coefficient S.E. Z P>∣z∣ Odds ratio 95% confidence interval
eff .07786** .00405 19.23 0.000 1.08097 .06993 .08580
price -.00066** .00004 -18.72 0.000 .99934 -.00073 -.00059
time -.01247** .00260 -4.80 0.000 .98761 -.01755 -.00738
dist .00189** .00015 12.28 0.000 1.00189 .00159 .00219
co2 -.00215** .00064 -3.38 0.001 .99785 -.00340 -.00090
LRχ2(5) 956.49**
Prob>χ2 0.0000
log L -3854.9477
Pseudo R2 0.1104
Note: **: Statistically significant at a one-percent level.
Table 4-7 lists the results of our indirect utility function analysis for the early majority, as shown in Figure 4-7. The null hypothesis that all the coefficients involved in the model would equal zero simultaneously is again dismissed at a significance level of one percent. The signs of the coefficients also confirm the prevailing commonsense assumptions. All the variables, including mileage, price, charging time, driving distance, and carbon dioxide emission coefficients are statistically significant at a one-percent level. The early majority is the only group that showed statistically significant coefficients for all the variables in our indirect utility function analysis.
Table 4-8. Indirect Utility Function Estimates (Early Adopters)
Variable Est. coefficient S.E. z P>∣z∣ Odds ratio 95% confidence interval
eff .05676** .00865 6.56 0.000 1.05839 .03980 .07371
price -.00047** .00007 -6.50 0.000 .99953 -.00061 -.00033
time -.00905 .00552 -1.64 0.101 .99099 -.01988 .00177
dist .00234** .00033 7.16 0.000 1.00235 .001701 .00298
co2 -.00015 .00134 -0.11 0.911 .99985 -.00278 .00248
LRχ2(5) 143.29**
Prob>χ2 0.0000
log L -849.967
Pseudo R2 0.0777
Note: **: Statistically significant at a one-percent level.
Table 4-8 lists the results of our indirect utility function analysis for the slow majority, as shown in Figure 4-7. The null hypothesis that all the coefficients involved in the model would equal zero simultaneously is again dismissed at a
significance level of one percent. The signs of the coefficients also confirm the prevailing commonsense assumptions.
While mileage, price, and driving distance coefficients are statistically significant at a one-percent level, charging time and carbon dioxide emissions fail to show a statistically significant coefficient even at a 10-percent level.
We can use the indirect utility functions estimated using the conjoint method and our conditional logit method to estimate the distribution of the probabilities of choosing vehicles of different fuel types.55
3)
In the equation above, i represents the consumer; x, the vector of the consumer’s idiosyncrasies, mileage, price, charging time, driving distance, and carbon dioxide emissions. Meanwhile, j represents the vehicle type (gasoline, diesel, hybrid, plug-in hybrid, or battery), and represents the vector of the estimated coefficients of different variables. In the next chapter, we will apply this equation and our estimates to find the distribution of probabilities of consumers choosing vehicles of different fuel types. We will then use this information to predict consumers’ selection/avoidance of EVs in response to possible changes in the subsidy policy.
Among Tables 4-4 through 4-8, only Tables 4-4 (for all consumers) and 4-7 (for the early majority) showed statistically significant coefficients with respect to all variables. The estimates listed in Table 4-4 will thus only be used in the next chapter, since estimating the probabilities of choice in light of how quickly consumers adapt to changing technology would not give us statistically significant information.
55 Choi and Lee (2011) explains (p. 72): “Assuming that V1 represents the probability variable and the J-number of error terms are independently and identically distributed with a type-I extreme value distribution, the probability of consumer i selecting j among the given alternatives” can be estimated by applying the equation herein.
Chapter 5. Simulated Analysis