Mileage-Based User Fee Winners and Losers - RAND Corporation

MPG Difference between Household’s Most and Least Efficient Vehicles
In this model, households are not allowed to change the number or type of vehicles owned
and how much these are driven in response to changes in tax policy. Further, in households owning
more than one vehicle, the share of annual VMT per vehicle is held constant. These are very strong
assumptions made to simplify the model that may or may not be reasonable. In fact, they may be
reasonable assumptions given the relatively small change in the price per mile for most households
for most of the alternatives. Households with more than one vehicle do have more short-run
flexibility that other households do not have and may be less sensitive to changes in price. It was
previously demonstrated that households with more than one vehicle have lower price elasticity. This
variable shows that households with vehicles of various fuel efficiencies have a “substitute” that
allows them to be less sensitive to changes in price because they can switch some driving to other
vehicles should the price increase or, for that matter, decrease. Instead of explicitly modeling how
much each household chooses to drive each vehicle, this model uses an interaction term to allow the
price elasticity to vary.
In previous research, a dummy variable has been used to indicate whether a household owns
a “substitute” vehicle. This variable is set equal to one if a household owns more than one type of
vehicle, for example an SUV and a pickup. This dummy variable is interacted with price and has the
effect of reducing the price elasticity of demand (McMullen, Zhang, and Nakahara 2010). While
multiple types of vehicles are positively correlated with VMT, the interaction term is not statistically
significant in McMullen, Zhang, and Nakahara (2010). This may be because the type of vehicle is
not a very good predictor of MPG; there are fuel efficient small pickups and fuel inefficient sports
cars, for example. The range of fuel efficiency is particularly large among automobiles. Therefore a
household can have a legitimate MPG substitute with two cars while another that owns a van and a
SUV may not have a legitimate MPG substitute.
Weatherford (2011) proposes an improvement to this approach by introducing a second
dummy variable indicating whether or not a household owns two or more vehicles where the MPG
of one of the vehicles is 20 percent or more fuel efficient than the average MPG of the household.
This variable more clearly indicates whether or not the household has a vehicle that is more, or less,
fuel efficient than the others owned by the household, regardless of type. It is problematic, however,
in that the 20 percent threshold is arbitrary.
This study introduces a continuous alternative to the MPG “substitute” variable in using the
percentage difference between the most fuel efficient and the least fuel efficient vehicle in the
household. This household MPG range variable addresses both of the concerns raised above and
indicates not only whether a household owns a vehicle that is a “substitute” based entirely on MPG
criteria, but also captures how good a substitute that vehicle is. Because the price elasticity works in
both directions, it is important to use a variable for which the coefficient will always have the same
sign.
The percentage difference is calculated by dividing the MPG of the household’s least
efficient vehicle from the MPG of the household’s most efficient vehicle and then dividing that
difference by the MPG of the most efficient vehicle. For this variable, 36 percent of households
have a value of zero because they either have only one vehicle or, in relatively rare cases, have two
vehicles with the same MPG. 33 The distribution of this variable, in Figure 3.4 shows that many
households with two or more vehicles have a non-trivial difference in the fuel economy between
their most and least fuel efficient vehicles. The percentage difference in MPG between the most and
33 Only 345 observations with a value of zero for this variable, less than 1 percent, own two or more vehicles.
Page 38 of 131