Mileage-Based User Fee Winners and Losers - RAND Corporation

A growing body of research suggests that price elasticity is not constant among households
(Blundell, Horowitz, and Parey 2011). Particularly relevant to this study are research demonstrating
that households with lower incomes are more price elastic than households with higher incomes
(Wadud, Graham, and Noland 2009; Bento et al. 2009; West 2005). 26 This can be incorporated into
the model developed here by adding a term that allows price to interact with income (Zhang et al.
2009; McMullen, Zhang, and Nakahara 2010; Weatherford 2011). The price elasticity is now a
function of the natural log of income and the coefficients on the natural log of price variable and
the interaction term. Price elasticity has also been shown to vary with other socio-economic
variables and population density (Bento et al. 2009; West 2005).
The model is also biased because vehicle choice is endogenous. The choices of whether to
own a vehicle, what type (truck or car, for example), how many vehicles of each type to own, and
how much to drive each vehicle are all separate decisions that households must make. Household
socioeconomics and geography predict these choices and, by not separately modeling those choices
the estimates are biased. The model compounds this problem by then holding current vehicle
ownership, and the proportion of household VMT per vehicle, fixed. This approach was chosen to
avoid the need to make certain simplifying assumptions, discussed in greater detail later in this
chapter, which would have prevented the disaggregation of households by certain socio-economic
details. This modeling approach is also relatively simple, the results are easier to interpret, and
requires no additional data in addition to the NHTS data. However, the resulting endogeneity bias
overestimates the price elasticity of demand for VMT.
To minimize this bias, the price elasticity is allowed to vary with characteristics of the
household’s vehicle stock. Households that own different types of vehicles have been found to be
less sensitive to changes in price (McMullen, Zhang, and Nakahara 2010; Weatherford 2011). For
this study, three variables are interacted with price. This specification, in Equation 3.2, allows
household price elasticity to vary with the number and the fuel economy of the vehicles owned by
each household:
lnM i = α + β 1 lnp i + β 2 lnY i + β 3 lnV i + β 4 lnDist i + β 5 lnDensity i + β 6 W i (3.2)
+ β 7 (lnp i *lnY i )+ β 8 (lnp i *MPG i ) + β V2 lnp i + β V3 lnp i
+ β MULTI + β TRANSIT + β HH_TYPE + β LIFECYCLE + β STATE + ε i
where:
lnp i *MPG i is the percentage difference in MPG between the most and least efficient vehicles
in household i interacted with the natural log of household i ’s price per mile,
and
β V2 & β V3 are two parameters on the natural log of price per mile that are estimated if
household i owns 2 vehicles or 3 or more vehicles.
The fourth column of Table 3.2 reports the fitted coefficient values and their robust standard errors
for the model with price interactions fitted using the pooled NHTS data. All of the coefficients are
statistically different from zero at a 1 percent significance level.
In this model there are 5 variables with price as a component. Consequently, it is incorrect to
simply interpret β 1 as the price elasticity. The price elasticity of demand for VMT now varies by
household with income and characteristics of the household’s vehicle stock. The price elasticity is
26 Blundell et al (2011) find that price elasticity may not vary with income monotonically and that both low income households and
high income households have lower price elasticities than do middle income households. This suggests that price increases may
make the fuel tax or MBUF more regressive than estimated in this study.
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