H.A. Kayser r Energy Economics 22 2000 331]348 336
Ž .
by Heckman 1976 and is known as the Heckman selection correction model. Gasoline demand is only observed when the household owns a car. Assume that «
i
and n have a bivariate normal distribution with zero means and correlation r. For
i
identification, s
2
is normalized to one. Then the expected gasoline demand can be
u
expressed as: Ž
X
. f
Z g
i X
X X
w Ž
. x
w x
Ž . E
ln g C 0 s E X b q « W g u s X b q rs 3
X i
i i
i i
i i
«
Ž .
F Z g
i
and the demand for gasoline becomes: Ž
X
. f
Z g
i X
Ž .
Ž . ln g s X b q b l q « l s
4
X i
i l
i i
i
Ž .
F Z g
i
In the Heckman selection correction specification, a Probit model is used for the car ownership equation to obtain an estimate for the selection correction term l .
i
An ordinary least squares regression for the gasoline demand equation which includes that estimated selection correction term will lead to consistent estimates
for the coefficients, b, even in the case where the error terms are correlated. For identification of the parameters in the two equations, one of two conditions
must hold. Either the error terms have to be uncorrelated, or if the error terms are correlated, there has to be at least one variable in the vector of explanatory
variables in the car choice equation, W, that is not included in the vector of Ž
explanatory variables in the gasoline demand equation, X Maddala, 1983, pp. .
231]234 . I include an imputed average price of cars for each state. The price of a vehicle should affect the likelihood of owning a car without having an effect on the
Ž . amount of driving. Given the specification in Eq. 4 I can determine the short-run
elasticities as follows: w
Ž .
x d
E ln g
X
i i
Ž .
Ž . h s
s b q b ln m
5
p 1
4
d p
w Ž
. x
d E
ln g X
i i
Ž .
Ž . Ž .
h s s b q
2b ln m q b ln p 6
m 2
3 4
d
m
where m is the mean of average income and p is the average gasoline price in the sample.
3. Data
To estimate the gasoline demand and car-ownership decisions I will use house- Ž
. hold data for 1981 from the Panel Study of Income Dynamics PSID . The data
may appear outdated and are certainly not representative any more in terms of the
H.A. Kayser r Energy Economics 22 2000 331]348 337
characteristics of the car fleet that travels the roads in the United States. However, data from 1981 are the most recent data for one year in which gasoline prices were
changing rather substantially. The year 1981 is the last year of a period of substantially fluctuating prices that followed the oil supply shocks of the late 1970s.
Ever since 1981, gasoline prices in the United States have fallen gradually in real terms. The 1981 data will therefore predict household responses to more substan-
tial increases in the price of gasoline through a carbon tax or any other form of gasoline tax more accurate than would estimates from more recent data.
The PSID is a panel data set that was started in 1968 with approximately 5000 American households. Since 1968 the PSID has collected data annually from the
households in the original sample as well as from any new household that was formed by members of the original families. Each sampled household responds to
approximately 2000 questions. Table A1 in Appendix B presents means and standard deviations for the variables that enter the empirical model. The list of
explanatory variables includes family composition dummies since one would expect households with a larger number of adults to drive more, while households with
children may both require additional transportation services and drive less by staying more in the vicinity of the home. Dummy variables indicating whether the
household is a one-adult household or one with more adults, and indicating whether the household has no children, one child or several children are thus part
of the list of independent variables.
Also included are a number of demographic variables that serve as proxies for unobservable taste differences. Among these characteristics are ethnicity, gender,
age, marital status, and educational attainment of the head.
8
These variables are chosen because they either significantly affect gasoline demand in the works by
Ž .
Ž .
Archibald and Gillingham 1980 , and Greening and Jeng 1994 , or because they are suggested as playing a role in household’s driving through differential treat-
ment by automobile insurance policies. The list of variables includes two variables that define the living environment of
the household: whether a household lives in a rural environment, and whether public transportation is available for the household members to get them to work.
It is likely that households living outside of metropolitan areas have different driving patterns than households who live in a large city or in the vicinity of a large
city. Traveling distances are presumably longer for rural households, and house- holds in rural areas are assumed to drive larger, less fuel-efficient cars. Both higher
annual mileage and lower fuel efficiency should increase the gasoline demand for rural households.
9
Economic factors are the household’s income, the price of gasoline for the household, and the employment status of the head of the household and the
8
Throughout the study I will use as head those designated head in the PSID. In a cohabitating couple this is generally the husband or male partner.
9
A dummy rather crudely classifies households as living in a rural setting if they do not live in or around Ž
. one of the 40 largest Metropolitan Statistical Areas MSA in the United States and if the nearest city
has fewer than 50 000 inhabitants.
H.A. Kayser r Energy Economics 22 2000 331]348 338
spouse. The appropriate measure of household income is controversial. Since annual income may fluctuate substantially from year-to-year, annual income may
not be the appropriate variable to measure a household’s well-being. Rather, according to Friedman’s permanent income hypothesis a better measure of a
household’s income would be a measure that smoothes out annual fluctuation but
Ž maintains variations across different stages in a household’s life-cycle Friedman,
. 1957 . Accordingly, in the empirical work I use an income measure that averages
household’s income over the 11-year period from 1976 to 1986, i.e. an average centered around the reference year of 1981.
10
Since the PSID does not contain information on gasoline prices, the prices used Ž
. in this study are those developed by Chernik and Reschovsky 1992 . Using data
from the Bureau of Labor Statistics, Chernik and Reschovsky assign average retail prices directly to households living in or around any of the 30 larger cities in the
United States for which gasoline price data are readily available. The rest of the sample is stratified according to four US regions and three city sizes, resulting in 42
different prices net of taxes. For each state, these prices are adjusted to include local, state and federal taxes when these are applicable. Because of regional
differences in the cost-of-living, all other prices are represented by a regional price index that reflects cost of living differences by state, as published by Fournier and
Ž .
Rasmussen 1986 for the year 1980. The PSID also does not contain information on gasoline consumption or on the
gas mileage which could be used to estimate households’ gasoline consumption. Consequently, prior studies have calculated each household’s gasoline consumption
by dividing the reported miles by the average national fuel efficiency. However, this is a crude measure that ignores any variation in the fuel efficiency of car fleets
across the population. In this study I adopt the following procedure to estimate gas
Ž .
mileage. Using the 1983 Survey of Consumer Finances SCF and the annual Gas Mileage Guides for New Car Buyers from the Environmental Protection Agency
Ž .
11
1974]1986 , I impute household specific gas mileage. The Survey of Consumer
Finances contains information on the number of cars as well as the make, model, and vintage of the first three cars in the household. I assign the fuel efficiency
values for each make, model, and year of a car from the Gas Mileage Guide to the corresponding cars in the SCF and take a simple average across the cars in a
household to arrive at an average fuel efficiency value of the household’s car fleet for all households in the SCF. In a second step I run an ordinary least squares
Ž .
regression of the imputed miles per gallon mpg , on a vector of explanatory variables, X, that includes household income, gender, ethnicity, and age of the
household head, employment information, and information about the residential location of the household. The coefficients from the regression using data from the
SCF, b
, are used to calculate predicted fuel efficiency values for each
83, SCF
household in the PSID according to the following equation:
10
Not all households are part of the survey for all 11 years, in which case the average is calculated from the years that are available.
11
Some descriptive statistics for this imputed fuel efficiency variable can be found in Appendix C.
H.A. Kayser r Energy Economics 22 2000 331]348 339
X
Ž . mpg
s b X
7
83 ,PSID 83,SCF
83,PSID
Table A2 in Appendix B shows the coefficients and standard errors of the mpg regression from which the coefficients b
are taken to impute fuel efficiency
83,SCF
Ž . value for households in the PSID according to Eq. 7 . Using this more disaggre-
gate measure of fuel efficiency, gasoline consumption is calculated by dividing the reported miles driven by the household-specific fuel efficiency. Since an imputed
value from another data set is used, gasoline consumption will be subject to errors in measurement that can lead to biased estimates.
12
I also impute the estimated cost of a car using the SCF. The SCF contains information about the bluebook value for each of the first three cars in the
household. For households with more than one car, the average car value was constructed. Regressing the average car value on household characteristics such as
work status, household income, region of residence, number of adults, number of children, gender, race, and marital status in the SCF, I estimate coefficients that I
can use to impute the average car value for all households in the PSID based on their household characteristic. Households that do not own a car thus also have a
value of a car assigned to them. This value serves as a proxy for the amount of money a household with the given characteristics can be expected to spend were
they to buy a car.
4. Estimation results
