Energy Economics 20 Ž1998. 273]295
Gasoline demand revisited: an international
meta-analysis of elasticities
Molly Espey U
Department of Applied Economics and Statistics, Uni¨ersity of Ne¨ada, Reno, NV 89557, USA
Abstract
Meta-analysis is used to determine if there are factors that systematically affect price and
income elasticity estimates in studies of gasoline demand. Four econometric models are
estimated, using long-run and short-run price and income elasticity estimates from previous
studies as the dependent variables. Explanatory variables include functional form, lag
structure, time span, national setting, estimation technique, and other features of the model
structure. Elasticity estimates are found to be sensitive to the inclusion or exclusion of some
measure of vehicle ownership. Static models appear to overestimate short-run elasticities,
underestimate long-run price elasticities, but pick up the full long-run income responsiveness. There is variation in the elasticity of demand across countries, especially in the
short-run, and gasoline demand appears to be getting more price-elastic and less incomeelastic over time. Q 1998 Elsevier Science B.V.
JEL classification: Q41
Keywords: Gasoline demand; Demand elasticities; Meta-analysis
1. Introduction
A large number of econometric studies of gasoline demand have been conducted
over the years, particularly during the 1970s and the early 1980s when fuel prices
were high and concerns about energy conservation and energy security were strong.
U
Tel.: q1 702 7841679; fax: q1 702 7841342.
0140-9883r98r$19.00 Q 1998 Elsevier Science B.V. All rights reserved
PII S0140-9883Ž97.00013-3
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M. Espey r Energy Economics 20 (1998) 273]295
Recent concerns about global warming and increasing levels of carbon in the
atmosphere have reignited interest in understanding the demand for gasoline,
particularly in explaining cross-country differences in gasoline consumption and
automobile driving and in predicting the impact of fuel tax changes on driving and
fuel consumption. Many gasoline demand studies have also been motivated by
interest in the role of income in gasoline demand, and how expected increases in
income over time would affect fuel consumption and automobile use. With automobile ownership and vehicle miles traveled increasing in virtually every country
over the past two decades, determining the role of fuel prices and income in fuel
consumption is integral to effective environmental policy-making at both the
national and international level.
A wide variety of models have been estimated, using different functional forms
and estimation techniques, covering different time periods and different parts of
the globe in the effort to better understand gasoline demand. This study summarizes and analyzes these efforts using a technique called meta-analysis. The models
used here follow the meta-analysis work conducted by Assmus et al. Ž1984. and
Tellis Ž1988. in marketing studies of sales elasticities, Smith and Kaoru Ž1990. in
recreation benefit estimates, and Espey et al. Ž1997. in residential water demand
analysis. Meta-analysis can be used to analyze estimates of price or income
elasticities and explain the variation by interstudy differences.
While there have been qualitative summaries of gasoline demand research
ŽDahl, 1986; Sterner, 1990; Dahl and Sterner, 1991. and some quantitative analysis
through stratification of results by model characteristics ŽDahl and Sterner, 1991.,
meta-analysis provides a complementary quantitative summary of past research.
Espey Ž1997. used meta-analysis to summarize studies of gasoline demand in the
United States. This paper expands upon that work by Ž1. using a more comprehensive set of studies from throughout the world, and Ž2. separately analyzing long-run
and short- or medium-run elasticity estimates.
2. Data
This study is based on a review of articles from a wide array of journals, reports,
and books, published between 1966 and 1997, covering the time period from 1929
to 1993. Many of these studies involved multiple models that differed by region, by
functional form, by estimation method, or by what variables were included. Those
models that estimated a positive price elasticity of demand or a negative income
elasticity of demand, usually the result of small samples and not statistically
significant, were excluded from this analysis.
Review of the literature yielded 277 estimates of long-run price elasticity, 245
estimates of long-run income elasticity, 363 estimates of short- or medium-run
price elasticity, and 345 estimates of short- or medium-run income elasticity. Sec. 3
discusses the categorization of estimates as long-run versus short- or medium-run
elasticities and the other characteristics of the meta-analysis model. The studies
included in this analysis are listed in Table 1.
M. Espey r Energy Economics 20 (1998) 273]295
Table 1
List of studies included in the meta-analysis
AuthorŽs.
Year published
Abdel-Khalek
Adams, Graham and Griffin
Al-Faris
Andreasson
Archibald and Gillingham
Archibald and Gillingham
Archibald and Gillingham
Arimany de Padlos
Baas, Hughes and Treloar
Baltagi and Griffin
Baltagi and Griffin
Beardsel, Bernard and Thivierge
Bentzen
Berkowitz, Gallini, Miller and Wolfe
Berndt and Botero
Berzeg
Blair, Kaserman and Tepel
Blum, Foos and Gaudry
Burright and Enns
Castenada
Dahl
Dahl
Danielson and Agarwal
Dargay
Dargay
Data Resources Inc.
Destais
Dewees et al.
Donnelly
Donnelly
Donnelly
Donnelly
Drollas
Elkhafif
Eltony
Eltony
Eltony
Eltony and Al-Mutairi
Fishelson
Flemig
Folie
Foos and Gaudry
Fotiadis, Hutzel et al.
Gallini
Garbacz
Garbacz
Garbacz
Gately
Gaudry
1988
1974
1993
1979
1978
1980
1981
1977
1982
1983
1997
1986
1994
1990
1985
1982
1984
1986
1974
1982
1978
1982
1976
1984
1988
1973
1985
1975
1981
1982
1984
1985
1984
1993
1993
1994
1996
1995
1982
1979
1977
1986
1980
1983
1986
1989
1993
1992
1984
275
276
M. Espey r Energy Economics 20 (1998) 273]295
Table 1 Ž Continued.
AuthorŽs.
Year published
Goel and Morey
Greene
Greene
Greene
Greene
Greening
Griffin
Hartman, Hopkins and Cato
Hein
Houthakker and Taylor
Houthakker, Verleger and Sheehan
Hsing
Hsing
Hughes
Hughes
Iqbal
Kennedy
Koshel and Bradfield
Kraft and Rodekohr
Kriegsman
Kwast
Lin, Botsas and Monroe
McGillivray
McRae
Mehta, Narasimham and Swamy
Miklius, Leung and Siddayao
Mount and Williams
Nilsson
Ostro and Naroff
Peleaz
Phlips
Pindyck
Proske
Puwein
Ramsey et al.
Reza and Spiro
Rodekohr
Schou and Johnson
Springer
Springer and Resek
Sterner
Stewart and Bennett
Suits and Wang
Tishler
Tishler
Tsurumi
1995
1979
1980
1981
1983
1995
1979
1981
1969
1966
1974
1990
1994
1980a
1980b
1985
1974
1977
1978
1980
1980
1985
1976
1994
1978
1986
1981
1986
1980
1981
1972
1979
1979
1981
1975
1979
1979
1979
1978
1981
1988
1975
1988
1980
1983
1980
M. Espey r Energy Economics 20 (1998) 273]295
277
Table 1 Ž Continued.
AuthorŽs.
Year published
Uri
Uri and Hassanein
Verleger
Wheaton
Wong, Venegas and Antiporta
Yang and Hu
1980
1985
1975
1982
1977
1984
Overall
1966]1997
3. Empirical model
Four models are estimated: two that explain the variation in the estimates of the
price elasticity of the demand for gasoline, one for long-run and one for short- or
medium-run estimates Žhereafter referred to simply as short-run., and two that
explain the variation in the estimates of the income elasticity of the demand for
gasoline, one for long-run and one for short-run estimates. Elasticity estimates,
rather than the coefficient estimates for price and income, are used as the
dependent variables because elasticities are unit-free, easily interpreted, and
comparable across studies.
Models with some sort of lagged structure produce both short- and long-run
elasticity estimates. Models that include some measure of vehicle ownership
andror fuel efficiency measure more of a short-run or medium-run elasticity. The
most debate over classification of estimates as short-run or long-run is probably
over static models that include price and income, but no measure of vehicle stock
or the fuel efficiency of that stock. Some researchers argue that because stock and
efficiency are not included, such models measure long-run responses to prices and
income. However, since responses to fuel price or income changes can take a
decade or more to be reflected through turnover of the vehicle stock, if the data
only covers a few years and includes only one country or countries with similar
prices and incomes, the data might not reflect the full long-run response, and
hence elasticity estimates might be better classified as short-run or medium-run.
In this study, if the elasticity estimates were not defined as short-run or long-run
by the author and were not possible to indisputably categorize them as one or the
other, they were included in both the long-run and the short-run models. As will be
discussed in Sec. 4, variables included in the meta-analysis model will make it
possible to distinguish among these different gasoline demand model characteristics.
Figs. 1]4 show the range of short-run and long-run price elasticity estimates and
short-run and long-run income elasticity estimates. Short-run price elasticity estimates for the demand for gasoline range from 0 to y1.36, averaging y0.26 with a
median of y0.23 for the studies included here. Long-run price elasticity estimates
range from 0 to y2.72, averaging y0.58 with a median of y0.43. Short-run
278
M. Espey r Energy Economics 20 (1998) 273]295
Fig. 1. Short-run price elasticity estimates for gasoline demand.
income elasticity estimates range from 0 to 2.91, averaging 0.47 with a median of
0.39, and long-run income elasticity estimates for these studies range from 0.05 to
2.73, averaging 0.88 with a median of 0.81.
The basic hypothesis of this analysis is that the variation in these elasticity
estimates arises because of differences in Ža. the assumptions inherent in the
behavioral model underlying the demand, including measures of quantity, price,
income, vehicle ownership, countries included, and the time frame of the data; Žb.
the specifications of the estimated demand function; andror Žc. the econometric
estimation technique.
These model characteristics have been categorized here as differences in the
following.
3.1. Demand specification
The inclusion or exclusion of potentially significant explanatory variables, including some measure of automobile ownership, vehicle characteristics such as fuel
economy, and other variables such as regional or seasonal dummy variables,
population density, the percentage of total vehicles that are trucks or busses, and
the percentage of the population in a certain age range, is part of the demand
specification. This demand specification category also includes functional form:
linear, multiplicative, or indirect. Indirect estimates of price and income elasticities
are derived from the results of two or more models of the separate components of
M. Espey r Energy Economics 20 (1998) 273]295
Fig. 2. Long-run price elasticity estimates for gasoline demand.
Fig. 3. Short-run income elasticity estimates for gasoline demand.
279
280
M. Espey r Energy Economics 20 (1998) 273]295
Fig. 4. Long-run income elasticity estimates for gasoline demand.
fuel consumption: driving, vehicle ownership, and fuel efficiency. The final demand
specification category is lag structure. A variety of lag structures have been used in
estimating gasoline demand, from inclusion of a lagged dependent variable in the
form of a partial adjustment model, to geometric lags and inverted-V lags. Since
there were few observations on any one lag structure other than the partial
adjustment model, all other lag structures were grouped in an ‘other lag’ category.
A variable is also included to distinguish between quarterly lags and annual lags.
3.2. Data characteristics
This category includes the measurement of the dependent variable, gasoline
consumption, as either an aggregate measure, consumption per capita, consumption per vehicle, or consumption per household. It also includes the time interval of
the data used in the study, either monthly, quarterly, or yearly, and whether the
data was time-series, cross-sectional, or cross-sectional time-series.
3.3. En¨ironmental characteristics
Environmental characteristics includes information about the level of the data,
the setting, and the time span analyzed. The level of the data is either panel data,
state or provincial level data, or national level data. Several models specifically
estimated demand for a state or a province and several others estimated a
‘regional’ demand Že.g. the New England region of the US.. Two dummy variables
M. Espey r Energy Economics 20 (1998) 273]295
281
were included to account for these studies. The various settings include the United
States, the United States pooled with some other countries Žtypically Europe or
Canada., European countries, and Australia, New Zealand, and Canada.1 All
others were grouped into an ‘other countries’ category and were typically studies of
developing countries with lower, but fast growing levels of vehicle ownership and
automobile driving. Finally, dummy variables are included for those studies for
which 75% or more of the data is either from before 1974, between 1974 and 1981,
or after 1981, when fuel prices began to fall.
3.4. Estimation method
There has been a wide range of methods used to estimate the demand for
gasoline. However, several methods were only used a few times. Ordinary least
squares ŽOLS., generalized least squares ŽGLS., maximum likelihood, error components, random coefficients, and seemingly unrelated regression models have all
been estimated a number of times. Box-Cox was included as a separate estimation
technique for the short-run models but since there were so few observations, it was
pooled with maximum likelihood Žsince it actually is a maximum likelihood technique. for the long-run models. Table 2 lists these model characteristics and their
frequency in previous gasoline demand models for both short-run and long-run
price elasticity estimates. Table 3 shows these frequencies for the short-run and
long-run income elasticity estimates.
4. Results
All of the models are estimated using a linear model specification and the White
Ž1980. heteroskedasticity-consistent estimation. The estimated coefficients for the
model of short-run price elasticity are shown in Table 4, for long-run price
elasticity in Table 5, short-run income elasticity in Table 6, and long-run income
elasticity in Table 7. In order to estimate the model and avoid perfect multicollinearity, several variables were omitted before estimation. Hence, the coefficient estimates shown in Tables 4]7 should be interpreted as deviations from the
base model comprised of the omitted variables. This base is OLS estimation of a
log-linear partial adjustment model with annual, national level, time series data for
the United States using aggregate gasoline consumption as the dependent variable
and gasoline prices and per capita income as the explanatory variables.
It is possible that the lack of independence across some of the observations,
where several elasticity estimates are drawn from the same data set, could affect
the standard errors and hence invalidate tests of hypotheses. The potential impact
of this was estimated by calculating the correlation among the error terms for each
1
Australia, New Zealand, and Canada were grouped together because of similar driving, vehicle
ownership, and fuel pricing characteristics, all of which are between the US and Europe.
282
M. Espey r Energy Economics 20 (1998) 273]295
Table 2
Frequency of variables included in the price elasticity meta-analysis
Variable class
Variable
Number of observations
Short-run
Demand specification
Data characteristics
Environmental characteristics
Estimation method
Total
Level of vehicle ownership included
Vehicle characteristics included
Other variables included
Functional form:
Linear
Multiplicative
Indirect
Lag structure:
Partial adjustment
Other lag
Static model
Quantity measure:
Aggregate
Per capita
Per vehicle
Per household
Time interval:
Monthly
Quarterly
Yearly
Time series
Cross-sectional
Cross-sectional-time series
Panel data
State or provincial data
National level data
Setting:
United States
US combined with others
Europe
Australia, New Zealand, or Canada
Other
Time span:
Pre-1974
1974 to 1981
Post-1981
Other
OLS
GLS
Box-Cox
Maximum likelihood
Error components
Random coefficients
SURE
Long-run
135
40
123
61
16
90
33
317
13
24
244
9
150
29
186
150
28
105
124
161
62
16
99
149
26
3
79
58
226
251
11
101
65
42
170
196
10
71
12
124
227
0
108
169
125
25
101
53
59
99
26
68
42
42
81
73
7
202
65
69
4
139
183
94
6
25
23
14
18
127
79
3
25
13
12
18
363
277
M. Espey r Energy Economics 20 (1998) 273]295
283
Table 3
Frequency of variables included in the income elasticity meta-analysis
Variable class
Variable
Number of observations
Short-run
Demand specification
Data characteristics
Environmental characteristics
Estimation method
Total
Level of vehicle ownership included
Vehicle characteristics included
Other variables included
Functional form:
Linear
Multiplicative
Indirect
Lag structure:
Partial adjustment
Other lag
Static model
Quantity measure:
Aggregate
Per capita
Per vehicle
Per household
Time interval:
Monthly
Quarterly
Yearly
Time series
Cross-sectional
Cross-sectional-time series
Panel data
State or provincial data
National level data
Setting:
United States
US combined with others
Europe
Australia, New Zealand, or Canada
Other
Time span:
Pre-1974
1974 to 1981
Post-1981
Other
OLS
GLS
Box-Cox
Maximum likelihood
Error components
Random coefficients
SURE
Long-run
128
31
112
34
12
81
28
310
7
20
218
7
141
29
175
130
23
98
118
151
62
14
96
140
9
0
71
56
218
238
11
96
59
42
144
186
6
53
11
116
218
0
103
142
115
26
96
49
59
87
7
70
41
40
81
67
6
191
62
61
2
120
169
84
5
25
23
14
18
112
62
3
24
12
13
18
345
245
284
M. Espey r Energy Economics 20 (1998) 273]295
Table 4
Meta-analysis coefficient estimates: short-run price elasticity of gasoline demand
Variable
Demand specification:
Level of vehicle ownership
Vehicle characteristics
Other variables
Functional form:
Linear model
Indirect estimate
Lag structure:
Quarterly lag
Other lags Žnot partial adjustment.
Static model
Data characteristics:
Quantity measure:
Per capita
Per vehicle
Per household
Time interval:
Monthly
Quarterly
Cross-sectional
Cross-sectional-time series
Environmental characteristics:
Panel data
State or provincial level data
State demand dummy
Regional demand dummy
Setting:
US plus other countries
Europe
Australia, New Zealand, or Canada
Other countries
Time span:
Pre-1974
1974 to 1981
Post-1981
Estimation technique:
Generalized least squares
Box-Cox
Maximum likelihood estimation
Random coefficients estimation
SUR estimation
Error components
Constant
Adjusted R2
Coefficient
T-statistic
0.055
0.093
0.049
1.64
2.43
1.53
y0.000
y0.036
y0.00
y0.76
0.106
0.006
y0.192
2.21
0.18
y5.54
y0.019
0.044
y0.067
y0.68
1.04
y0.77
y0.054
0.018
y0.282
0.052
y1.41
0.46
y3.93
1.82
y0.260
y0.057
0.096
y0.043
y2.73
y1.28
1.36
y0.44
y0.188
y0.092
y0.002
y0.026
y3.32
y2.95
y0.07
y0.94
y0.108
0.049
0.404
y2.89
1.40
2.65
0.029
0.031
y0.126
0.166
0.033
0.067
y0.159
0.82
0.77
y3.07
2.57
0.63
1.52
y5.03
0.3442
M. Espey r Energy Economics 20 (1998) 273]295
285
Table 5
Meta-analysis coefficient estimates: long-run price elasticity of gasoline demand
Variable
Demand specification:
Level of vehicle ownership
Vehicle characteristics
Other variables
Functional form:
Linear model
Indirect estimate
Lag structure:
Quarterly lag
Other lags Žnot partial adjustment.
Static model
Data characteristics:
Quantity measure:
Per capita or per household
Per vehicle
Time interval:
Monthly
Quarterly
Cross-sectional
Cross-sectional-time series
Coefficient
T-statistic
0.218
0.078
0.074
2.05
0.46
0.86
y0.110
y0.337
y1.46
y1.66
0.368
y0.092
0.253
2.48
y0.93
3.12
y0.031
y0.160
y0.31
y1.28
0.030
0.169
y0.148
0.090
0.18
1.37
y0.82
0.76
y0.158
0.499
y0.136
y1.10
2.41
y0.61
Environmental characteristics:
State or provincial level data
State demand dummy
Regional demand dummy
Setting:
US plus other countries
Europe
Australia, New Zealand, or Canada
Other countries
Time span:
Pre-1974
1974 to 1981
Post-1981
y0.205
0.082
0.226
y0.052
y1.27
0.75
2.91
y0.42
y0.082
y0.205
y0.508
y0.92
y1.30
y1.97
Estimation technique:
Generalized least squares
Maximum likelihood estimation
Random coefficients estimation
SUR estimation
Error components
Constant
0.103
y0.062
0.355
0.060
0.166
y0.814
0.87
y0.58
3.00
0.36
1.12
y6.22
Adjusted R2
0.2806
286
M. Espey r Energy Economics 20 (1998) 273]295
Table 6
Meta-analysis coefficient estimates: short-run income elasticity of gasoline demand
Variable
Demand specification:
Level of vehicle ownership
Vehicle characteristics
Other variables
Functional form:
Linear model
Indirect estimate
Lag structure:
Quarterly lag
Other lags Žnot partial adjustment.
Static model
Data characteristics:
Quantity measure:
Per capita
Per vehicle
Per household
Time interval:
Monthly
Quarterly
Cross-sectional
Cross-sectional-time series
Environmental characteristics:
Panel data
State or provincial level data
State demand dummy
Regional demand dummy
Setting:
US plus other countries
Europe
Australia, New Zealand, or Canada
Other countries
Time span:
Pre-1974
1974 to 1981
Post-1981
Estimation technique:
Generalized least squares
Box-Cox
Maximum likelihood estimation
Random coefficients estimation
SUR estimation
Error components
Constant
Adjusted R2
Coefficient
T-statistic
y0.155
y0.101
y0.060
y2.73
y1.74
y1.08
0.010
y0.018
0.16
y0.15
0.207
0.062
0.454
1.97
1.01
7.58
y0.034
y0.023
0.015
y0.75
y0.28
0.11
y0.199
y0.051
y0.257
y0.024
y2.03
y0.44
y1.49
y0.35
0.095
y0.11
0.273
y0.198
0.55
y1.59
2.89
y2.20
0.253
0.176
0.049
0.137
2.50
2.85
0.82
1.99
0.065
y0.056
0.138
1.07
y0.85
0.61
y0.106
y0.120
y0.109
0.261
0.033
y0.097
0.316
y2.12
y1.08
y1.66
3.07
0.34
y1.34
4.68
0.2850
M. Espey r Energy Economics 20 (1998) 273]295
287
Table 7
Meta-analysis coefficient estimates: long-run income elasticity of gasoline demand
Variable
Demand specification:
Level of vehicle ownership
Vehicle characteristics
Other variables
Functional form:
Linear model
Indirect estimate
Lag structure:
Quarterly lag
Other lags Žnot partial adjustment.
Static model
Data characteristics:
Quantity measure:
Per capita or per household
Per vehicle
Time interval:
Monthly
Quarterly
Cross-sectional
Cross-sectional-time series
Coefficient
T-statistic
y0.384
y0.244
0.025
y2.96
y1.17
0.23
y0.025
0.496
y0.21
1.14
y0.085
0.022
y0.030
y0.38
0.22
y0.30
0.080
0.218
0.83
1.11
y0.011
0.058
y0.213
0.025
y0.05
0.24
y0.68
0.21
0.253
y0.521
y0.329
1.92
y2.12
y1.17
Environmental characteristics:
State or provincial level data
State demand dummy
Regional demand dummy
Setting:
US plus other countries
Europe
Australia, New Zealand, or Canada
Other countries
Time span:
Pre-1974
1974 to 1981
0.106
0.298
y0.211
0.281
0.57
2.70
y2.21
2.20
y0.037
y0.182
y0.38
y1.63
Estimation technique:
Generalized least squares
Maximum likelihood estimation
Random coefficients estimation
SUR estimation
Error components
Constant
y0.040
y0.068
0.075
y0.213
y0.349
0.900
y0.23
y0.68
0.40
y0.96
y2.46
7.02
Adjusted R2
0.2642
288
M. Espey r Energy Economics 20 (1998) 273]295
of the studies with four or more elasticity estimates drawn from the same data set.
This allowed at least seven values from which to calculate the correlation coefficient.
In each of the models in this study, there were several sets of observations for
which these correlations were relatively high. These correlations suggest biased
error terms within these sets of observations. However, the studies with errors
biased in either direction made up at most 7.5% of the sample for the four models
estimated here, suggesting that the dependence across elasticity estimates is not a
major concern. Simply including a dummy variable for each set of observations
with highly correlated errors would produce consistent estimates unless the new
dummy variable is correlated with some other variable in the model. While some of
the correlated observation dummy variables were correlated with some of the other
variables in the model, inclusion of these addition dummy variables did not
substantially affect the model results. Since inclusion of these dummy variables
does not enhance the interpretive usefulness of the meta-analysis, they are not
included in the results shown in Tables 4]7.
4.1. Price elasticity
Gasoline demand is affected by distance driven, the number of vehicles being
driven, and the fuel efficiency of those vehicles. Models that include some measure
of vehicle ownership and fuel efficiency capture the ‘shortest’ short-run elasticities
by effectively measuring the influence of price and income changes on driving only.
Models that omit one or both of these variables would measure changes in
consumption through driving as well as through changes in vehicle ownership
andror fuel efficiency Žall implicitly., hence measuring an intermediate or long-run
elasticity, depending on other features of the model and data. The results of this
meta-analysis corroborate this hypothesis. Models that include some measure of
vehicle ownership andror vehicle characteristics such as fuel efficiency produce
less price-elastic estimates for the short-run. While there was no significant
influence of fuel efficiency on long-run price elasticity estimates, inclusion of
vehicle ownership also resulted in less elastic long-run estimates.
While there was no significant difference between the results derived from
linear, log-linear Žor other multiplicative., and indirect models for the short-run,
both linear and indirect models produced more elastic estimates for long-run price
elasticity. While the coefficient on ‘linear’ is significant at the 10% level, most
researchers who have tested the appropriateness of the linear and log-linear
models for gasoline consumption have rejected the linear, but not the log-linear
ŽDahl, 1986..
Models that use only a quarterly lag produce less elastic estimates for both the
short-run and the long-run and are likely not picking up all of the adjustment to
price changes. Static models produced more elastic short-run estimates and less
elastic long-run estimates, reinforcing the idea that perhaps these models produce
intermediate-run elasticities. These findings are similar to those found by Dahl and
Sterner Ž1991. in their analysis of gasoline demand elasticities. In contrast to these
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results, there was not found to be any significant difference between the partial
adjustment model and models using other lag structures. This absence of a
difference across dynamic models is particularly interesting as the structure of the
lag has been a major focus of many studies of gasoline demand. That there is a
difference between static and dynamic models is also significant, as this suggests
there is some lagged response to fuel price changes. This difference is relatively
small though, with the coefficient on the static model dummy variable implying
about a 30% reduction in the long-run price elasticity relative to the overall
average. This suggests that around 70% of the response to changes in fuel prices
occurs within the time frame of the static models, most of which use yearly data.
Models using gasoline consumption specified either per capita, per vehicle, or
per household did not produce significantly different elasticity estimates from
aggregate consumption models for either the short-run or the long-run at the 5%
level of significance. Interestingly, this study found long-run estimates derived from
models using monthly or quarterly data were not significantly different from those
using yearly data, but models with monthly data had significantly more elastic
short-run estimates at the 10% level. It makes sense that data with a shorter
periodicity could pick up more subtle short-run responses, resulting in more
price-elastic short-run estimates, but this contrasts with the finding in Dahl and
Sterner Ž1991. who concluded that elasticities estimated from monthly and quarterly data were less than those estimated from yearly data. This result also suggests
that the short-run response of gasoline demand to price changes is quick, with
virtually all of the short-run response occurring within a month. On the other hand,
there is no reason to expect differences in long-run estimates due to the periodicity
of the data. A properly specified model with a dynamic structure should be able to
capture the same long-run effects using monthly, quarterly, or yearly data.
In general, cross-sectional studies tended to produce significantly more elastic
short-run estimates for price elasticity while cross-sectional-time series data produced less elastic short-run estimates when compared to pure time-series studies.
However, there was no difference in the long-run estimates among time series,
cross-sectional, and cross-sectional-time series studies.
While there was not a significant difference between studies that used state or
provincial level and those using national level data, there was a significant difference between the estimates from panel data and those from national level data,
with panel data producing more elastic short-run estimates. This might be due to
the greater level of detail and variation in the data available in panel studies which
may capture more subtle responses resulting in more elastic estimates. The dummy
variable used to account for the regional level studies was not statistically significant and the dummy variable used to account for the state demand studies was
only significant at the 5% level for the long-run estimate, implying a less elastic
estimate. This may be because less variation likely exists in the data within any one
state over time compared to many states or countries over time, resulting in the
measurement of smaller responses and a less elastic estimate for demand. While
the correlation between ‘state level data’ and the ‘state demand dummy’ is 0.62, if
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the state demand dummy is omitted from the model, ‘state level data’ is still not
statistically significant at the 5% or the 10% level.
While there may not be much difference between estimates from state level and
national level studies, there appears to be a significant difference in elasticity
estimates across studies depending on which countries were included in the
analysis. Those studies that combined US data with data from other countries
Žusually Canada or European countries. estimated the demand for gasoline to be
significantly more elastic in the short-run than those models that just used US data,
although there was no statistically significant difference in the long-run. It is
possible that other countries are more price responsive in the short-run than the
United States, hence pooling increases the estimated elasticity. This idea is
supported by the negative coefficient on ‘Europe’ which implies that studies using
European data found more elastic short-run estimates than those using US data
but again, there was no difference in the long-run. There was no significant
difference in the short-run estimates between models using US data and those
using data from Australia, New Zealand, or Canada nor between the US and other
non-European countries. However, Australia, New Zealand, and Canada were
found to be less price responsive than the US in the long-run.
Short-run gasoline demand price responsiveness appears to have declined over
time, yet the long-run price elasticity appears to have increased over time. At first
this result might seem contradictory, but it is reasonable to believe that as prices
rose during the 1970s and people made some initial adjustments in driving habits
and bought more fuel-efficient vehicles, there were fewer options for further
short-run responses to price changes. However, as automobile fuel efficiency
technology improved during the late 1970s and early to mid-1980s, long-run
responses to fuel price changes were larger than before 1974.
Finally, maximum likelihood and random coefficients estimation produced significantly different values for the short-run price elasticity than the other models,
with maximum likelihood resulting in more elastic estimates and random coefficients producing less elastic estimates than other models. For the long-run elasticity estimates, only random coefficients estimation was statistically significant. Since
there is no technical reason why these estimation techniques should produce
different elasticity estimates, this difference might be attributable to some other
feature that these studies had in common. For example, 72% of the maximum
likelihood estimates were from one study ŽDrollas, 1984. and 83% of the random
coefficients estimates were from either Rodekohr Ž1979. or Kraft and Rodekohr
Ž1978., 93% from the United States, and none included data beyond 1978.
4.2. Income elasticity
In the estimation of the income elasticity of the demand for gasoline, the
inclusion of some measurement of vehicle ownership and of vehicle characteristics
significantly influences the results. Those models that include some measure of
vehicle ownership estimate the income elasticity of the demand for gasoline to be
significantly lower, in both the short-run and the long-run, than those models that
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291
exclude vehicle ownership. This may be due in part to the fact that models that
include vehicle ownership do not capture the full long-run influence of income
changes on gasoline demand, as income also affects vehicle ownership which, in
turn, influences gasoline consumption. Models that exclude any measure of vehicle
ownership, however, exclude a significant explanatory variable in the demand for
gasoline, a variable that is positively correlated with both the dependent variable,
gasoline consumption, and an included variable, income. Exclusion of vehicle
ownership would be expected to positively bias the estimated coefficient on
income. However, any model that includes vehicle ownership will only measure the
direct impact of income changes on gasoline consumption, not the indirect impact
working through changes in the level of vehicle ownership.
Similarly, exclusion of vehicle characteristics such as vehicle fuel economy, size
or power also would be expected to bias the estimate of income elasticity if these
characteristics are significant explanatory variables of the demand for gasoline and
are correlated with income. Fuel economy, for example, is negatively correlated
with gasoline demand. If it is also negatively correlated with income, its inclusion
from a model of gasoline demand would be expected to result in lower estimates of
the income elasticity as was found in this study for the short-run. As with vehicle
ownership, inclusion of fuel economy in a model of the demand for gasoline more
likely captures only the direct impacts of income on fuel consumption. In order to
capture both the direct and the indirect impacts of income Žworking through
changes in vehicle ownership and fuel economy levels., it is more appropriate to
also model vehicle ownership and fuel economy, rather than to simply exclude
them from a model of the demand for gasoline.
Interestingly, however, such indirect estimates of gasoline demand did not
produce statistically significantly different income elasticity estimates from direct
log-linear models. This suggests that the simple partial adjustment models with
price and income as explanatory variables picks up the same long-run income
effect as the more complex multiple model indirect estimates. The advantage to the
more complex models, though, is that the income effect is clearly broken down into
component effects on driving, vehicle ownership, and fuel economy. Indirect
estimates have this same advantage over linear models as well but, despite the
preference in past research for the log-linear model, the estimates derived from
linear models are not statistically different from those derived from log-linear
models.
Static models were found to produce significantly higher short-run income
elasticity estimates than the partial adjustment models, but there is no statistically
significant difference in the long-run estimates. This corresponds to the finding by
Dahl and Sterner Ž1991., who concluded that ‘the simple static models on annual
data seem to measure only an intermediate price elasticity but an income elasticity
closer to the long-run’. Neither was there a statistically significant difference in the
long-run income elasticity estimates between the partial adjustment models using
annual data and those using quarterly lags or other dynamic models. While this
suggests that the lag structure Žor absence thereof. does not matter in the long-run,
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M. Espey r Energy Economics 20 (1998) 273]295
more research into the dynamics of the adjustment process would likely be
enlightening.
There was no significant difference, at the 95% confidence level, between
models that used a non-aggregate measure of gasoline consumption Žper capita,
per household, or per vehicle. and those that used aggregate consumption. There
was also no significant difference, at the 95% confidence level, between the
long-run income elasticity estimates from studies that used yearly data and those
that used monthly or quarterly data. This contrasts significantly with Dahl and
Sterner Ž1991. who concluded that monthly or quarterly data were ‘inappropriate
particularly for long-run adjustments’. Their analysis technique, however, does not
allow for the separation of other features of the models that might have contributed to the finding of different elasticity estimates. This econometric study
suggests monthlyrquarterly data are appropriate for estimating long-run adjustments, as long as care is taken in model selection to account for the shorter
periodicity of the data. For example, a 1-month lag likely is not enough to capture
long-run income effects. In contrast to the consistency across long-run estimates,
models that used monthly data produced less income-elastic short-run estimates.
This would be expected, however, as the response to income changes likely takes
some time so yearly data would pick up more of a response than monthly data. This
contrasts to the result for price elasticity which implied that the full short-run price
response occurs within a month.
Cross-sectional studies tended to produce less elastic short-run income estimates
Žat the 10% level., but there was not a statistically significant difference in the
long-run estimates for cross-sectional and time series studies. Cross-sectional-time
series studies did not produce significantly different estimates of the income
elasticity for the short-run or the long-run.
Studies using panel data did not produce significantly different short-run income
elasticity estimates. There were not enough observations using panel data to
include this variable in the long-run model. The regional demand dummy variable
was statistically significant at the 5% level in the short-run model, suggesting a less
elastic short-run demand for regional studies. The ‘state level data’ and the ‘state
demand’ dummy variables were both statistically significant at the 5% level in the
long-run model and at the 10% Žstate level data. and 5% Žstate demand. levels in
the short-run model. However, they had opposite signs from each other and
opposite signs for the short-run and the long-run. Since there is a relatively high
correlation between these two variables Ž0.62., these estimates are probably not
very reliable. If ‘state demand’ is omitted from the estimation, ‘state level data’ is
not statistically significant in either income elasticity model.
As with price elasticity estimates, there was a significant difference across studies
related to which countries were included. Studies that combined US data with data
from other countries estimated the income elasticity to be significantly higher in
the short-run than those that used data just from the United States. This implies,
perhaps, that gasoline consumers in other countries are more income sensitive
than consumers in the US, hence pooling increases the estimated elasticity. If
income elasticity declines as income increases, as has been estimated ŽGriffin,
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293
1979., income differentials across countries could explain the differences in income
elasticity estimates between the US models and the pooled models. The estimated
income elasticity was also found to be significantly higher in studies using data
from European countries and ‘other countries’ for both the short-run and the
long-run. Studies using data from Australia, New Zealand, and Canada, however,
resulted in short-run income elasticity estimates very close to those studies using
US data and slightly lower long-run income elasticity estimates.
It does not appear that the short-run income elasticity has changed over time,
but the long-run income elasticity might be decreasing. There were not enough
observations post-1981 to include this as a variable in the long-run model, but the
dummy variable for studies between 1974 and 1981 was significant at the 10% level
Žand almost at the 5% level with a t-statistic of y1.626.. If income elasticity
declines as income increases as has been hypothesized, a declining income elasticity over time makes sense as, in general, incomes have been rising over time.
Error components models produced significantly lower long-run income elasticity estimates while GLS and maximum likelihood produced lower short-run income
elasticity estimates and the random coefficients models resulted in higher short-run
estimates. None of the other various estimation techniques produced significantly
different estimates of the income elasticity from ordinary least squares.
5. Conclusions
Gasoline demand has been studied extensively over the past two decades. These
studies have utilized a wide range of data sets and model assumptions, and a wide
range of price and income elasticities have been estimated quantitatively. Metaanalysis is used to summarize these diverse studies and to determine if there are
factors that systematically affect the elasticity estimates.
Among the factors that were found to have a significant influence was the
inclusion of some measure of vehicle ownership in the model. Vehicle ownership is
certainly a significant explanatory variable for the demand for gasoline, and
exclusion of such a measure would be expected to bias the results. Exclusion of
vehicle ownership generally results in more price and more income-elastic estimates. Linear models were not found to be significantly different from log-linear
models in terms of any of the elasticity estimates but indirect estimation of
gasoline demand, derived from models for driving, vehicle ownership, and fuel
economy, produced more price-elastic long-run estimates of demand. While the
other elasticity estimates were not significantly different from the log-linear,
indirect estimates provide much more information about the structure of the
response to price and income changes by breaking the response into the component parts of gasoline demand.
Models with just a quarterly lag produced elasticity estimates that differed from
those with annual lags, but there was no other difference across the various
dynamic models that have been estimated. This is an interesting result, but it does
not imply that the lag specification is not important. Much work needs to be done
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to understand the dynamics of the response of gasoline demand to price and
income changes. Different dynamic models may produce the same long-run estimates, but they imply different things about how long it takes to make that
long-run adjustment and how much of the adjustment occurs in the first year
versus the second year versus the years thereafter. Policy makers interested in
welfare effects should be especially interested in knowing more about the dynamics
of the adjustment process.
Except for the short-run income elasticity, the periodicity of the data did not
affect the elasticity estimates and in general, studies using state or regional level
data did not produce significantly different elasticity estimates than those using
national level data. There is perhaps some comfort in knowing this as often only
annual national level data is available. On the other hand, studies using panel level
data estimated a more price-elastic short-run demand, but found no difference in
the income responsiveness in the short-run. There were no long-run elasticity
estimates from panel data studies, perhaps another area ripe for further analysis.
Pooling the US with other countries was found to significantly influence the
estimate of both the short-run income and the short-run price elasticities, making
both more elastic. Studies using data from European countries, Australia, New
Zealand, Canada, and other countries also found significantly different estimates
of the elasticity of gasoline demand from studies using US data. This indicates that
the demand for gasoline is not necessarily the same in the US as it is in other
countries, and if different countries are to be pooled, care should be taken to
account for such differences, for example, through the use of country dummy
variables. The fact that cross-sectional studies produced significantly different
short-run elasticity estimates from time-series studies also indicates a need for care
in pooling diverse countries in one study.
The finding of different elasticity estimates using data prior to 1974 and data
after 1974 suggests the need for updated studies and for care to be taken in
extrapolating into the future using elasticity estimates from the 1970s or even the
1980s.
One variable that was not included in this meta-analysis but has been found to
play an important role in the estimation of elasticities is the way ‘gasoline’ is
defined. Jorgenson Ž1976. analyzed the differences in elasticity estimates from the
use of different ‘gasoline’ data series that included motor gasoline, motor fuel, and
gasoline used on the highway. Schipper et al. Ž1993. also pointed out the significance of using different definitions for the consumption variable, comparing
elasticity estimates using ‘gasoline’ and ‘automobile fuel’. Since the consumption
series was not always clearly defined and can vary so much across countries, this
influencing factor was not included here.
The price elasticity of the demand for gasoline appears to be relatively homogeneous across some research settings. For example, there is not generally a significant difference between those models that used state level data and those that
used national level data, nor between those that used monthly or quarterly data
and those that used yearly data. There is also a fair degree of consistency across
functional forms and estimation techniques. This does not mean, necessarily, that
M. Espey r Energy Economics 20 (1998) 273]295
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the estimation technique or the choice of functional form is not important, but
elasticity estimates do appear to be fairly robust. As illustrated by Sterner Ž1991.,
researchers should take care to estimate the demand using different functional
forms and estimation techniques to determine if there are differences for their
data set. The meta-analytic process cannot indicate what is the ‘right’ way of
modeling demand, but it is valuable in evaluating the sensitivity of estimates to
modeling assumptions and data characteristics.
Acknowledgements
This research was conducted under funding from the University of Nevada
Agricultural Experiment Station Project No. 5138.
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