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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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

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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

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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

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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.

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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

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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.

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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

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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

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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

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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

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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

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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

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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

290

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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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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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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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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

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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.

References Assmus, G., Farley, J.U., Lehmann, D.R., 1984. How advertising affects sales: meta-analysis of econometric results. Journal of Marketing Research 21, 65]74. Dahl, C., 1986. Gasoline demand survey. The Energy Journal 7, 67]82. Dahl, C., Sterner, T., 1991. A survey of econometric gasoline demand elasticities. International Journal of Energy Systems 11, 53]76. Drollas, L.P., 1984. The demand for gasoline: further evidence. Energy Economics 6, 71]82. Espey, M., 1997. Explaining the variation in elasticity estimates of gasoline demand in the United States: a meta-analysis. Energy Journal 17, 49]60. Espey, M., Espey, J., Shaw, W.D., 1997. Price elasticity of residential demand for water: a meta-analysis. Water Resources Research 33, 1369]1374. Griffin, J.M., 1979. Energy Consumption in the OECD: 1880]2000. Ballinger, Cambridge, MA. Jorgenson, D., ŽEd.., 1976. Econometric Studies of US Energy Policy. North-Holland, Amsterdam. Kraft, J., Rodekohr, M., 1978. Regional demand for gasoline: a temporal cross-section specification. Journal of Regional Science 1, 45]55. Rodekohr, M.E., 1979. Demand for transportation fuels in the OECD: a temporal cross-section specification. Applied Energy 22 Ž3., 223]231. Schipper, L., Figueroa, M.J., Price, L., Espey, M., 1993. Mind the gap: the vicious circle of measuring automobile fuel use. Energy Policy ŽDecember. 1173]1190. Smith, V.K., Kaoru, Y., 1990. Signals or noise? Explaining the variation in recreation benefit estimates. American Journal of Agricultural Economics May, 419]433. Sterner, T., 1990. The Pricing of and Demand for Gasoline. Swedish Transport Research Board, TFB-Report no. 9. Sterner, T., 1991. Gasoline demand in the OECD: choice of model and data set in pooled estimation. OPEC Review Summer, 91]101. Tellis, G.J., 1988. The price elasticity of selective demand: a meta-analysis of econometric models of sales. Journal of Marketing Research 25, 331]341. White, H., 1980. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817]838.