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ORNL/TM-2018/1070
Using Meta-Analysis to Estimate World
Crude Oil Demand Elasticity
Rocío Uría-Martínez
Paul N. Leiby
Gbadebo Oladosu
David C. Bowman
Megan M. Johnson
12/10/2018
Approved for public release.
Distribution is unlimited.
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ORNL/TM-2018/1070
Environmental Sciences Division
Using Meta-Analysis to Estimate World Crude Oil Demand Elasticity
Rocío Uría-Martínez
Paul N. Leiby
Gbadebo Oladosu
David C. Bowman
Megan M. Johnson
Date Published: 12/10/2018
Prepared by
OAK RIDGE NATIONAL LABORATORY
Oak Ridge, TN 37831-6283
managed by
UT-BATTELLE, LLC
for the
US DEPARTMENT OF ENERGY
under contract DE-AC05-00OR22725
iii
TABLE OF CONTENTS
TABLE OF CONTENTS ............................................................................................................................. iii
LIST OF FIGURES ..................................................................................................................................... iv
LIST OF TABLES ....................................................................................................................................... iv
ABSTRACT .................................................................................................................................................. 5
1. INTRODUCTION ................................................................................................................................ 6
2. META-ANALYSIS DATABASE DESCRIPTION ............................................................................. 8
3. METAREGRESSION ANALYSIS: METHODS AND EXPLANATORY VARIABLES ............... 11
3.1 EXPLANATORY VARIABLES .............................................................................................. 13
4. RESULTS FROM METAREGRESSION ANALYSIS ..................................................................... 16
4.1 WORLD CRUDE OIL ELASTICITY DEMAND ESTIMATION .......................................... 27
4.2 COMPARISON TO OTHER WORLD ELASTICITY ESTIMATES ..................................... 29
5. CONCLUSIONS ................................................................................................................................ 31
6. REFERENCES ................................................................................................................................... 32
APPENDIX. LIST OF REFERENCES USED IN META-ANALYSIS .................................................... 35
iv
LIST OF FIGURES
Figure 1. Periods of analysis in studies included in elasticity meta-analysis database ................................. 8
Figure 2. Forest plot of demand elasticities with respect to price and income ........................................... 10
Figure 3. Funnel plots by elasticity grouping ............................................................................................. 12
Figure 4. Estimated short-run and long-run world crude oil demand elasticities with respect to
price (including income effect) ...................................................................................................... 29
Figure 5. Short-run price elasticities of world crude oil demand (metaregression vs. other
published results) ........................................................................................................................... 30
LIST OF TABLES
Table 1: Likelihood Ratio Tests Comparing Fit of Linear Mixed Effects and Weighted Least
Squares Metaregression Specifications .......................................................................................... 16
Table 2: Results from Short-Run Price Elasticity Metaregressions (Transportation) ................................. 17
Table 3: Results from Short-Run Price Elasticity Metaregressions (Non-Transportation)......................... 19
Table 4: Results from Long-Run Price Elasticity Metaregressions (Transportation) ................................. 20
Table 5: Results from Long-Run Price Elasticity Metaregressions (Non-Transportation) ......................... 22
Table 6: Results from Short-Run Income Elasticity Metaregressions (Transportation) ............................. 23
Table 7: Results from Short-Run Income Elasticity Metaregressions (Non-Transportation) ..................... 24
Table 8: Results from Long-Run Income Elasticity Metaregressions (Transportation) ............................. 25
Table 9: Results from Long-Run Income Elasticity Metaregressions (Non-Transportation) ..................... 26
Table 10. Estimated Elasticities (Fitted Means and Baselines) .................................................................. 28
5
ABSTRACT
Crude oil demand elasticities are important behavioral parameters for assessing the effectiveness of many
energy policy proposals and the economic impact of crude oil market shocks. Most of the literature on
crude oil demand computes elasticities for one specific petroleum product in a country or group of
countries. There are fewer published values for world crude oil demand elasticity because it requires more
complex estimation methods. Since world crude oil demand and price are simultaneously determined, the
reduced-form single equation approach used in much of the petroleum product demand literature leads to
endogeneity bias when applied to global demand. This study uses meta-analysis techniques to compute
world crude oil demand elasticity. Metaregressions are first conducted to identify sources of variation in
elasticity estimates for transportation and non-transportation sectors collected from 75 studies published
from 2000 to 2015 using a consistent set of explanatory variables identified in the literature. The
estimated coefficients from the metaregressions are then summarized into elasticity baseline values for
several combinations of explanatory variable values. Finally, a global crude oil demand elasticity is
computed as the consumption-weighted average of the two sectoral elasticities. Resulting mean values for
the short-run crude oil demand elasticities with respect to price range from -0.07 to -0.14 depending on
the attributes selected for the price variable. As expected from theory and empirical studies, crude oil
demand is more price-responsive in the long run than in the short run. Long-run mean values range from
-0.26 to -0.83.
6
1. INTRODUCTION
Crude oil demand elasticities are important behavioral parameters for assessing the effectiveness of many
energy policy proposals and the economic impact of crude oil market shocks. Estimation of these
parameters became a focus of attention during the crude oil crises of the 1970s, as the governments of
industrialized countries looked for ways to improve energy efficiency and advance energy security, and it
has remained an active research topic ever since. Elasticities must be periodically re-estimated to
incorporate the effects of changes in technology, policy, and market factors.
With improvements in the availability and quality of energy consumption data (particularly for non-
OECD countries) and the development of new econometric methods that enable better analysis of time
series and panel data, demand elasticity estimation approaches have changed substantially over time.
Estimation methodology also varies across petroleum products. Basso and Oum (2007) review the
evolution of preferred model specifications for estimation of petroleum product demand in the light-duty
transportation sector. Static demand equations and partial adjustment models were the most common
choices for estimation of petroleum product demand in the transportation sector in the 1970s and 1980s.
In the 1990s, econometricians introduced error correction and co-integration techniques for the analysis of
time-series data and their application in transportation fuel demand elasticity estimation has steadily
gained popularity (see Banerjee et al. (1993) for a detailed exposition of these techniques).
1
Even though
the model specifications used to analyze vehicle fuel demand are sometimes applied to studies of other
sectors, non-transportation petroleum product demand is often explored with distinct methodologies. For
instance, interfuel substitution models are frequently used to estimate petroleum product own-price and
cross-price elasticities in the industrial sector and at the household level.
Most of the literature on crude oil demand computes elasticities for one particular region and/or
petroleum product. There are fewer published values for world crude oil demand elasticity because
estimating it is more difficult. For world crude oil demand, crude oil price is not exogenous and the
reduced-form single equation approach used in much of the petroleum product demand literature leads to
endogeneity bias. Instead, most estimations of world crude oil demand elasticities are based on systems of
equations. Within this group, recent structural vector autoregression (SVAR) models whose results
challenge the prevailing view that short-run world crude oil demand elasticity is very low have garnered
much attention. For instance, Kilian and Murphy (2014) find world crude oil demand elasticities in the
range of -0.26 to -0.44 in the first month after a supply shock using 1973-2009 data. Baumeister and
Peersman (2013) obtain an average elasticity of -0.26 for that same period, but they allow for time-
varying parameters which reveal a substantial steepening of the crude oil supply and demand curves after
the mid-1980s. IMF (2011) employ a different approach to correct for endogeneity bias in their
exploration of world crude oil demand elasticity and find a much lower elasticity (in absolute value).
Taking advantage of cross-sectional variation in a 45-country data panel, they estimate fixed-effect
models of OECD and non-OECD crude oil demand and average the resulting elasticities, using
consumption weights, into short-run world elasticities of -0.04 using 1965-2009 data and -0.02 for the
more recent 1990-2009 subperiod.
2
Together, the three studies referenced in this paragraph result in a
1
Because researchers are typically interested in measuring demand responsiveness over a specific time period, time-series data
have generally been considered more appropriate than cross-sectional data for estimating elasticities. However, crude oil demand
analysis based on cross-sectional data has remained a parallel track. These studies produce long-run elasticities that summarize
responses to all price and income conditions experienced by the survey respondents until the data collection period.
2
The authors of the IMF study contend that any remaining endogeneity bias using their approach should be small because
country-specific demand shocks will have little or no effect on the world crude oil price and common demand shocks are
accounted for through inclusion of GDP as one of the explanatory variables.
7
very wide range of world crude oil demand elasticity estimates. Section 4.2 attempts to explain some of
the reasons for these diverging findings.
We contribute to the existing literature by constructing a “bottom-up” world crude oil demand elasticity,
based on hundreds of estimates from dozens of studies focused on different portions of global crude oil
demand. Several studies explore differences in crude oil demand responsiveness across uses and/or
countries (Dargay and Gately, 2010; Dargay et al., 2007; Dees et al., 2007; IMF, 2011). These studies
have agreed in their finding that crude oil demand elasticities in OECD countries have been higher than in
other regions. As for sectors, Dargay et al. (2007) and Dargay and Gately (2010) argue that the OECD has
already largely abandoned crude oil consumption in those uses where fuel switching was easier (e.g.,
electricity generation, space heating). Both of these studies conclude that world crude oil demand
elasticity should be expected to decrease as the fraction of total oil demand originating in more inelastic
regions and sectors increases. However, technology, policy, and/or behavioral changes could result in
different future crude oil demand elasticity trends. For instance, elasticity in the transportation sector
might increase as alternative fuels continue to be adopted and the non-OECD region might become more
price responsive if price subsidies on petroleum products are phased out and economic growth sets the
region in a trajectory that converges toward that of OECD countries.
Although other researchers have used metaregressions in surveys of the demand elasticities of gasoline
(Espey,1998; Brons et al., 2008; Havranek et al., 2012; Havranek and Kokes, 2015), petroleum products
for industrial use (Stern, 2009), or multiple energy products (Labandeira et al., 2017), our study is the first
that applies this methodology to gain insight on the value of world crude oil demand elasticity computed
as a weighted average of the price responsiveness of two sectors (transportation and non-transportation).
In specifying the metaregression model and selecting an econometric estimation approach, we aim to
mitigate potential biases associated to the use of meta-data (Borenstein et al., 2009; Nelson and Kennedy,
2009): variance heterogeneity, publication bias, and within-study correlation of residuals. We weigh
elasticity estimates by the inverse of their precision to avoid excessive influence of large, imprecise
estimates. We test for publication bias—the idea that our metadata is not a random sample of the entire
population of elasticity estimates due to higher likelihood of a study being published when estimate size
or magnitude is consistent with economic theory and statistically significant. If publication bias is present,
we add the variance of estimates as one of the explanatory variables in the metaregression to control for
the relationship between the magnitude of an elasticity estimate and its variance. Finally, we use two
alternative approaches to account for the lack of independence of residuals corresponding to elasticity
estimates obtained from the same study: cluster-robust standard errors or addition of study-level random
intercepts. Our choice of explanatory variables is driven by the objective of identifying sources of
variation that are important to produce adequate elasticity values for specific empirical applications. For
instance, a model exploring multi-year period responses to a policy (e.g., international carbon tax) and a
model that depicts short-run responses to a crude oil supply shock require different elasticity inputs. We
also pay attention to the relationship between elasticities and cross-sectional differences in price and
income levels and assess the specific length of run (number of years) of long-run elasticity estimates.
8
2. META-ANALYSIS DATABASE DESCRIPTION
We performed queries in Google Scholar and Econlit as well as snowball searches to identify peer-
reviewed journal articles and working papers published between 2000 and 2015 containing primary
estimates of crude oil or petroleum product demand elasticities. We discarded studies that did not provide
standard errors or other related information (t-statistic, p-value or confidence intervals) to infer the
precision of the elasticity estimates. We excluded estimates with an absolute value outside of (-5,5)
interval as well as observations that cannot be assigned to OECD/nonOECD regions or
transportation/non-transportation sectors. Finally, we dropped observations for which the value of any of
the explanatory variables to be included in the metaregression analysis are not available. The resulting
dataset to be used in the metaregression analysis consists of 1983 observations from the 75 papers listed
in Appendix A. Figure 1 shows the initial and final year of the data period considered in each of the
papers in our database.
Figure 1. Periods of analysis in studies included in elasticity meta-analysis database
Even though 40 of the 75 papers in the database were published after 2009, only 12 contain data for 2010
or later. The average lag between publication year and end of analysis period is approximately 5 years.
Studies based on time series data tend to analyze longer periods and result in average elasticities that
might be less representative of recent conditions than those from studies using more recent data panels.
3
3
The average length of data period covered by papers in our database using time series and panel data is 28 and 17 years
respectively.
9
The average years in this database are 1989, 1994, and 2004 for subsets of studies using time series,
panel, and cross-sectional data respectively.
Beyond segmentations by type (price or income) and length of time (short- or long-run), we also segment
the database by sector (transportation or non-transportation) because the data sources and estimation
methods used by studies generating these two elasticities tend to be different.
4
Segmentation by sector
also enables a more tailored selection of explanatory variables for the metaregression analysis. We
considered further segmenting the data by region (OECD versus non-OECD) but some of the resulting 16
groupings contained few observations making the validity of a metaregression analysis approach
questionable. Instead, to control for regional differences, we include regional dummies and cross-sections
of price and income levels as explanatory variables in the metaregressions.
Accounting for response period is important when comparing elasticity estimates across studies. All else
equal, demand responsiveness is expected to increase with the length of the period over which the
response is measured. We consider short-run elasticities as those that convey a first-period response: one
year, one quarter, or one month depending on the data frequency used in each study. In addition,
whenever possible, we assign long-run estimates a specific response length (in years). Dynamic demand
specifications typically include a variable (lagged demand for partial adjustment models or error
correction term in error correction models) whose estimated coefficient can be used to estimate the length
of run implied by the long-run elasticities.
5
To our knowledge, this is the first meta-analysis that extracts
this more detailed information on length of run from long-run elasticities. We classify most of the
elasticities from cross sectional studies as long-run and assign them a length of run in years equal to the
average adjustment period for long-run elasticities in the same sector.
6
As an initial exploratory step, Figure 2 displays unweighted means alongside the fixed effect and random
effects means typically computed in meta-analyses, for the 8 elasticity groupings being analyzed: 2 types
(price and income) times 2 lengths of run (short and long) times two sectors (transportation and non-
transportation). Fixed effect means are appropriate when all elasticities in a given group originate from
the same population and the only reason why they differ is sampling error. In that case, estimates with
lowest standard errors should be weighted more heavily and vice versa. On the other hand, random effects
means assume that variability in a given set of elasticities is partly due to inherent differences in the true
effect sizes (e.g., the true population mean is different across countries, over time and/or based on other
attributes). The weights applied to random effects means include an extra component to account for
between-estimate variation (Borenstein et al., 2009). As in most social sciences applications of meta-
analysis, the random effects model is most appropriate to describe our dataset because there is no single
true value for petroleum product demand elasticity.
4
Gasoline or diesel demand elasticities were assigned to the transportation sector unless the study mentioned explicitly that its
consumption data corresponded to a different sector. Elasticities in the non-transportation category include elasticities for
petroleum demand in the industrial sector, residential sector (for uses other than transportation) or petroleum products used in
those sectors (industrial use of diesel and gas oil, fuel oil, kerosene, liquefied petroleum gas, residual fuel oil, other petroleum
products). Even though aviation is a transportation activity, jet fuel demand was assigned to the non-transportation category.
5
Balcombe et al. (2004) show that the number of periods to achieve 90% of the long-run elasticity estimated using and ARDL
specification can be calculated as ln(1 − 0.9)/ln(
).
is the estimated coefficient on lagged demand in a partial adjustment
model; for error correction models the formula is ln(1 − 0.9)/ln(
) + 1.
6
The only cross-sectional elasticities classified as short-run are from 3 studies that used data from household surveys where the
same household is interviewed multiple times at intervals equal or less than one year (e.g., Frondel et al.,(2008)). Alternatively,
data from these studies could have been categorized as a (very unbalanced) panel.
10
Note: Colored dots and black dots correspond to weighted and unweighted means, respectively.
Figure 2. Forest plot of demand elasticities with respect to price and income
All weighted and unweighted means are less than one in absolute value (i.e., inelastic). For both types of
elasticity and both lengths of run, the unweighted average elasticities are greater for the transportation
sector than for other sectors. The same result is true for the random effects means but not for the long-run
fixed effect means. For all elasticity groupings except long-run non-transportation, the random effects
mean is an intermediate value between the unweighted and fixed effect means. This result is consistent
with a data set where the smaller effect sizes (elasticities in this case) are the most precisely measured.
For long-run, nontransportation elasticities, fixed effect means are the largest. This result indicates that
the relationship between effect size and precision of the estimate is weaker for that elasticity grouping.
11
3. METAREGRESSION ANALYSIS: METHODS AND EXPLANATORY VARIABLES
Our model specification and estimation method choices address the econometric issues that are typically
present in energy and resource economics meta-analyses applications (e.g., Bel and Gradus (2016);
Havranek and Kokes (2015); Ma et al. (2015); Daniel et al. (2009)). The starting point for metaregression
specification is a linear relationship between a set of i elasticity estimates
i, an intercept
0, the set of k
explanatory variables associated to the i elasticity estimates Xi,k, and a residual for each elasticity estimate,
.
a) Variance heterogeneity (heteroskedasticity)
When the variances of the elasticity estimates
i are known, Borenstein et al. (2009) and Nelson and
Kennedy (2009) recommend giving more weight to the more precise ones. We follow that approach to
address the issue of variance heterogeneity and estimate the model using weighted least squares with the
inverse of standard error of each estimate (1/sei) as weights.
b) Publication bias
Publication bias arises when the sample of published estimates is not a random sample of the full
population of estimates. The bias results from researchers being more likely to submit, and journals being
more likely to publish, studies finding larger effect sizes and/or estimates conforming to the theoretically
expected sign. The panels in Figure 3 are funnel plots showing the relationship between the inverse of the
standard error (i.e., precision) on the y-axis and the effect size on the x-axis for each of the 8 elasticity
groupings. The more asymmetric a funnel plot is around the most precise estimate, the stronger
publication bias there is (Havranek et al., 2012). Funnel asymmetry tests confirmed statistically
significant asymmetry at the 10% confidence level in 7 of the 8 metaregressions. Long-run income
elasticities in non-transportation sector is the only grouping for which funnel asymmetry can be rejected
at the 10% confidence level.
12
Figure 3. Funnel plots by elasticity grouping
To correct for publication bias, we implement the precision-effect estimate with standard error (PEESE)
method outlined in Stanley and Doucouliagos (2007) in which the variance of the effect sizes is included
as one of the explanatory variables in a weighted least squares estimation. PEESE is a modified version of
the Heckman regression used to address sample selection bias. PEESE uses the heteroscedastic nature of
standard errors in a meta-analysis database to capture the relationship between the precision of elasticity
estimates and their probability of being published.
c) Within-study correlation of residuals
Most primary studies produce more than one elasticity estimate. In our database, we find that multiple
effect sizes from the same paper typically result from authors reporting results from multiple estimation
methods or segmenting their datasets by household characteristics, geographical units, or time periods.
Each additional estimate from the same study provides less additional information that an estimate from a
different study and should be weighted accordingly in the metaregression.
7
Nelson and Kennedy (2009)
7
We argue that overweighting of individual estimates from a single study will be less severe if the metaregression includes
explanatory variables to capture their attributes. We computed the number of “unique” observations in each grouping as those for
which at least one of the explanatory variables (other than VARIANCE) differs from all the other observations in the grouping.
Standard error clustering should be strongest for the subgroups with the lowest fraction of unique observations out of their total
number of observations: short-run nontransportation price (23%) and short-run transportation income (38%) elasticities.
13
advise researchers to control for the clustering of standard errors that results from having multiple effect
sizes from the same study. Depending on the sample size and number of studies, it sometimes is advisable
to just pick the mean estimate from each paper or select a preferred estimate. Here, such approach would
result in very small sample sizes for some of the metaregressions.
We apply two alternative approaches to control for within-study correlation of residuals. The first
approach adds a correction to the standard errors of parameter estimates to control for the correlation
among residuals from each study.
8
In what follows, we refer to that specification as weighted-least
squares (WLS) with cluster-robust standard errors. Without correction, WLS would tend to underestimate
the variance of the estimated model coefficients (Cameron and Miller, 2015). The second variant is a
linear mixed effects (LME) specification which acknowledges the presence of study-level clusters in the
database more explicitly. In the LME specification, model variables and their standard errors have an
extra index j that indicates the study (i.e., cluster) from which each elasticity estimate originated and the
residual has a study-level component vj and an observation-level component uij. where i represents a study
and j an elasticity estimate.
3.1 EXPLANATORY VARIABLES
We use a general-to-specific approach to select explanatory variables for the metaregressions. The most
general specification includes the subset of the explanatory variables listed below that are applicable to
each elasticity grouping. In order to alleviate multicollinearity concerns, when the variance inflation
factors (VIFs) of the estimated metaregressions are above 5 for any of the variables, we drop one
explanatory variable at a time until all the VIFs are below 5.
9
• YrAvg (all metaregressions): average year of the period of analysis in the study that
produced the elasticity estimate
• SPEEDYRS (long-run elasticity metaregressions): length of adjustment period (in years).
• Quarterly (short-run elasticity metaregressions): indicator variable that takes the value 1 for
elasticity estimates obtained from quarterly data.
• Monthly (short-run elasticity metaregressions): indicator variable that takes the value 1 for
elasticity estimates obtained from monthly data.
• CS (long-run metaregressions): indicator variable that takes the value 1 for elasticity estimates from
cross-sectional studies.
8
The cluster-robust standard errors were computed using the cluster.vcov function from the multiwaycov package in R. They
incorporate degree of freedom corrections to mitigate over-rejection of the null hypothesis in coefficient tests when small number
of clusters prevents application of asymptotic theory assumptions. The number of clusters in our database ranges between 13 for
short-run income elasticities in non-transportation sectors and 58 for transportation short-run price elasticities.
9
The VIF for estimated coefficient k is calculated as VIFk = 1/(1 – R2k) where R2k is the proportion of variability in the
independent variable Xk explained by a regression of Xk on the rest of independent variables in the model. VIF thresholds used in
the literature as indicative of serious multicollinearity range from 5 to 10 (Menard, 1995; Hair et al., 1995).
14
• CSTS (all metaregressions): indicator variable that takes the value 1 for elasticity estimates
from panel data analyses.
• Pmax (price elasticity metaregressions): indicator variable that takes the value 1 if the elasticity is with
respect to a new historical price maximum in the country or region being studied rather than an average
elasticity over the full period of analysis.
• Ymax (income elasticity metaregressions): indicator variable that takes the value 1 if the
elasticity estimate is with respect to a new historical income maximum in the country or region being
studied rather than an average elasticity over the full period of analysis.
10
• StaticP (price elasticity metaregressions): indicator variable that takes the value 1 for elasticities
estimated using static demand equations (in long-run metaregressions, all cointegration equations are
codified with StaticP = 1).
• StaticY (income elasticity metaregressions): indicator variable that takes the value 1 for
elasticities estimated using static demand equations (in long-run metaregressions, all cointegration
equations are codified with StaticY = 1).
• StaticP.CS (short-run price elasticity metaregressions): interaction dummy that takes the value 1 for
elasticities from cross-sectional studies estimated using static demand specifications.
• StaticY.CS (short-run income elasticity metaregressions): interaction dummy that takes the
value 1 for elasticities from cross-sectional studies estimated using static demand specifications.
• PRICE.1998 (transportation sector price elasticity metaregressions): average 1998 price for crude oil
(Brent) or the relevant petroleum product in the country/region to which the elasticity refers (in dollars
per liter).
11
• rgdpe_cap.1998 (income elasticity metaregressions): 1998 GDP per capita in real terms for the country
or group of countries to which the elasticity estimate refers (in thousands of dollars).
12
• EndUserP (non-transportation sector metaregressions): indicator variable that takes the value 1 if the
elasticity is measured with respect to a petroleum product price and 0 if it is an elasticity with respect to
the crude oil price.
• DslTransp (transportation sector metaregressions): indicator variable that takes the value 1 if
the elasticity estimate corresponds to diesel consumption.
10
Dargay (2007) and Dargay and Gately (2010) are the only two studies in our dataset that estimate multiple income elasticities
for periods of income increases, income decreases, and new income maxima to detect asymmetries and nonlinearities in crude oil
demand responsiveness to changes in income. They only apply this decomposition to explain crude oil demand decisions of oil
exporting countries.
11
Cross-sectional 1998 price data comes from the GIZ survey (https://www.giz.de/expertise/html/4317.html). Although the
survey also includes prices for non-transportation related oil consumption, the number of countries with missing observations
was large and would have severely cut the sample size for those metaregressions. The year 1998 was chosen because it is close to
the average year analyzed by the studies in our dataset (1992) and covered the most countries out of all the available versions of
the GIZ survey conducted in the mid to late 1990s.
12
The source for the 1998 GDP per capita data is the Penn World Table, version 9.0 (www.ggdc.net/pwt)
15
• VehStk (transportation sector metaregressions): indicator variable that takes the value 1 if the elasticity
estimate comes from a study that includes a measure of vehicle stock as one of the explanatory variables
for fuel demand.
13
• FuelSwitch (non-transportation sector metaregressions): indicator variable that takes the value 1 if the
elasticity estimate refers to a product or sector with abundant fuel switching options (residential or
electricity generation sectors following the categorization in Dargay and Gately (2010)).
• VARIANCE (included in all metaregressions that require a correction for publication bias): the variance
of the elasticity estimate.
• CALC_STERROR (all metaregressions): indicator variable that takes the value 1 if the study
did not report the standard error or t-statistic of the elasticity estimate but was calculated instead as a
function of the standard error of other estimated coefficients using the Gaussian error propagation
formula.
14
In his meta-analysis of the price elasticity of beer, Nelson (2014) finds that calculated standard
errors tend to be larger than those directly reported in the papers.
15
To correct for possible bias, Nelson
(2014) introduces a dummy variable in the metaregression that takes the value 1 for calculated standard
errors. We use the same approach.
Continuous variables (except VARIANCE) are centered around the average value within their grouping.
For PRICE.1998, centering is around the Brent crude oil price. With centered variables, the
metaregression intercept has a straightforward interpretation as the elasticity evaluated at the average
values of the continuous variables and zero values for the indicator variables.
13
Havranek and Kokes(2015) found that studies of gasoline demand omitting this variable result in significantly larger income
elasticity values.
14
Given random variables x and y measured with standard errors d(x) and d(y) and assuming that x and y are uncorrelated, the
Gaussian error propagation formula for the standard error of q = f(x,y) is
15
We conducted two tests to evaluate whether calculated standard errors appear to be biased. First, as recommended in Nelson
(2014), we regressed standard errors on the elasticities and a dummy that takes the value 1 for calculated standard errors. The
estimated coefficients were positive in most cases but only statistically significant for the short-run, transportation income
elasticity and the long-run, nontransportation price elasticity. Second, we calculated standard errors for a subset of long-run
elasticities for which directly reported standard errors were also available. The ratio of reported to calculated standard errors in
that subset was 0.946 and 0.877 for price and income elasticities respectively. These results suggest that calculated standard
errors tend to be larger although not by a large amount.
16
4. RESULTS FROM METAREGRESSION ANALYSIS
For each of the 8 elasticity groupings considered in this analysis, we estimate metaregressions using both
the WLS and LME approaches introduced in Section 3 and conduct likelihood ratio tests to select which
of the two model specifications provides the best fit. The null hypothesis tested by the likelihood ratio is
that the more parsimonious model (WLS) is the “true” model.
16
Table 1 shows the results from the tests.
Table 1: Likelihood Ratio Tests Comparing Fit of Linear Mixed Effects and Weighted Least Squares
Metaregression Specifications
Grouping
Log
Likelihood
LME
Log
Likelihood
WLS
Statistic
Degrees
of
Freedom
p
value
Number
of
Clusters
Price-SR-
Transport
351.72
302.14
99.16
1
0
58
Price-SR-
NonTransport
201.88
201.88
0
1
1
18
Price-LR-
Transport
-26.97
-49.08
44.22
1
0
48
Price-LR-
NonTransport
-27.50
-30.16
5.32
1
0.02
20
Income-SR-
Transport
64.15
52.88
22.53
1
0
50
Income-SR-
NonTransport
-38.47
-38.98
1.01
1
0.31
13
Income-LR-
Transport
-114.16
-125.42
22.51
1
0
48
Income-LR-
NonTransport
-62.39
-62.39
0
1
1
17
Based on the likelihood ratio test results, we conclude that the LME estimation is preferred for all the
price elasticity metaregressions—except short-run, non-transportation—as well as for the transportation
income elasticity metaregressions. For the remaining 3 metaregressions (short-run, nontransportation
price, short-run nontransportation income, and long-run nontransportation income), the addition of a
random intercept for each within-study cluster of elasticity estimates does not lead to a statistically
significant improvement in model fit and the simpler WLS specification is preferred. The number of
clusters (i.e., number of studies) in each metaregression are also included in Table 1. The discussion of
estimated metaregression coefficients in Table 2 through Table 9 focuses on the preferred specification in
each case, but the results of the alternative specification are also shown in the tables for reference.
16
The likelihood ratio test statistic follows a chi-squared distribution with degrees of freedom equal to the difference in degrees
of freedom between the two compared models.
17
Table 2: Results from Short-Run Price Elasticity Metaregressions (Transportation)
WLS cluster-robust.se LME
---------------------------------------------------------------------
YrAvg 0.0029* 0.0044***
(0.0016) (0.0012)
Quarterly -0.0648 -0.0476
(0.0567) (0.0421)
Monthly -0.0333 -0.0568
(0.0288) (0.0526)
CSTS -0.0355 -0.0005
(0.0230) (0.0199)
Pmax -0.0206 -0.0381*
(0.0350) (0.0203)
OECD 0.0380 0.0172
(0.0240) (0.0180)
StaticP -0.0984*** -0.0577***
(0.0358) (0.0169)
StaticP.CS -0.2421*** -0.2771***
(0.0502) (0.0711)
PRICE.1998 -0.0850** -0.0706***
(0.0335) (0.0255)
DslTransp -0.0163 -0.0078
(0.0117) (0.0110)
VehStk -0.0247 -0.0771**
(0.0295) (0.0350)
VARIANCE -0.1704 -0.0308
(0.1614) (0.1010)
CALC_STERROR -0.0192 -0.0308
(0.0275) (0.0371)
Constant -0.0370** -0.0809***
(0.0158) (0.0224)
Observations 432 432
R2 0.4048
Adjusted R2 0.3862
Log Likelihood 351.7215
Akaike Inf. Crit. -671.4429
Bayesian Inf. Crit. -606.3481
Residual Std. Error 0.5428 (df = 418)
F Statistic 21.8641*** (df = 13; 418)
-----------------------------------------------------------
Notes: Significant at the 1% level (***), 5% level (**), 10% level (*).
Table 1 indicated that LME is the preferred model for explaining short-run transportation price
elasticities. The estimated intercept (-0.0809) in Table 2 can be interpreted as the baseline elasticity. The
baseline is the value of the elasticity when all indicator variables are zero and all continuous variables are
equal to their sample means.
Table 2 shows that the estimated coefficient on the YrAvg variable is 0.0044. This can be interpreted as a
decreasing trend (i.e., smaller absolute value over time) on the short-run price responsiveness of the
transportation sector. The baseline elasticity corresponds to 1993—the average year of the datasets in the
studies that produced the elasticity estimates being explained by this metaregression. All else equal, the
baseline elasticity for 1994 would be -0.0765.
18
In agreement with results from previous meta-analyses of gasoline demand, static model specifications
yield larger (in absolute value) short-run price elasticities of transportation demand (Espey, 1998; Brons
et al., 2008). The combination of static specification and cross-sectional data leads to even larger
elasticities. Relative to the baseline elasticity of -0.0809, elasticities from models using cross-sectional
data and a static specification are, on average, more than 4 times larger (-0.358).
The estimated coefficient on VehStk is -0.0771 almost doubling price responsiveness relative to the
baseline. The sign of this coefficient is contrary to the argument that elasticities from models accounting
for changes in vehicle stock should be smaller (in absolute value) because they do not conflate demand
responses to price with demand changes due to the evolution of average fleet attributes. However, since
changes in stock are almost negligible within the length of period (one-year or less) considered in short-
run elasticities, the argument for smaller elasticities resulting from models including that variable seems
more relevant for the long-run elasticity metaregressions.
Short-run transportation fuel demand responsiveness to price is positively correlated with price level both
when we compare price levels across countries at one point in time (PRICE.1998) and when we compare
responsiveness to a new price maximum versus average price responsiveness (Pmax). All else equal,
estimated price responsiveness increases by 7.06 percentage points with each additional dollar in the 1998
price level (in $/liter) in the country or region of study relative to the price of Brent.
17
In addition,
estimated price responsiveness is 3.81 percentage points larger when the observed price level is a new
price maximum for the country or region being studied.
Based on the estimated coefficients for the Quarterly, Monthly, CSTS, and DslTransp variables, estimated
elasticities from studies using quarterly, monthly, panel, or diesel data are larger (in absolute value) than
the baseline of annual, time series, non-diesel demand data. However, these four effects are not
statistically significant. Also statistically insignificant is the estimated coefficient on OECD which
indicates that, all else equal, short-term price responsiveness is smaller in studies using data for OECD
countries than non-OECD countries. Finally, neither VARIANCE nor CALC_STERROR display a
statistically significant coefficient meaning that 1) publication bias does not remain a concern after
controlling for the effect of all other explanatory variables and 2) elasticity estimates for which the
standard error was not displayed in the study and had to be calculated based on other parameters are not
introducing bias into the metaregression.
17
The values of the PRICE.1998 variable range from -0.07$/liter for Iran and Iraq to 1.11 $/liter for Italy. Differences among the
prices of most countries or regions are in the order of cents or tenths of dollars.
19
Table 3: Results from Short-Run Price Elasticity Metaregressions (Non-Transportation)
WLS cluster-robust.se LME
---------------------------------------------------------------
YrAvg -0.0004 -0.0004
(0.0017) (0.0014)
Monthly 0.1579** 0.1579
(0.0790) (0.2082)
CSTS 0.0563*** 0.0563***
(0.0107) (0.0185)
OECD -0.0195 -0.0195
(0.0122) (0.0128)
Pmax -0.0251*** -0.0251**
(0.0034) (0.0119)
StaticP 0.0255 0.0255
(0.0181) (0.0176)
EndUserP -0.0444*** -0.0444***
(0.0130) (0.0146)
FuelSwitch 0.0158 0.0158
(0.0109) (0.0249)
VARIANCE -0.4368 -0.4368
(0.4809) (0.2944)
Constant -0.0653*** -0.0653***
(0.0142) (0.0195)
Observations 244 244
R2 0.2453
Adjusted R2 0.2163
Log Likelihood 201.8780
Akaike Inf. Crit. -379.7560
Bayesian Inf. Crit. -337.7900
Residual Std. Error 0.4619 (df = 234)
F Statistic 8.4529*** (df = 9; 234)
-----------------------------------------------------------
Notes: Significant at the 1% level (***), 5% level (**), 10% level (*).
As indicated by Table 1, the LME estimation approach does not improve the fit of the short-run
nontransportation price elasticity metaregression. Thus, the WLS model with cluster-robust standard
errors is the preferred specification to be discussed next.
Table 3 displays 4 statistically significant effects as well as a statistically significant baseline short-run
non-transportation price elasticity of -0.0653. All else equal, elasticities from the subset of studies using
panel data are 5.63 percentage points smaller in absolute value than the time-series baseline. The effect of
Monthly, studies based on monthly rather than annual data, is even larger (0.1579) such that keeping all
other attributes from the baseline elasticity constant, it would result in a positive price elasticity.
18
The
estimated coefficient for EndUserP (-0.0444) indicates that, all else equal, the demand response to an
increase in the end user price of a petroleum product is 4.444 percentage points larger than the response to
the same percentage increase in the price of crude oil. In addition, all else equal, elasticity with respect to
a new price maximum is 2.51 percentage points larger than the average elasticity across all price levels in
the period of analysis.
18
Vásquez-Cordano (2005) is the only study in the dataset that uses monthly data to estimate price elasticities outside of the
transportation sector. The two elasticity estimates from that study going into this metaregression are for kerosene (0.269) and
liquefied petroleum gas (-0.333) in Peru.
20
The rest of estimated coefficients shown in Table 3 are not statistically significant. Lack of statistical
significance and very small magnitude of the estimated coefficient on YrAvg mean that there is no visible
trend in short-run non-transportation elasticities over time in these metadata. All else equal, estimated
elasticities are 1.95 percentage points larger (i.e., more negative) for the subset of OECD elasticities than
for the rest of the world. Contrary to the negative estimated coefficient for the StaticP variable for the
transportation sector discussed in Table 2, using static model specifications to explain non-transportation
crude oil demand leads to elasticities that are 2.55 percentage points smaller (less negative) than those
from dynamic models. According to the estimated coefficient on FuelSwitch, the elasticities for petroleum
products whose uses present more opportunities for fuel switching (residential, electricity generation)
were not significantly different than those in other non-transportation activities during the period covered
by the studies in this metaregression. Finally, the lack of statistical significance on the VARIANCE
variable suggests that publication bias is not of key concern in this metaregression.
Table 4: Results from Long-Run Price Elasticity Metaregressions (Transportation)
WLS cluster-robust.se LME
---------------------------------------------------------------
YrAvg -0.0064* -0.0016
(0.0036) (0.0034)
SPEEDYRS -0.0111*** -0.0118***
(0.0029) (0.0021)
CS -0.3773*** -0.2810*
(0.0999) (0.1552)
CSTS -0.0129 -0.0081
(0.0548) (0.0570)
Pmax -0.5281*** -0.4712***
(0.1417) (0.1429)
OECD 0.2431*** 0.1449**
(0.0803) (0.0644)
StaticP -0.0413 0.0309
(0.0622) (0.0927)
PRICE.1998 -0.6395*** -0.5343***
(0.1727) (0.1244)
DslTransp -0.0012 0.0224
(0.0353) (0.0379)
VehStk 0.1262 0.0331
(0.0884) (0.0897)
VARIANCE -0.0228* -0.0199*
(0.0119) (0.0104)
CALC_STERROR -0.0821 -0.0463
(0.0815) (0.0950)
Constant -0.1729* -0.2621***
(0.0882) (0.1012)
Observations 259 259
R2 0.4078
Adjusted R2 0.3790
Log Likelihood -26.9662
Akaike Inf. Crit. 83.9324
Bayesian Inf. Crit. 137.2849
Residual Std. Error 0.7437 (df = 246)
F Statistic 14.1192*** (df = 12; 246)
-----------------------------------------------------------
Notes: Significant at the 1% level (***), 5% level (**), 10% level (*).
21
Table 1 showed that the LME estimation method is preferred for transportation sector long-run price
elasticities. According to the estimated intercept in Table 4, the baseline value for this elasticity grouping
is -0.2621. The estimated coefficient on SPEEDYRS indicates that, for every extra year of adjustment, the
estimated elasticity increases by 1.18 percentage points. To place that number into context, the baseline
elasticity of -0.2621 is for the sample mean adjustment period length (9.3 years); all else equal, the
estimated elasticity would become -0.2739 if the adjustment period were 10.3 years instead. Based on the
estimated coefficient on CS, elasticities from studies using cross sectional data are, on average, 28.1
percentage points larger (more negative) than those based on time series data.
The estimated Pmax coefficient implies that responsiveness to a new price maximum is 47.12 percentage
points larger than the average price responsiveness and the estimated coefficient on PRICE.1998 means
that for each dollar per liter the 1998 price of transportation fuel increases relative to the price of Brent,
demand responsiveness increases by 53.43 percentage points. OECD countries tend to have higher
transportation fuel prices than the rest of the world, mostly due to higher taxes. However, for OECD
countries, the effect of high price level on elasticity embodied in the PRICE.1998 variable is partly offset
by the estimated coefficient on OECD which is of the opposite sign (0.1449). The estimated coefficient
on VARIANCE (-0.0199) is indicative of publication bias as it means that elasticity estimates with larger
variances tend to also be larger in absolute value. However, the effect is small. Without controlling for
this effect, the estimated baseline would be -0.2820 instead of -0.2621.
The remaining estimated coefficients are not statistically significant. Those on YrAvg (-0.0016) and CSTS
(-0.0081) are also small in magnitude suggesting no clear trend in long-run price responsiveness in the
transportation sector and no significant differences in elasticity estimates from studies using panel (CSTS)
versus time series data. Estimated coefficients on StaticP, DslTransp, and VehStk all imply decreases in
price responsiveness in the 2-3 percentage point range associated with the use of static models, diesel
(versus other transportation fuel) data, and the inclusion of vehicle stock as an explanatory variable. The
lack of statistical significance of the CALC_STERROR variable indicates that elasticity estimates for
which the standard error was not displayed in the study and had to be calculated based on other
parameters are not introducing bias into the metaregression.
22
Table 5: Results from Long-Run Price Elasticity Metaregressions (Non-Transportation)
WLS cluster-robust.se LME
--------------------------------------------------------------------
YrAvg -0.0076 -0.0021
(0.0064) (0.0043)
SPEEDYRS -0.0152*** -0.0144***
(0.0014) (0.0017)
CSTS 0.1425* 0.1288*
(0.0853) (0.0773)
OECD -0.0541 -0.0363
(0.0797) (0.0551)
Pmax -0.1891*** -0.1825***
(0.0335) (0.0623)
EndUserP -0.1358*** -0.1346**
(0.0522) (0.0613)
VARIANCE -0.1143 -0.1365
(0.1364) (0.0910)
CALC_STERROR -0.0063 0.0427
(0.0850) (0.0828)
Constant -0.3053*** -0.3397***
(0.0953) (0.0789)
Observations 136 136
R2 0.8095
Adjusted R2 0.7975
Log Likelihood -27.5043
Akaike Inf. Crit. 77.0085
Bayesian Inf. Crit. 109.0477
Residual Std. Error 0.7837 (df = 127)
F Statistic 67.4568*** (df = 8; 127)
-----------------------------------------------------------
Notes: Significant at the 1% level (***), 5% level (**), 10% level (*).
Based on the likelihood ratio test p-value discussed in Table 1, LME is the preferred specification for this
elasticity grouping. Table 5 displays the baseline elasticity (-0.3397) and estimated effects of the
explanatory variables. Similar to the transportation sector findings in Table 4, each additional year of
response period (SPEEDYRS) leads to an increase of elasticity (in absolute value) of 1.4 percentage
points. Long-run price elasticities outside of the transportation sector are, on average, 12.88 percentage
points larger in studies that use panel data rather than time series. Responsiveness to a new price
maximum (Pmax) is 18.25 percentage points larger than the average price responsiveness. The estimated
coefficient for EndUserP indicates that for a same percentage increase in the price of crude oil versus the
end user price of a petroleum product, the demand response is 13.46 percentage points larger in the latter
case.
The estimated coefficients on YrAvg (-0.0021) and OECD (-0.0363) imply slight increase in price
responsiveness over time and greater responsiveness in the OECD region versus the rest of the world, but
neither of these two effects are statistically significant. Finally, the coefficients on VARIANCE and
CALC_STERROR are not statistically significant either which means that publication bias does not appear
of grave concern within the set of studies considered in this metaregression and no sizable bias results
from using error propagation methods to compute the standard errors of elasticity estimates in cases when
those numbers are not directly published in the study.
23
Table 6: Results from Short-Run Income Elasticity Metaregressions (Transportation)
WLS cluster-robust.se LME
---------------------------------------------------------------------
YrAvg 0.0046* 0.0033
(0.0027) (0.0025)
Monthly -0.1140* -0.0886
(0.0664) (0.0917)
CSTS -0.0920** -0.1426***
(0.0456) (0.0422)
Ymax 0.0921** 0.0329
(0.0424) (0.0995)
StaticY 0.5638*** 0.5337***
(0.0680) (0.0392)
StaticY.CS -0.4340*** -0.4424***
(0.0949) (0.1312)
rgdpe_cap.1998 -0.0008 -0.0012
(0.0016) (0.0011)
DslTransp -0.0069 0.0602**
(0.0448) (0.0283)
VehStk -0.0254 -0.0365
(0.0323) (0.0545)
VARIANCE 0.1350 0.0996
(0.1166) (0.1252)
Constant 0.2095*** 0.2625***
(0.0398) (0.0331)
Observations 355 355
R2 0.5993
Adjusted R2 0.5876
Log Likelihood 64.1476
Akaike Inf. Crit. -102.2952
Bayesian Inf. Crit. -51.9577
Residual Std. Error 0.7227 (df = 344)
F Statistic 51.4463*** (df = 10; 344)
--------------------------------------------------------------
Notes: Significant at the 1% level (***), 5% level (**), 10% level (*).
As discussed in Table 1, the likelihood ratio test indicates that inclusion of a study-level random effect is
appropriate for the metaregression of short-run income elasticities in the transportation sector. Thus, the
discussion of results from Table 6 focuses on the LME specification. According to the estimated
intercept, the baseline income elasticity for the transportation sector demand is 0.2625. One of the
attributes of that baseline elasticity value is that it corresponds to income elasticities of gasoline demand
or overall transportation fuel demand. For studies of diesel demand, the estimated coefficient on
DslTransp indicates that income elasticities are 6 percentage points larger. Studies based on panel data
(CSTS) yield income elasticities 14.26 percentage points lower than those from studies using time series
data. More than 80% of elasticities from panel data studies in this metaregression are for OECD countries.
Thus, the CSTS variable might be partly reflecting lower income elasticities for that set of countries.
Static model specifications (StaticY) result in 53.37 percentage points greater estimated income
elasticities. For gasoline demand, Espey (1998) found a similarly large effect for this variable. However,
for the subset of elasticities obtained from static models using cross sectional data, the effect of StaticY is
largely offset by the opposite effect of the interaction dummy StaticY.CS.
24
The GDP per capita cross-sectional variable (rgdpe_cap.1998) suggests this elasticity is largely flat across
income levels. For every additional thousand dollars of gpd per capita relative to the sample mean,
income elasticity becomes 0.12 percentage points lower.
19
Within a given country or region,
responsiveness to a new maximum income level (Ymax) is 3.29 percentage points larger than the average
responsiveness. However, neither of the two estimated coefficients related to income levels (Ymax and
rgdpe_cap.1998) are statistically significant at the 10% level in the preferred LME specification. As
found in previous meta-analyses of gasoline demand (e.g., Espey, 1998; Havranek and Kokes, 2015),
including vehicle stock in the demand model (VehStk) results in smaller estimates of income elasticity.
However, the magnitude of this coefficient is small (-0.0365) and it is not statistically significant. Finally,
the lack of statistical significance on the VARIANCE variable suggests that, after controlling for the rest of
explanatory variables, publication bias is not significantly affecting the estimated baseline for this
elasticity.
Table 7: Results from Short-Run Income Elasticity Metaregressions (Non-Transportation)
WLS cluster-robust.se LME
--------------------------------------------------------------
YrAvg -0.0091 -0.0158*
(0.0117) (0.0088)
Monthly 0.5751*** 0.6098
(0.1504) (0.3927)
CSTS 0.0953 0.1087
(0.0659) (0.0684)
Ymax 0.0011 0.0203
(0.0285) (0.0500)
StaticY 0.6444*** 0.6534***
(0.0856) (0.0690)
rgdpe_cap.1998 -0.0002 0.0000
(0.0009) (0.0013)
FuelSwitch -0.0781 -0.0266
(0.0519) (0.0934)
VARIANCE 0.1597 0.1941
(0.2012) (0.2138)
Constant 0.0134 -0.0015
(0.0602) (0.0536)
Observations 127 127
R2 0.4563
Adjusted R2 0.4195
Log Likelihood -38.4718
Akaike Inf. Crit. 98.9436
Bayesian Inf. Crit. 130.2296
Residual Std. Error 0.8989 (df = 118)
F Statistic 12.3806*** (df = 8; 118)
--------------------------------------------------------------
Notes: Significant at the 1% level (***), 5% level (**), 10% level (*).
The results of likelihood ratio tests in Table 1 showed that the WLS model specification with standard
errors clustered at the study level is preferred to the LME specification for analyzing the variability in
short-run income elasticities outside of the transportation sector. The strongest effect revealed by the
WLS metaregression in Table 7 is that of static versus dynamic model specifications. The estimated
19
The sample mean of 1998 real GDP per capita is $27,173 and the range spans from $408 for Nigeria to $76,100 for the United
Arab Emirates.
25
coefficient on StaticY indicates that using a static model results in 64.44 percentage points larger income
elasticities for this portion of crude oil demand. This large effect is consistent with the interpretation of
elasticities from static models as medium run rather than short-run (Espey, 1998). The only other
statistically significant effect in the WLS specification in Table 7 is the one from the use of monthly data
(Monthly) which results in an increase in income elasticity of 57.51 percentage points. However, this
result should not be viewed as general or extrapolated outside of this specific metadata sample because it
is based on only two elasticity estimates from a single study.
20
The rest of estimated effects—increasing trend over time, larger elasticities from studies using panel data,
larger responsiveness to a new GDP per capita maximum than other income levels, smaller income
elasticities for higher income countries, smaller elasticities from studies of crude oil demand in the
residential and electricity generation sectors, and direct relationship between elasticity estimates and their
variance—are not statistically significant.
Table 8: Results from Long-Run Income Elasticity Metaregressions (Transportation)
WLS cluster-robust.se LME
-------------------------------------------------------------------
YrAvg -0.0091 -0.0077
(0.0063) (0.0050)
SPEEDYRS -0.0141*** -0.0068**
(0.0031) (0.0029)
CSTS 0.0808 -0.0419
(0.0713) (0.0883)
Ymax 0.4998*** 0.4012
(0.1211) (0.2768)
rgdpe_cap.1998 -0.0034* -0.0023
(0.0020) (0.0016)
DslTransp 0.4783*** 0.5096***
(0.0983) (0.0689)
VehStk -0.1018** -0.1032
(0.0502) (0.0949)
VARIANCE 0.0002*** 0.0001
(0.0001) (0.0002)
CALC_STERROR -0.3362*** -0.1858**
(0.0989) (0.0846)
Constant 0.6282*** 0.6917***
(0.0411) (0.0569)
Observations 226 226
R2 0.4661
Adjusted R2 0.4439
Log Likelihood -114.1655
Akaike Inf. Crit. 252.3310
Bayesian Inf. Crit. 293.3774
Residual Std. Error 0.9194 (df = 216)
F Statistic 20.9539*** (df = 9; 216)
--------------------------------------------------------------
Notes: Significant at the 1% level (***), 5% level (**), 10% level (*).
20
As for the counterpart price elasticities, Vásquez-Cordano (2005) is the only study in the dataset that uses monthly data to
estimate income elasticities outside of the transportation sector. The two elasticity estimates from that study going into this
metaregression are for kerosene (0.702) and liquefied petroleum gas (0.101) in Peru.
26
For long-run income elasticities in the transportation sector, the likelihood ratio test in Table 1 indicates
that the LME specification is preferred. Results from that preferred specification in Table 8 indicate that
the long-run responsiveness of transportation fuel demand to income is almost double for diesel versus
other petroleum-based transportation fuels. The baseline elasticity value indicated by the intercept
(0.6917) corresponds to studies using gasoline or aggregate transportation fuel demand data. All else
equal, diesel demand studies find elasticities of 1.20. None of the studies on long-run income elasticity of
diesel demand are for the United States. Most elasticity estimates in this category are for European
countries or low-income countries. Higher elasticities for diesel in Europe can be partly explained by the
policy shift toward diesel consumption in that region in the 1990s and 2000s. As for high income
elasticities for diesel in low-income countries, this result is consistent with the negative coefficient on
1998 income level (rgdpe_cap.1998). Contrary to the idea of larger demand responses over longer
adjustment periods, within the set of studies included in this metaregression, long-run income elasticity in
the transportation sector slightly decreases, by 0.68 percentage points, for each additional year of
adjustment. The large negative effect of calculated standard errors (CALC_STERROR) on effect size is
indicative of bias in the calculated standard errors relative to those directly reported in the studies.
The rest of estimated effects—decreasing trend over time, smaller elasticities from studies using panel
data, larger responsiveness to a new GDP per capita maximum than other income levels, smaller income
elasticities for higher income countries, smaller elasticities from studies including vehicle stock as one of
their explanatory variables, and direct relationship between elasticity estimates and their variance—are
not statistically significant.
Table 9: Results from Long-Run Income Elasticity Metaregressions (Non-Transportation)
WLS cluster-robust.se LME
--------------------------------------------------------------------
YrAvg 0.0137*** 0.0137***
(0.0030) (0.0035)
SPEEDYRS -0.0007 -0.0007
(0.0052) (0.0052)
CSTS 0.1643 0.1643
(0.1064) (0.1059)
Ymax 0.3802** 0.3802
(0.1569) (0.2594)
rgdpe_cap.1998 -0.0022* -0.0022
(0.0012) (0.0019)
CALC_STERROR -0.4301*** -0.4301***
(0.0986) (0.1015)
Constant 0.6716*** 0.6716***
(0.0549) (0.0585)
Observations 97 97
R2 0.6362
Adjusted R2 0.6119
Log Likelihood -62.3939
Akaike Inf. Crit. 142.7878
Bayesian Inf. Crit. 165.9602
Residual Std. Error 0.9822 (df = 90)
F Statistic 26.2301*** (df = 6; 90)
--------------------------------------------------------------
Notes: Significant at the 1% level (***), 5% level (**), 10% level (*).
27
For long-run, income elasticities outside the transportation sector, the likelihood ratio test displayed in
Table 1 indicates that the WLS specification is preferred. Table 9 shows that the baseline elasticity value
implied by the intercept (0.6716) is similar to the one for the transportation sector (0.6917) as is the
magnitude of the CALC_STERROR coefficient—indicative of bias from the calculated standard errors
that were not reported in the studies.
21
The estimated coefficient on YrAvg is indicative of an increasing
trend—1.37 percentage points increase per year—in income elasticity for the demand of petroleum
products outside of the transportation sector. Income elasticities in response to a new GDP per capita
maximum (Ymax) are 38.02 percentage points larger than for other income levels. The estimated
coefficient on rgdpe_cap.1998 means that long-run income elasticity outside of the transportation sector
decreases by 0.22 percentage points for each additional thousand dollars 1998 GDP per capita. The other
two estimated effects—decreasing elasticity as length of adjustment period increases and larger
elasticities from studies using panel data—are not statistically significant.
4.1 WORLD CRUDE OIL ELASTICITY DEMAND ESTIMATION
To translate the metaregression results into an estimate of world crude oil demand elasticity, a further
processing step is required. Table 10 displays multiple summary metrics for each of the 8
metaregressions. Fitted means result from computing the sumproduct of the estimated coefficients and the
sample mean values of the explanatory variables. The fitted means are generally smaller but not much
different from the raw mean elasticities for each grouping. The remaining columns in Table 10 display
alternative estimated baselines and their standard errors. Each baseline is constructed as the sumproduct
of the estimated coefficients and a value of either 0,1, or the sample mean for each of the explanatory
variables.
22
The 3 alternative baselines differ on the values at which price level-related explanatory
variables are evaluated. The first baseline bsl should be interpreted as the demand elasticity with respect
to the average crude oil price (PRICE.1998 and EndUserP evaluated at zero in the transportation and non-
transportation metaregressions respectively and Pmax and Ymax also evaluated at zero). The second
baseline bsl.max is the demand elasticity with respect to a new crude oil price maximum or income
maximum; it differs from the first in that Pmax and Ymax are assigned a value of 1 for the multiplication
by their estimated coefficients. Finally, the third baseline bsl.prodpmax evaluates Pmax, Ymax at one,
PRICE.1998 at the mean, and EndUserP at 1 and it conveys the demand responsiveness with respect to a
new observed maximum in the petroleum product prices paid by final customers. The standard errors of
the three alternative baselines are calculated using the Gaussian error propagation formula.
21
VARIANCE was not included as an explanatory variable in this metaregression because the funnel asymmetry test did not find
a statistically significant relationship between effect size and precision of the estimate.
22
YrAvg, rgdpe_cap.1998, DslTransp, FuelSwitch, SPEEDYRS, CS, CSTS, OECD, Monthly, and Quarterly are evaluated at their
mean values. StaticP, StaticY, StaticP.CS, StaticY.CS are evaluated at 0 for short-run elasticities and at their mean for long-run
elasticities. VehStk is evaluated at the mean for short-run elasticities and at zero for long-run elasticities. The rest of the
explanatory variables are evaluated at zero.
28
Table 10. Estimated Elasticities (Fitted Means and Baselines)
Grouping
Fitted
mean
bsl
bsl.max
bsl.prodpmax
Price-SR-
Transport
-0.168
-0.080
0.028
-0.118
0.035
-0.149
0.037
Price-SR-
NonTransport
-0.105
-0.060
0.017
-0.085
0.017
-0.129
0.022
Price-LR-
Transport
-0.452
-0.184
0.113
-0.656
0.182
-0.928
0.193
Price-LR-
NonTransport
-0.451
-0.321
0.091
-0.504
0.110
-0.638
0.126
Income-SR-
Transport
0.338
0.195
0.040
0.228
0.107
0.228
0.107
Income-SR-
NonTransport
0.225
0.054
0.068
0.055
0.074
0.055
0.074
Income-LR-
Transport
0.661
0.771
0.069
1.172
0.285
1.172
0.285
Income-LR-
NonTransport
0.486
0.733
0.069
1.114
0.171
1.114
0.171
We construct world price and income elasticities as weighted averages of the baseline elasticities of the
transportation and non-transportation sectors presented in Table 10. The weights are based on crude oil
consumption projections for the year 2017 from EIA’s International Energy Outlook 2013 (56%
transportation and 44% non-transportation). As additional step, we adjust the resulting short and long-run
world crude oil demand price elasticities to include changes in income as an indirect mechanism by which
demand responds to price shocks according to the formula
D,P =
D,P +
D,Y *
GDP,P where
A,B is the
elasticity of A with respect to B, D is demand, P is price, Y is income, and GDP is gross domestic
product.
23
Using a value of -0.02 for the elasticity of GDP with respect to crude oil price
GDP,P (Oladosu
et al., 2018), this second-order effect does not increase the price elasticity value significantly. The mean
and 68% confidence interval for the resulting world crude oil demand price elasticities, based on results
from 20,000 random draws from normal distributions truncated at mean +/- one standard deviation for
each of the 8 type-sector baselines, are shown in Figure 4. All the elasticities in Figure 4 are evaluated at
the average length of run of the elasticity data points included in the metaregression analysis. The average
length of run is 0.9 and 11.3 years for the short-run and long-run elasticities respectively.
23
Combining the direct and indirect effect (via income) of an oil price increase on demand is common when crude oil demand
elasticity is used to assess the costs of oil supply shocks (e.g., Brown and Huntington, 2013) because those events have a well-
documented macroeconomic impact. For different applications of the elasticity parameter, this adjustment might not be
appropriate..
29
Figure 4. Estimated short-run and long-run world crude oil demand elasticities with respect to price
(including income effect)
4.2 COMPARISON TO OTHER WORLD ELASTICITY ESTIMATES
Figure 5 places the world crude oil demand elasticities (with respect to crude oil price or a new crude oil
price maximum) from the metaregression in the context of other world crude oil demand elasticity
estimates in the literature and highlights attributes that can help understanding and, to some extent,
reconciling the large differences in value.
30
Figure 5. Short-run price elasticities of world crude oil demand (metaregression vs. other published
results)
First, except for IMF (2011), all other primary studies in Figure 5 estimate systems of equations:
simultaneous equations (Krichene, 2002; Askari and Krichene, 2010), structural VARs (Baumeister and
Peersman, 2013; Kilian and Murphy, 2014) or a dynamic stochastic general equilibrium model
(Bodenstein and Guerrieri, 2011). In all those systems, the quantity variable refers to crude oil production
data and changes in consumption are assumed to be equal to changes in crude oil output. The resulting
demand elasticities with respect to price can be referred to as “elasticities-in-production”—terminology
introduced in Kilian and Murphy (2014)—and they tend to overstate demand responsiveness because they
do not take into account the smoothing role of inventories. Kilian and Murphy (2014) address this
shortcoming by also computing a substantially smaller “elasticity-in-use” (-0.26 for the “elasticity-in-use”
versus -0.44 for the “elasticity-in-production”).
24
In contrast, the majority of studies included in the
metaregressions discussed in the previous section (as well as IMF(2011)) estimate reduced form
equations with crude oil consumption data as the dependent variable.
Second, studies that consider the possibility of time-varying elasticities find crude oil demand elasticity to
be declining over time (e.g., Baumeister and Peersman, 2013; Askari and Krichene, 2010). The crude oil
market has experienced structural changes since the 1970s that have reduced crude oil demand
24
Krichene (2002) and Askari and Krichene (2010) are exceptions to the otherwise larger “elasticities-in-production”
summarized in Figure 5. However, their authors acknowledge the limitations of their two-stage least squares approach which
takes GDP, natural gas prices, and exchange rates as exogenous. These estimates might be downward-biased due to endogeneity
bias.
31
responsiveness: the advent of liquid spot and future markets where participants can hedge their physical
positions (Baumeister & Peersman, 2013); the reduced ability of the OECD non-transportation sector to
substitute or reduce crude oil consumption after having taken advantage of “low hanging fruit”
adjustments in the wake of the crude oil crises of the 1970s (Dargay and Gately, 2010); a given reduction
in miles traveled provides progressively smaller fuel savings as vehicle fuel efficiency improves (Hughes
et al., 2008). Thus, papers that compute a single elasticity over the long time period including the 1970s
and early 1980s will likely obtain a larger elasticity than those starting later or allowing elasticity to vary
over time.
Third, crude oil demand elasticities recovered from SVAR impulse response functions represent
responses to shocks and those shocks are normalized to always result in a crude oil price increase. In
contrast, elasticities estimated using reduced form equations typically correspond to the average
responsiveness over shocked and unshocked periods and various types of shocks implying crude oil price
increases and decreases. The strong effect of the Pmax variable in the metaregressions is consistent with a
larger responsiveness during that specific type of price increase. Relatedly, IMF (2011) finds world crude
oil elasticity for the subset of observations in which price level was above the average price level (-0.038)
to be double the average elasticity for the full price history (-0.019).
Not all authors using SVARs agree on the magnitude of crude oil demand elasticities. Imposing bounds
on the value of crude oil demand elasticity has become a common part of the strategy for identification of
structural parameters in SVAR crude oil market models. As shown in Caldara et al. (2016), the two
observed patterns of 1) larger volatility in crude oil prices than crude oil output and 2) near-zero
covariance between reduced form residuals for global crude oil output and crude oil price are consistent
with a wide range of choices for supply and demand elasticity bounds. With many feasible combinations,
the choice of bounds must rely on external information which involves either a literature review or
primary estimation. In some cases, the selected pair of bounds involves a very small supply elasticity
(0.025) and larger demand elasticity (-0.8) (Killian and Murphy (2014); Baumeister and Peersman
(2013)) and in other cases the bounds or, in Bayesian SVARs, priors are similar in absolute value for
supply and demand (e.g., 0.10 and -0.10 respectively in Baumeister and Hamilton (2015) and Caldara et
al. (2016)).
25
Results from our metaregression generally agree with a short-run world crude oil demand
elasticity of approximately -0.1.
5. CONCLUSIONS
The aggregate response of global crude oil demand to a price or income change is the combination of
responses from multiple regions and sectors. Building on that idea, we construct a world crude oil demand
elasticity based on a meta-analysis of elasticities for individual regions and sectors/petroleum products
obtained from 75 studies published from 2000 to 2015. We then compare the metaregression results to
other estimates of the world crude oil demand elasticity in the literature.
Global short-run elasticities with respect to crude oil price obtained from the metaregression are low (0.08
and -0.06 for transportation and non-transportation sectors respectively). Estimated long-run elasticities
reflecting decade-long adjustments are -0.18 for the transportation sector and -0.32 for other end uses. All
estimated elasticities increase (in absolute value) when they convey response to a new price or income
maximum and when they reflect response to end-use product prices rather than crude oil prices. The
25
The -0.8 bound on crude oil demand impulse elasticity is based on a single paper that estimates long-run price elasticity of
gasoline for the United States using results from a household survey conducted in 1979 and 1988 (Hausman and Newey, 1995).
32
consumption-weighted average of elasticities from both sectors ranges, depending on details about the
price baseline, from -0.074 to -0.143 in the short-run. The long-run range is wider (-0.260, -0.823).
Results indicate a slightly decreasing trend in short-run transportation elasticity over time. The estimated
coefficient on the trend variable for the other price-elasticities is consistent with them increasing over
time but it is not statistically significant. For income elasticities, statistically significant trends only
appear for the non-transportation sector and suggest that short-run income elasticity has been decreasing
but long-run elasticity has been increasing. We find that countries with higher end-use price levels
(inclusive of taxes) are more price elastic. The estimated relationship between income elasticities and a
cross-section of income levels is weaker but consistent with higher-income countries being less income-
elastic.
No single study can produce an elasticity value well-suited for every empirical application. However,
applied economists can benefit from systematic literature reviews and meta-analyses to select elasticity
values useful to their specific research question. Attentiveness to key aspects of empirical application
(e.g., duration of adjustment period being investigated, normal market conditions vs. disrupted market
conditions) are important in selecting a value of crude oil demand elasticity. We illustrate these
considerations by computing multiple elasticity baseline values.
Even though there is an extensive body of literature on petroleum product demand elasticity estimation, it
continues to be unbalanced toward study of transportation demand in high-income countries. In addition,
changes in demand elasticity due to technological and policy changes are often observed in the literature
with a considerable lag since most studies compute average elasticities over decades-long analysis
periods. This is particularly the case for studies using time series data since they need to cover a longer
time period than studies using data with a cross-sectional dimension to ensure sufficient degrees of
freedom in the estimation. Thus, there continues to be room for new estimates to balance out the body of
estimates from different regions and sectors and to capture evolution of elasticities over time.
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