LOG-LINEAR MODELS OF PETROLEUM PRODUCT DEMAND:
AN INTERNATIONAL STUDY
by
Ross J. Heide
July 1978
MIT-EL-79-006WP
4
Log-Linear Models of Petroleum Product Demand:
An International Study
1. Introduction
The purpose of this work is to describe a set of log-linear models
of petroleum product demand and to document the estimation results.
This
effort is part of an overall study to understand and model the world oil
market.
As results obtained here will be used to construct portions of
a larger simulation model, this paper is intended to serve as a reference
to the methodology employed in obtaining the results.
More encompassing and sophisticated translog models have been used
to analyze total energy demand and oil's share of the demand for about
ten major Western countries.
The relatively simple log-linear specifi-
cation for demand equations is used here for two purposes.
The first is
to provide preliminary estimates of demand response to price and income
changes in the major consuming ("primary") countries for the main product
groups.
The intent is to provide a starting point by constructing
equations which can be used in a simulation model and can be replaced
as other segments of the overall study are completed.
The second purpose is to provide "final" equations and estimates
for what will be referred to as "secondary" countries.
These are coun-
tries which because of data availability problems and/or relatively less
significant quantities of demand are placed outside the scope of current
plans for more detailed modeling.
See Pindyck [1], [2].
-2-
No explicit distinction is made between "primary" and "secondary"
countries in this segment of the study.
Both secondary and primary
countries are pooled together.to obtain joint estimates.
But if sensible
results were obtained using the translog formulation, efforts were more
readily redirected if reasonable results could not be obtained for loglinear models.
The 20 countries represented in this work are listed below:
Europe
Asia
Austria
Belgium
Denmark
France
Greece
Ireland
Italy
Netherlands
Norway
Spain
Sweden
Switzerland
Turkey
United Kingdom
West Germany
Japan
North America
Canada
United States
South America
Brazil
Mexico
Exhibit 1 shows their relative size as oil consumers.
The above 20
countries accounted for 82.3% (based on weight) of the 1974 total oil
demand, excluding the U.S.S.R., Eastern Europe and China, or 68.1% of
the world total including those countries with controlled economies.
-3-
Exhibit 1
World Oil Consumption 1975 and 1974
Million Tonnes
1975
1974
U.S.A.
764.2
82.5
Canada
Total North America
846.7
Latin America
173.9
[TOTAL WESTERN HEMISPHERE 1,020.6
10.6
Austria
27.1
Belgium & Luxembourg
Denmark
15.5
5.2
Eire
11.9
Finland
France
109.3
Greece
10.2
0.6
Iceland
Italy
95.6
34.8
Netherlands
8.0
Norway
6.8
Portugal
43.4
Spain
Sweden
26.4
12.5
Switzerland
13.6
Turkey
United Kingdom
92.1
West Germany
128.6
11.4
Yugoslavia
1.1
Cyprus/Gibraltar/Malta
Total Western Euro e
664.7
Middle East
70.4
Africa
51.4
South Asia
28.5
South East Asia
81.3
Japan
239.8
35.6
Australasia
U.S.S.R.
370.0
84.0
Eastern Europe
China
55.5
TOTAL EASTERN HEMISPHERE ;1,681.2
World 2,701.8
WORLD (Excl. U.S.S.R.,
2,192.3
E. Europe & China)
782.6
84.8
867.4
171.3
1,038.7
10.7
28.1
16.0
5.4
11.6
121.0
9.4
0.6
100.8
35.4
7.7
6.5
41.1
27.1
13.0
12.5
105.9
134.3
11.5
1.3
699.9
68.6
50.3
27.7
77.7
258.9
36.0
341.5
81.0
48.5
1,690.1
2,728.8
Country/Area
2,257.8
Thousand
Barrels Daily
Percentagef
1975 I Change
Share
of
1975
over
T
10Q7A
1Q7n/107
17 1 It
17
V/ 13
I
4-1
Lvc-
l
Annual
Average
28.3%
-2.3% +1.9%
3.1% -2.7% +2.5%
31.4i1 -2.4% +2.0%
6.4- +i 5X
+4.9%X
37.8
-1.7% +2.4%
0.4%
-1.3%
+2.5%
1.0% -3.4% -0.6%
0.6% -3,0% -3.6%
0.2% -3.3% +4.8%
0.4% +3.3% +2.1%
4.1% -9.7% +3.0%
0.4% +8.7%
+8.7%
--2.5% +0.9%
3.5% -5.1% +1.8%
1.3%
-1.7% -1.0%
0.3% +4.3%
-0.7%
0.2% +5.1% +8.2%
1.6% +5.7% +9.1%
1.0% -2 .5% -2.4%
0.5% -4.4% -0.1%
0.5% +9.1% +12.1%
3.4%1-13.0%
-2.0%
4.8% -4.3%
-0.4% -0.6% +10.3%
--12.8% +1.1%
24.6% -5.0% +1.2%
2.6% +2.7% +7.3%
1.9% +2.2% +4.3%
1.0% +2.9%
+1.0%
3.0% +4.7% +6.4%
8.9% -7.4% +3.8%
1.3% -0.9% +3.4%
13.7% +8.3% +7.1%
3.1% +3.7% +8.7%
2.1% +14.4% +22.6%
62.2%
-0.5% +4.2%
100.0% -1.0% +3.5%
81.1%
-2.9%
+2.5%
J1
1Q07I
J1
1?07A
..
I
15,845*
1,735
17.580
3 660
21240
215
545
310
105
235
2,240
205
10
1,925
710
165
140
880
530
260
275
1,875
2,665
230
20
13,540
1,390
1,050
575
1,615
4,905
750
7,480
1,725
1 105
34,135
55,375
16,150*
1,785
17.935
3 595*
21 530
215
560
320
110
230
2,460
185
15
2,015
725
160
135
820
540
270
255
2,145
2,760
235
25
14,180
1,355
1,020
560
1,540
5,270
755
6905
1,660
970
34,215
55,745
45,065
46,210
I
Differences between production and consumption are accounted for by stock changes and
unknown military liftings.
*U.S. processing gain has been deducted from total domestic product demand. tBased on weight. 4Brazil 35.2, Mexico 29.1.
**Brazil 855,
Mexico 707.
Source: BP Statistical Review of the World Oil Industry 1975 [4].
-4-
2.
The Log-Log Specification
The log-log equation sets the log of the variable to be explained
equal to a linear combination of the logs of the independent variables,
hence its name.
log qijt
The basic static demand equation for fuel i is:
=
aij + 0ilog
ijt + Yilog Pijt
+
ijt
(1)
where j is the country index and t the time index, qi is per capita
consumption of fuel i, yj is the per capita gross domestic product in
constant currency units of country j, and Pij is the fuel price in real
units of local currency.
Adding the subscript j to the constant term
(using intercept dummies) allows estimating an equation across countries
with different units for the same variable.
The a..'s account for scale
differences because they are multiplicative terms.
This is one of the
conveniences of the log-log formulation, allowing pooling of various
countries' time series without performing the often difficult task of
conversion to a common unit of currency.
Unfortunately this same property eliminates the ability to pick up
inter-country differences in estimating the elasticities.
But if the
true elasticities are the same in the pooled countries, pooling results
in more efficient estimates.
Alternative poolings can be used to test
for differences in elasticities across countries.
By differentiating equation (1) with respect to P and y and multiplying by P/Q and y/Q respectfully, one obtains the price and income
elasticities:
=
dq
p
dp
-
P
(2)
-5-
ny
y
dq xP
y
dy
=
(3)
i
The elasticities can be read directly as one of the estimated coefficients
and the elasticities are constant, i.e. identical for all values of q, P,
and y.
If q is a "habit" level of consumption, or is consumed by a capital
stock, the new equilibrium level of q after a sustained change in P or y
One
This is a lagged adjustment process.
is not reached instantaneously.
type of lagged adjustment is the Koyck or geometric lag, where the adjustment
that takes place in each period is a constant portion of the difference
between the current level of consumption and the equilibrium or "desired"
level.
A dynamic version of equation (1) containing a Koyck lag is:
log qijt
=
i'log Yjt + Yi' log Pijt
ij +
+ Xilog qij,t-1
+
ijt
(4)
where 1-X (O < X < 1) is the portion of adjustment between the current
and equilibrium value of q that takes place in a given period.
In the
long-run equilibrium, which strictly speaking is reached only after an
infinite number of periods, qt equals qt-l'
Therefore substituting qt
for qt-l in equation (4) and resolving for the log of qt results in:
log q
ijt
+
-
i
log Pijt + 1-X
log yt
(5)
From this we see that the total long-run elasticities are the short-run
(one period) elasticities,
i
and Yi, divided by (l-X).
-6-
The fraction of the total adjustment to the new equilibrium t
periods after a maintained change in P or y at t=O is:
qo - qt
q0
t
=
1 -
t
(6)
qeq
A useful measure when discussing and comparing lags is the median lag,
T , or the value of t in equation (6) for which the fraction of the
total adjustment completed equals one half.
.5
=
1-
T
X m
or
T
m
=
log (.5)/log (X)
(7)
For example, if X = .7 which implies a 30% adjustment to the-long-run
equilibrium in each period, the median lag is approximately 1.9 periods.
-7-
3. Data
This section provides a brief summary of the data used in estimating
the previously described equations for the twenty countries.
Also
presented are the methods of transforming the data into the exact forms
in which they were used in the estimating equations.2
Product Quantities:
The annual consumption by product type comes from two sources, each
having a different category breakdown.
They are each described below.
The source of the quantity data for 18 countries (all except Brazil and
Mexico) is OECD's Energy Statistics.
For these countries there are nine
fuel categories:
1. Aviation gasoline (AG)
2. Diesel fuel (DS)
3. Industrial fuel oil (INDFO)
4. Jet fuel (JF)
5. Kerosene (KS)
6. Liquified petroleum gases (LPG)
7. Motor gasoline (MG)
8. Other fuel oil -- other than industrial (RESFO)
9. Other petroleum products (FOPET) -- petroleum chemical
feedstocks, fuel oil and LPG used to generate
electricity and steam
2
The data employed are part of a large international data base.
complete details, see Chapter 5 of the Users Guide [3].
For
-8-
Fuel consumption data for Brazil and Mexico were obtained from the UN's
World Energy Supplies.
For these two countries there are four fuel
categories:
1.
Fuel oil -- consumption by all sectors, also diesel fuel
2.
Gasolines -- motor and aviation gasolines
3.
Kerosenes -- kerosene including jet fuel
4.
LPG -- Liquified petroleum gases consumed by all sectors
The units of all of the above categories are Tcals per million capita per
year.
Tcals, a measure of the heat content of a fuel, is an abbreviation
of teracalories or 1012 calories.
A Tcal is the equivalent of 3.968x10 9
BTU, or approximately 685 barrels of crude oil.
Prices:
For the nineteen countries other than the United States the prices
of all petroleum products, retail price of gas, coal, and electricity
and the industrial price of gas, coal, and electricity, were obtained
from the international energy statistics compiled by the Federal Energy
Administration.3
In the data base the data are converted from various
units to units of local currency per Tcal.
Price series for jet fuel and aviation gasolines were not available
for any of the twenty countries.
The price of kerosene was used as a
proxy for the price of jet fuel and the price of motor gasoline was used
in place of the price of aviation gasoline.
Although the markets are
different, the products are physically very similar.
Prices for the U.S.
were obtained from the Bureau of Mines and Department of Commerce.
Details for each series may be found in Table 5-5 of the User's Guide [3].
With the exception of Brazil and Mexico, these data are proprietary
and not described in the above mentioned User's Guide.
-9-
For the countries with an "other petroleum products" category an average
of the prices of No. 2 and No. 6 fuel oils was used to approximate the
price movements of those products. When used in estimating equations,
all prices are deflated using the implicit gross domestic product
deflator with 1970 as a base year.
Therefore, the units are constant
1970 units of local currency for Tcal.
Price of Energy:
In estimating the demand for fuel oils, the products most susceptible to substitution of alternative fuels, a measure of the aggregate
price of energy was needed.
Translog price aggregators have been esti-
mated for nine countries (residential price of energy) and ten countries
(industrial price of energy).
countries included here.
Both groups are subsets of the 18 OECD
The coefficients estimated for these subsets
were used with the prices of oil, gas, electricity, and coal in each
country to generate a price index of energy for the entire group of 18
countries.
Three indices were used: a four fuel residential index for
European countries, a three fuel residential index for the U.S. and
5
Canada, and a four fuel index using industrial prices. The appropriate
set of coefficients were used in each case, but no attempt was made to
scale the index as the input prices were in each country's local currency.
The units of the price of energy indices are not defined, but since
they are constructed from nominal local currency prices, the indices are
deflated (using the implicit GDP deflator) when used in the estimating
4
For a detailed description of the energy price aggregators, see Pindyck
[1], [2].
Virtually no coal is used in the residential sectors of either the U.S.
or Canada.
-
equations.
10 -
The hope is that the indices capture the movement of the
price of energy within each country.
Other Variables:
Series for gross domestic product, population, and temperature
were also used.
Gross domestic product data were obtained from the
OECD's National Accounts and the UN's National Account Statistics.
units are 1970 local currency per capita.
The
The implicit deflators were
derived from the same sources by using the ratios of the GDP in current
purchasers' values to the GDP in constant purchasers' values (1970 base
year).
Data for the total population of each country, used to transform
fuel quantities and income to per capita bases, come from the UN Demographic Yearbook.
The temperature series represent the average temperature over the
five winter months (November-March) of the major city or cities of each
country.
The source is the U.S. Weather Bureau's Monthly Climatic Data
for the World, and the units of measurement are degrees Fahrenheit.
Table 1 shows the range of data available for the variables
described above.
The range of values used for estimation is only the
intersection of the range for each variable included.6
Table 2 gives the
relative consumption of each fuel category for two different years.
The
total consumption in 1,000's of Tcals is also shown for the same years.
One may observe that although the shares may differ drastically between
countries, they are relatively stable over time within each country.
6 For some fuel categories the range includes zero values (no consumption)
which can not be used in log equations.
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4. Statistical Results
In this section we present the estimation results for the models
described above.
The twenty countries are pooled into five groups and
alternative model specifications are explored for each product category
within each group.
The five groups are:
1. North America (2 countries):
2. Europe (12 countries):
United States and Canada
Austria, Belgium, Denmark, France,
Ireland, Italy, Netherlands, Norway, Sweden, Switzerland,
United Kingdom and West Germany
3. Southern Europe (3 countries):
Greece, Spain and Turkey
4. Japan (1 country)
5. South America (2 countries): Brazil and Mexico
This grouping is based upon geographic proximity and broad similarity
of economic characteristics, such as degree of development and growth
rate.
Many other possible combinations of countries exist along with
valid arguments for their use.
Alternative poolings have not yet been
completed, as each requires a bare amount of computer work.
One or two
different poolings for a few of the equations should be estimated to
test the validity of the selected pooling.
For each of the groups a subset of the estimated equation specifications are presented in Tables 3 through 7. All regressions were done
using the ordinary least squares (OLS) program of TROLL.
As opposed to
a verbal description of the information contained in these tables, a
general outline of the estimation work is presented.
For each product
type in each of the country groups the "preferred" specification is
- 15 -
NOTES TO TABLES 3A THROUGH 7
When a variable is indicated,.the coefficient is that of the log of that
variable.
The lagged dependent variable is the value of the left-hand side variable
in the previous year.
The T statistic for each coefficient appears in parentheses below the
coefficient.
NOB = number of observations
F = F statistic
T = median lag in years
m
MG = motor gasoline
DS = diesel fuel
KS = kerosene
JF = jet fuel
AG = aviation gasoline
LPG = liquified petroleum gases
INDFO = industrial fuel oil
RESFO = residential (other) fuel oil
FOPET = other petroleum products
* indicates preferred specification
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indicated with an asterisk.
Not a precise term, "preferred" indicates a
combination of significance and correct sign in the elasticities and
reasonable behavior in the lag structure.
An attempt has been made to
show the logical alternative(s) to the preferred specification.
The
most common reason for selecting an equation which excludes a variable
which should in theory be included (such as price) is an incorrect sign
for the coefficient of that variable (such as a positive elasticity for price).
In the case of motor gasolines and diesel fuel where, strictly
speaking, other fuels do not compete for the same uses, alternative
specifications attempted include only the basic equations.
That is,
only the static and dynamic version where product price and income are
used as explanatory variables.
For the fuel oils the appropriate prices
(retail or industrial) of alternative fuels were used; generally with
poor result.
Alternatively the respective constructed price of energy
was used in the fuel oil equations for each group (regressions not shown
for every case) also with mixed results.
For other fuel oil, the major
use of which is space heating, an average temperature variable was
included.
Good results were achieved using the temperature variable in
equations for Europe and North America.
Fuels used to generate electricity
constitute a significant portion of the category "other petroleum products"
(FOPET).
Therefore the price of electricity was employed and expected to
have a negative coefficient.
A time variable was used in some specifications
for aviation gasoline in an attempt to account for the replacement over time of
internal conbustion engines by jet engines in most commercial aircraft.
As
would be expected, jet fuel has a high income elasticity in most cases; higher
than would be expected to hold after the above mentioned replacement has been
more or less completed.
- 28 -
The results in many cases indicate a negative income elasticity for
kerosene.
It is reasonable that kerosene is an inferior good, being
replaced by more convenient heating and cooking fuels as incomes rise.
LPG, only recently a significant consumption category, generally displays
a very high positive income elasticity.
elasticities to hold in the long run.
One would not expect these high
- 29 -
REFERENCES
1.
Pindyck, R. S., "International Comparisons of the Residential Demand
for Energy", MIT Energy Laboratory Working Paper #MIT EL 77-027
WP, August 1977.
2.
Pindyck, R. S., "Interfuel Substitution and the Industrial Demand for
Energy: An International Comparison", MIT Energy Laboratory
Working Paper #MIT EL 77-026 WP, August 1977.
3.
Carson, J., "A User's Guide to the World Oil Project Demand Database",
Working Paper MIT-EL-78-016, August, 1978.
4.
British Petroleum Co. Ltd., "BP Statistical Review of the World Oil
Industry 1975", Britannic House, London, 1976.