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Demand for non-energy petroleum products
Demand for non-energy petroleum products The case of QuCbec
Davy B&anger, Jean-Thomas Bernard and RCmyDubois
Non-energy petroleum products (NEPP) refer to petroleum products which, once refined, are used either as final goo& or as intermediate inputs for other non-energy producing processes. They fall into jive categories: petrochemical feedstocks, asphalt, petroleum coke, lubricating oils/greases and naphtha specialties. While being of some sign@ance, they have received little attention inprevious petroleum demandstudies. The heterogeneous nature of the products may be part of the explanation for the lack of interest. The main results of the econometric analysis are:first, all own-price elasticities except for petroleum coke are quite low, that is, less than one in absolute value. Second, asphalt,petroleum coke, and lubes/greases dtiplay income elasticities which are close to one while petrochemical fee&tocks has an output elasticity above one and income appears to play no role in explaining the demand for naphtha specialties. Finally, petrochemical feedrtocks are a statistically significant substitute for capital and energy, but not for labour, in the QuPbec chemical industry. Keywork
Petroleum demand; Non-energy petroleum products; Econometric analysis
Non-energy petroleum products (NEPP) refer to petroleum products which, once refined, are used either as final goods or as intermediate inputs for other nonenergy producing processes. They fall into five categories - petrochemical feedstocks, asphalt, petroleum coke, lubricating oils/greases, and finally, naphtha specialties.’ Together, theymadeup9.0% and 10.6% of all petroleum products consumed in the province of Qukbec and in Canada in1986.2 While being of some significance, they have received little attention in previous petroleum demand studies. Bohi [3] provides a comprehensive survey of energy demand analysis, including petroleum products as of 1980; however, non-energy petroleum products are ignored. The
heterogeneous nature of the products may be part of the explanation for the lack of interest.3 The main purpose of this paper is to show the results of an econometric analysis of NEPP demand in the province of QuCbec. First, there is a description of the evolution of Quebec NEPP consumption from 1962 to 1986. Second, the approaches and the main conclusions of some related works in the Canadian context are summarized. Third, the specification ofthemodels used to estimate Qutbec NEPP demand is described. A discussion of the empirical results follows. The main results of the econometric analysis are: first, all own-price elasticities except for petroleum coke are quite low, ie less than one in absolute value. Second,
The authors are with GREEN, Dtpartement d’ficonomique,
‘There is also a residual category, that can be referred to as ‘other non-energy petroleum products’, which accounted for 1.8% of total Quebec NEPP in 1986. This residual category is not analyzed in this paper. %tatistics Canada, No 57-003, Tables 1D and 7D, 1986-IV. “Some unpublished works on Canadian total energy demand incorporate non-energy petroleum products as separate items and they are discussed further later.
Universitt
Laval, Ste-Foy,
QuCbec, Canada
GlK
7 P4.
We are grateful for financial support from the SSHRC, Ottawa, and from the Fonds FCAR, Minis&e de l’fiducation, Quebec. Thanks are due to J. Roberts for providing research assistance. Final manuscript received 8 February 1990.
0140-9883/90/030177-08 0 1990 Butterworth-Heinemann Ltd
Demandfor non-energy petroleum products: D. BPlanger et a]
asphalt, petroleum coke and lubes/greases display income elasticities which are close to one while petrochemical feedstocks have an output elasticity above one and income appears to play no role in explaining the demand for naphtha specialties. Finally, petrochemical feedstocks are a statistically significant substitute for capital and energy, but not for labour, in the Quebec chemical industry.
Consumption in Quebec non-energy petroleum products 1962436 In order to single out the main features of Quebec NEPPconsumption from 1962 to 1986, the first oilcrisis in 1973 serves as a benchmark to identify two subperiods. As can be seen from Table 1, the average annual growth rate of NEPP consumption was 9.2% over the first subperiod and -4.0% over the second. This growth pattern increased the share of NEPP in total petroleum product consumption from 6.6% in 1962 to 10.0% in 1977. In that year, NEPP consumption reached a peak of 2942000m3. Thereafter the decline has been rather steady matching the reduction of totalpetroleumproductconsumption.Thedeclineisthe result of both higher oil prices and the 1982 world recession. Petrochemical feedstocks and asphalt are the two largest single components of NEPP and together they form more than 50% of the total. Petrochemical feedstock consumption increased rapidly in the first subperiod at an average of 13.9%/year outpacing total petroleum product growth. Peak consumption was reached in 1979 followed by a sharp decline. Accounting for 52.2% of total NEPP consumption in 1978, petrochemical feedstocks fell to 13.2% in 1986. Asphalt consumption displays a steadier pattern of evolution. The rapid average growth rate in the first subperiod (7.5% year) was followed by a slight reductionin the second. In 1986, asphalt accounted for42.0% of NEPP. Naphtha specialties display a pattern similar to petrochemical feedstocks: rapid growth in the first subperiod with a peak in 1973 followed by a fall. The two other products, lubes/greases and petroleum coke present a more stable pattern; the latter product is the only one to show positive growth from 1973 to 1986. Our aim is to estimate econometric models which can be used to determine whether variations in Quebec NEPP consumption, as shown in Table 1, can be explained using standard economic variables such as income and relative prices.
Previous studies Energy, Mines and Resources Canada and the National Energy Board have developed demand models by sector
178
and by province for the Canadian economy. These are called respectively the Interfuel Substitution Demand Model (IFSD) and the Energy Demand Model (EDM) and they include some non-energy petroleum products.4 Petrochemical feedstocks and petroleum coke are excluded. However, asphalt, lubes and naphtha are treated as separate final goods and they are assumed to depend in a log-linear functional form on the following variables: real domestic product, oil price, degree-days,5 and finally, the lagged dependent variable. Table 2 displays a summary of short-run and longrun price and income elasticities for the relevant products. All price elasticities both in the short run and in the long-run are less than one, except for lubes and greases in the long run (EDM). With the exception of asphalt in the long run, all income elasticities are also less than one. The elasticity estimates for both models are somewhat close for asphalt; however, there are significant differences for lubes and greases and naphtha.
Tbe models Two distinct models are adopted to model Quebec NEPP demand. The choice between the two is based on practical grounds and data availability. One approach is adopted for asphalt, petroleum coke, lubes and naphtha, and a different approach is adopted for petrochemical feedstocks. Asphalt, petroleum coke, lubes and naphtha
For each product, a single equation was estimated relating the quantity by a log-linear function to real prices and income. Despite its theoretical shortcomings6 the log-linear model can still be of some usefulness in situations where a model with a better theoretical basis cannot be used, as is the case here.’ Then, following the method of Anderson and Blundell [l], each of the four equations is imbedded into a dynamic structure and they are estimated jointly using Zellner’s seemingly unrelated regression procedure. The main advantage of the Anderson and Blundell specification is that it allows for a fairly flexible dynamic adjustment mechanism while making it easy to retrieve the long-run equilibrium relationships by setting all ‘Energy, Mines and Resources Canada (Spring 1985) and National Energy Board (July 1985). See also Sahi and Erdmann [II] and Preece el al [IO]. ‘Degree-days is introduced as an explanatory variable to capture the effect of weather on the product mix coming out of the refining process. For instance, in colder periods, more heavy fuel oil is produced for heating purposes at the expense of asphalt production. Usually, this phenomenon would be captured by relative price changes between the two products. Unfortunately, data availability precludes such an approach. %ee Plourde and Ryan [9]. ‘See the discussion dealing with the log-linear model presented by Deaton and Muellbauer [4], pp 17-18.
ENERGY ECONOMICS
July 1990
\o
z
g
G
2 q
1032 850 606 453 208
I101
mJx 1W 256 298 510 525 655 740 712 728 896 899 951 1075 975 817 1116 I333 1512 1518 1296
13.9 - 11.9
(%) 25.4 26.5 34.2 35.9 37.6 41.9 39.5 39.0 43.6 43.1 43.3 40.4 38.5 39.7 46.8 45.3 52.2 52.0 47.7 43.9 46.8 40.2 31.0 26.2 13.2
7.5 -1.5
m’x 1W 365 397 517 504 560 505 513 525 553 586 672 809 743 641 709 782 736 777 698 619 544 567 586 651 661
Aspbalt
(%) 36.3 35.2 34.7 34.5 32.1 28.6 28.5 28. I 26.9 28. I 30.6 30.4 29.3 31.1 29.8 26.6 25.4 26.7 25.7 24.7 24.7 26.8 30.0 37.7 42.0
4.6 2.7
m’x 1Y 216 254 259 199 275 271 328 355 360 271 215 354 425 315 245 441 314 281 430 458 367 417 530 392 503
Petroleum coke
(%) 21.5 22.6 17.4 13.6 15.8 15.3 18.2 19.0 17.5 13.0 9.8 13.3 16.8 15.3 10.3 15.0 10.8 9.6 15.8 18.3 16.6 19.7 27.1 22.7 32.0
Lubesand
4.5 - 2.4
m3x 1W 117 122 130 I41 147 158 156 166 I53 164 173 191 190 191 195 184 208 199 170 180 147 I45 158 I52 138
gre(%) 11.6 10.8 8.7 9.6 8.4 9.0 8.7 8.9 7.4 7.9 7.9 7.2 7.5 9.3 8.2 6.3 7.2 6.8 6.3 7.2 6.7 6.9 8.1 8.8 8.8
13.8 - 13.0
m3x 1Y 52 55 63 83 89 84 85 89 87 155 155 213 103 75 80 71 79 87 78 84 68 82 54 43 35
Naphtha specialties
(%) 5.1 4.9 4.2 5.7 5.1 4.7 4.7 4.7 4.2 7.4 7.1 8.0 4. I 3.6 3.4 2.4 2.7 3.0 2.9 3.3 3.1 3.9 2.7 2.5 2.2
Sources: 1962 to 1975, Srafisfics Cumzdu, No45-004; 1976 to 1986, Smisrics Canada, No 57-003. From 1962 to 1976, data on petroleumcokeconsumption bank. Since non-energy petroleum products include the miscellaneous residual category (see footnote 1). percentages (%) do not sum to 100%.
1962-73 1973-86
AMII~ rate of growth
I%2 1963 1964 1965 1966 1967 1968 1969 I970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
Petrochemical feed&&s
Table I. Breakdown of Qu&ec non-energy petroleum products consumption from 1962 to 1986 (quantity and percentage of total).
9.2 -4.0
6.4 -4.1
‘u
5Y In
& a. ij
G
2
S3
3 2 P b 2 2
:
$
9.9 9.8 9.6 9.8 9.8 10.5 10.2 9.7 9.0
2
3
B
7.1 7.8
IO.0
6.6 6.9 8.3 7.4 8.3 7.8 7.3 7.1 7.5 7.8 7.7 8.8 8.5
NEPP as % of total petroleum ,products
from the EDM data
m’x 1W 15307 16231 18052 19656 21069 22769 24657 26411 27561 26728 28352 30278 29912 29164 30441 29499 29132 29678 28167 25515 22423 20089 19275 17863 17510
Total petroleum products
have been borrowed
m3x 1W 1007 1127 1492 1464 1744 1767 1800 1870 2054 2085 2196 2662 2534 2059 2381 2942 2898 2916 2718 2506 2206 2112 1958 1727 1573
Non-energy petroleum products
DemandJor uon-etlergy petroleum products: D. BClanger et al / I Table 2. Previous studies: NEPP price and
income elasticities (Quibec).
Price elasticity Short run
Long run
Income elasticity Short run
Long run
- 0.28 - 0.25
-0.51 - 0.63
0.95 0.53
1.73 1.33
-0.13 -0.41
- 0.30 -1.17
0.36 0.23
0.82
-
0.67
-
- 0.27
0.28
0.70
Asphalt JFSD EDM
Lubes and greases IFSD EDM
0.66
Naphtha specialties IFSD
-0.10
EDM
-0.1
S~x~ccs: IFSD,
I
Energy, Mines and Resources Canada,
Spring 1985; and EDM,
variable changes to ze~o.~ Unfortunately there is no direct price information on the above products. To get around this difficulty, use is made of available price data on other products which are closely related to those under study in the refining process and which are substitutes to them at the production stage.’ The four equations are the following: rlnASP=a,,
+a,Ja,.,lnRHFP(u13”16+
- 1) l)+ai3u,slnQRDP(-
(1)
rlnPC=uzlrlnRHFP+
u&nPC( - 1)
+ u2,u,,ln RHFP( - 1) + a,,uz51nQlRDP( - 1) + u23”26 + (I2 (2) rlnLUBE=u3,rlnRLFP+ u32rhQiRDP-u331nLUBE(
- 1)
+ u33u341nRLFP( - 1) + u,,u,,lnQlRDP(
- 1) +
(3)
u3
rlnNAPH=u,,rlnRCOP+ ub2AlnRPDIH - a,,lnNAPH( + u43u,SlnRCOP( u43”46
+
u4
- 1)
- 1) + a43u451nRPDfH(
- 1) +
(4)
where A
&j
ASP LUBE NAPH
frst difference operator coelhcient of explanatory variable j for products = asphalt (m3) = lubes and greases (m3) = naphtha specialties per household (m’) =
=
‘The major difference between the approach taken here and the more encompassing one sugges:ed by Anderson and Blundcll [I]. is tha[ no interaction occurs across equations besides the error terms. 9No close substitute with price information is available for naphtha specialties and the crude oil price at refinery gate in Montreal is used.
180
PC QIRDP
= petroleum coke (m3) = QuCbec industrial real domestic product
QRDP
= Quebec real domestic product
RCOP
= crude oil price at Montreal refinery gate
(billion $ 197 1) (billion $ 1971)
RHFP
=
RLFP
=
RPDIH
=
U,
=
1)+
uI
u2,rlnQIRDP-
+
Energy Board, July 1985.
rlnRHFP+
a,2rlnQRDP-a,JlnASP(
a33036
National
deflated by the implicit price deflator of consumer expenditure excluding direct energy (1971= 1) heavy fuel price deflated by the GDP price deflator (1971= 1) light fuel price deflated by the GDP price deflator (1971= 1) personal disposable income per household deflated by the CPI (1971= 1) error term of equation s
Petrochemical feedstock demand is treated as a derived demand and is considered as one of the inputs in the production process of the chemical industry along with capital, labour and energy. Due to the large number of parameters to be estimated when several inputs are considered simultaneously in unrestricted form, we adopt the nested twolevel model along lines originally suggested by Fuss [6]. At the first or aggregated level, the producer is assumed to choose the mix of capital (K), labour (L), energy (E) and petrochemical feedstocks (fl which minimizes production cost for a given output level (Q), while taking into account the relative input prices. At the second level, the price of energy (PE) is obtained from a unit cost function which also represents the cost minimizing behaviour of the producer which seeks the optimal mix of electricity (EL), natural gas (G+)and oil (0) for a given energy level. The price of energy (PE) bridges the link between the first and the second level. Finally, at both levels, production factor demand functions can be derived by applying Shephard’s lemma.
ENERGY ECONOMICS
July 1990
Demandfor non-energy petroleum products: D. BP/anger
The aggregate level: capital (K), labour (L), energy (E) and petrochemical feeristocks (F). Materials (IV) are assumed to enter the production process in a fixed proportion o!to output and no-substitution is allowed to occur between materials and other inputs. The restrictive assumption is made because of data limitations: Q = min{f(K, L, E, F), aM)
(5)
Cost minimization implies that:
Price elasticities associated with the translog cost function are:’ ’ Eii= @ii+ Siz - Si)/Si for i= K, L, E, F Eu=(/?v+S;Si)/Si for i,j=K, L. E. Fand i #j (11) The energy level: electricity (EL), naturalgas (G) andfuel oil (0). Finally, the price of aggregate energy (PE) is obtained from a unit cost function which is again approximated by a second-order translog function: lnPE=r],+C,ql
Q = f(K, L, E, F)
(6)
We suppose that the function f(K, L, E, F) is quasiconcave and increasing in terms of K, L, E and F. Then, from duality theory, there exists a unique cost function which is homogeneous of degree one, concave with respect to factor prices and increasing in output: CQ = cQ(pK,
PL. pE> pF>
Q>
(7)
where C, = total cost Pi= the price of factor i= K, L, E, F
lnCQ=a,+ xi ailnPi+ a&Q+
1/2C,~,@$nPilnPj
+ C,PiQlnPilnQ + 1/2&$lnQ)’
lnP,+ 1/2C,Cs & lnP, lnP,
Again, applying Shephard’s lemma gives each energy input share in total energy cost: S, = q1+ 1, UnP,
(13)
where t,s= EL, G, 0. Finally, we impose the following restrictions: t;
s ‘S &, = 65,
1, & = 0 (adding-up) (homogeneity) (symmetry)
Price elasticities, for a given total energy level, can be computed from functions (11) when they are expressed in terms of energy. ’ *
(8)
Empirical results
The application of Shephard’s lemma to the translog cost function yields the cost share (Si) associated with each production factor:
Asphalt, petroleum coke, lubes and naphtha
(9)
where i, j= K, L, E. F. In order for the system of demand equations to satisfy the adding-up criterion (c,Si= 1) and the properties of neoclassical production theory, the following parameter restrictions are required and they are imposed at the estimation stage.” C,ai= 1, C#~=C,@i~=O
(adding-up)
C,&=O
(homogeneity)
Pp=
(symmetry)
Pji
(10)
where i, j= K, L, E, F. ‘“Neoclassical production theory requires that the cost function be concave with respect to factor prices. The restriction cannot be expressed as simple linear relationships involving parameters only and it has not been imposed at the estimation stage. A necessary condition is that price elasticities be negative and this is verified below.
ENERGY ECONOMICS
July 1990
(14)
where t, s= EL, G, 0.
where i, j= K, L, E, F.
Si= tli + x,@&Pj + /?iplnQ
(12)
where t, s = EL, G, 0.
g,;
To represent empirically this cost function, we have arbitrarily chosen the translog function, which provides a second-order approximation of any function:
et al
Table 3 shows price and income elasticities computed from the estimation results for the model described earlier. The statistical fit of the sytem as measured by R2, is acceptable and most of the variables related to the dynamic specification are statistically different from zero. It should be noted that two variables are deleted because of non-significant statistical results in light of theoretical expectations: income per household in the naphtha specialties equation and price in the petroleum coke equation. It is seen that all long-run own-price elasticities are quite low and that long-run income elasticities are close to one. If we compare the results in Table 3 with those of previous studies as shown in Table 2, it can be seen that our estimates of long-run price and income elasticities for asphalt are lower than those of both the IFSD and EDM. The results for lubes are closer to those appearing in IFSD than in EDM. As for naphtha specialties, no statistically significant relation with income is indica“See Fuss [6]. ‘%ee Fuss [6].
181
Demandfor non-energy petroleum products: D. BP/anger et
al Table 4. Energy sources: empirical results for 1962 to 1984.
Table 3. Final goods demand models: price and income elasticities. Long runn Asphalt Price elasticity Income elasticity DW=1.90SER=0.07 Lubes Price elasticity Income elasticity DW = 1.76SER = 0.05 Naphtha Price elasticity Income elasticity DW=2.15 SER=0.19 Coke Price elasticity Income elasticity DW= 1.53 SER=0.21 Overall measure to fit R2: = 0.6 1b
-0.21 (- 1.85) 1.01 (3.80)
-0.38 (- 5.45) 0.96 (6.21)
Parameter k VE
no 6EG SE0 6 GO
SER DW Overall measure
Estimate( x W) 0.68 0.62 0.32 -0.19 - 0.03 0.08 Unit energy Electricity cost function cost share 0.01 0.04 0.73 0.53 to fit: R2L = 0.73”
“As defined in Bewley [2]. SER and DW are presented statistics only.
-0.65 (-4.15)
t-statistics 0.48 138.29 45.15 - 10.37 - I .46 1.86 Fuel oil cost share 0.07 0.34
as descriptive
-
0.92 (3.81)
Table 5. Own- and cross-price elasticities (with constant total energy).
PEL
Nore; DW: Durbin-Watson statistic; SER: standard error of regression; both are presented as descriptive statistics only. “f-statistics are in parentheses. bAs defined in McElroy [7].
PC
PO
EL -0.06 (- 2.42) -0.21 (- 5.70) 0.27 (7.80)
G - 0.62 (- 5.70) - 0.20 (-0.61) 0.82 (3.07)
0 0.43 (7.80) 0.43 (3.07) - 0.86 (- 6.39)
ted when consumption is expressed per household while its price elasticity is significantly higher than in previous Canadian studies.
Nofe; Price elasticities are computed at the mean exogeneous variables. r-statistics are in parentheses.
Petrochemicalfeedrtocks Since the systems (9) and (13) of cost shares must sum to unity, an estimation of all share equations would result in singularity of the error covariance matrix. Hence, to overcome this difficulty, we omit one cost share equation in both estimations and employ an estimation method which is invariant with respect to the omitted equation. I3 Afterwards, the omitted coefficients are computed by making use of the appropriate constraints. Finally, since we have a recursive model, consistent parameter estimates at the aggregate level can be obtained by using lnPE as instrument for lnPE; lnPE is obtained from the energy source level.r4
stayed rather constant at less than 8% from 1962 to 1974 and it increased to 34.8% in 1984. Our aim is to test whether the changes of energy source cost shares can be explained in terms of their relative prices through the translog model. Table 4 presents the estimated coefficients for the energy source level. First, one can see that in general the coefficients are statistically significant and that the fit as measured by RzL is rather tight. However the DurbinWatson statistics for each of the three estimated equations are quite low; this is a recurring problem in the application of the translog function. l6 Own-price and cross-price elasticities are shown in Table 5. Own-price elasticities are negative, as expected on theoretical grounds and with the exception of natural gas, they are statistically significant. One can see that electricity/oil and natural gas/oil are significant substitutes while electricity/natural gas are complements. The estimated parameters of the unit energy cost function are used to construct an energy price index which then serves as an instrument for lnPE at the next level.
Energy sources. Over the sample periodI from 1962 to 1984, electricity accounted for the largest cost share among the energy sources of the Quebec chemical industry. The electricity share decreased from 73.7% in 1962 to 47.5% in 1978 and then increased to 55.4% in 1984. The oil cost share increased from 2 1.1% in 1962 to reach a peak of 39.4% in 1974 and afterward declined steadily to 9.8% in 1984. The natural gas cost share iaWe which ‘%ee “The
182
use the Zellner iterated seemingly unrelated equation method has this property. Fuss [6]. sample period is limited to 1984 because of data availability.
value
of
Factors of production. From 1962 to 1983, capital accounted for the largest cost share decreasing from i6This feature may be due to model static formulation.
ENERGY ECONOMICS
July 1990
Demandfor non-energy petroleum products: D. BPIanger et al 58.8% in 1962 to 48.7% in 1983. The labour cost share was stable around 30% up to 1974 and then decreased gradually to 24.4% in 1982. The energy cost share was also stable at less than 9% up to 1976 and then it moved up to 12.1% in 1983. The petrochemical feedstock cost share increased steadily from 3.4% in 1962 to 14.8% in 1983. Over the sample period, the prices of capital and labour increased the least with annual nominal growth rates of 5.1% and 8.3% respectively, while energy and petrochemical feedstock prices went up by 9.7% and 12.1% a year. Production increased at an average annual rate of 6.6% from 1962 to 1973 and 1.3% from 1973 to 1983. This is a summary of the statistical data used to estimate Equations (8) and (9) subject to constraints (lo), and the results appear in Table 6. Most of the estimated coefficients are significantly different from zero and, in particular, the underlying production function is non-homothetic since BpL and fleF are significantly different from zero.” The fit of each equation is rather tight; however, the DurbinWatson statistics are low for the total cost and the petrochemical feedstock cost share equation. Table 7 displays the estimated price elasticities for a constant output level. Own-price elasticities have negative signs as expected theoretically; however, they are not significantly different from zero for labour and energy. Furthermore all own-price and cross-price elasticities are less than one in absolute value; this result indicates limited adjustment to price changes. Crossprice elasticities reveal that substitutability is the rule across factors of production, except for labour and energy which are complements. It is also seen that petrochemical feedstocks cannot be aggregated with energy into a single input since the two inputs have different substitution/complementary relationships with capital and labour. Table 7 also shows in the last row output elasticities which are less than one for capital and labour and greater than one for energy and petrochemical feedstocks.
Conclusion This paper deals with the demand for non-energy petroleum products. Although these products are of some importance, they have received little attention until now due to their heterogeneous nature and data availability. Econometric analysis was applied simultaneously to Qdbec asphalt, petroleum coke, lubes and naphtha specialties as final goods. Petrochemical feed“The multiple comparisons required to test for non-homotheticity are carried through the Bonferonni procedure, see Savin [12]. BQx= /lQr = ~QE= /?QF= 0 implies that the underlying production is homothetic. Furthermore, if jIQQ= 0, then the production function exhibits constant returns to scale and if up = I, it is homogeneous of degree one.
ENERGY ECONOMICS
July 1990
Table 6. Tbe aggregate model parameter estimates or 1962 to 1%3. t-statistics
Estimate
Parameter
12.55 0.54 0.32
BZ
XK aL (IF
1019.13 107.99 54.31
@Q
0.08 0.88
16.04 20.92
1;;
-0.06 -0.03 0.01
- 2.84 I .09 1.71
BLE
-
SLF
-
BFE
BQK BQL
0.08 0.03 0.001
- 0.05 - 0.08
BQF
BQQ Total cost
0.10 0.33 Capital share Labour share
SER 0.05 0.01 0.01 DW 0.82 2.05 2.11 Overall measures of fit: RzL = 0.67a
- 8.48 - 2.61 0.29 - 1.85 - 2.88 6.66 1.38 Feedstocks share
0.01 0.92
“As defined in Bewley (0~ tit Ref 2). Note: SER and DW are presented as descriptive statistics only.
Table 7. Aggregate price and output elasticities (with constant output). Elasticity of
K
PK
-0.33 (- 5.74) 0.15 (2.13) 0.11 (6.51) 0.07 (3.66) 0.89 (13.03)
PL PE
PF
Q
0.28 (2.13) - 0.09 (-0.51) -0.21 (-5.91) 0.01 (0.36) 0.68 (5.91)
0.61 (6.51) - 0.63 (-5.91) -0.12 (- 1.36) 0.14 (2.49) 1.27 15.48)
0.29 (3.66) 0.03 (0.36) 0.10 (2.49) - 0.42 (- 5.98) 1.80 (12.78)
Nore: Elasticities are computed at the mean value of exogeneous variables. t-statistics are in parentheses.
stocks were analysed along with other factors of production of the chemical industry. The analysis intended to determine whether Qdbec demand for these products can be explained in terms of the standard economic variables of prices and income. The econometric results show that long-run ownprice elasticities are less than one for all of the above products. Long-run income elasticities are equal to one for asphalt, and close to but less than one for petroleum coke and lubes and output elasticity is above one for petrochemical feedstocks. The above results are useful in the development of a total petroleum demand model which includes both energy and non-energy components.
References G. J. Anderson and R. W. Blundell, ‘Estimation and hypothesis testing in dynamic singular equations systems’, Econometrica, Vol50, No 6, November 1982, pp 1559-1572.
183
Demandfor
non-energy petroleum products: D. Belanger et al
2 R. A. Bewley, ‘Goodness-of-fit Economics Letters, Vol 17,
3
4 5
6
7
8 9
10
for allocation models’, No3, March 1985,
pp 227-229. D. Bohi, Analysing Demand Behavior: a Study of Demand Elasticities, Johns Hopkins University Press, Baltimore, 1981. A. S. Deaton and J. Muellbauer, Economics and Consumer Behavior, Cambridge University Press, 1980. Energy, Mines and Resources Canada, Market Analysis and Statistics Division, Energy Strategy Branch, IFSD Interfuel Substitution Demand Model, Spring 1985. M. A. Fuss, ‘The demand for energy in Canadian manufacturing: an example of the estimation structures with many imputs’, Journal of Econometrics, Vol5, No 1, January 1977, pp 89-l 16. M. B. McElroy, ‘Goodness of fit for seemingly unrelated regressions: Glahn’s R’y.x and Hooper’s P’, Journal of Econometrics, Vo16, No 3, November 1977, pp 381-387. National Energy Board, Economics Branch, Energy Demand Model, July 1985. A. Plourde and D. Ryan, ‘On the use of double-log form in energy demand analysis,’ The Energy Journal, Vo16, No 4, October 1985, pp 105-l 14. R. A. Preece et al, ‘The energy demand forecasting system
184
of the national energy board’, in W. T. Ziemba et al, eds. Energy Policy Modeling: United States and Canadian Experiences, Vol 1, Martinus Nijhoff, Boston, 1980,
pp 16-33. 11 R. K. Sahi and R. W. Erdmann, ‘A policy model of Canadian interfuel substitution demands’, in W. T. Ziemba et al, eds, Energy Policy Modeling: United States and Canadian Experiences, Vol 1, Martinus Nijhoff. Boston, 1980, pp 34-49. 12 N. E. Savin, ‘The Bonferroni and the Scheffe multiple, comparison procedures’, Review of Economic Studies, Vo147, 1980, pp 255-273. 13 W. T. Ziemba et al, eds, Energy Policy! Modeling: United States and Canadian Experiences, Vol 1, Martinus, Nijhoff, Boston, 1980.
Data sources Statistics Canada, Quarterly Report on Energy Supply Demand in Canada, No 57-003, quarterly. Statistics Canada, Refined Petroleum Products, NO 45-004, monthly.
ENERGY
ECONOMICS
July 1990
Davy B&anger, Jean-Thomas Bernard and RCmyDubois
Non-energy petroleum products (NEPP) refer to petroleum products which, once refined, are used either as final goo& or as intermediate inputs for other non-energy producing processes. They fall into jive categories: petrochemical feedstocks, asphalt, petroleum coke, lubricating oils/greases and naphtha specialties. While being of some sign@ance, they have received little attention inprevious petroleum demandstudies. The heterogeneous nature of the products may be part of the explanation for the lack of interest. The main results of the econometric analysis are:first, all own-price elasticities except for petroleum coke are quite low, that is, less than one in absolute value. Second, asphalt,petroleum coke, and lubes/greases dtiplay income elasticities which are close to one while petrochemical fee&tocks has an output elasticity above one and income appears to play no role in explaining the demand for naphtha specialties. Finally, petrochemical feedrtocks are a statistically significant substitute for capital and energy, but not for labour, in the QuPbec chemical industry. Keywork
Petroleum demand; Non-energy petroleum products; Econometric analysis
Non-energy petroleum products (NEPP) refer to petroleum products which, once refined, are used either as final goods or as intermediate inputs for other nonenergy producing processes. They fall into five categories - petrochemical feedstocks, asphalt, petroleum coke, lubricating oils/greases, and finally, naphtha specialties.’ Together, theymadeup9.0% and 10.6% of all petroleum products consumed in the province of Qukbec and in Canada in1986.2 While being of some significance, they have received little attention in previous petroleum demand studies. Bohi [3] provides a comprehensive survey of energy demand analysis, including petroleum products as of 1980; however, non-energy petroleum products are ignored. The
heterogeneous nature of the products may be part of the explanation for the lack of interest.3 The main purpose of this paper is to show the results of an econometric analysis of NEPP demand in the province of QuCbec. First, there is a description of the evolution of Quebec NEPP consumption from 1962 to 1986. Second, the approaches and the main conclusions of some related works in the Canadian context are summarized. Third, the specification ofthemodels used to estimate Qutbec NEPP demand is described. A discussion of the empirical results follows. The main results of the econometric analysis are: first, all own-price elasticities except for petroleum coke are quite low, ie less than one in absolute value. Second,
The authors are with GREEN, Dtpartement d’ficonomique,
‘There is also a residual category, that can be referred to as ‘other non-energy petroleum products’, which accounted for 1.8% of total Quebec NEPP in 1986. This residual category is not analyzed in this paper. %tatistics Canada, No 57-003, Tables 1D and 7D, 1986-IV. “Some unpublished works on Canadian total energy demand incorporate non-energy petroleum products as separate items and they are discussed further later.
Universitt
Laval, Ste-Foy,
QuCbec, Canada
GlK
7 P4.
We are grateful for financial support from the SSHRC, Ottawa, and from the Fonds FCAR, Minis&e de l’fiducation, Quebec. Thanks are due to J. Roberts for providing research assistance. Final manuscript received 8 February 1990.
0140-9883/90/030177-08 0 1990 Butterworth-Heinemann Ltd
Demandfor non-energy petroleum products: D. BPlanger et a]
asphalt, petroleum coke and lubes/greases display income elasticities which are close to one while petrochemical feedstocks have an output elasticity above one and income appears to play no role in explaining the demand for naphtha specialties. Finally, petrochemical feedstocks are a statistically significant substitute for capital and energy, but not for labour, in the Quebec chemical industry.
Consumption in Quebec non-energy petroleum products 1962436 In order to single out the main features of Quebec NEPPconsumption from 1962 to 1986, the first oilcrisis in 1973 serves as a benchmark to identify two subperiods. As can be seen from Table 1, the average annual growth rate of NEPP consumption was 9.2% over the first subperiod and -4.0% over the second. This growth pattern increased the share of NEPP in total petroleum product consumption from 6.6% in 1962 to 10.0% in 1977. In that year, NEPP consumption reached a peak of 2942000m3. Thereafter the decline has been rather steady matching the reduction of totalpetroleumproductconsumption.Thedeclineisthe result of both higher oil prices and the 1982 world recession. Petrochemical feedstocks and asphalt are the two largest single components of NEPP and together they form more than 50% of the total. Petrochemical feedstock consumption increased rapidly in the first subperiod at an average of 13.9%/year outpacing total petroleum product growth. Peak consumption was reached in 1979 followed by a sharp decline. Accounting for 52.2% of total NEPP consumption in 1978, petrochemical feedstocks fell to 13.2% in 1986. Asphalt consumption displays a steadier pattern of evolution. The rapid average growth rate in the first subperiod (7.5% year) was followed by a slight reductionin the second. In 1986, asphalt accounted for42.0% of NEPP. Naphtha specialties display a pattern similar to petrochemical feedstocks: rapid growth in the first subperiod with a peak in 1973 followed by a fall. The two other products, lubes/greases and petroleum coke present a more stable pattern; the latter product is the only one to show positive growth from 1973 to 1986. Our aim is to estimate econometric models which can be used to determine whether variations in Quebec NEPP consumption, as shown in Table 1, can be explained using standard economic variables such as income and relative prices.
Previous studies Energy, Mines and Resources Canada and the National Energy Board have developed demand models by sector
178
and by province for the Canadian economy. These are called respectively the Interfuel Substitution Demand Model (IFSD) and the Energy Demand Model (EDM) and they include some non-energy petroleum products.4 Petrochemical feedstocks and petroleum coke are excluded. However, asphalt, lubes and naphtha are treated as separate final goods and they are assumed to depend in a log-linear functional form on the following variables: real domestic product, oil price, degree-days,5 and finally, the lagged dependent variable. Table 2 displays a summary of short-run and longrun price and income elasticities for the relevant products. All price elasticities both in the short run and in the long-run are less than one, except for lubes and greases in the long run (EDM). With the exception of asphalt in the long run, all income elasticities are also less than one. The elasticity estimates for both models are somewhat close for asphalt; however, there are significant differences for lubes and greases and naphtha.
Tbe models Two distinct models are adopted to model Quebec NEPP demand. The choice between the two is based on practical grounds and data availability. One approach is adopted for asphalt, petroleum coke, lubes and naphtha, and a different approach is adopted for petrochemical feedstocks. Asphalt, petroleum coke, lubes and naphtha
For each product, a single equation was estimated relating the quantity by a log-linear function to real prices and income. Despite its theoretical shortcomings6 the log-linear model can still be of some usefulness in situations where a model with a better theoretical basis cannot be used, as is the case here.’ Then, following the method of Anderson and Blundell [l], each of the four equations is imbedded into a dynamic structure and they are estimated jointly using Zellner’s seemingly unrelated regression procedure. The main advantage of the Anderson and Blundell specification is that it allows for a fairly flexible dynamic adjustment mechanism while making it easy to retrieve the long-run equilibrium relationships by setting all ‘Energy, Mines and Resources Canada (Spring 1985) and National Energy Board (July 1985). See also Sahi and Erdmann [II] and Preece el al [IO]. ‘Degree-days is introduced as an explanatory variable to capture the effect of weather on the product mix coming out of the refining process. For instance, in colder periods, more heavy fuel oil is produced for heating purposes at the expense of asphalt production. Usually, this phenomenon would be captured by relative price changes between the two products. Unfortunately, data availability precludes such an approach. %ee Plourde and Ryan [9]. ‘See the discussion dealing with the log-linear model presented by Deaton and Muellbauer [4], pp 17-18.
ENERGY ECONOMICS
July 1990
\o
z
g
G
2 q
1032 850 606 453 208
I101
mJx 1W 256 298 510 525 655 740 712 728 896 899 951 1075 975 817 1116 I333 1512 1518 1296
13.9 - 11.9
(%) 25.4 26.5 34.2 35.9 37.6 41.9 39.5 39.0 43.6 43.1 43.3 40.4 38.5 39.7 46.8 45.3 52.2 52.0 47.7 43.9 46.8 40.2 31.0 26.2 13.2
7.5 -1.5
m’x 1W 365 397 517 504 560 505 513 525 553 586 672 809 743 641 709 782 736 777 698 619 544 567 586 651 661
Aspbalt
(%) 36.3 35.2 34.7 34.5 32.1 28.6 28.5 28. I 26.9 28. I 30.6 30.4 29.3 31.1 29.8 26.6 25.4 26.7 25.7 24.7 24.7 26.8 30.0 37.7 42.0
4.6 2.7
m’x 1Y 216 254 259 199 275 271 328 355 360 271 215 354 425 315 245 441 314 281 430 458 367 417 530 392 503
Petroleum coke
(%) 21.5 22.6 17.4 13.6 15.8 15.3 18.2 19.0 17.5 13.0 9.8 13.3 16.8 15.3 10.3 15.0 10.8 9.6 15.8 18.3 16.6 19.7 27.1 22.7 32.0
Lubesand
4.5 - 2.4
m3x 1W 117 122 130 I41 147 158 156 166 I53 164 173 191 190 191 195 184 208 199 170 180 147 I45 158 I52 138
gre(%) 11.6 10.8 8.7 9.6 8.4 9.0 8.7 8.9 7.4 7.9 7.9 7.2 7.5 9.3 8.2 6.3 7.2 6.8 6.3 7.2 6.7 6.9 8.1 8.8 8.8
13.8 - 13.0
m3x 1Y 52 55 63 83 89 84 85 89 87 155 155 213 103 75 80 71 79 87 78 84 68 82 54 43 35
Naphtha specialties
(%) 5.1 4.9 4.2 5.7 5.1 4.7 4.7 4.7 4.2 7.4 7.1 8.0 4. I 3.6 3.4 2.4 2.7 3.0 2.9 3.3 3.1 3.9 2.7 2.5 2.2
Sources: 1962 to 1975, Srafisfics Cumzdu, No45-004; 1976 to 1986, Smisrics Canada, No 57-003. From 1962 to 1976, data on petroleumcokeconsumption bank. Since non-energy petroleum products include the miscellaneous residual category (see footnote 1). percentages (%) do not sum to 100%.
1962-73 1973-86
AMII~ rate of growth
I%2 1963 1964 1965 1966 1967 1968 1969 I970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
Petrochemical feed&&s
Table I. Breakdown of Qu&ec non-energy petroleum products consumption from 1962 to 1986 (quantity and percentage of total).
9.2 -4.0
6.4 -4.1
‘u
5Y In
& a. ij
G
2
S3
3 2 P b 2 2
:
$
9.9 9.8 9.6 9.8 9.8 10.5 10.2 9.7 9.0
2
3
B
7.1 7.8
IO.0
6.6 6.9 8.3 7.4 8.3 7.8 7.3 7.1 7.5 7.8 7.7 8.8 8.5
NEPP as % of total petroleum ,products
from the EDM data
m’x 1W 15307 16231 18052 19656 21069 22769 24657 26411 27561 26728 28352 30278 29912 29164 30441 29499 29132 29678 28167 25515 22423 20089 19275 17863 17510
Total petroleum products
have been borrowed
m3x 1W 1007 1127 1492 1464 1744 1767 1800 1870 2054 2085 2196 2662 2534 2059 2381 2942 2898 2916 2718 2506 2206 2112 1958 1727 1573
Non-energy petroleum products
DemandJor uon-etlergy petroleum products: D. BClanger et al / I Table 2. Previous studies: NEPP price and
income elasticities (Quibec).
Price elasticity Short run
Long run
Income elasticity Short run
Long run
- 0.28 - 0.25
-0.51 - 0.63
0.95 0.53
1.73 1.33
-0.13 -0.41
- 0.30 -1.17
0.36 0.23
0.82
-
0.67
-
- 0.27
0.28
0.70
Asphalt JFSD EDM
Lubes and greases IFSD EDM
0.66
Naphtha specialties IFSD
-0.10
EDM
-0.1
S~x~ccs: IFSD,
I
Energy, Mines and Resources Canada,
Spring 1985; and EDM,
variable changes to ze~o.~ Unfortunately there is no direct price information on the above products. To get around this difficulty, use is made of available price data on other products which are closely related to those under study in the refining process and which are substitutes to them at the production stage.’ The four equations are the following: rlnASP=a,,
+a,Ja,.,lnRHFP(u13”16+
- 1) l)+ai3u,slnQRDP(-
(1)
rlnPC=uzlrlnRHFP+
u&nPC( - 1)
+ u2,u,,ln RHFP( - 1) + a,,uz51nQlRDP( - 1) + u23”26 + (I2 (2) rlnLUBE=u3,rlnRLFP+ u32rhQiRDP-u331nLUBE(
- 1)
+ u33u341nRLFP( - 1) + u,,u,,lnQlRDP(
- 1) +
(3)
u3
rlnNAPH=u,,rlnRCOP+ ub2AlnRPDIH - a,,lnNAPH( + u43u,SlnRCOP( u43”46
+
u4
- 1)
- 1) + a43u451nRPDfH(
- 1) +
(4)
where A
&j
ASP LUBE NAPH
frst difference operator coelhcient of explanatory variable j for products = asphalt (m3) = lubes and greases (m3) = naphtha specialties per household (m’) =
=
‘The major difference between the approach taken here and the more encompassing one sugges:ed by Anderson and Blundcll [I]. is tha[ no interaction occurs across equations besides the error terms. 9No close substitute with price information is available for naphtha specialties and the crude oil price at refinery gate in Montreal is used.
180
PC QIRDP
= petroleum coke (m3) = QuCbec industrial real domestic product
QRDP
= Quebec real domestic product
RCOP
= crude oil price at Montreal refinery gate
(billion $ 197 1) (billion $ 1971)
RHFP
=
RLFP
=
RPDIH
=
U,
=
1)+
uI
u2,rlnQIRDP-
+
Energy Board, July 1985.
rlnRHFP+
a,2rlnQRDP-a,JlnASP(
a33036
National
deflated by the implicit price deflator of consumer expenditure excluding direct energy (1971= 1) heavy fuel price deflated by the GDP price deflator (1971= 1) light fuel price deflated by the GDP price deflator (1971= 1) personal disposable income per household deflated by the CPI (1971= 1) error term of equation s
Petrochemical feedstock demand is treated as a derived demand and is considered as one of the inputs in the production process of the chemical industry along with capital, labour and energy. Due to the large number of parameters to be estimated when several inputs are considered simultaneously in unrestricted form, we adopt the nested twolevel model along lines originally suggested by Fuss [6]. At the first or aggregated level, the producer is assumed to choose the mix of capital (K), labour (L), energy (E) and petrochemical feedstocks (fl which minimizes production cost for a given output level (Q), while taking into account the relative input prices. At the second level, the price of energy (PE) is obtained from a unit cost function which also represents the cost minimizing behaviour of the producer which seeks the optimal mix of electricity (EL), natural gas (G+)and oil (0) for a given energy level. The price of energy (PE) bridges the link between the first and the second level. Finally, at both levels, production factor demand functions can be derived by applying Shephard’s lemma.
ENERGY ECONOMICS
July 1990
Demandfor non-energy petroleum products: D. BP/anger
The aggregate level: capital (K), labour (L), energy (E) and petrochemical feeristocks (F). Materials (IV) are assumed to enter the production process in a fixed proportion o!to output and no-substitution is allowed to occur between materials and other inputs. The restrictive assumption is made because of data limitations: Q = min{f(K, L, E, F), aM)
(5)
Cost minimization implies that:
Price elasticities associated with the translog cost function are:’ ’ Eii= @ii+ Siz - Si)/Si for i= K, L, E, F Eu=(/?v+S;Si)/Si for i,j=K, L. E. Fand i #j (11) The energy level: electricity (EL), naturalgas (G) andfuel oil (0). Finally, the price of aggregate energy (PE) is obtained from a unit cost function which is again approximated by a second-order translog function: lnPE=r],+C,ql
Q = f(K, L, E, F)
(6)
We suppose that the function f(K, L, E, F) is quasiconcave and increasing in terms of K, L, E and F. Then, from duality theory, there exists a unique cost function which is homogeneous of degree one, concave with respect to factor prices and increasing in output: CQ = cQ(pK,
PL. pE> pF>
Q>
(7)
where C, = total cost Pi= the price of factor i= K, L, E, F
lnCQ=a,+ xi ailnPi+ a&Q+
1/2C,~,@$nPilnPj
+ C,PiQlnPilnQ + 1/2&$lnQ)’
lnP,+ 1/2C,Cs & lnP, lnP,
Again, applying Shephard’s lemma gives each energy input share in total energy cost: S, = q1+ 1, UnP,
(13)
where t,s= EL, G, 0. Finally, we impose the following restrictions: t;
s ‘S &, = 65,
1, & = 0 (adding-up) (homogeneity) (symmetry)
Price elasticities, for a given total energy level, can be computed from functions (11) when they are expressed in terms of energy. ’ *
(8)
Empirical results
The application of Shephard’s lemma to the translog cost function yields the cost share (Si) associated with each production factor:
Asphalt, petroleum coke, lubes and naphtha
(9)
where i, j= K, L, E. F. In order for the system of demand equations to satisfy the adding-up criterion (c,Si= 1) and the properties of neoclassical production theory, the following parameter restrictions are required and they are imposed at the estimation stage.” C,ai= 1, C#~=C,@i~=O
(adding-up)
C,&=O
(homogeneity)
Pp=
(symmetry)
Pji
(10)
where i, j= K, L, E, F. ‘“Neoclassical production theory requires that the cost function be concave with respect to factor prices. The restriction cannot be expressed as simple linear relationships involving parameters only and it has not been imposed at the estimation stage. A necessary condition is that price elasticities be negative and this is verified below.
ENERGY ECONOMICS
July 1990
(14)
where t, s= EL, G, 0.
where i, j= K, L, E, F.
Si= tli + x,@&Pj + /?iplnQ
(12)
where t, s = EL, G, 0.
g,;
To represent empirically this cost function, we have arbitrarily chosen the translog function, which provides a second-order approximation of any function:
et al
Table 3 shows price and income elasticities computed from the estimation results for the model described earlier. The statistical fit of the sytem as measured by R2, is acceptable and most of the variables related to the dynamic specification are statistically different from zero. It should be noted that two variables are deleted because of non-significant statistical results in light of theoretical expectations: income per household in the naphtha specialties equation and price in the petroleum coke equation. It is seen that all long-run own-price elasticities are quite low and that long-run income elasticities are close to one. If we compare the results in Table 3 with those of previous studies as shown in Table 2, it can be seen that our estimates of long-run price and income elasticities for asphalt are lower than those of both the IFSD and EDM. The results for lubes are closer to those appearing in IFSD than in EDM. As for naphtha specialties, no statistically significant relation with income is indica“See Fuss [6]. ‘%ee Fuss [6].
181
Demandfor non-energy petroleum products: D. BP/anger et
al Table 4. Energy sources: empirical results for 1962 to 1984.
Table 3. Final goods demand models: price and income elasticities. Long runn Asphalt Price elasticity Income elasticity DW=1.90SER=0.07 Lubes Price elasticity Income elasticity DW = 1.76SER = 0.05 Naphtha Price elasticity Income elasticity DW=2.15 SER=0.19 Coke Price elasticity Income elasticity DW= 1.53 SER=0.21 Overall measure to fit R2: = 0.6 1b
-0.21 (- 1.85) 1.01 (3.80)
-0.38 (- 5.45) 0.96 (6.21)
Parameter k VE
no 6EG SE0 6 GO
SER DW Overall measure
Estimate( x W) 0.68 0.62 0.32 -0.19 - 0.03 0.08 Unit energy Electricity cost function cost share 0.01 0.04 0.73 0.53 to fit: R2L = 0.73”
“As defined in Bewley [2]. SER and DW are presented statistics only.
-0.65 (-4.15)
t-statistics 0.48 138.29 45.15 - 10.37 - I .46 1.86 Fuel oil cost share 0.07 0.34
as descriptive
-
0.92 (3.81)
Table 5. Own- and cross-price elasticities (with constant total energy).
PEL
Nore; DW: Durbin-Watson statistic; SER: standard error of regression; both are presented as descriptive statistics only. “f-statistics are in parentheses. bAs defined in McElroy [7].
PC
PO
EL -0.06 (- 2.42) -0.21 (- 5.70) 0.27 (7.80)
G - 0.62 (- 5.70) - 0.20 (-0.61) 0.82 (3.07)
0 0.43 (7.80) 0.43 (3.07) - 0.86 (- 6.39)
ted when consumption is expressed per household while its price elasticity is significantly higher than in previous Canadian studies.
Nofe; Price elasticities are computed at the mean exogeneous variables. r-statistics are in parentheses.
Petrochemicalfeedrtocks Since the systems (9) and (13) of cost shares must sum to unity, an estimation of all share equations would result in singularity of the error covariance matrix. Hence, to overcome this difficulty, we omit one cost share equation in both estimations and employ an estimation method which is invariant with respect to the omitted equation. I3 Afterwards, the omitted coefficients are computed by making use of the appropriate constraints. Finally, since we have a recursive model, consistent parameter estimates at the aggregate level can be obtained by using lnPE as instrument for lnPE; lnPE is obtained from the energy source level.r4
stayed rather constant at less than 8% from 1962 to 1974 and it increased to 34.8% in 1984. Our aim is to test whether the changes of energy source cost shares can be explained in terms of their relative prices through the translog model. Table 4 presents the estimated coefficients for the energy source level. First, one can see that in general the coefficients are statistically significant and that the fit as measured by RzL is rather tight. However the DurbinWatson statistics for each of the three estimated equations are quite low; this is a recurring problem in the application of the translog function. l6 Own-price and cross-price elasticities are shown in Table 5. Own-price elasticities are negative, as expected on theoretical grounds and with the exception of natural gas, they are statistically significant. One can see that electricity/oil and natural gas/oil are significant substitutes while electricity/natural gas are complements. The estimated parameters of the unit energy cost function are used to construct an energy price index which then serves as an instrument for lnPE at the next level.
Energy sources. Over the sample periodI from 1962 to 1984, electricity accounted for the largest cost share among the energy sources of the Quebec chemical industry. The electricity share decreased from 73.7% in 1962 to 47.5% in 1978 and then increased to 55.4% in 1984. The oil cost share increased from 2 1.1% in 1962 to reach a peak of 39.4% in 1974 and afterward declined steadily to 9.8% in 1984. The natural gas cost share iaWe which ‘%ee “The
182
use the Zellner iterated seemingly unrelated equation method has this property. Fuss [6]. sample period is limited to 1984 because of data availability.
value
of
Factors of production. From 1962 to 1983, capital accounted for the largest cost share decreasing from i6This feature may be due to model static formulation.
ENERGY ECONOMICS
July 1990
Demandfor non-energy petroleum products: D. BPIanger et al 58.8% in 1962 to 48.7% in 1983. The labour cost share was stable around 30% up to 1974 and then decreased gradually to 24.4% in 1982. The energy cost share was also stable at less than 9% up to 1976 and then it moved up to 12.1% in 1983. The petrochemical feedstock cost share increased steadily from 3.4% in 1962 to 14.8% in 1983. Over the sample period, the prices of capital and labour increased the least with annual nominal growth rates of 5.1% and 8.3% respectively, while energy and petrochemical feedstock prices went up by 9.7% and 12.1% a year. Production increased at an average annual rate of 6.6% from 1962 to 1973 and 1.3% from 1973 to 1983. This is a summary of the statistical data used to estimate Equations (8) and (9) subject to constraints (lo), and the results appear in Table 6. Most of the estimated coefficients are significantly different from zero and, in particular, the underlying production function is non-homothetic since BpL and fleF are significantly different from zero.” The fit of each equation is rather tight; however, the DurbinWatson statistics are low for the total cost and the petrochemical feedstock cost share equation. Table 7 displays the estimated price elasticities for a constant output level. Own-price elasticities have negative signs as expected theoretically; however, they are not significantly different from zero for labour and energy. Furthermore all own-price and cross-price elasticities are less than one in absolute value; this result indicates limited adjustment to price changes. Crossprice elasticities reveal that substitutability is the rule across factors of production, except for labour and energy which are complements. It is also seen that petrochemical feedstocks cannot be aggregated with energy into a single input since the two inputs have different substitution/complementary relationships with capital and labour. Table 7 also shows in the last row output elasticities which are less than one for capital and labour and greater than one for energy and petrochemical feedstocks.
Conclusion This paper deals with the demand for non-energy petroleum products. Although these products are of some importance, they have received little attention until now due to their heterogeneous nature and data availability. Econometric analysis was applied simultaneously to Qdbec asphalt, petroleum coke, lubes and naphtha specialties as final goods. Petrochemical feed“The multiple comparisons required to test for non-homotheticity are carried through the Bonferonni procedure, see Savin [12]. BQx= /lQr = ~QE= /?QF= 0 implies that the underlying production is homothetic. Furthermore, if jIQQ= 0, then the production function exhibits constant returns to scale and if up = I, it is homogeneous of degree one.
ENERGY ECONOMICS
July 1990
Table 6. Tbe aggregate model parameter estimates or 1962 to 1%3. t-statistics
Estimate
Parameter
12.55 0.54 0.32
BZ
XK aL (IF
1019.13 107.99 54.31
@Q
0.08 0.88
16.04 20.92
1;;
-0.06 -0.03 0.01
- 2.84 I .09 1.71
BLE
-
SLF
-
BFE
BQK BQL
0.08 0.03 0.001
- 0.05 - 0.08
BQF
BQQ Total cost
0.10 0.33 Capital share Labour share
SER 0.05 0.01 0.01 DW 0.82 2.05 2.11 Overall measures of fit: RzL = 0.67a
- 8.48 - 2.61 0.29 - 1.85 - 2.88 6.66 1.38 Feedstocks share
0.01 0.92
“As defined in Bewley (0~ tit Ref 2). Note: SER and DW are presented as descriptive statistics only.
Table 7. Aggregate price and output elasticities (with constant output). Elasticity of
K
PK
-0.33 (- 5.74) 0.15 (2.13) 0.11 (6.51) 0.07 (3.66) 0.89 (13.03)
PL PE
PF
Q
0.28 (2.13) - 0.09 (-0.51) -0.21 (-5.91) 0.01 (0.36) 0.68 (5.91)
0.61 (6.51) - 0.63 (-5.91) -0.12 (- 1.36) 0.14 (2.49) 1.27 15.48)
0.29 (3.66) 0.03 (0.36) 0.10 (2.49) - 0.42 (- 5.98) 1.80 (12.78)
Nore: Elasticities are computed at the mean value of exogeneous variables. t-statistics are in parentheses.
stocks were analysed along with other factors of production of the chemical industry. The analysis intended to determine whether Qdbec demand for these products can be explained in terms of the standard economic variables of prices and income. The econometric results show that long-run ownprice elasticities are less than one for all of the above products. Long-run income elasticities are equal to one for asphalt, and close to but less than one for petroleum coke and lubes and output elasticity is above one for petrochemical feedstocks. The above results are useful in the development of a total petroleum demand model which includes both energy and non-energy components.
References G. J. Anderson and R. W. Blundell, ‘Estimation and hypothesis testing in dynamic singular equations systems’, Econometrica, Vol50, No 6, November 1982, pp 1559-1572.
183
Demandfor
non-energy petroleum products: D. Belanger et al
2 R. A. Bewley, ‘Goodness-of-fit Economics Letters, Vol 17,
3
4 5
6
7
8 9
10
for allocation models’, No3, March 1985,
pp 227-229. D. Bohi, Analysing Demand Behavior: a Study of Demand Elasticities, Johns Hopkins University Press, Baltimore, 1981. A. S. Deaton and J. Muellbauer, Economics and Consumer Behavior, Cambridge University Press, 1980. Energy, Mines and Resources Canada, Market Analysis and Statistics Division, Energy Strategy Branch, IFSD Interfuel Substitution Demand Model, Spring 1985. M. A. Fuss, ‘The demand for energy in Canadian manufacturing: an example of the estimation structures with many imputs’, Journal of Econometrics, Vol5, No 1, January 1977, pp 89-l 16. M. B. McElroy, ‘Goodness of fit for seemingly unrelated regressions: Glahn’s R’y.x and Hooper’s P’, Journal of Econometrics, Vo16, No 3, November 1977, pp 381-387. National Energy Board, Economics Branch, Energy Demand Model, July 1985. A. Plourde and D. Ryan, ‘On the use of double-log form in energy demand analysis,’ The Energy Journal, Vo16, No 4, October 1985, pp 105-l 14. R. A. Preece et al, ‘The energy demand forecasting system
184
of the national energy board’, in W. T. Ziemba et al, eds. Energy Policy Modeling: United States and Canadian Experiences, Vol 1, Martinus Nijhoff, Boston, 1980,
pp 16-33. 11 R. K. Sahi and R. W. Erdmann, ‘A policy model of Canadian interfuel substitution demands’, in W. T. Ziemba et al, eds, Energy Policy Modeling: United States and Canadian Experiences, Vol 1, Martinus Nijhoff. Boston, 1980, pp 34-49. 12 N. E. Savin, ‘The Bonferroni and the Scheffe multiple, comparison procedures’, Review of Economic Studies, Vo147, 1980, pp 255-273. 13 W. T. Ziemba et al, eds, Energy Policy! Modeling: United States and Canadian Experiences, Vol 1, Martinus, Nijhoff, Boston, 1980.
Data sources Statistics Canada, Quarterly Report on Energy Supply Demand in Canada, No 57-003, quarterly. Statistics Canada, Refined Petroleum Products, NO 45-004, monthly.
ENERGY
ECONOMICS
July 1990