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Tests for structural change in US oil consumption, 1967–1982
Tests for structural change in US oil consumption, 1967-1982 Anthony E. Bopp
The purpose of this paper is to test US oil consumption for structural change over the period 1967-I 982. A frequently used functional form is posited for total petroleum consumption as well as for gasoline, distillate, and residual fuel. Tests for abrupt change (Chow) and gradual or conservation-like change (Durbin, Brown, Evans and Farley, Hinnich, McGuire) are employed at special break points (1973 embargo, I979 Iranian crisis, 1980 recession) to check for abrupt changes and across years in general to detect gradual shifts. Both abrupt and gradual changes are found, although the last five years may be the beginning of a new non-changing period. Keywords:
This paper presents a number of tests for structural change in US oil consumption from 1967 to 1982. Figure 1 shows the steady growth in oil consumption from 1967 to 1973, the dramatic effect of the Arab embargo in early 1974, the renewed growth in 1976, and the again dramatic effect of the Iranian crisis in 1979. The 1980-1982 consumption levels reflect the prolonged US recession. However, some of these changes in consumption levels can be explained by changes in macroeconomic activity, prices or weather (1978 was a particularly cold year). That is, structurally 1981 may be similar to 1972. Consumption in 1981 was down because GNP was down, prices were up, and the weather was warm. In 1972 consumption was up for precisely opposite reasons. This paper posits a relationship between oil consumption and important factors such as macroeconomic activity, oil prices and weather, and tests the various periods for structural change of two types: dramatic and subtle. Dramatic shifts such as the Arab embargo or Iranian crisis are almost obvious. However, ever since 1974 the USA may have been gradually reducing its oil consumption past the level explained by higher The author is with the Department of Information and Decision Sciences, James Madison University, Harrisonburg, VA 22807, USA. The author acknowledges the assistance of Or George in making clear what is meant by ‘structural change’. Final manuscript
M. Lady
received 27 March 1984.
0140-9883/84/040223-08
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0 1984 Butterworth
Oil consumption;
Structural
1976
1976
change; USA
1980
1982
Figure 1. Historical US oil consumption.
prices, reduced GNP, and warmer weather because of a gradual, less dramatic, but nevertheless significant shift favouring conservation. As a consequence, a variety of tests will be employed to attempt to detect both dramatic and subtle shifts in the relationship between US oil consumption and its explanatory factors. It is important to specify what is meant by the term ‘structural change’, because there are a variety of meanings. The idea developed in this work is that in the early 1960s there was a predictable and stable relationship between oil consumption and macroeconomic activity, oil prices, and weather. What is tested here is the stability of that posited relationship. Thus, if
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Tests for struchual change in US oil consumption, 196 7-l 982: A. E. Bopp macroeconomic activity, prices, or weather changes in the 1974-1982 period account for the changes in oil consumption, then no structural change can be assumed even though the pattern of consumption obviously has changed (see Figure 1). For other purposes some would label any change in the pattern of consumption as one of ‘structural change’. Here, only those instances of changing patterns that are not explained by corresponding changes in the listed explanatory factors are labelled ‘structurally changed’. Also, a period such as 1978 where the pattern is not changed (growth in 1978 followed closely that of 1976-1977 and seems to validate a return to pre-embargo growth rates) but where weather is colder than normal might also be labelled one of ‘structural change’. There is an advantage and a disadvantage to this approach. The advantage is that more factors than simply consumption can be examined. Economic theory can be used along with statistical tests to examine the stability of a relationship - not just a single series. 1980-1982 is an interesting period of declining consumption. However, the USA was in a severe recession in those years. If there has been no structural change then when the US economy recovers, so should oil consumption. If the historical relationship between oil consumption and macroeconomic activity has been changed, then as the USA recovers, its oil usage may not. Thus the importance of an enlarged notion of structural change. The disadvantage is that the enlarged notion is vitally dependent upon the notion of a ‘posited’ relationship between oil consumption and the explanatory factors. Always at issue will be the question ‘is the posited the true relation?‘. Furthermore, any empirical single equation relationship may not conform to all of the theoretical restrictions that economic theory has to offer, and any empirical relationship may have statistical shortcomings of a minor-to-serious nature. By adopting the device of a ‘posited’ relationship, a period can be identified only as experiencing or not experiencing a change in the pattern. When a period of structural change is so identified, the cause of the change is not also identified with the tests employed here. There are at least four different circumstances that could cause a period to be so identified. If an omitted variable (interest rates, for example) began to behave differently in relation to included variables, such a change would be identified. If a simple functional form that well approximated over a base period the correct but more complicated true functional form became a worse approximation with different values for the exogenous variables, then the same result would be obtained. Also, if the true relationship simply changed (because of a basic change in preferences) or if it were only temporarily disrupted (by an embargo), then the tests would still only reveal structural change. All of these cases are possible with energy consumption functions and any of these cases is described here as one of ‘structural change’ in the posited relationship. The following sections will examine the relationship actually posited here and will then explain the design of the experiments performed. The method for choosing
224
periods to be tested and the types ‘of tests employed are discussed. Test results are then presented and the modifications in the original design, precipitated by those test results. are presented. The sensitivity tests are presented and a comparison of 1960 and 1980 estimations is made to illustrate the meaning of some of the test results.
Functional form There are a number of considerations to be taken into account in choosing a functional form so that stability tests between oil consumption and explanatory factors can be performed. First, the functional form should be representative of forms used in energy and petroleum studies. This criterion makes the tests useful immediately, because even if other functional forms reveal different answers, relative to the studies or models that use this particular form, these results are pertinent. Second, the functional form should be amenable to performing structural change tests. Some attractive forms such as polynomial distributed lags, dynamic demand models, and Hannon estimators are not well suited for these tests because their advantage-specificity in modelling the lag structure - coupled with the number of new terms introduced by the structural change tests - so reduces the degrees of freedom as to greatly weaken the tests. Often three periods (and sometimes four periods) are needed to test for stability - thus the parameter requirements are three (or four) times those of the original case. Any form that uses a large number of parameters in the fust case is too severely taxed in the structural change cases. It ‘is beyond the scope of this study to employ a simultaneous equation system to completely model a system of interdependencies between oil prices, oil consumption, macroeconomic activity and other prices. Some of the simultaneity problem is addressed by using crude oil prices as an identifying variable for explaining refined oil prices or for explaining disposable income, but in the single equation context using the instrumental variable approach. The approach used here is to specify a partial adjustment demand equation It is well suited to energy demand studies in that it allows for instantaneous and non-instantaneous consumption adjustments to price, income, and weather changes. This specification has appeared in a variety of studies in the energy and consumer durable literature (see for example Kennedy,’ Bopp,2 US Department of Energy3) and is referenced by Phlips4 as one ad hoc specification frequently used because of goodness-of-fit considerations. It is used ln energy studies for that reason and for the reason that once the following equation is estimated: lnQ,=a+blnP’+cln
Y,tdlnW,
+elnQ,-rs+U, where Q, = monthly petroleum in million bbl
consumption
in the USA
ENERGY ECONOMICS October 1984
Tests for structural change in US oil consumption, 196 7- I982. A. E. Bopp Pt = wholesale price index for petroleum products deflated by the wholesale price index Y, = disposable national income in 1972 dollars IV,= heating degree days Qt_rz = petroleum consumption lagged one year (this lag better reflects seasonal decisions for heating or driving rather than monthly ones) U, = assumed white noise error term the coefficients b, c, d are short-term (instantaneous) elasticity estimates and these estimates multiplied by l/( 1 - e) are long-term estimates of the same elasticities - some of the most critical elements in energy studies. The main statistical problem with this specification is the complicating error structure resulting from the presence of a lagged endogenous variable. If autocorrelated disturbances are also present, quasi-first differences using maximum-likelihood methods or two-step procedures discussed in Hatanaka’ must be estimated. Fortunately, here almost all of the reported DW statistics are very close to 2.0 so that computed h-statistics did not indicate the presence of autocorrelated disturbances. Also, only the periods that show structural change are the ones with DW statistics not close to 2.0, suggesting that an important variable might be omitted during these special periods. Some view DW statistics as a structural change test itself. Most of the tests employed over 60 (some over 180) monthly observations so that, hopefully, the small sample bias of the specification is diluted in the large sample tests.
Test statistics employed Perhaps the most widely used test for structural change is the Chow or F-test.6 When the point of change is known, this test is most powerful. It is employed two ways here. In some cases the break point is suggested by other events: the 1973/74 embargo, the 1979 Iranian crisis. In these cases, the classic Chow test is performed; that is, the sum of squared residuals from the linear model YT = XTB + UT is compared with the sum from
point is to be specified. However, if a change has occurred, this test will not reveal its date. Next, again for the case of unknown break point, Durbin and Brown’ have proposed a series of graphical tests that test the actual cumulative sum of squared residuals against an ideal sum. If there is no structural change, then with n observations, each residual should make a proportionate contribution to the sum of squared residuals. A serious departure from this rule suggests change in a graphical way (see Appendix 2). Their test may be the weakest, but is also the most suggestive in indicating when a change has occurred. Finally, there is the question: why not test for change in a subset of coefficients? The problem is the number of tests this demands. Not only should single coefficients be tests but also pairs and combinations. The number of tests becomes immense. Furthermore, a change in preferences could very well affect all of the coefficients - at least enough evidence of such change is found here that searching for further evidence of change seems unwarranted.
Test results: total petroleum products The previous sections detailed which variables are used to construct the X matrix in estimating the linear model of US oil consumption: Y,=XTB+U, Now consider possible time divisions for i? If the preand post-embargo periods are the same (and, of course, assuming that there is something special about the embargo period) then only 2 Bs are to be estimated since, in that case, XT, = pre-embargo values prior to 1973: 12 0 for 1973:12 to 1974:4 post-embargo values after 1974:4, and XT, = embargo values for 1973: 12 to 1974:4 and 0 elsewhere, inthemodelYT=[xi’
x:1::
tUT
However, there may be numerous post-embargo periods (as well as pre-embargo ones). Consider some of the following possible divisions for the X matrix: where T, + Tz = T and Tz corresponds to the period of interest. When the point for breaking the data into TI and Tz subsets is not known, then Tl and Tz are constructed to divide T evenly. However, in that case, other statistics may be more powerful and are also used. The Farley-Hinich-McCuire (FHM) test’ allows for an unknown break point and also allows for a gradual rather than a dramatic shift. Here the model is Y, = WTB •tXTTT-y = U,, where T, is a simple time trend variable (it takes values from l/n, 2/n , . . ., l), and the test is obtained by testing for the significance of 7 with an F-test in the multivariate case. If the break is not in the middle of T, then this test is more powerful than the Chow test. The advantage here is that no break
ENERGY ECONOMICS October 1954
XT, = pre-embargo period XT2 = embargo period XT, = post-embargo and pre-Iranian crisis XT, = Iranian crisis XT, = post-lranian crisis and pre-prolonged XT, = prolonged recession XT, = post-prolonged recession.
recession
Such a scheme would then involve the estimation of several sets of Bs. The procedure used here is first to determine if the period 1966-1973 was homogeneous - that is, without structural change. These test statistics suggest that the 1966-1973 period was one when a stable
225
Tests for structural change in US oil consumption, 1967-I 982: A. E. Bopp relationship between oil consumption and macroeconomic activity, prices, and weather existed. First, a Chow test was performed that divided 1966-1973: 11 into two even parts. This test revealed no structural change. Appendix 1 contains all of the information used to generate these statistics and all of the test results. Table 1 summarizes the results. A FHM test for gradual change was also performed over the period and revealed no change. In the fall of 1973, OPEC met and in response to actions of its Arab members became an effective cartel by raising crude oil prices from $5.25/bbl to over $12/bbl. At that time an embargo on direct sales to the USA was also imposed. The embargo ended in April 1974. Thus the period December 1973 to April 1974 represents a potential structural change period. The second Chow test tested 1966-1974:5 versus 1966-1973: 11 and 1973: 12-1974:5, and found significant structural change. (A regression was also attempted for 1966 to the end of 1974. Large errors occurred only in these months. By May 1974 things appeared to return to their previous pattern.) From 1974 to 1979 there were no dramatic events to disrupt the oil market, but oil prices were higher than in the earlier period. Figure 1 suggests that oil consumption levels may have returned to their preembargo patterns. To test this, the sum of squared residuals from a regression that employed the following time division: XT, = pre-embargo period XT, = embargo period XT, = post-embargo period to 1979:7 was compared to a sum from a regression employed two divisions: XT, = pre- and post-embargo XT, = embargo period
that
only
period
This Chow test revealed no structural change and suggested that consumption levels had, in fact, returned to pre-embargo patterns. Bopp and Lady9 have reported similar results only for 1974-1976. However, for
T&k
1. A summary of patrolaum consumption
atructuml
change teat maults. Test no la lb 2 3 4 5 6a 6b 7 ae 8b
226
Type of test
Result
Chow test over 19&6-1973:ll FHM test over 1966-1973:ll Embargo period 1973: 12-l 974:4 Pre- V. post-embargo 1966-1979:7 Iranian crisis period 1979:81979:12 1980 y. earlier periods 1980 v. 1966-1979 Chow test over 1975-l 979 FHM test over 1975-1979 Chow test ovar 1978-l 991 Chow test over 1978-l 992 FHM test over 1978-1982
No structural change No structural change Structural change No structural change No structural
change
Structural change Structural change Structural change No structural change No structural change No structural change
reasons discussed later, this test failed to detect actual change. When product specific tests are performed over the same period, significant change is found. The next section reports on these tests. However, when all fuels are aggregated, those changes are not detected. The next step was to check the Iranian crisis period. In 1979, especially from August to December, events in Iran pushed world oil prices from $18 to $36/bbl. Another Chow test that allowed for pre-embargo values in one regression (with post values ending December 1979) and that allowed for a separate period over 1979:8 to 1979: 12 was performed. It showed no change, again at the aggregate level, suggesting that consumption levels were responding in a predictable way to the higher prices. (In the fuel specific section, gasoline consumption will show change over this period while other fuels will not.) 1980 was then tested against previous periods. This test was originally performed allowing for only one special period (the embargo period) but was repeated (after the fuel specific tests showed change over the Iranian period) using two special periods. These tests revealed structural change. The test was repeated using just post-embargo data and change was still revealed. Here the importance of establishing the ‘sameness’ of the 1967-1973 period should be emphasized. The data, function, and tests that indicated so much change in 1980 are the same as those that revealed no change in 1966-1973. 1980 could have been the beginning of a new period, 1980 could have been uniquely different, or 1974- 1979 perhaps was not structurally the same. Two tests were first performed on the 1975- 1979:7 period (1975 was chosen over 1974 to be sure all traces of the direct impact of the embargo were removed.) A Chow test and a FHM test were performed and each revealed change over 1975-1979. Next, the periods 1978-1981 and 1978-1982 were tested for sameness. A Chow test was used in each case, and a FHM and a Durbin-Brown test over 1978-l 982. (Again each test was performed twice, once allowing for a special period for the Iranian crisis and once without it.) None of the tests revealed change. The DurbinBrown test was also performed over 1980- 1982, because this period constitutes the ‘most recent’ past and it is important to be sure that the last years are a period without change. The 1980- 1982 Durbin-Brown graph is in Appendix 2. Table 1 presents a summary of these test results. This section has presented tests that suggest that in the period 1978- 1982, US oil consumption followed a pattern different from the past. Moreover, this pattern has gradually emerged in response to the events of the 1970s.
Sensitivity
analyses
There are a variety of other tests that could be performed. Other functions could be employed, but degrees of freedom limit the choices available. (Test 5, for
ENERGY ECONOMICS October 1984
Tests for structural change in US oil consumption, I96 7-1982: example, allows for four distinct periods.) Other variables could be employed and other factors considered indirectly here could be explicitly modelled. However, two important variations were tested here, and both do support the previous results that 1978-1982 is a stable period, but one that is different from earlier times; A serious simultaneous bias resulting from the interdependencies of oil consumption, oil prices, macroeconomic activity, and other prices almost surely exists. A number of the tests reported here were repeated in two different ways. In one case, crude oil prices were used as an instrumental variable to first estimate refined product prices. In the second case, crude oil prices were used to first estimate macroeconomic activity and hence correct for ‘GDP feedback’ bias. Then the test statistics were re-estimated. In no case did these corrections affect the significance of the test results, although individual parameter estimates were, of course, affected. However, at the sum of the squared residuals level this usually complicating factor was not so here. A more serious problem is that of aggregation bias Motor gasoline, aviation gasoline, diesel fuel, distillate fuel oil, residual fuel oil, jet fuel oil (of two types) and 20 other products have been aggregated into ‘refined petroleum products’. How serious is aggregating these fuels for the test purposes used here? To answer this, all eight tests were repeated with similar data and functional form for motor gasoline, distillate fuel oil and residual fuel oil - about 80% of all products. Product specific prices replaced the aggregate price index. Test results for these fuels are reported in Table 2 and the detailed statistics are in Appendix 3. During the pre-embargo period, all tests agree and continue to do so through the embargo, except for residual fuel. The third period - the post-embargo period - is the most striking one in this table. The category ‘all oils’ showed no change, yet each separate fuel did. It thus appears that when there is little change at the fuel level, then the fuels can be aggregated, but the only way to test this is at the fuel level. The Iranian period is also interesting. The categories all oils, distillate, and residual exhibited no change, but gasoline (about 45% of all oils) did. Over 1975-1979 these categories reversed roles - only gasoline failed to show change. Fortunately, over 1978- 198 1 and 1978-l 982 all tests agree, again except for residual in 1982. The middle tests in the previous sections are thus reversed by the product specific ones (tests 3,4,6) but the pre-embargo
Tablo 2. A summary of
the product
and the post-1978 tests present the same results and suggest that data over the last five years can be used to forecast 1983 and beyond.
Conclusions For a variety of reasons (many of which have been discussed earlier) it is doubtful if there can be a ‘defmitive’ study about structural change in US oil consumptin over 1966-1982. However, this study does suggest and support the following claims: from 1966 to 1973, oil consumption in the USA was consistently related to oil prices, macroeconomic activity, and weather changes; that pattern was interrupted by the embargo of 1973174; following the embargo, a subtle shift in the pattern began to take place; those changes were again interrupted by the Iranian crisis (for gasoline, at least); since 1978, another and new pattern has been emerging and 1981 and 1982 have followed this new pattern. Finally, to conclude this work and to illustrate the above mentioned points, consider the following parameter estimates for the periods 1966- 1973 and 1978- 1982:
Price elasticity Macroeconomic activity elasticity Weather coefficient g2
1966-1973 -0.148
1978-1982 -0.195
0.713 0.103 0.96
0.314 0.0298 0.90
These data suggest that during the last five years (relative to the pre-embargo period), oil consumption is slightly more responsive to price changes and much less so to macroeconomic activity and weather changes. There are many hypotheses to explain this, but better insulated homes and factories, more fuel-efficient automobiles, and, in general, a more fuel-conscious society, would account for these changes.
References 1 M. Kennedy, ‘An economic model of the world oil market’, Bell Journal of Economics, Vol 5, No 2, Autumn 1974.
specific test results.
Test
All petrdeum
Gaeoline
Distillete
1 2 3 4 5 6 7 8
No change Change No change No change Change Change No change No change
No change Change Change Change Change No change No change No change
No change Change Change No change Change Change No change No change
Pre-embargo Embargo Post-embargo Iran 1980 1975-1979 1978-I 981 1978-1982
A. E. Bopp
ENERGY ECONOMICS October 1984
No change No charge Change No change Change Chenga No change Change
227
Tests for structural change in US oil consumption,
1967-1982:
2 A. Bopp, ‘The demand for kerosene: a modem Giffen good’, Applied Economics, Vol 15, No 1, February 1983. 3 US Department of Energy, Short Term Energy Outlook, US Government printing Office, Washington, DC, August 1982. 4 L. Phlips, Applied Consumption Analysis, NorthHolland, Amsterdam, 1974. 5 M. Hatanaka, ‘An efficient two-step estimator for the dynamic adjustment model with autoregressive errors’, Journal of Econometrics, Vol 2, No 3, September 1974. 6 F. Fisher, ‘Tests of equality between sets of coeffi-
A. E. Bopp cients in two linear regressions: an expository note’, Econometrica, Vol38, No 2, March 1970. 7 J. Farley, M. Hinnich and T. McGuire, ‘Some comparisons of tests for a shift in the slope of a multivariate linear time series model’, Journal of Econometrics, Vol 3, No 3, September 1975. 8 J. Durbin, R. Brown and J. Evans, ‘Techniques for testing the constancy of regression relationships over time’, Journal of the Royal Statistical Society (Series B), Vol37, No 2, April 1975. in US 9 A. Bopp and G. Lady, ‘Conservation petroleum consumption, t974- 1976’, Energy, Vol 3, No 4, August 1978.
Appendix 1 Test statistic results A. Chow Test: Date
tests
kl= number SSRl = sum of kz = number SSRz = sum of NOB = number test statistic
_ WR2
of parameters, unrestricted case (separate Bs) squared residuals, unrestricted case of parameters, restricted case (Bs equal across periods) squared residuals, restricted case of observations -
SSW(4
-
SSR,/(NOB
k2)
- kI) Test statistic
Test 1: Pre-embargo
1966-1973:
k,= 10 k2 = 5
SSRl = 0.0584 SSR2 = 0.0646
Test 2: Embargo 1966-1974:4 kI= 10 k2 = 5
kI= 15 k2= 10
v. 66-73:
Critical F
11 1.80
2.35
3.14
2.34
2.07
2.28
0.759
2.27
DW = 1.45
7.23
2.25
DW = 1.86
9.57
2.45
DW = 1.85
0.192
2.52
DW = 2.04
11 and 73: 12-74:4 NOB = 100 R2 = 0.96
1966-1973:ll 1966-1973:ll
DW = 1.99
t 1974:5-79:7 and 1973:l l-19745 and 1973:12-19745 and 1974:5-1979:7
SSRl = 0.1526 SSR2 = 0.1632
Test 4: Iranian crisis* 66-73:
11 and 69: 12-73:
NOB = 95 I?’ = 0.96
SSRl = 0.0646 SSRl = 0.0759
Test 3: Post-embargo* k,= 15 k2= 10
11 v, 66:01-69:
NOB = 164 I?’ = 0.96
11 t 74:5-79:
SSRl = 0.1814 SSR2 = 0.1859
DW = 1.48
12 v. 66. 73: 11 t 79:8-79: NOB = 168 R2 = 0.95
12
DW = 1.50
Tesr 5: 1980 v, earliert kI = 20 k2= 15
SSR, = 0.168 SSR2 = 0.206
I?’ = 0.96 NOB= 180
*Each period had a dummy for the embargo. tlranian period also dummied.
Test 6: May 1975-June kI= 10 k, = 5 Test 7: 1978-1979 k,= 15 k2 = 10
1977 Y. July 1977-August
SSRl = 0.168 SSR2 = 0.036 and 1980-1981 SSR, = 0.0275 SSR2 = 0.0283
1979
rT2 = 0.89 NOB= 51 v. 1978-1981s X2 = 0.93 NOB = 48
ENERGY ECONOMICS October 1984
Tests for structural change in US oil consumption, 196 7-1982: Test 8a: 1978-1981
$ Iranian
and 1982 v. 1978-1982f SSR, = 0.0407 SSR2 = 0.0525
kl= 15 k2= 10
A. E. Bopp
R2 = 0.88 NOB = 60
DW = 1.88
2.37
2.44
R2 = 0.89 NOB = 60
DW = 1.89
2.30
2.44
period also dummied.
Test 8b: SSR, = 0.0441 SSR2 = 0.0554
kI= 15 k2= 10
B. Farley-Hinich-McGuire tests (NOB - 2p) SSR2 - SSRl * The test statistic is SSRl P where p = number of parameters allowed to shift. Test statistic
Critical F
Test 1: Pre-embargo 95 - 8 0.0646 - 0.0614
SSR2 = 0.0646
Test F= - 4
SSRl = 0.06 14 Test 6: May 197%August SSR2 = 0.0783
=
1.13
2.70
12.18
2.60
0.44
2.18
1979 Test F =
SSRl = 0.0367
0.0614
0.0783 - 0.0367 0.0367
51 -8 4
=
Test 8: 1978-19828 SSR2 = 0.0526
Test F =
SSRl = 0.0483 PAllowing
0.0526 - 0.0483 0.0483
56-=
16 8
for a special period for the Iranian crisis.
These last 3 tests support the earlier tests that show no change over 1966-1973, change over 1978-1982.
change over 1975- 1979 and no
Appendix 2 Durbin-Brown
plots
Appendix 2 shows three Durbin-Brown plots. In the ideal case of absolutely no structural change the plots of the cumulative sum of squared residuals will follow the line through the points (0, 0) and (1, 1) in the sum of squared residuals/time space. Durbin and Brown’ have provided confidence bands about the ideal to reveal structural change graphically. Below (Figures 2-4) are the plots for 1973-1975 (showing change during the embargo period), 1975-1982 (showing change again) and for 1980-1982 (showing no change).
1.0 -
Figure 2. Durbin-Brown
ENERGY ECONOMICS October 1984
plot: 1973-1975
(embargo).
229
Tests for structural change in US oil consumption,
196 7-1982:
A. E. Bopp
I .o Y .j
0.0
L
B i
0.6
6
E 304 8, p E p 0.2
0
Figure 3. Durbin-Brown
plot: 1975-l
982.
Figure 4. Durbin-Brown
Appendix 3
plot: 1980-1982.
4. Iranian crisis Number of observations SSRl 0.100 0.597 SSR? 0.121 0.626 Test F/ 6.82/2&I 1.2212.44 critical F change no change
Product specific Chow tests
5. 1980~. earlier Number SSRl 0.1068 SSRz 0.1276 Test Ff 6.83/2.43 critical F change
= 139 1.067 1.121 1.3212.44 no change
of observations 0.6227 0.8014 7.8lj2.27 change
= 146 1.076 1.356 7.0812.27 change
Test
Motor gasoline*
1. Pre-embargo SSRl SSRz Test F/ critical F
Number of observations 0.0276 0.1574 0.1878 0.0306 2.3512.36 1.67/2.5 1 no change no change
= 71 0.2708 0.3042 15012.36 no change
6. 1975-1979 SSRl SSRz Test F/ critical F
Number of observations 0.0272 0.1326 0.0285 0.2207 0.5212.6 1 5.5812.45 no change change
= 52 0.2423 0.4076 5.7312.45 change
2. Embargo SSRl SSRB Test F/ critical F
Number of observations = 76 0.1878 0.3042 0.0306 0.3457 0.2604 0.0360 5.1Ol2.35 1.8012.35 3.011252 change no change change
7. 1978-1982 SSRl SSRz Test F/ critical F
Number of observations 0.033 0.140 0.035 0.176 0.7312.58 2.312.43
= 48 0.175 0.228 2.812.43
Distillate
Number of observations 3. Post-embargo 0.072 0.429 SSR, 0.100 0.598 SSRz Test F/ 12.3612.45 9.7012.29 change change critical F
Residual
= 134 0.784 1.067 8.912.29 change
These tests support tural change over 1975-1979 (Test (Test 7). However, embargo periods are
the ‘all oil’ tests to show no struc1966-1973 (Test l), change over 6), no change over 1978-1982 the suggestion that pre- and postthe same is refuted (Test 3).
ENERGY ECONOMICS October 1984
The purpose of this paper is to test US oil consumption for structural change over the period 1967-I 982. A frequently used functional form is posited for total petroleum consumption as well as for gasoline, distillate, and residual fuel. Tests for abrupt change (Chow) and gradual or conservation-like change (Durbin, Brown, Evans and Farley, Hinnich, McGuire) are employed at special break points (1973 embargo, I979 Iranian crisis, 1980 recession) to check for abrupt changes and across years in general to detect gradual shifts. Both abrupt and gradual changes are found, although the last five years may be the beginning of a new non-changing period. Keywords:
This paper presents a number of tests for structural change in US oil consumption from 1967 to 1982. Figure 1 shows the steady growth in oil consumption from 1967 to 1973, the dramatic effect of the Arab embargo in early 1974, the renewed growth in 1976, and the again dramatic effect of the Iranian crisis in 1979. The 1980-1982 consumption levels reflect the prolonged US recession. However, some of these changes in consumption levels can be explained by changes in macroeconomic activity, prices or weather (1978 was a particularly cold year). That is, structurally 1981 may be similar to 1972. Consumption in 1981 was down because GNP was down, prices were up, and the weather was warm. In 1972 consumption was up for precisely opposite reasons. This paper posits a relationship between oil consumption and important factors such as macroeconomic activity, oil prices and weather, and tests the various periods for structural change of two types: dramatic and subtle. Dramatic shifts such as the Arab embargo or Iranian crisis are almost obvious. However, ever since 1974 the USA may have been gradually reducing its oil consumption past the level explained by higher The author is with the Department of Information and Decision Sciences, James Madison University, Harrisonburg, VA 22807, USA. The author acknowledges the assistance of Or George in making clear what is meant by ‘structural change’. Final manuscript
M. Lady
received 27 March 1984.
0140-9883/84/040223-08
303.00
0 1984 Butterworth
Oil consumption;
Structural
1976
1976
change; USA
1980
1982
Figure 1. Historical US oil consumption.
prices, reduced GNP, and warmer weather because of a gradual, less dramatic, but nevertheless significant shift favouring conservation. As a consequence, a variety of tests will be employed to attempt to detect both dramatic and subtle shifts in the relationship between US oil consumption and its explanatory factors. It is important to specify what is meant by the term ‘structural change’, because there are a variety of meanings. The idea developed in this work is that in the early 1960s there was a predictable and stable relationship between oil consumption and macroeconomic activity, oil prices, and weather. What is tested here is the stability of that posited relationship. Thus, if
& Co (Publishers) Ltd
223
Tests for struchual change in US oil consumption, 196 7-l 982: A. E. Bopp macroeconomic activity, prices, or weather changes in the 1974-1982 period account for the changes in oil consumption, then no structural change can be assumed even though the pattern of consumption obviously has changed (see Figure 1). For other purposes some would label any change in the pattern of consumption as one of ‘structural change’. Here, only those instances of changing patterns that are not explained by corresponding changes in the listed explanatory factors are labelled ‘structurally changed’. Also, a period such as 1978 where the pattern is not changed (growth in 1978 followed closely that of 1976-1977 and seems to validate a return to pre-embargo growth rates) but where weather is colder than normal might also be labelled one of ‘structural change’. There is an advantage and a disadvantage to this approach. The advantage is that more factors than simply consumption can be examined. Economic theory can be used along with statistical tests to examine the stability of a relationship - not just a single series. 1980-1982 is an interesting period of declining consumption. However, the USA was in a severe recession in those years. If there has been no structural change then when the US economy recovers, so should oil consumption. If the historical relationship between oil consumption and macroeconomic activity has been changed, then as the USA recovers, its oil usage may not. Thus the importance of an enlarged notion of structural change. The disadvantage is that the enlarged notion is vitally dependent upon the notion of a ‘posited’ relationship between oil consumption and the explanatory factors. Always at issue will be the question ‘is the posited the true relation?‘. Furthermore, any empirical single equation relationship may not conform to all of the theoretical restrictions that economic theory has to offer, and any empirical relationship may have statistical shortcomings of a minor-to-serious nature. By adopting the device of a ‘posited’ relationship, a period can be identified only as experiencing or not experiencing a change in the pattern. When a period of structural change is so identified, the cause of the change is not also identified with the tests employed here. There are at least four different circumstances that could cause a period to be so identified. If an omitted variable (interest rates, for example) began to behave differently in relation to included variables, such a change would be identified. If a simple functional form that well approximated over a base period the correct but more complicated true functional form became a worse approximation with different values for the exogenous variables, then the same result would be obtained. Also, if the true relationship simply changed (because of a basic change in preferences) or if it were only temporarily disrupted (by an embargo), then the tests would still only reveal structural change. All of these cases are possible with energy consumption functions and any of these cases is described here as one of ‘structural change’ in the posited relationship. The following sections will examine the relationship actually posited here and will then explain the design of the experiments performed. The method for choosing
224
periods to be tested and the types ‘of tests employed are discussed. Test results are then presented and the modifications in the original design, precipitated by those test results. are presented. The sensitivity tests are presented and a comparison of 1960 and 1980 estimations is made to illustrate the meaning of some of the test results.
Functional form There are a number of considerations to be taken into account in choosing a functional form so that stability tests between oil consumption and explanatory factors can be performed. First, the functional form should be representative of forms used in energy and petroleum studies. This criterion makes the tests useful immediately, because even if other functional forms reveal different answers, relative to the studies or models that use this particular form, these results are pertinent. Second, the functional form should be amenable to performing structural change tests. Some attractive forms such as polynomial distributed lags, dynamic demand models, and Hannon estimators are not well suited for these tests because their advantage-specificity in modelling the lag structure - coupled with the number of new terms introduced by the structural change tests - so reduces the degrees of freedom as to greatly weaken the tests. Often three periods (and sometimes four periods) are needed to test for stability - thus the parameter requirements are three (or four) times those of the original case. Any form that uses a large number of parameters in the fust case is too severely taxed in the structural change cases. It ‘is beyond the scope of this study to employ a simultaneous equation system to completely model a system of interdependencies between oil prices, oil consumption, macroeconomic activity and other prices. Some of the simultaneity problem is addressed by using crude oil prices as an identifying variable for explaining refined oil prices or for explaining disposable income, but in the single equation context using the instrumental variable approach. The approach used here is to specify a partial adjustment demand equation It is well suited to energy demand studies in that it allows for instantaneous and non-instantaneous consumption adjustments to price, income, and weather changes. This specification has appeared in a variety of studies in the energy and consumer durable literature (see for example Kennedy,’ Bopp,2 US Department of Energy3) and is referenced by Phlips4 as one ad hoc specification frequently used because of goodness-of-fit considerations. It is used ln energy studies for that reason and for the reason that once the following equation is estimated: lnQ,=a+blnP’+cln
Y,tdlnW,
+elnQ,-rs+U, where Q, = monthly petroleum in million bbl
consumption
in the USA
ENERGY ECONOMICS October 1984
Tests for structural change in US oil consumption, 196 7- I982. A. E. Bopp Pt = wholesale price index for petroleum products deflated by the wholesale price index Y, = disposable national income in 1972 dollars IV,= heating degree days Qt_rz = petroleum consumption lagged one year (this lag better reflects seasonal decisions for heating or driving rather than monthly ones) U, = assumed white noise error term the coefficients b, c, d are short-term (instantaneous) elasticity estimates and these estimates multiplied by l/( 1 - e) are long-term estimates of the same elasticities - some of the most critical elements in energy studies. The main statistical problem with this specification is the complicating error structure resulting from the presence of a lagged endogenous variable. If autocorrelated disturbances are also present, quasi-first differences using maximum-likelihood methods or two-step procedures discussed in Hatanaka’ must be estimated. Fortunately, here almost all of the reported DW statistics are very close to 2.0 so that computed h-statistics did not indicate the presence of autocorrelated disturbances. Also, only the periods that show structural change are the ones with DW statistics not close to 2.0, suggesting that an important variable might be omitted during these special periods. Some view DW statistics as a structural change test itself. Most of the tests employed over 60 (some over 180) monthly observations so that, hopefully, the small sample bias of the specification is diluted in the large sample tests.
Test statistics employed Perhaps the most widely used test for structural change is the Chow or F-test.6 When the point of change is known, this test is most powerful. It is employed two ways here. In some cases the break point is suggested by other events: the 1973/74 embargo, the 1979 Iranian crisis. In these cases, the classic Chow test is performed; that is, the sum of squared residuals from the linear model YT = XTB + UT is compared with the sum from
point is to be specified. However, if a change has occurred, this test will not reveal its date. Next, again for the case of unknown break point, Durbin and Brown’ have proposed a series of graphical tests that test the actual cumulative sum of squared residuals against an ideal sum. If there is no structural change, then with n observations, each residual should make a proportionate contribution to the sum of squared residuals. A serious departure from this rule suggests change in a graphical way (see Appendix 2). Their test may be the weakest, but is also the most suggestive in indicating when a change has occurred. Finally, there is the question: why not test for change in a subset of coefficients? The problem is the number of tests this demands. Not only should single coefficients be tests but also pairs and combinations. The number of tests becomes immense. Furthermore, a change in preferences could very well affect all of the coefficients - at least enough evidence of such change is found here that searching for further evidence of change seems unwarranted.
Test results: total petroleum products The previous sections detailed which variables are used to construct the X matrix in estimating the linear model of US oil consumption: Y,=XTB+U, Now consider possible time divisions for i? If the preand post-embargo periods are the same (and, of course, assuming that there is something special about the embargo period) then only 2 Bs are to be estimated since, in that case, XT, = pre-embargo values prior to 1973: 12 0 for 1973:12 to 1974:4 post-embargo values after 1974:4, and XT, = embargo values for 1973: 12 to 1974:4 and 0 elsewhere, inthemodelYT=[xi’
x:1::
tUT
However, there may be numerous post-embargo periods (as well as pre-embargo ones). Consider some of the following possible divisions for the X matrix: where T, + Tz = T and Tz corresponds to the period of interest. When the point for breaking the data into TI and Tz subsets is not known, then Tl and Tz are constructed to divide T evenly. However, in that case, other statistics may be more powerful and are also used. The Farley-Hinich-McCuire (FHM) test’ allows for an unknown break point and also allows for a gradual rather than a dramatic shift. Here the model is Y, = WTB •tXTTT-y = U,, where T, is a simple time trend variable (it takes values from l/n, 2/n , . . ., l), and the test is obtained by testing for the significance of 7 with an F-test in the multivariate case. If the break is not in the middle of T, then this test is more powerful than the Chow test. The advantage here is that no break
ENERGY ECONOMICS October 1954
XT, = pre-embargo period XT2 = embargo period XT, = post-embargo and pre-Iranian crisis XT, = Iranian crisis XT, = post-lranian crisis and pre-prolonged XT, = prolonged recession XT, = post-prolonged recession.
recession
Such a scheme would then involve the estimation of several sets of Bs. The procedure used here is first to determine if the period 1966-1973 was homogeneous - that is, without structural change. These test statistics suggest that the 1966-1973 period was one when a stable
225
Tests for structural change in US oil consumption, 1967-I 982: A. E. Bopp relationship between oil consumption and macroeconomic activity, prices, and weather existed. First, a Chow test was performed that divided 1966-1973: 11 into two even parts. This test revealed no structural change. Appendix 1 contains all of the information used to generate these statistics and all of the test results. Table 1 summarizes the results. A FHM test for gradual change was also performed over the period and revealed no change. In the fall of 1973, OPEC met and in response to actions of its Arab members became an effective cartel by raising crude oil prices from $5.25/bbl to over $12/bbl. At that time an embargo on direct sales to the USA was also imposed. The embargo ended in April 1974. Thus the period December 1973 to April 1974 represents a potential structural change period. The second Chow test tested 1966-1974:5 versus 1966-1973: 11 and 1973: 12-1974:5, and found significant structural change. (A regression was also attempted for 1966 to the end of 1974. Large errors occurred only in these months. By May 1974 things appeared to return to their previous pattern.) From 1974 to 1979 there were no dramatic events to disrupt the oil market, but oil prices were higher than in the earlier period. Figure 1 suggests that oil consumption levels may have returned to their preembargo patterns. To test this, the sum of squared residuals from a regression that employed the following time division: XT, = pre-embargo period XT, = embargo period XT, = post-embargo period to 1979:7 was compared to a sum from a regression employed two divisions: XT, = pre- and post-embargo XT, = embargo period
that
only
period
This Chow test revealed no structural change and suggested that consumption levels had, in fact, returned to pre-embargo patterns. Bopp and Lady9 have reported similar results only for 1974-1976. However, for
T&k
1. A summary of patrolaum consumption
atructuml
change teat maults. Test no la lb 2 3 4 5 6a 6b 7 ae 8b
226
Type of test
Result
Chow test over 19&6-1973:ll FHM test over 1966-1973:ll Embargo period 1973: 12-l 974:4 Pre- V. post-embargo 1966-1979:7 Iranian crisis period 1979:81979:12 1980 y. earlier periods 1980 v. 1966-1979 Chow test over 1975-l 979 FHM test over 1975-1979 Chow test ovar 1978-l 991 Chow test over 1978-l 992 FHM test over 1978-1982
No structural change No structural change Structural change No structural change No structural
change
Structural change Structural change Structural change No structural change No structural change No structural change
reasons discussed later, this test failed to detect actual change. When product specific tests are performed over the same period, significant change is found. The next section reports on these tests. However, when all fuels are aggregated, those changes are not detected. The next step was to check the Iranian crisis period. In 1979, especially from August to December, events in Iran pushed world oil prices from $18 to $36/bbl. Another Chow test that allowed for pre-embargo values in one regression (with post values ending December 1979) and that allowed for a separate period over 1979:8 to 1979: 12 was performed. It showed no change, again at the aggregate level, suggesting that consumption levels were responding in a predictable way to the higher prices. (In the fuel specific section, gasoline consumption will show change over this period while other fuels will not.) 1980 was then tested against previous periods. This test was originally performed allowing for only one special period (the embargo period) but was repeated (after the fuel specific tests showed change over the Iranian period) using two special periods. These tests revealed structural change. The test was repeated using just post-embargo data and change was still revealed. Here the importance of establishing the ‘sameness’ of the 1967-1973 period should be emphasized. The data, function, and tests that indicated so much change in 1980 are the same as those that revealed no change in 1966-1973. 1980 could have been the beginning of a new period, 1980 could have been uniquely different, or 1974- 1979 perhaps was not structurally the same. Two tests were first performed on the 1975- 1979:7 period (1975 was chosen over 1974 to be sure all traces of the direct impact of the embargo were removed.) A Chow test and a FHM test were performed and each revealed change over 1975-1979. Next, the periods 1978-1981 and 1978-1982 were tested for sameness. A Chow test was used in each case, and a FHM and a Durbin-Brown test over 1978-l 982. (Again each test was performed twice, once allowing for a special period for the Iranian crisis and once without it.) None of the tests revealed change. The DurbinBrown test was also performed over 1980- 1982, because this period constitutes the ‘most recent’ past and it is important to be sure that the last years are a period without change. The 1980- 1982 Durbin-Brown graph is in Appendix 2. Table 1 presents a summary of these test results. This section has presented tests that suggest that in the period 1978- 1982, US oil consumption followed a pattern different from the past. Moreover, this pattern has gradually emerged in response to the events of the 1970s.
Sensitivity
analyses
There are a variety of other tests that could be performed. Other functions could be employed, but degrees of freedom limit the choices available. (Test 5, for
ENERGY ECONOMICS October 1984
Tests for structural change in US oil consumption, I96 7-1982: example, allows for four distinct periods.) Other variables could be employed and other factors considered indirectly here could be explicitly modelled. However, two important variations were tested here, and both do support the previous results that 1978-1982 is a stable period, but one that is different from earlier times; A serious simultaneous bias resulting from the interdependencies of oil consumption, oil prices, macroeconomic activity, and other prices almost surely exists. A number of the tests reported here were repeated in two different ways. In one case, crude oil prices were used as an instrumental variable to first estimate refined product prices. In the second case, crude oil prices were used to first estimate macroeconomic activity and hence correct for ‘GDP feedback’ bias. Then the test statistics were re-estimated. In no case did these corrections affect the significance of the test results, although individual parameter estimates were, of course, affected. However, at the sum of the squared residuals level this usually complicating factor was not so here. A more serious problem is that of aggregation bias Motor gasoline, aviation gasoline, diesel fuel, distillate fuel oil, residual fuel oil, jet fuel oil (of two types) and 20 other products have been aggregated into ‘refined petroleum products’. How serious is aggregating these fuels for the test purposes used here? To answer this, all eight tests were repeated with similar data and functional form for motor gasoline, distillate fuel oil and residual fuel oil - about 80% of all products. Product specific prices replaced the aggregate price index. Test results for these fuels are reported in Table 2 and the detailed statistics are in Appendix 3. During the pre-embargo period, all tests agree and continue to do so through the embargo, except for residual fuel. The third period - the post-embargo period - is the most striking one in this table. The category ‘all oils’ showed no change, yet each separate fuel did. It thus appears that when there is little change at the fuel level, then the fuels can be aggregated, but the only way to test this is at the fuel level. The Iranian period is also interesting. The categories all oils, distillate, and residual exhibited no change, but gasoline (about 45% of all oils) did. Over 1975-1979 these categories reversed roles - only gasoline failed to show change. Fortunately, over 1978- 198 1 and 1978-l 982 all tests agree, again except for residual in 1982. The middle tests in the previous sections are thus reversed by the product specific ones (tests 3,4,6) but the pre-embargo
Tablo 2. A summary of
the product
and the post-1978 tests present the same results and suggest that data over the last five years can be used to forecast 1983 and beyond.
Conclusions For a variety of reasons (many of which have been discussed earlier) it is doubtful if there can be a ‘defmitive’ study about structural change in US oil consumptin over 1966-1982. However, this study does suggest and support the following claims: from 1966 to 1973, oil consumption in the USA was consistently related to oil prices, macroeconomic activity, and weather changes; that pattern was interrupted by the embargo of 1973174; following the embargo, a subtle shift in the pattern began to take place; those changes were again interrupted by the Iranian crisis (for gasoline, at least); since 1978, another and new pattern has been emerging and 1981 and 1982 have followed this new pattern. Finally, to conclude this work and to illustrate the above mentioned points, consider the following parameter estimates for the periods 1966- 1973 and 1978- 1982:
Price elasticity Macroeconomic activity elasticity Weather coefficient g2
1966-1973 -0.148
1978-1982 -0.195
0.713 0.103 0.96
0.314 0.0298 0.90
These data suggest that during the last five years (relative to the pre-embargo period), oil consumption is slightly more responsive to price changes and much less so to macroeconomic activity and weather changes. There are many hypotheses to explain this, but better insulated homes and factories, more fuel-efficient automobiles, and, in general, a more fuel-conscious society, would account for these changes.
References 1 M. Kennedy, ‘An economic model of the world oil market’, Bell Journal of Economics, Vol 5, No 2, Autumn 1974.
specific test results.
Test
All petrdeum
Gaeoline
Distillete
1 2 3 4 5 6 7 8
No change Change No change No change Change Change No change No change
No change Change Change Change Change No change No change No change
No change Change Change No change Change Change No change No change
Pre-embargo Embargo Post-embargo Iran 1980 1975-1979 1978-I 981 1978-1982
A. E. Bopp
ENERGY ECONOMICS October 1984
No change No charge Change No change Change Chenga No change Change
227
Tests for structural change in US oil consumption,
1967-1982:
2 A. Bopp, ‘The demand for kerosene: a modem Giffen good’, Applied Economics, Vol 15, No 1, February 1983. 3 US Department of Energy, Short Term Energy Outlook, US Government printing Office, Washington, DC, August 1982. 4 L. Phlips, Applied Consumption Analysis, NorthHolland, Amsterdam, 1974. 5 M. Hatanaka, ‘An efficient two-step estimator for the dynamic adjustment model with autoregressive errors’, Journal of Econometrics, Vol 2, No 3, September 1974. 6 F. Fisher, ‘Tests of equality between sets of coeffi-
A. E. Bopp cients in two linear regressions: an expository note’, Econometrica, Vol38, No 2, March 1970. 7 J. Farley, M. Hinnich and T. McGuire, ‘Some comparisons of tests for a shift in the slope of a multivariate linear time series model’, Journal of Econometrics, Vol 3, No 3, September 1975. 8 J. Durbin, R. Brown and J. Evans, ‘Techniques for testing the constancy of regression relationships over time’, Journal of the Royal Statistical Society (Series B), Vol37, No 2, April 1975. in US 9 A. Bopp and G. Lady, ‘Conservation petroleum consumption, t974- 1976’, Energy, Vol 3, No 4, August 1978.
Appendix 1 Test statistic results A. Chow Test: Date
tests
kl= number SSRl = sum of kz = number SSRz = sum of NOB = number test statistic
_ WR2
of parameters, unrestricted case (separate Bs) squared residuals, unrestricted case of parameters, restricted case (Bs equal across periods) squared residuals, restricted case of observations -
SSW(4
-
SSR,/(NOB
k2)
- kI) Test statistic
Test 1: Pre-embargo
1966-1973:
k,= 10 k2 = 5
SSRl = 0.0584 SSR2 = 0.0646
Test 2: Embargo 1966-1974:4 kI= 10 k2 = 5
kI= 15 k2= 10
v. 66-73:
Critical F
11 1.80
2.35
3.14
2.34
2.07
2.28
0.759
2.27
DW = 1.45
7.23
2.25
DW = 1.86
9.57
2.45
DW = 1.85
0.192
2.52
DW = 2.04
11 and 73: 12-74:4 NOB = 100 R2 = 0.96
1966-1973:ll 1966-1973:ll
DW = 1.99
t 1974:5-79:7 and 1973:l l-19745 and 1973:12-19745 and 1974:5-1979:7
SSRl = 0.1526 SSR2 = 0.1632
Test 4: Iranian crisis* 66-73:
11 and 69: 12-73:
NOB = 95 I?’ = 0.96
SSRl = 0.0646 SSRl = 0.0759
Test 3: Post-embargo* k,= 15 k2= 10
11 v, 66:01-69:
NOB = 164 I?’ = 0.96
11 t 74:5-79:
SSRl = 0.1814 SSR2 = 0.1859
DW = 1.48
12 v. 66. 73: 11 t 79:8-79: NOB = 168 R2 = 0.95
12
DW = 1.50
Tesr 5: 1980 v, earliert kI = 20 k2= 15
SSR, = 0.168 SSR2 = 0.206
I?’ = 0.96 NOB= 180
*Each period had a dummy for the embargo. tlranian period also dummied.
Test 6: May 1975-June kI= 10 k, = 5 Test 7: 1978-1979 k,= 15 k2 = 10
1977 Y. July 1977-August
SSRl = 0.168 SSR2 = 0.036 and 1980-1981 SSR, = 0.0275 SSR2 = 0.0283
1979
rT2 = 0.89 NOB= 51 v. 1978-1981s X2 = 0.93 NOB = 48
ENERGY ECONOMICS October 1984
Tests for structural change in US oil consumption, 196 7-1982: Test 8a: 1978-1981
$ Iranian
and 1982 v. 1978-1982f SSR, = 0.0407 SSR2 = 0.0525
kl= 15 k2= 10
A. E. Bopp
R2 = 0.88 NOB = 60
DW = 1.88
2.37
2.44
R2 = 0.89 NOB = 60
DW = 1.89
2.30
2.44
period also dummied.
Test 8b: SSR, = 0.0441 SSR2 = 0.0554
kI= 15 k2= 10
B. Farley-Hinich-McGuire tests (NOB - 2p) SSR2 - SSRl * The test statistic is SSRl P where p = number of parameters allowed to shift. Test statistic
Critical F
Test 1: Pre-embargo 95 - 8 0.0646 - 0.0614
SSR2 = 0.0646
Test F= - 4
SSRl = 0.06 14 Test 6: May 197%August SSR2 = 0.0783
=
1.13
2.70
12.18
2.60
0.44
2.18
1979 Test F =
SSRl = 0.0367
0.0614
0.0783 - 0.0367 0.0367
51 -8 4
=
Test 8: 1978-19828 SSR2 = 0.0526
Test F =
SSRl = 0.0483 PAllowing
0.0526 - 0.0483 0.0483
56-=
16 8
for a special period for the Iranian crisis.
These last 3 tests support the earlier tests that show no change over 1966-1973, change over 1978-1982.
change over 1975- 1979 and no
Appendix 2 Durbin-Brown
plots
Appendix 2 shows three Durbin-Brown plots. In the ideal case of absolutely no structural change the plots of the cumulative sum of squared residuals will follow the line through the points (0, 0) and (1, 1) in the sum of squared residuals/time space. Durbin and Brown’ have provided confidence bands about the ideal to reveal structural change graphically. Below (Figures 2-4) are the plots for 1973-1975 (showing change during the embargo period), 1975-1982 (showing change again) and for 1980-1982 (showing no change).
1.0 -
Figure 2. Durbin-Brown
ENERGY ECONOMICS October 1984
plot: 1973-1975
(embargo).
229
Tests for structural change in US oil consumption,
196 7-1982:
A. E. Bopp
I .o Y .j
0.0
L
B i
0.6
6
E 304 8, p E p 0.2
0
Figure 3. Durbin-Brown
plot: 1975-l
982.
Figure 4. Durbin-Brown
Appendix 3
plot: 1980-1982.
4. Iranian crisis Number of observations SSRl 0.100 0.597 SSR? 0.121 0.626 Test F/ 6.82/2&I 1.2212.44 critical F change no change
Product specific Chow tests
5. 1980~. earlier Number SSRl 0.1068 SSRz 0.1276 Test Ff 6.83/2.43 critical F change
= 139 1.067 1.121 1.3212.44 no change
of observations 0.6227 0.8014 7.8lj2.27 change
= 146 1.076 1.356 7.0812.27 change
Test
Motor gasoline*
1. Pre-embargo SSRl SSRz Test F/ critical F
Number of observations 0.0276 0.1574 0.1878 0.0306 2.3512.36 1.67/2.5 1 no change no change
= 71 0.2708 0.3042 15012.36 no change
6. 1975-1979 SSRl SSRz Test F/ critical F
Number of observations 0.0272 0.1326 0.0285 0.2207 0.5212.6 1 5.5812.45 no change change
= 52 0.2423 0.4076 5.7312.45 change
2. Embargo SSRl SSRB Test F/ critical F
Number of observations = 76 0.1878 0.3042 0.0306 0.3457 0.2604 0.0360 5.1Ol2.35 1.8012.35 3.011252 change no change change
7. 1978-1982 SSRl SSRz Test F/ critical F
Number of observations 0.033 0.140 0.035 0.176 0.7312.58 2.312.43
= 48 0.175 0.228 2.812.43
Distillate
Number of observations 3. Post-embargo 0.072 0.429 SSR, 0.100 0.598 SSRz Test F/ 12.3612.45 9.7012.29 change change critical F
Residual
= 134 0.784 1.067 8.912.29 change
These tests support tural change over 1975-1979 (Test (Test 7). However, embargo periods are
the ‘all oil’ tests to show no struc1966-1973 (Test l), change over 6), no change over 1978-1982 the suggestion that pre- and postthe same is refuted (Test 3).
ENERGY ECONOMICS October 1984