Modeling the high frequency demand for energy

Applied Energy 19 (1985) 49 59

Modeling the High Frequency Demand for Energy* Noel D. Uri Bureau of Economics, Federal Trade Commission, Washington, DC 20580 (USA)

and

Saad A. Hassanein Department of Economics and Business, The Catholic University of America, Washington, DC 20064 (USA)

SUMMARY This paper looks at the nature and length off,the impact that prices and economic activity have on the demand ff,or motor gasoline and distillate fuel oil in the United States. A general approach is presented and implemented to aid any energy analyst m gaining insights into the modeling activity. The results suggest that price changes affect the quantity of motor gasoline and distillate fuel oil demanded for as long as two years after an initial change, while changing personal income has an impact ff,br about a year.

INTRODUCTION Modeling the demand for energy on a high frequency basis (e.g. monthly) has proved to be an elusive proposition. For example, a concensus on a reliable estimate of the elasticity demand for motor gasoline has not emerged. Estimates 11 range between - 0 . 0 7 and -0-47. Analogously, short-run demand elasticity estimates 1 for home heating oil (i.e. distillate * The views expressed are those of the authors and do not necessarily represent the policies of the institutions with which they are affiliated. 49

Applied Energy 0306-2619/85/$03"30 4") Elsevier Applied Science Publishers Ltd, England, 1985. Printed in Great Britain

50

Noel D. Uri, Saad A. Hassanein

fuel oil), range between - 0 . 1 2 and -0.41. Such variability in estimates can be most problematical when there is a need to infer the potential impacts of policy initiatives or when the objective is to forecast demand over some given horizon. In fact, the issue of an accurate assessment of a motor gasoline price elasticity is so muddled that, in the model used to forecast the short-term demand for energy employed by the US Department of Energy, a value of - 0 . 1 5 is subjectively assumed. 2 Even if a correct single period value could be determined, there are other issues of relevance. As noted by Uri, 3 important questions that need to be addressed in energy modeling include identification (i.e. can the demand equation be distinguished from the supply equation) and the dynamic consideration. In this latter instance, the notion of a distributed lag is important. A change in price, for example, will only partially affect the quantity demanded in any given period and this impact can be expected to be spread out over several periods. It is typical, in energy modeling, to specify a single period distributed lag and some sort of adjustment process whereby the future quantity demanded adjusts to this single-period price movement. The analyst just does not devote the requisite time needed to determine the number of periods over which the price impact is spread. Given the need to establish reliable estimates of price and income elasticities, in particular, in energy modeling (see, for example, Energy Modeling Forum 4) and the inherent limitations in the approaches currently used, this paper utilizes an infrequently employed technique to demonstrate how any analyst can go about resolving (1) whether any single variable de facto impact causes another and (2) if there is such an impact, the length of the period over which the effect of one variable is felt by the other. This paper uses two specific energy types as examples-motor gasoline and distillate fuel oil--but the methodology has much broader applications. It can be employed in any modeling activity where the interrelationships between the variables need to be determined. Before actually employing the technique, it will be useful to discuss it briefly.

TESTING FOR CAUSATION The notion of causation rests on the ability of a given series to explain another series better than the second series can explain itself, based on its

Modeling the high frequency demand for energy

51

own past alone. This suggests relating the first series, say X, to that part of the second series, say Y, which cannot be explained by its own past history. The mechanics of doing this are as follows. To obtain that portion of Y which cannot be explained by its own past history requires that the series be whitened. 5 There are a variety of approaches that can be used to achieve this whitening. Each, however, is equivalent to estimating univariate model filters F(B)and G(B)for X, and Y, (where the subscript t has been added to denote the period). The method here is to use the approach of Box and Jenkins. 6 In this, one obtains estimates, F(B) and G(B), of the true whitening filters and residuals, U, and V,, as given by: (], = [:(O)X,

(1)

•, = d(B)Y,

(2)

The analysis is carried out using the sample residual cross-correlations: ik =

Y

~-~2-~)2

(3)

In order to use the statistics given by eqn. (3) to test the hypothesis about the series of interest (i.e. about causality), it is necessary to know the approximate sampling distribution under the null hypothesis that the type of causality being tested for is absent. Consider the hypothesis that X and Y are independent. Under this presumption, it has been shown that the residual cross-correlations given by eqn. (3) and the white noise crosscorrelations have the same asymptotic distribution.7 In particular, the test statistic: M

= T ~ ' (ik)2 / k=l

(4)

d

is distributed as a chi-square with n degrees of freedom. 8 From this it follows that causation can be examined by substituting, in eqn. (4), the particular sample residual cross-correlation, rk, corresponding to the population white noise correlations. For example, it can be concluded that X causes Y at significance level, ~, if: m

T~-~ 0:k) 2 > Z~Z(rn) k=l

52

Noel D. Uri, Saad A. Hassane&

where the right-hand side of the inequality is the upper percentage point of the zZ(m) distribution, m is the number of degrees of freedom and T is the number of observations. Analogously, the hypothesis that X and Y are unrelated would not be rejected at significance level, ~, if, and only if: T~--~ (t:k)2 < Z2(2m + 1) k=l

where m is chosen to be large enough to include expected nonnegligible, non-zero coefficients. It is informative, before actually implementing this test, to reflect on its origin. The definition of causation employed here is based on the predictability of a series (Y). If another series (X) contains information in past terms that helps the prediction of Y, and if this information is obtained in no other series used in the prediction, then Xis said to cause Y. The time element is obviously central to this consideration. EMPIRICAL RESULTS The focus of concern is on high frequency (i.e. monthly) demand for motor gasoline and distillate fuel oil. Monthly data on the quantity of motor gasoline demanded and the quantity of distillate fuel oil demanded were obtained for the period 1968 to March, 1983, from the Minerals Industry Yearbook 1° (for 1968-1973) and from the Monthly Energy Review of the Department of Energy (for 1974-1983). 1~ Factors commonly recognized which influence demand include own prices, competing prices, economic activity, the weather, etc. (see Blattenberger et al.12). Prices (in real terms) are measured as an index for motor gasoline and distillate fuel oil and were obtained from the Bureau of Labor Statistics. Weather data (measured as heating degree days) were obtained from the National Oceanic and Atmospheric Administration. Personal income data, used to reflect changes in economic activity, were obtained from the Bureau of Economic Analysis of the US Department of Commerce. Other variables potentially important in explaining demand were tried (e.g. mass transportation prices (for motor gasoline) and natural gas prices (for distillate fuel oil)) but no identifiable relationships were found. Consequently, they are excluded from the discussion.

Modeling the high frequency demand for energy

53

The data interval (1968-1983) was selected to cover a period of no energy crisis and fairly constant prices, an energy crisis with oil embargoes and significantly changing prices and periods of economic expansion and decline. With regard to the impact of weather on energy demand, there was a clear effect in the coincident period (i.e. contemporaneously) but no lag effect was observed. That is, in colder weather (as measured by increased heating degree days), cars run less efficiently and hence motor gasoline demand increases. Similarly, the amount of distillate fuel oil consumed for heating purposes increases as it gets colder. In neither of these instances, however, does this impact spread over to succeeding months-hence the absence of any empirical findings on the distributed lag impacts of weather. The approach used in applying the test discussed in the previous section is to first determine appropriate filters (i.e. estimate F(B) and G(B) as autoregressive-integrated-moving-average (ARIMA) models) that remove the autocorrelation in the series of interest. The resulting residuals are then used as the basis of the analysis. Table 1 gives the filters, determined via the Box Jenkins approach, estimated to accomplish this. Note that, as a result of the filtering process, there are 159 residuals common across all series. TABLE 1 A R I M A Models

Series

(1) Motor gasoline demand (2) Motor gasoline price (3) Distillate fuel oil demand (4) Distillate fuel oil price

(5) Personal income

Estimated ARIMA modelsa'b (in autoregressive form) (1 - 0 . 7 4 5 7 B - 0.5606B 2) (1 + 0-7818B12) -I (0.066 2) (0.066 1) (0-054 7) (1 + 0.866 6B - 0.470 IB 2) (1 + 0.766 2B + 0.201 0B 14 - 0.269 IB 16) - 1 (0-0806) (0.0686) (0-0673) (0.0686) (0.0691) (l+0.3092B+0.2312B4+0.2250B ~) ~ (1+0.7125B~2) -a (0.069 2) (0.0726) (0.071 6) (0.067 6) (1 - 0.482 6B 2 - 0.473 8B 4 - 0.230 9B s - 0.676 3B 2° + 0.255 8B 22) (0.067 3) (0.067 9) (0.071 8) (0.083 4) (0.104 8) (1 - 0.3200B 11 + 0.559 3B 13 _ 0.357 4B t6 + 0.207 1B22) - 1 (0.069 4) (0.057 1) (0.048 8) (0.095 9) (1 - 0 . 3 4 7 6 B 17) (1 + 0 . 8 2 9 3 B - 0 . 1 9 3 7 B 1 7 ) - l (0.085 11) (0.0326) (0.036 3)

Standard errors of estimates in parentheses. b Note that B is general operator notation, that is, B~Z~ = Z t - i. a

Noel D. Uri, Saad A. Hassanein

54

The cross-correlations of the ARIMA residuals were examined to determine the nature and extent of associations between the variables. Table 2 gives the results for motor gasoline demand and the price of motor gasoline lagged. Tables 3, 4 and 5 present results for motor gasoline demand and lagged personal income, distillate fuel oil and lagged distillate fuel oil price and distillate fuel oil and lagged personal income, respectively. Finally, Tables 6 and 7 report the results for the prices of motor gasoline and distillate fuel oil and their respective quantities lagged. No results are reported for personal income and lagged values of the variables. There is no evidence of causation. Also, lagged cross-correlations are not reported for more than twenty-four periods, although they were computed. Uniformly, they did not prove to be significant and provide no further information. Table 2 shows the cross-correlations between the quantity of motor gasoline demanded and lagged motor gasoline price to be supportive of causation. Specifically, for the quantity of motor gasoline demanded and lagged values of the prices of motor gasoline: 12

(?~k) 2 =

26.78 > Z20"05(12) = 21"03

k=l

and: 24

T~

(t~k)2 = 38-43 > Z20-05(24) = 36.42

k=l

In other words, the demand for motor gasoline can be better predicted from changes in the price of motor gasoline than from its own past alone. Additionally, the impact of any price movement is spread over twentyfour months. That is, there is an identifiable causal impact over twelve months, as well as over twenty-four months. After that time, however, the impact wanes and is not statistically observable. There are several reasons why one, a priori, would expect to witness this. In the immediate period (i.e. the first few months), consumers adjust their driving habits, including reducing the use of their cars, consciously combining shopping trips, joining car pools for the journey to and from work and improving the maintenance of their cars. In the longer run, we find, in addition,

55

Modeling the high f r e q u e n c y demand f o r energy

I

I

"-66

I oo

----6 6 I oo

oo

oo r.~ t"q

I

I

"~

°_66

°_66

°_66

I

¢;

t'q

:2

~66

I

I

c~66 I

a~

I

e~ oo

I

©

0

t'q

oo66

~66

o~66

oo66 I

r,.

I

t"q

t'q

¢.

r~66

r~-7.~.

r~o6 I

~a

~66 I

I

I

,,rlt¢~ ¢,q

~66

r=

©

66

~66 I

0 0

0

6

t"q

r~

~66

I

0

I

I t'q

0"~ t'q

~66

~66

~ro6

.-2

0

6

I

~r e~

~66

6

66

I

0 ~r

~66 I

.o

o

I o

a C7~

I

I

o

?

I

'

?

I

I

I t~l ¢.q

or)

,d

~0

~0

o

?

2 ol)

,d

56

Noel D. Uri, Saad A. Hassanein

-~do ~ pq~ k~ 6

~" oo

o

oo

I

6 6 6

'

oo

b , -0o

0

I

--66

~ 6 6

I

oo

°66

I

°_66 I

I

e~

o~.o. 0

0

~66

0

6 6 6 I

I

0

D.

~66

o

o

~66

I

I

I

6 6 6 " I

!

o~

!

0 "~" t'N IIn , . ~

r-66

0

6 6 6 I

I

'~66 I

©

~

~66

66 ¢",1

©

I

~66

6 6 6

I

I

._= o

"~'66

I

I

a~ e., o

6

~D

6 6 6

I

~ 1 I'N

~66

H .0

6

I

I

0 6 6 6 I

I 0

o

o 6

0~

I

I

I

I

,o ~J I

0

Y ~,1 e',,I

6 6 6 0

0

0

0

p

I

66~ r

o r.)

c~ ..1

,.d

,...1

.,d

Modeling the high J?equency demandJor energy

57

consumers switching to more energy-efficient capital equipment (i.e. to cars and trucks with associated better gas mileages) and altering their lifestyles so that motor gasoline-consuming equipment is less intensively relied upon. In employing the chi-square test for the relationship between motor gasoline price and the quantity of motor gasoline demanded, the results (from Table 6) are: T ~ (rk) 2 = 1'99 < Z20"05(24) =21'03 T~

(rk) 2 = 2.37 < •20"05(24) = 36.42

indicating that causation does not run from the quantity of motor gasoline demanded to motor gasoline prices. This is not surprising. Given the regulated nature of the price of motor gasoline over most of the period of investigation, price movements were a supply side phenomenon and not exactly determined by market interaction. The identifiable impact that personal income has on the quantity of motor gasoline demanded is much shorter lived, not extending beyond twelve months (Table 3). Consumers adjust their lifestyles in response to increases or decreases in personal income. This can be seen in driving related activities as income increases, including longer distance vacations, more trips to recreational sites, substituting cars for public transport on the journey to work, etc. With regard to the quantity of distillate fuel oil demanded and the price of distillate fuel oil, lagged results, analogous to those of motor gasoline, apply. It is two years before the impact of price changes is exhausted. Again, there are the immediate phenomena in response to rising distillate prices, including lowering domestic thermostats, living with a somewhat cooler house, keeping doors and windows closed and repairing broken windows. In the longer run, the thermal integrity of a house can be enhanced and new, more energy-efficient capital can be employed (i.e. by replacing the old central space heater with a newer, more efficient one). Again, because the price of distillate was regulated over most of the sample period, there is no identifiable causative link between the quantity demanded and price. Personal income does make a perceptible impact on the quantity of distillate demanded over about a one-year period. This is primarily due to householders raising their domestic thermostats, in order to be more comfortable, as their incomes rise.

58

Noel D. Uri, Saad A. Hassanein

IMPLICATIONS AND CONCLUSIONS What can be concluded from the foregoing analysis ? First, the quantity of motor gasoline consumed is causally related to the price of motor gasoline over about twenty-four months and to personal income over about twelve months. Hence, any attempt to model the demand for motor gasoline must explicitly represent these dynamic distributed lag relationships. An analogous comment holds for distillate fuel oil. Secondly, there is no suggestion that there is a causative relationship between the quantity of motor gasoline or distillate fuel oil demanded and the price of the respective fuels. This means that the problem of simultaneous equation bias need not be addressed when endeavouring to model demand. ~3 That is, a simultaneous equation system explicitly representing supply and demand is not required. Thirdly, the impact of weather is identifiable only contemporaneously. Distributed lag concerns do not apply.

REFERENCES 1. L. D. Taylor, The demand for energy: A survey, University of Arizona, Tuscon, AZ, USA, 1976. 2. Department of Energy, Short-term energy outlook, US Government Printing Office, Washington, February, 1983. 3. N. D. Uri, Estimation of demand elasticities: A reflection on the issues, Applied Energy, 9 (1981), pp. 243-56. 4. Energy Modeling Forum, Aggregate elasticity of energy demand, Stanford University, Palo Alto, 1980. 5. C. W. J. Granger and P. Newbold, Forecasting economic time series, Academic Press, New York, 1977. 6. G. E. P. Box and G. M. Jenkins, Time series analysis: Forecasting and control, Holden-Day Inc., San Francisco, 1970. 7. L.D. Haugh, Checking the independence of two covariance-stationary time series: A univariate residual cross-correlation approach, Journal of the American Statistical Association, 71 (1976), pp. 378-85. 8. J. M. Durbin, Tests for serial correlation in regression analysis based on the periodogram of least squares residuals, Biometrika, 56 (1969), pp. 1-15. 9. F. L. Feige and D. Pearce, The causality relationship between money and income: A time series approach. Paper presented to the Midwest Economic Association, Chicago, IL, USA, 1974. 10. Department of the Interior, Minerals Industries Yearbook, US Government Printing Office, Washington. (Annually.)

Modeling the high]requency demandfor energy

59

11. Department of Energy, Monthly Energy Review, US Government Printing Office, Washington. (Monthly.) 12. G. Blattenberger, L. D. Taylor and P. K. Verlager, The demandfor energy, Electric Power Research Institute, Palo Alto, CA, USA, 1978. 13. J. Kmenta, Elements of econometrics, Macmillan Publishing Company, New York, 1971.