Electrical energy usage over the business cycle

Transcription

1 Energy Economics 26 (2004) Electrical energy usage over the business cycle Mark Thoma* Department of Economics, University of Oregon, Eugene, OR , USA Available online 24 May 2004 Abstract Causality from macroeconomic conditions to electrical usage overall and in the residential, commercial, industrial, and other sectors is examined. The paper shows that changes in macroeconomic conditions cause significant changes in electrical usage in the commercial and industrial sectors, and overall. In addition, the paper shows that causality occurs at business cycle frequencies and that there are asymmetries over the business cycle. An implication is that forecasts used to assess the probability of exceeding capacity constraints should incorporate forecasts of macroeconomic conditions, asymmetries over the cycle, and how the commercial and industrial sectors will respond to such changes. D 2004 Elsevier B.V. All rights reserved. JEL classification: Q43 Energy and the Macroeconomy Keywords: Causality; Electricity; Business cycle; Sectors 1. Introduction What effect does variation in output over the business cycle have on electrical energy usage? Surprisingly, little empirical evidence exists on the time-series properties of electrical usage, the causal relationship between the state of the macroeconomy and electrical energy usage, or on how variations in the composition of output affects electrical energy usage. 1 This paper fills this void by providing an econometric model linking macroeconomic conditions to energy usage by sector and showing that a causal relationship exists, by demonstrating that the linkage operates at business cycle frequencies, and by showing that there are asymmetries in the effect of output movements on energy usage over the business cycle. * Tel.: ; fax: address: mthoma@uoregon.edu (M. Thoma) /$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi: /j.eneco

2 464 M. Thoma / Energy Economics 26 (2004) There are several reasons to be interested in these results. First, with peak annual demand for electricity near or above capacity in recent years in states such as California, accurate forecasts of energy needs are essential. The model proposed here is useful for adjusting forecasts of the demand for electricity according to expected changes in macroeconomic conditions. Second, the model allows the effect on energy usage from expected changes in the composition of output such as a change in the percentage of total output accounted for by the industrial and commercial sectors to be estimated providing an additional means for improving forecasts of electricity usage. Third, firms operating in futures markets for electricity usage have a keen interest in forecasting future energy usage. Forecasts of future macroeconomic conditions can be used to guide electricity futures market decisions and to improve the assessment of the probability of a blackout. In addition, one goal of demand side management policies such as peak load pricing, load management, and strategic load growth directed at electrical energy usage is to shift the demand for energy so as to attenuate the cyclic variation in energy usage at daily, monthly, and business cycle frequencies. Efficient implementation of these policies requires precise knowledge of energy usage at each of these frequencies. If energy usage is affected by changes in the macroeconomy, and if such changes are unaccounted for, then load management and strategic load growth policies will not be as effective as they could be by accounting for such variation. Estimates of future energy usage that do not account for variation in actual or expected macroeconomic conditions will not allow the most efficient implementation of energy management policy. There is a literature linking electricity usage to macroeconomic variables, but where significant results are obtained, it is generally for countries other than the U.S. For example, as noted by Stern (2000), research by Kraft and Kraft (1978), Akarca and Long (1980), Yu and Hwang (1984), Abosedra and Baghestani (1991) uses Granger causality tests to assess whether causality exists between energy use and measures of aggregate output or output growth. The results are, in general, inconclusive. Stronger results are obtained for countries such as Japan (Erol and Yu, 1987a), the Philippines and South Korea (Yu and Choi, 1985), Ghana (Ammah-Tagoe, 1990), or industrialized countries in general (Erol and Yu, 1987a), but the results are not uniformly conclusive and the data sets used are not very recent. Other papers using data for countries other than the U.S. are Yang 1 The San Jose Mercury News (March 18, 2001, page 16A, San Jose Mercury News, CA) reported the following statements from Thom Kelly, assistant executive director of the California Energy Commission: Measuring the effects of an economic downturn on power is so difficult and complicated that the energy commission never before attempted to calculate it, Kelly said. It varies according to what s going on in the economy, Kelly said. Our economy is moving away from industrial plants and into service industries; therefore, our energy intensity seems to be falling. We re able to produce a lot using less energy. Trying to calculate a figure is like going to a turkey shoot with your gun which I ve never used and it s peasoup fog, Kelly added. The silver lining is that it s likely to force demand down a little bit, said Thom Kelly, assistant executive director of the California Energy Commission. And since this year we re really tight, that s good news. It s bad for the economy, but for electricity it s a good deal.

3 M. Thoma / Energy Economics 26 (2004) (2000) and Cheng and Tin (1997) who look at causal relationships and cointegration between energy usage and the macroeconomy in Taiwan, Glasure and Lee (1998) who examine cointegration between energy and GDP in South Korea, Harvie and Hoa (1993) who look at cointegration issues in resource markets in Australia, Pepper (1985) who performs a Box-Jenkins analysis for forecasting energy demand in the UK, and Masih and Masih (1996) who perform a multi-country analysis of cointegration and causality between real income and energy consumption. There are far fewer papers examining the time-series properties and causality relationships for U.S. data. Stern (1993, 2000) focuses on the U.S. and reports evidence of causality from energy usage to macroeconomic variables, but does not find a strong relationship running from macroeconomic variables to energy usage and this is not the main focus of the investigation. There are also papers by Silk and Joutz (1997) looking at cointegration of short- and long-run elasticities for energy demand, Yu and Jin (1992) who look for cointegration between energy usage, income, and employment, and Erol and Yu (1987b) who look at causality from energy usage to employment, but, again, the main focus of these papers is not causality from macroeconomic variables to sectoral energy usage. Thus, whether there are important causal linkages that run from the macroeconomy to energy usage is an open question. As noted above, the methodology proposed in this paper examines and quantifies the extent to which shocks to the macroeconomy affect energy usage overall and also by sector. The paper demonstrates a methodology for examining the relationship between macroeconomic conditions and energy usage, shows that there are significant effects, and quantifies the relationship amongst the key variables and sectors, results that should be of value in guiding forecasts of energy usage. In addition, the paper shows how changes in the composition of output across sectors affects energy usage, a topic not addressed in previous work. While a careful examination of the time-series properties and causal structure of energy usage and macroeconomic conditions as measured by aggregate output is a useful exercise, particularly given the small number of papers that formally examine causality and time-series properties such as unit roots and cointegration for the U.S., that there is causality from aggregate output to energy usage is not surprising. For example, many energy consumption forecasting models assume causality exists and include macroeconomic variables as explanatory variables in the econometric model. What has not been examined is the cyclical frequency at which the relationship between aggregate output and energy usage operates (papers by Erol and Yu, 1990 and Serletis and Hulleman, 1994 are remotely related). Whether this is a high or low frequency relationship is an important question for energy policy. Policies will differ if the relationship is due, for example, to 3- to 6-month cycles in the data rather than 3- to 5-year business cycle frequency movements. This paper uses band spectral regression techniques to identify the cycles in aggregate output generating changes in energy usage as well as the frequency of cycles in energy usage caused by the movements in output. The results show that causality between aggregate output and energy usage is primarily from low frequency, business cycle movements in output generating low frequency movement in energy usage, useful information for energy policy. Having established that the causality is due to low frequency movements in the data rather than high frequency movements, the next step is to investigate potential asymme-

4 466 M. Thoma / Energy Economics 26 (2004) tries in causality over the business cycle. For example, it is possible that trough energy usage is unaffected by changes in output even though there is significant causality overall. That is, suppose that over the business cycle there is a strong causal relationship between output and energy usage at the midpoint and peak of cycles, but the relationship is weak near the trough of cycles. Then, although significant causality will be in evidence in the data due to the association between the variables away from the trough of cycles, there is not a causal relationship near the trough of cycles. This is important to examine because if this were the case, it would undermine forecasting models that do not recognize this asymmetry over the cycle. A forecasting model that does not allow for the coefficient on aggregate output to vary over the business cycle, i.e. be small or zero in the trough of cycles and rise as the cyclical peaks are approached, will not produce the best possible forecasts. This paper estimates models of energy usage for peak annual usage, average annual usage, and minimum annual usage and shows that there are asymmetries over the business cycle in particular sectors and overall. In general, the association between energy usage and output is strongest at the peak of cycles and lowest, sometimes insignificant, at the midpoint or trough of cycles. Thus, energy forecasting models that include aggregate output as an explanatory variable need to allow for the coefficient on output to vary over the business cycle, something not currently done. The paper proceeds as follows. First, the data and data transformations are described. This is followed by a discussion of the econometric model and estimation technique used to investigate the time-series properties and causality. Next, the causality results are presented. This is followed by the discussion and estimation of the band spectral regression model used to uncover the cyclical frequencies where causality is most important. Then, potential asymmetries over the business cycle are investigated. The final section contains the conclusions. 2. The data The data used in the study are derived from two sources. Macroeconomic variables are obtained from the Citibase data set, and data on energy usage for the U.S. are from the tables in The Monthly Energy Review. 2 The data are monthly and range from 1973:01 to 2000:01. The variable used to measure the state of the economy is the log of monthly industrial production. 3 Data on energy usage for the U.S. are monthly and are the log of total electricity end use, and for the sub-categories of commercial, residential, industrial, and other sectors (which together sum to total usage). 4 In 2001, residential usage accounted for 2 The data can be found at 3 It is possible to replace industrial production with other indications of the state of the economy such as the unemployment rate, or to expand the list to include variables such as interest rates, the price level, money, and oil prices to provide a broader set of indications of the state of the economy. It would also be possible partition shocks into permanent (supply) and temporary (demand) components using typical identifying restrictions to see if the type of shock is important for energy usage. 4 The category Other is public street and highway lighting, other sales to public authorities, sales to railroads and railways, and interdepartmental sales.

5 M. Thoma / Energy Economics 26 (2004) Table 1 Augmented Dickey Fuller unit root tests AR model with constant and trend AR model with constant 1st unit root 2nd unit root 1st unit root 2nd unit root IP *** *** RES * *** *** COM *** *** IND * *** *** OTH * *** *** TOT *** *** The critical values for the first two columns are 3.96, 3.41, and 3.12 for the 1%, 5%, and 10% levels of significance. For the second two columns, the critical values are 3.43, 2.86, and A single * indicates significant at the 10% level, ** indicates 5%, and *** indicates 1%. The number of lags is 12. All variables are seasonally adjusted. 35% of retail sales of electricity, commercial 32%, industrial 29%, and other 3% (Monthly Energy Review, April 2002). That energy usage and industrial production move together over time is not surprising. At issue here is whether fluctuations in industrial production from trend towards a booming economy or towards a recession bring about predictable changes in energy usage. Thus, the issue of how to properly detrend energy usage and industrial production must be addressed. To examine this issue, Dickey and Fuller (1981) augmented unit root tests are conducted on all variables. Tests are conducted using 12 lags and the energy usage data are deseasonalized by using the residual from a regression of energy usage on 12 monthly dummies. 5 Because the variables trend upwards in the sample, the Dickey and Fuller tests allow for a deterministic trend in the alternative hypothesis. However, tests where only a constant is included are also presented. The results of these tests are shown in Table 1. The variables shown in the table are industrial production (IP), and residential (RES), commercial (COM), industrial (IND), other (OTH), and total (TOT) energy usage. As can be seen from the table, the null of a unit root is not rejected in any case at the 5% level of significance. The presence of a second unit root is rejected at a high level of significance in every case. Thus, all of the variables used in the econometric model appear to have a single unit root. However, because these tests are known to have low power, particularly when the span of the data is relatively short, these results are not necessarily conclusive. Thus, as a robustness check, all of the estimation is conducted using two models, one assuming a stochastic trend, the other a deterministic trend. 6 Because electricity usage and industrial production both appear to contain unit roots, that is they are both integrated variables of order one, the possibility that they share a common trend, or are cointegrated, must be investigated. This information will be used to 5 The number of lags was determined using the Akaike (1970, 1974) Information Criterion (AIC) both with and without seasonally adjusting the energy data, and with and without differencing the data. The lag length results were not sensitive to seasonal adjustment or differencing. The unit root tests are robust to different specifications of the lag length and to seasonal adjustment of energy usage. 6 A third model is also examined as discussed below.

6 468 M. Thoma / Energy Economics 26 (2004) Table 2 Co-integration tests IP, RES IP, COM IP, IND IP, OTH IP, TOT The critical values are 3.43, 2.86, and 2.57 for the 1%, 5%, and 10% levels of significance. A single * indicates significant at the 10% level, ** indicates 5%, and *** indicates 1%. All variables are seasonally adjusted. determine if a standard VAR in differences is appropriate, as it would be if the variables are not cointegrated, or whether an error correction model is the appropriate specification. In the bivariate model used here, the cointegration tests are very simple and amount to a linear regression of one of the variables on the other, and then testing for the presence of a unit root in the estimated residuals using a Dickey and Fuller test (see Engle and Granger, 1987). If a unit root is present in the residuals, the null of cointegration is rejected. The outcome of these tests is summarized in Table 2. 7 The results presented in the table do not show, somewhat surprisingly, any evidence of cointegration between industrial production and energy usage. However, as a check of the robustness of the results, a model in levels is also estimated since levels models contain both differenced models and error-correction models as special cases. Overall, the unit root and co-integration tests indicate that a VAR model in differences is the preferred model for examining causal relationships, a result that is robust to the number of lags used in the tests, and whether or not the energy data is seasonally adjusted. However, in recognition of the low power of unit root tests when the span of the data is relatively short, a VAR model in levels that includes a deterministic time trend is also estimated. In addition, as a robustness check against co-integration, a model in levels without a deterministic trend that contains differences and error-correction specification as special cases is also used to examine causal relationships. 3. The econometric model and estimation The following three models are estimated: VAR in Differences DY t ¼ a 0 þ Xk a Y j DY t j þ Xk a E j DE t j þ l Y t ð1þ DE t ¼ b 0 þ Xk b Y j DY t j þ Xk b E j DE t j þ l E t 7 The results do not change if the data is not seasonally adjusted.

7 M. Thoma / Energy Economics 26 (2004) VAR in Levels with trend Y t ¼ a 0 þ a 1 t þ Xk a Y j Y t j þ Xk a E j E t j þ l Y t ð2þ E t ¼ b 0 þ b 1 t þ Xk b Y j Y t j þ Xk b E j E t j þ l E t VAR in Levels Y t ¼ a 0 þ Xk a Y j Y t j þ Xk a E j E t j þ l Y t ð3þ E t ¼ b 0 þ Xk b Y j Y t j þ Xk b E j E t j þ l E t where Y t is the log of industrial production, E t is the log of total electrical energy usage, or one of the sub-categories of residential usage, commercial usage, industrial usage, or other usage, DY t is the change in the log of industrial production, and DE t is the change in the log of total electrical energy usage or one of the sub-categories. The number of lags, k, is Results The results from Granger (1969) causality tests are presented in Table 3. The table shows the F-statistics for causality from industrial production to residential, commercial, industrial, other, and total energy usage. Causality for each of the three models (Eqs. (1), (2), and (3)) are shown. The results are consistent across the three models and show that there is significant causality from industrial production to commercial, industrial, and total electrical energy usage. Causality is insignificant from industrial production to residential and other electrical energy usage. Thus, changes in macroeconomic conditions have significant impacts on the industrial and commercial sectors which account for approx- Table 3 F-statistics and P-values for causality tests from IP to energy usage Differences model (1) Levels model with trend (2) Levels model (3) RES (0.1358) (0.4724) (0.4630) COM *** (0.0015) *** (0.0010) *** (0.0015) IND *** (0.0000) 5.509*** (0.0000) *** (0.0000) OTH (0.3628) (0.6313) (0.3514) TOT *** (0.0001) *** (0.0000) *** (0.0000) A single * indicates significant at the 10% level, ** indicates 5%, and *** indicates 1%. P-value in parentheses.

8 470 M. Thoma / Energy Economics 26 (2004) imately 60% of energy usage, as well as overall, but do not affect residential and other electrical usage. An implication of these results is that during an economic downturn, the commercial and industrial sectors will experience significant declines in energy usage. During an economic boom, these sectors will increase their energy usage significantly. Thus, efforts to forecast energy usage over the business cycle with the aim of ensuring adequate supplies during economic boom periods should focus attention on predicting variation in usage over the business cycle in the commercial and industrial sectors. In addition, the sectoral composition of output is important. If the sectoral composition of aggregate output changes over time, either from structural change or business cycle variation, the results indicate that sectoral change affecting the industrial or commercial sectors in particular will have the largest impact on energy usage. Table 4 shows reverse causality from electricity usage by sector and in total to industrial production. Interestingly, there is no significant relationship between shocks to energy usage and subsequent changes in industrial production for any of the three econometric models examined here. To examine how important macroeconomic fluctuations are in explaining variation in electrical energy usage, variance decompositions are presented in Table 5. The table shows the percentage of the variance of each sector s electricity usage explained by shocks to industrial production at horizons of 1, 4, 8, 12, 24, 48, and 60 months. Results for (1), (2), and (3) are presented. Note that the variance decompositions for model (1) are for the growth rate in each sector s electricity usage while the results for models (2) and (3) are for the variance in the level of electrical usage. Thus, the results for model (1) are not directly comparable to those in models (2) and (3). To overcome this, the differences model was estimated, transformed into a levels representation, and the variance decompositions for the levels calculated. These results are in parentheses and are listed beside the results for the differences model (Eq. (1)). With the results for model (1) expressed in levels, the percentage of the variance in electrical usage for each sector explained by shocks to industrial production are fairly consistent across (1), (2), and (3). For example, consider the commercial and industrial sectors, and the results for total usage, the three results for which F-statistics indicated significant causality from industrial production to electrical energy usage. At the 60-month horizon, the percentage of the variance in commercial usage explained by industrial production is 20% for model (1) expressed in levels, 12% for model (2), and 9% for model (3). The figures for industrial usage are 47% for model (1) expressed in levels, 54% for model (2), and 77% for model (3). The results from (1), (2), Table 4 F-statistics and P-values for causality tests from energy usage to IP Differences model (1) Levels model with trend (2) Levels model (3) RES (0.3430) (0.4451) (0.2384) COM (0.4959) (0.3797) (0.1726) IND (0.4846) (0.3910) (0.5438) OTH (0.7964) (0.8312) (0.5336) TOT (0.4312) (0.4098) (0.3109) A single * indicates significant at the 10% level, ** indicates 5%, and *** indicates 1%. P-value in parentheses.

9 M. Thoma / Energy Economics 26 (2004) Table 5 Variance decompositions, percentage of the variance of the listed variable explained by industrial production Steps Residential Commercial Industrial Other Total Model (1) differences (levels) (3.70) 4.27 (4.27) 7.67 (7.67) 0.02 (0.02) 6.05 (6.05) (3.99) 4.68 (3.57) (28.63) 0.80 (2.75) 5.61 (9.51) (5.23) 4.72 (5.12) (46.21) 1.48 (4.15) 5.99 (15.10) (7.50) 6.45 (12.39) (49.40) 1.92 (4.93) 6.36 (24.99) (7.34) 7.07 (14.52) (48.62) 2.49 (10.07) 6.45 (28.94) (7.48) 7.12 (18.72) (47.36) 2.57 (14.20) 6.51 (33.65) (7.58) 7.13 (20.00) (47.10) 2.57 (15.23) 6.51 (35.15) Model (2) levels with trend Model (3) levels (1), (2), and (3) are defined in the text. Data are seasonally adjusted. The results for model (1) in parentheses are for the levels representation implied by the estimated differences model. and (3) for total usage are 35%, 27%, and 32%. For the two sectors where causality as assessed by F-statistics is insignificant, residential and other, the percentages are 8%, 9%, and 14% for residential usage and 15%, 5%, and 14% for other usage in (1), (2), and (3) at the 60-month horizon. 8 Finally, the results are further elucidated by examining the impulse responses of electrical energy usage arising form a shock to industrial production. These results are presented in Figs Each graph shows the response of electrical energy usage to a shock to industrial production along with two standard deviation confidence bands. 9 Fig. 1 shows the response of residential electrical energy usage after a shock to industrial production. There is a significant positive response in the first 2 months 8 The variance decomposition results for differences, i.e. from model (1), are generally smaller than for the levels models. This is expected as it is generally the case in VAR models. 9 The impulse responses for models (1) and (3), the differences and levels models, are very similar when the differences responses from model (1) are accumulated into levels. The responses for model (2), the model with a deterministic trend, differ from those for models (1) and (3). The two standard confidence bands are based on 100,000 replications.

10 472 M. Thoma / Energy Economics 26 (2004) Fig. 1. Impulse response of residential electricity usage to a shock to industrial production. after the shock, and some evidence of significant responses around months and months 21 23, but the most significant and noteworthy response is in the first 2 months immediately following the shock when residential electrical energy usage increases. Fig. 2 shows the impulse response for the commercial sector. The impulse response for the commercial sector due to a shock to industrial production follows a pattern similar to the response of the residential sector. In the first month following the shock Fig. 2. Impulse response of commercial electricity usage to a shock to industrial production.

11 M. Thoma / Energy Economics 26 (2004) Fig. 3. Impulse response of industrial electricity usage to a shock to industrial production. to industrial production, there is a significant increase in energy usage, and some evidence of a significant response, though not as strong as the initial response, at months Fig. 3 illustrates the impulse response of industrial electricity usage in response to a shock to industrial production. The response is positive and highly significant over the entire 60-month horizon shown in the graph. There is an initial positive response that increases for the first 6 months after the shock, then levels off and trends gently downward after 6 months. 10 Fig. 4 shows the impulse response for other usage. The response is very small and insignificant over the 60-month horizon shown in the graph indicating that other electrical usage does not show any significant response to shocks to industrial production. Finally, Fig. 5 shows the response of total energy usage to industrial production shocks. The response is positive, fairly level though it does trend downward slightly, and significant over the first 26 months after the shock. Overall, the results indicate that a shock to industrial production will significantly increase electricity usage in the residential, commercial, and industrial sectors in the 10 The most recent peak in industrial production was in June of 2000 when it was The most recent trough was in December 2001 when it was Using the June 2000 figure as the base, this represents a 7.14% fall in industrial production. The largest impulse response of industrial production over the 60-month horizon is billion kw h (Fig. 3 shows the log of industrial electricity usage, this figure is for the actual industrial sector usage, i.e. for the unlogged value). The shock is a due to a 1% change in industrial production. This means that a 7.14% change in industrial production will decrease energy usage in the industrial sector by billion kw h, a decline in mean monthly usage of 9.84%. Thus, a 1% decline in industrial production results in a 1.38% decline in industrial electricity usage. The corresponding figures for the other sectors are similar in magnitude.

12 474 M. Thoma / Energy Economics 26 (2004) Fig. 4. Impulse response of other electricity usage to a shock to industrial production. first month or two following a shock, and that the significant positive response will continue in the industrial sector for several years following the shock. For the other energy usage sector, the response is insignificant in all time periods. When all sectors are combined into total energy usage, the picture that emerges is a significant and positive response for the first 26 months following the shock. Fig. 5. Impulse response of total electricity usage to a shock to industrial production.

13 M. Thoma / Energy Economics 26 (2004) Causality results across spectral frequency bands In previous sections, the time-series properties of the data are carefully examined and causality from aggregate output to commercial, industrial, and total energy usage is established through Granger causality tests, impulse response functions, and variance decompositions. That Granger causality from macroeconomic variables to energy usage can be established is not particularly surprising and forecasting models for energy usage often implicitly assume a causal relationship between macroeconomic conditions and energy usage in the forecasting equations. It is also implicitly assumed that the relationship between movements in macroeconomic variables and energy usage is due to business cycle variation in the data. However, to date, no studies examine the cyclical frequency at which the relationship between aggregate output and energy usage exists, an important consideration in, for example, demand management strategies. Given that a causal relationship exists, what types of fluctuations underlie it, high frequency monthly variation or low frequency business cycle variation? If the relationship is due to cyclical variation in the data of, say, 3 or 4 months, then the policies to manage demand will be different from strategies designed to manage annual variation or business cycle frequency variation. Which frequency movements in the measures of aggregate activity and energy usage are responsible for the causality results? Following the methodology set forth in Thoma (1992, 1994), the procedure used to answer this question is to transform the data to the frequency domain, zero out some of the frequencies, transform the data back to the time domain, perform causality tests, and compare the tests to the baseline, unfiltered results. Following Engle (1974, 1978), define the row vector w k as w k ¼ð1; e ih k ; e 2ih k ; :::::: ; e ðt 1Þih k Þ ð4þ where h k =2pk/T. Now, consider a particular element of the vector Z t, say Y t. Let Y=[ Y 0, Y 1,..., Y T 1 ] T, and define Ỹ = WY where W=[w 0, w 1,..., w T 1 ] T. Ỹ is an element vector with complex entries, each of which corresponds to a different frequency. The objective is to exclude some of the frequencies from Ỹ. To accomplish this, construct a T T matrix S, where S has ones on the diagonal elements corresponding to included frequencies and is zero elsewhere, and obtain SỸ Finally, define Y*=W y SWY = W y SỸ where y means the complex conjugate of the transpose. This is the inverse Fourier transform of SỸ. The next step is to let Z t Y* =[ Yt *, E t ] T. Then write the new VAR model: Z Y t * ¼ XJ A j Z Y* t j þ u t ð5þ This is the VAR model with designated frequencies removed from one of the variables, in this case from Y. This model is estimated with cycles from 2 to 48

14 476 M. Thoma / Energy Economics 26 (2004) months removed from income or energy usage 11 and the F-statistics for causality are compared to the significant baseline results from Table 3, i.e. those for commercial, industrial, and total energy usage. 12 If the excluded frequencies are responsible for the causality results, the F-statistics from model (5) should drop below the baseline results from Table The causality statistics are presented in Figs. 6 8 where cycles from 2 to 48 months in duration are removed one at a time from industrial production and energy usage. The results are plotted on a diagram with the F-statistics for causality on the vertical axis, and the period of the cycle removed on the horizontal axis (the baseline results from Table 3 and 5% significant lines are also shown as horizontal lines in the diagrams, the baseline result is the uppermost line and the 5% level the line below it). 14 Fig. 6 shows the results for the difference model (Eq. (1)). The left-hand side of Fig. 6 shows the effects of removing cycles from commercial energy usage, industrial energy usage, and total energy usage. The results are very clear and very consistent across the three measures of energy usage. Removing cycles from 2 to 22 months causes a slight fall in the F-statistics for commercial and total energy usage, and removing cycles from 12 to 22 months results in a slight decline in the F-statistics for industrial energy usage, but it is cycles from approximately 23 to 30 months that cause the largest fall in the F-statistics, enough so that the F-statistics become insignificant around 25-month cycles for all three measures of energy usage. The statistics remain insignificant when cycles longer than 30 months are removed. Thus, the main affect of variation in industrial production is to produce cycles in energy usage of 22 or longer, cycles consistent with a business cycle interpretation. It is possible for both high and low frequency cycles in industrial production to produce either high or low frequency cycles in energy usage. What frequency cycles in industrial production are responsible for the month cycles in energy usage? The right-hand side of Fig. 6 shows how the F-statistics change as cycles are removed one at a time from industrial production. The results are very consistent across the different measures of energy usage. When cycles from approximately 2 to 22 months are removed, the F-statistics are not much affected. The F-statistics for industrial energy usage increase slightly indicating that these cycles are noise that obscure the causal relationship, and the F-statistics for commercial and total usage stay very close to the unfiltered, baseline result. Removing cycles from 22 to 35 months causes the F-statistics to decline rapidly and become insignificant, and from 36 months onward the F-statistics increase slightly then level off very near the 5% significance line. Overall, the results for the differences model (Eq. (1)) are very consistent and very clear. Cycles of 23 months or longer in industrial production cause cycles of 23 months or 11 The bandwidth of the excluded frequencies is 0.01 of a cycle. Both the fundamental and harmonic frequencies are excluded. 12 Geweke (1984) presents a decomposition of directional linear feedback by frequency. The procedures developed in Thoma (1992, 1994), which are similar to Engle (1974, 1978), are much easier to apply. 13 As noted in Thoma (1992), Monte Carlo simulations show that filtering cycles from the data in this manner does not affect the distribution of the test statistics for causality under the null hypothesis. 14 The F-statistics shown in the figures are smoothed using a symmetric rectangular window of width five. The smoothed statistics are superimposed upon the raw statistics to give an indication of the local movement in the F-statistics.

15 M. Thoma / Energy Economics 26 (2004) Fig. 6. Band spectral regression-differences model. (a) Model: COM cycles removed from COM. (b) Model: COM cycles removed from IP. (c) Model: IND cycles removed from IND. (d) Model: IND cycles removed from IP. (e) Model: TOT cycles removed from TOT. (f) Model: TOT cycles removed from IP. longer in energy usage. Thus, the causality results in Table 3 arise primarily from business cycle fluctuations in industrial production producing similar cycles in energy usage. There is some indication of higher frequency cycles in commercial energy usage and in total

16 478 M. Thoma / Energy Economics 26 (2004) energy usage (see Fig. 6a and e) also arising from low frequency cycles in industrial production, but the relationship appears strongest a business cycle frequencies. Figs. 7 and 8 show the results for models (2) and (3), the levels model with a trend term included, and the levels model with no trend. As in Fig. 6, the left-hand side shows the results of removing cycles from the measures of energy usage and the right-hand side the results from removing cycles from industrial production. The results differ from those obtained from the differences model. 15 Removing cycles from the energy usage measures in the levels model with a trend, as shown on the left-hand side of Fig. 7, cause an immediate and substantial decline in the F-statistics. In Fig. 7a which shows the result for commercial usage, the F-statistic falls below the 5% significance level when 2-month cycles are removed, level off at the lower level for cycles from 3 to 15 months, then increase back to the baseline result from 13- to 24-month cycles, then decline again for cycles 25 months or longer. This indicates that industrial production causes both high frequency (2 to 12 month) cycles and low frequency (25 months or longer) cycles in commercial energy usage. Fig. 7c shows the results for industrial energy usage. In this case, the F-statistics decline rapidly when cycles from 5- to 12-month cycles are removed, then level off thereafter at the lower level. This indicates that changes in industrial production induce cycles of 6 months or longer in duration in industrial energy usage. The results for total energy usage in Fig. 7e reflect the results for the commercial and industrial sectors and show that industrial production causes cycles 2 months or longer in energy usage. Overall, industrial production causes much higher frequency cycles in energy usage for the model with the trend term included than is evident in the differences model results shown in Fig. 6. The right-hand side of Fig. 7 shows the frequency of the cycles in industrial production that cause the high frequency variation in energy usage. Fig. 7b shows the effects on causality from industrial production to commercial energy usage from removing cycles from industrial production. The figure shows that 8 32-month cycles in industrial production are behind the causality results. When 2 7-month cycles are removed the F-statistics remain near the baseline result, the F-statistics decline from 8 to 15 months, level off, then increase back to baseline from 23 to 32 months. Thus, Fig. 7a and b taken together implies that 8 32-month cycles in industrial production cause 2 to 12 and 25 month or longer cycles in commercial energy usage. In Fig. 7d and f, the results on causality statistics for industrial and total energy usage from removing cycles from industrial production are very similar. In both figures, the F- statistics begin declining immediately reaching a minimum at around 12 months and level off or increase slightly from 12 months onward. This indicates that cycles 2 months are longer cause the cycles in energy usage. More particularly, cycles of 2 months or longer cause cycles 6 months or longer in industrial energy usage, and cycles 2 months or longer cause cycles 2 months or longer in total energy usage. Finally, Fig. 8 shows the results for the levels model. When cycles are removed from industrial production, as shown on the right-hand side of the figure, the results are nearly identical to the levels model with trend. There are differences when cycles are removed 15 Recall that the impulse responses discussed above for the levels and differences model are similar, while the trend model produces different results.

17 M. Thoma / Energy Economics 26 (2004) Fig. 7. Band spectral regression-levels model with trend. (a) Model: COM cycles removed from COM. (b) Model: COM cycles removed from IP. (c) Model: IND cycles removed from IND. (d) Model: IND cycles removed from IP. (e) Model: TOT cycles removed from TOT (f) Model: TOT cycles removed from IP. from the measures of energy usage as shown on the left-hand side of the figure. Fig. 8a and b together shows that cycles from 8 to 32 months in industrial production cause cycles from 2 to 12 months and 24 months or longer in commercial energy usage. Fig. 8c and d together indicates that cycles 2 months or longer in industrial production cause cycles from

18 480 M. Thoma / Energy Economics 26 (2004) Fig. 8. Band spectral regression-levels model. (a) Model: COM cycles removed from COM. (b) Model: COM cycles removed from IP. (c) Model: IND cycles removed from IND. (d) Model: IND cycles removed from IP. (e) Model: TOT cycles removed from TOT. (f) Model: TOT cycles removed from IP. 5 to 12 months and 16 months or greater in industrial energy usage. The results for total energy usage are very similar. Fig. 8e and f shows that cycles 2 months or longer in industrial production cause cycles from 2 to 12 months and 16 months or longer in total energy usage.

19 M. Thoma / Energy Economics 26 (2004) Overall, the implication of the results depends upon which of the three models, differences, linear trend, or levels is used. For the differences model, which is supported above as the best fit for the data, the implication is that the association between industrial production and energy usage is low frequency and consistent with a business cycle interpretation. For the trend and levels model, there is evidence of a high frequency association and, in most cases, a low frequency association as well. Thus, the levels and trend models support a business cycle interpretation as well as a higher frequency association between the variables. Summarizing, the causal relationship between growth rates of industrial production and energy usage appears to be due to business cycle frequency movements in both variables, while causality between the level of these variables or the deviation of the variables from trend occurs at higher frequencies as well as at business cycle frequencies. Thus, all models support the idea of a low frequency association, but in the levels and trend models the relationship is not exclusively low frequency as it is with the differences model. 6. Asymmetries in causality over the business cycle The previous section establishes that there is a relationship between business cycle frequency variation in industrial production and similar frequency movements in energy usage. However, this does not establish that there are significant changes in peak energy usage arising from variation in aggregate output. That is, it is possible that the significant causal relationship between industrial production and energy usage is from an association between the variables at the midpoint or the trough of business cycles and not at the peak. If the relationship does vary over the business cycle, then this is important for forecasting energy usage for peak load planning because this implies that small changes in industrial production, either up or down, near the peak of cycles does not significantly affect energy usage. Instead, a decline in energy usage would only occur if there was a large change industrial production, e.g., a movement back to trend or lower. However, if there is a significant relationship between peak energy usage and variation in industrial production, then peak load planning can make use of this information. In particular, forecasting models can be amended to allow the coefficient capturing the relationship between aggregate output and energy usage to vary over the business cycle thereby improving the efficiency of the forecasts and the efficacy of demand management policies. To examine potential asymmetries over the business cycle, a forecasting model for peak, average, and trough energy usage for each year in the sample is estimated. After examining a variety of models, the following model was chosen E j t ¼ b 0 þ b 1 E j t 1 þ b 2Y t þ b 3 P E t þ b 4 FF t þ e t ð6þ where E t j is the log of either peak energy usage, mean energy usage, or minimum energy usage over the year in sector j, Y t is the log of industrial production, P t E is the log of the producer price index for energy, and FF t is the federal funds rate. This equation includes variables typically included in forecasting models designed to capture the effects of macroeconomic variables on energy usage. All data is annual and for the same range as

20 482 M. Thoma / Energy Economics 26 (2004) Table 6 Significance of IP in the forecasting equation Max Mean Min RES (0.021) (0.156) (0.159) COM (0.111) (0.109) (0.304) IND (0.006) (0.011) (0.010) OTH (0.000) (0.002) (0.223) TOT (0.016) (0.013) (0.011) The table shows the t-statistics. Significance level in parentheses. above, The sectors are as above, residential, commercial, industrial, other, and total energy usage. Thus, 15 forecasting models are estimated. That is, for each of the five sectors there is one model for peak usage, one for average energy usage, and one for minimum usage. 16 The results are summarized in Table 6. The table shows the t-statistics for b 2, the coefficient on industrial production in the forecasting equations, along with the p-values. Thus, the table shows the extent to which variation in industrial production explains peak, average, and minimum energy usage in each sector. Examination of the table shows that the significance level is generally higher for maximum energy usage than for mean energy usage, and the significance level for mean energy usage is generally higher than for minimum energy usage as evidenced both by the number of sectors exhibiting significant coefficients and from the p-values. When peak annual energy usage is the dependent variable, the coefficient on industrial production is significant at the 5% level for residential, industrial, other, and total usage. Only the coefficient for the commercial sector is insignificant, but even here the p-value is.11. For average energy usage, the coefficient on industrial production is significant for industrial, other, and total usage, but not for commercial and residential usage. Finally, for minimum annual energy usage, there is significance for the industrial and total energy usage sectors. Residential, commercial, and other energy usage are not significantly related to industrial production. Thus, moving from minimum to maximum energy usage increases the number of sectors with significance. Furthermore, there is generally an increase in the significance level as well. Thus, importantly for peak load planning and demand management, the results indicate that causality from industrial production to energy usage arises mainly from changes in energy at the peak of cycles rather than at the midpoint or troughs. 17 Forecasting equations designed to identify future periods of high-energy usage commonly include a measure of aggregate output in the specification. These results imply that the models should also 16 The results are similar if the 3-month treasury bill secondary market rate is used instead of the federal funds rate, and if disposable income is used instead of industrial production. Serial correlation is eliminated by the presence of the lagged dependent variable on the right-hand side of the equation. Adding lagged values of industrial production, the producer price index for energy, and the federal funds rate does not change the results but does lower the significance levels as would be expected from adding insignificant variables to the equation. Estimation by IV, where lagged values of right-hand side variables are used as instruments, does not appreciably change the results. 17 Had the result been reversed, then changes in macroeconomic conditions would not need to be accounted for in peak load planning.

21 M. Thoma / Energy Economics 26 (2004) allow the coefficient measuring the effect of output on energy usage to vary over the business cycle to produce the best possible forecasts. 7. Conclusion The electrical energy crisis in California in the summer of 2000 resulted in rolling blackouts due to insufficient supply. At the time, there was speculation that an economic slowdown that appeared to be on the horizon would alleviate, if not eliminate the problem giving the state time to ensure adequate future supplies. However, little empirical evidence exists on the relationship between changes in the state of the macroeconomy and changes in energy usage. This paper shows that some sectors of the economy, in particular the commercial and industrial sectors which account for approximately 60% of total electrical energy usage, are responsive to variations in aggregate output as measured by industrial production, a result documented using F-tests, variance decompositions, and impulse response functions. The results also demonstrate that it is business cycle fluctuations in the data that produce these results and that causality is asymmetric and stronger at the peak of cycles than at the troughs. An implication of these results is that during an economic downturn from a peak, the commercial and industrial sectors will experience significant declines in energy usage. During an economic boom, these sectors will increase their energy usage significantly. Thus, efforts to forecast energy usage over the business cycle with the aim of ensuring adequate supplies during economic boom periods should focus attention on predicting variation in usage over the business cycle in the commercial and industrial sectors. The results also imply that the sectoral composition of output is important. To the extent that the sectoral composition of aggregate output changes over time, either from structural change or business cycle variation, the results of this paper indicate that changes in the sectoral composition affecting the industrial or commercial sectors will have the largest impact on energy usage and thus should guide forecasts of future energy demand. Electrical utility demand side management programs can be placed into three broad categories, conservation programs, load management programs, and strategic load growth programs. Conservation programs reduce energy use through means such as programs to improve the efficiency of equipment (lighting and motors, for example), buildings, and industrial processes. Load management programs redistribute energy demand to spread it more evenly throughout the day, week, year, or over the business cycle, e.g., load shifting programs (reducing air conditioning loads during periods of peak demand and shifting these loads to less critical periods), time-of-use rates (charging more for electricity during periods of peak demand), and interruptible rates (providing rate discounts in exchange for the right to reduce customers electricity allocation during the few hours each year with the highest electricity demand). Strategic load growth programs increase energy use during some periods, e.g., programs that encourage cost-effective electrical technologies that operate primarily during periods of low electricity demand. The results of this paper can be used to assist in the development of load management and strategic load growth strategies such as time-of-use rates, interruptible rates, load shifting rates, as an aid to the design of