Long memory in US disaggregated petroleum consumption: Evidence from univariate and multivariate LM tests for fractional integration

ARTICLE IN PRESS Energy Policy 37 (2009) 3205–3211

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Long memory in US disaggregated petroleum consumption: Evidence from univariate and multivariate LM tests for fractional integration Hooi Hooi Lean a, Russell Smyth b, a b

Economics Program, School of Social Sciences, Universiti Sains Malaysia, Malaysia Department of Economics, Monash University, Australia

a r t i c l e in fo

abstract

Article history: Received 7 January 2009 Accepted 7 April 2009 Available online 9 May 2009

Previous studies that have tested for a unit root in aggregate energy consumption have potentially reached misleading conclusions because they fail to allow for the possibility that energy consumption might be fractionally integrated and do not distinguish between different types of energy consumption. This study tests for long memory in disaggregated petroleum consumption in the United States using univariate and multivariate Lagrange multiplier (LM) tests for fractional integration. The results point strongly to the need to distinguish between different forms of energy consumption and allow for a generalization of the I(0)/I(1) dichotomy when considering the order of integration of energy consumption. Allowing for short-run dynamics, the univariate test suggests that less than 50% of the series are fractionally integrated. Consistent with expectations the non-stationary series are found to have the highest mean and standard deviation. The multivariate test suggests that petroleum consumption in the commercial and industrial sectors is clearly fractionally integrated when allowing for short-run dynamics, and, as such, exhibits persistent effects, while petroleum consumption in the residential sector is a stationary process. & 2009 Elsevier Ltd. All rights reserved.

Keywords: Energy consumption Fractional integration Long memory

1. Introduction There is an emerging literature that tests for a unit root in energy consumption. Some studies have used univariate unit root tests with and without structural breaks (see e.g. Altinay and Karagol, 2004; Lee and Chang, 2005; Narayan and Smyth, 2005). Other studies have used panel unit root tests with and without structural breaks (see Al-Iriani, 2006; Chen and Lee, 2007; Hsu et al., 2008; Joyeux and Ripple, 2007; Lee, 2005; Lee and Chang, 2008; Mishra et al., 2009; Narayan and Smyth, 2007). There are related literatures that test for a unit root in energy production (Maslyuk and Smyth, 2009; Narayan et al., 2008) and for a unit root in energy spot and futures prices (see e.g. Elder and Serletis, 2008; Serletis, 1992; Lee and Lee, 2009; Maslyuk and Smyth, 2008). Whether energy consumption is stationary or contains a unit root is important for several reasons, which are now well documented in the literature (see e.g. Hsu et al., 2008, pp. 2317–2318; Lee and Lee, 2009, p. 469; Mishra et al., 2009, pp. 2318–2319). First, if energy consumption is stationary, shocks to energy consumption will be temporary; however, if energy consumption contains a unit root, shocks to energy consumption will have

 Corresponding author.

E-mail address: [email protected] (R. Smyth). 0301-4215/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.enpol.2009.04.017

persistent effects. Second, if shocks to energy consumption are persistent, given the importance of energy to other sectors in the economy, key macroeconomic variables can be expected to inherit that persistence. Third, whether key macroeconomic variables are stationary has important implications for alternative economic theories, which suggest different conclusions on the issue of the desirability and efficacy of government intervention through the use of macroeconomic stabilization policies. Fourth, the analysis in this article addresses sectoral energy use, which implies that our findings are also relevant for industrial policies and firm level strategies (i.e. investment in renewable energy sources) as well as macroeconomic policies. Fifth, the issue of whether energy consumption is stationary has important implications for modelling. The correct approach to modelling, for example, energy demand or Granger causality between energy consumption and real output, which both have important policy implications, depend on whether energy consumption contains a unit root. Fifth, the issue of whether energy consumption is stationary has important implications for forecasting energy consumption. If energy consumption is stationary, it is possible to forecast future movements in energy consumption based on past behaviour. However, if energy consumption is non-stationary then past behaviour is of no value in forecasting future demand and one would need to look at other variables explaining energy consumption in order to generate forecasts of energy demand into the future.

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Studies have reached mixed conclusions about whether energy consumption is stationary. The results from univariate unit root tests have failed to reach a consensus (see Chen and Lee, 2007 for a review). Among studies that have employed panel data tests, Lee (2005), Joyeux and Ripple (2007) and Narayan and Smyth (2007) find evidence of a panel unit root, Chen and Lee (2007) and Mishra et al. (2009) find evidence of panel stationarity and Hsu et al. (2008) reach different conclusions according to regional panels. These inconclusive findings might reflect two limitations with the extant literature, which this paper seeks to address. First, the existing literature uses data on aggregate energy consumption, but different forms of energy consumption might exhibit different types of unit root behaviour. Yang (2000) argued that the use of aggregate energy data does not capture the degree to which different countries or industries depend differently on energy. The use of disaggregated data facilitates comparisons of relative energy intensities across uses by energy source (Ewing et al., 2007; Sari, et al., 2008). In the specific context of testing for a unit root in energy consumption, some end users are large consumers, while others are less so. Energy consumption is more likely to be non-stationary in sectors that are large consumers. The rationale is that for large consumers, shocks will generate a bigger deviation from the long-run equilibrium path, resulting in a higher level of persistence (Hsu et al., 2008). Second, some forms of energy consumption might be more volatile or more prone to disruption. Forms of energy and/or end users which experience high volatility in energy consumption are more likely to be associated with non-stationary energy consumption. The reasoning is that for forms of energy use and/or end users that experience high volatility in energy consumption, deviations from the long-run equilibrium path, due to shocks that create volatility in the first place, will be larger. Thus departure from the equilibrium path will be less likely to be temporary (see Maslyuk and Smyth, 2009; Mishra et al., 2009; Narayan et al., 2008). Second, the existing literature fails to consider that energy consumption might be a long memory, fractionally integrated process. The presence of long memory can be defined from an empirical data-oriented approach in terms of the persistence of autocorrelations. The extent of the persistence is consistent with essentially a stationary process, but where the autocorrelations take much longer to decay than the exponential rate associated with the ARMA class (Baillie, 1996). Chen and Lee (2007) attribute failure to reject the unit root in energy consumption in some studies to failure to take account of the existence of structural break(s), which lowers the power of conventional tests (see Perron, 1989). However, equally, it is well known that standard unit root tests, such as the Augmented Dickey-Fuller test, have low power if the alternatives are of a fractional form (see e.g. Diebold and Rudebusch, 1991; Hassler and Wolters, 1995; Lee and Schmidt, 1996; Caporale and Gil-Alana, 2008). Fractional integration was first observed by statisticians in the natural sciences in areas as diverse as climatology, geophysics and hydrology (see e.g. Hurst, 1951, 1957; Mandelbrot and Wallis, 1968; Mandelbrot, 1972; McLeod and Hipel, 1978). Testing for fractional integration in econometrics is a more recent phenomenon dating from the 1980s (Baillie, 1996). Several studies exist, testing for fractional integration in macroeconomic variables. These include studies for gross domestic product (Diebold and Rudebusch, 1989, 1991; Gil-Alana, 2002b, 2003), inflation (Baillie et al., 1996; Kumar and Okimoto, 2007), exchange rates (Diebold et al., 1991; Baillie, 1996; Gil-Alana, 2002a), stock prices (Assaf, 2007) and unemployment (Caporale and Gil-Alana, 2008; Gil-Alana, 2002b). There are also a series of studies in the tourism economics literature, testing for fractional integration in international tourist arrivals for a range of countries including Spain and the United States (Cunado et al., 2004, 2008; Gil-Alana et al.,

2004). There is only one related study in the energy unit root literature. Elder and Serletis (2008) test for fractional integration in energy futures prices and find evidence that energy future prices are long memory processes. While much of the literature that has tested for a unit root in energy consumption has emphasised the role of persistence of shocks, testing for the presence of unit roots in autoregressive representations of univariate and vector processes that are integrated of order zero (I(0)) and integrated of order one (I(1)) can be far too restrictive. Fractionally integrated processes represent a halfway house between I(0) and I(1) paradigms (Baillie, 1996). Moreover, fractional integration provides a means to isolate persistence that is not consistent with either I(0) or I(1) processes. For this reason, fractional integration can be considered a generalization of the I(0)/I(1) dichotomy (Kumar and Okimoto, 2007). Apart from the fact that fractional integration provides a more general framework to consider whether there is persistence in energy consumption, another reason for considering fractional integration is increasing evidence of non-linearities in energy markets. Serletis and Gogas (1999) tested for deterministic chaos in seven Mont Belview Texas hydrocarbon markets – crude oil, natural gas, ethane, propane, normal butane, iso-butane and naptha – and find evidence consistent with a chaotic non-linear process in the five natural gas liquid markets. More recently, Maslyuk and Smyth (2009) find evidence of non-linearities in crude oil production for 17 OECD and non-OECD countries using monthly data over the period January 1973 to December 2007. Assaf (2007) and Elder and Serletis (2008) note that long memory indicates evidence of non-linear dependence in the first and second moments. This paper applies univariate and multivariate Lagrange multiplier (LM) tests for fractional integration proposed by Nielsen (2005) to monthly data on disaggregated petroleum consumption in the United States over the period January 1973 to July 2008. The univariate LM test for fractional integration is applied to 24 series of alternative forms of petroleum consumption. The multivariate LM test for fractional integration is applied to five sector-based panels. The Nielsen (2005) multivariate LM test for fractional integration generalizes the univariate tests developed by Robinson (1994) and Tanaka (1999) among others. The multivariate fractional integration test has the advantage over the univariate test applied to multiple time series that it is less cumbersome and takes account of potentially important correlations between the elements of the multiple time series (Nielsen, 2005). We employ the Nielsen (2005) LM test for fractional integration in preference to other available multivariate tests for fractional integration such as those proposed by Breitung and Hassler (2002) and Gil-Alana (2003) because evidence from simulation studies reported in Nielsen (2005) suggests that the Nielsen (2005) test performs better in terms of finite sample properties.

2. Disaggregated energy consumption in the United States In the United States expenditure on energy accounts for 7% of gross domestic product (Sari et al., 2008). In 2002, the commercial and residential sectors together accounted for 39.4% of energy consumption, the industrial sector accounted for 33.4% of energy consumption and the transportation sector accounted for 27.2% of energy consumption (Ewing et al., 2007). Approximately 20% of the United States energy needs are imported with petroleum comprising the United States largest imported energy source. This feature means that any disruption in oil production in other parts of the world has the potential to result in significant disruptions to

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the United States economy (Kilian, 2008). If shocks to petroleum production, and disaggregated petroleum consumption, have persistent effects, disruptions to petroleum production and consumption will have persistent effects on the United States economy. In this case, diversification away from petroleum production is most desirable since it would lessen dependence on foreign energy and reduce the effects of oil disruptions on the United States real economy. Such policies would be consistent with the development of renewable technologies and the more efficient use of petroleum products via implementation of demand management policies (Economic Report of the President, 2004). However, if energy production and consumption is an I(0) process, disruptions to petroleum production and consumption will be fleeting and the economy will return to its long-run equilibrium path (Narayan and Smyth, 2007; Narayan et al., 2008). If this is the case, this makes the search for alternatives to petroleum products less pressing.

3. Econometric methodology We employ univariate and multivariate LM tests for fractional integration proposed by Nielsen (2005). Suppose we observe {yt, t ¼ 1, y, n} generated by ð1 þ LÞdþy yt ¼ et IðtX1Þ;

t ¼ 0; 1; 2; . . .

(1)

where I(.) denotes the indicator function and et is I(0); i.e., it is covariance stationary and has spectral density that bounded away from zero at the origin. The process yt generated by Eq. (1) is well defined for all d, where d+y is the fractional order of integration, and is sometimes called a multivariate type II fractionally integrated process. The process in Eq. (1) allows a uniform definition, valid for all d and y, whereas the alternative definition without truncation is valid only for d þ y 2 ð12; 12Þ and partial summation would be needed to generate a process with integration order outside this range. Deterministic terms can be added to Eq. (1), allowing for nonzero mean and trend. In Eq. (1), we assume that d is specified a priori and wish to test the hypothesis H0 : y ¼ 0

(2)

against the alternative H1: ya0. For instance, the unit root hypothesis and the hypothesis of joint stationary (or more precisely, weak dependence) of yt are given by Eqs. (1) and (2) with d ¼ 1 and d ¼ 0, respectively. The objective is to test if an observed K-vector time series yt is integrated of order d, denoted I(d), against the hypothesis that it is I(d+y) for ya0. By differencing the observed time series, this is equivalent to testing if xt ¼ (1L)dyt is I(0) against I(y). To put it in different terms, we test the null hypothesis, H0: I(0), jointly stationary against H1: I(y), fractional integration. The LM statistic, which is chi-squared with one degree of freedom under the null, is LM ¼

P1 trð ^ S10 Þ2 P1 trð ^ M 11 Þ

where S10 ¼

n X

xt1 x0 t ;

xt1 ¼

t¼2

M 11 ¼ S11 þ 12ðS20 þ S0 20 Þ

t1 X j¼1

j1 xtj

S11 ¼

n X

0

xt1 xt1 ;

t¼2

3207

S20 ¼

n X t¼1

0 x t2 x t ;

x t2 ¼

t2 X

j1 xtj1

j¼1

4. Data We examine 24 series of petroleum consumption by five sectors for the United States. The five sectors are residential, commercial, industrial, transportation and electric power. The series are monthly consumption of different petroleum types measured in thousand of barrels per day and are extracted from the Monthly Energy Review of the Energy Information Administration. The sample period covered is from January 1973 to July 2008. The data were transformed to natural logarithms prior to analysis. The 24 series broken down by sector are as follows: Distillate Fuel Oil Consumed by the Residential Sector; Liquefied Petroleum Gases Consumed by the Residential Sector; Distillate Fuel Oil Consumed by the Commercial Sector; Liquefied Petroleum Gases Consumed by the Commercial Sector; Motor Gasoline Consumed by the Commercial Sector; Residual Fuel Oil Consumed by the Commercial Sector; Asphalt and Road Oil Consumed by the Industrial Sector; Distillate Fuel Oil Consumed by the Industrial Sector; Liquefied Petroleum Gases Consumed by the Industrial Sector; Lubricants Consumed by the Industrial Sector; Motor Gasoline Consumed by the Industrial Sector; Petroleum Coke Consumed by the Industrial Sector; Residual Fuel Oil Consumed by the Industrial Sector; Other Petroleum Products Consumed by the Industrial Sector; Aviation Gasoline Consumed by the Transportation Sector; Distillate Fuel Oil Consumed by the Transportation Sector; Jet Fuel Consumed by the Transportation Sector; Liquefied Petroleum Gases Consumed by the Transportation Sector; Lubricants Consumed by the Transportation Sector; Motor Gasoline Consumed by the Transportation Sector; Residual Fuel Oil Consumed by the Transportation Sector; Distillate Fuel Oil Consumed by the Electric Power Sector; Petroleum Coke Consumed by the Electric Power Sector; Residual Fuel Oil Consumed by the Electric Power Sector. Table 1 presents descriptive statistics for the 24 series of petroleum consumption. Motor Gasoline Consumed by the Transportation Sector has the highest mean and standard deviation while Liquefied Petroleum Gases Consumed by the Transportation Sector has the lowest mean and standard deviation.

5. Results The results of the univariate LM test for fractional integration are reported in Table 2. We allow for a nonzero mean following Nielsen (2005). We report the results without allowing short-run dynamics (p ¼ 0) as well as allowing VAR(p) dynamics with p ¼ 1, p ¼ 2, p ¼ 3 and p ¼ 4 in each case. When p ¼ 0, the univariate LM test rejects the null hypothesis for all 24 series at the 1% level. When p40 the results are more mixed. If p ¼ 1, the null hypothesis is rejected for 15 of the 24 series or 62.5% at the 5% level or better. If p ¼ 2, the null hypothesis is rejected for 7 of the 24 series or 29.2% at the 5% level or better. If p ¼ 3, the null hypothesis is rejected for 9 of the 24 series or 37.5% at the 5% level or better. If p ¼ 4, the null hypothesis is rejected for 11 of the 24 series or 45.8% at the 5% level or better. Thus, allowing a nonzero mean and short-run dynamics, we are generally able to reject the null hypothesis less than 50% of the time. A possible explanation why the results with and without allowing for short-run dynamics differ is that the presence of noise in the data due to measurement errors, outliers and

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Table 1 Descriptive statistics of petroleum consumption by sector. Variables

Mean

Std. Dev.

Distillate Fuel Oil Consumed by the Residential Sector Liquefied Petroleum Gases Consumed by the Residential Sector Distillate Fuel Oil Consumed by the Commercial Sector Liquefied Petroleum Gases Consumed by the Commercial Sector Motor Gasoline Consumed by the Commercial Sector Residual Fuel Oil Consumed by the Commercial Sector Asphalt and Road Oil Consumed by the Industrial Sector Distillate Fuel Oil Consumed by the Industrial Sector Liquefied Petroleum Gases Consumed by the Industrial Sector Lubricants Consumed by the Industrial Sector Motor Gasoline Consumed by the Industrial Sector Petroleum Coke Consumed by the Industrial Sector Residual Fuel Oil Consumed by the Industrial Sector Other Petroleum Products Consumed by the Industrial Sector Aviation Gasoline Consumed by the Transportation Sector Distillate Fuel Oil Consumed by the Transportation Sector Jet Fuel Consumed by the Transportation Sector Liquefied Petroleum Gases Consumed by the Transportation Sector Lubricants Consumed by the Transportation Sector Motor Gasoline Consumed by the Transportation Sector Residual Fuel Oil Consumed by the Transportation Sector Distillate Fuel Oil Consumed by the Electric Power Sector Petroleum Coke Consumed by the Electric Power Sector Residual Fuel Oil Consumed by the Electric Power Sector

540.3524 334.2098 251.1784 58.97820 37.75951 115.1384 466.1105 593.2772 1338.701 78.99796 115.3892 315.3257 316.1405 1348.353 25.97950 1852.114 1369.891 19.64550 74.44845 7469.993 381.9936 66.26098 30.47199 647.5584

269.0433 84.21856 87.59911 14.86210 16.21899 95.96501 200.8024 153.3840 312.6678 10.07910 36.70115 75.59020 259.3488 229.3466 10.12646 615.2228 265.7272 9.165747 9.237673 919.1389 109.7621 44.46513 33.45523 448.3971

Table 2 Univariate LM test for fractional integration with nonzero mean. Sector

Zt ¼ 1

p¼0

p¼1

p¼2

Residential

Distillate fuel oil Liquefied petroleum gases

857.00*** 1021.4***

106.27*** 27.049***

11.018 2.9775

Commercial

Distillate fuel oil Liquefied petroleum gases Motor gasoline Residual fuel oil

281.70*** 1021.4*** 1683.6*** 2096.7***

114.30*** 27.049*** 3.0250* 22.629***

Industrial

Asphalt and road oil Distillate fuel oil Liquefied petroleum gases Lubricants Motor gasoline Petroleum coke Residual fuel oil Other petroleum products

127.71*** 280.18*** 1266.9*** 141.00*** 1899.7*** 1497.4*** 2317.4*** 1284.0***

111.21*** 30.513 35.480*** 67.733 7.0519*** 2.7839 54.106*** 733.18***

27.968*** 36.189 2.0846 6.8805 0.10123 13.461 7.6109*** 9.6911***

0.064291 8.2690 5.0138 6.2425 0.16623 36.461*** 6.7692*** 4.0031**

155.14*** 80.748 5.6405 4.6751 0.38796 8.5052*** 11.091*** 5.4671**

Transportation

Aviation gasoline Distillate fuel oil Jet fuel Liquefied petroleum gases Lubricants Motor gasoline Residual fuel oil

1039.7*** 2922.9*** 2153.6*** 1198.4*** 125.78*** 2602.4*** 314.96***

3.4338 33.519*** 67.376*** 3.7215* 93.372 49.142*** 18.497

2.1814 2.4500 25.756*** 0.57662 10.358 6.4683** 3.9661

1.6040 9.3694*** 17.994*** 4.7899** 7.7110 5.8171** 6.1432

2.7543 8.8451*** 10.829*** 6.0046** 6.8597 8.8695*** 6.6043

Electric Power

Distillate fuel oil Petroleum coke Residual fuel oil

625.79*** 2427.4*** 2074.1***

10.397 7.3199*** 4.9250**

13.017 9.2697*** 46.563***

0.79633 10.321*** 32.727***

* ** ***

, ,

0.60743 2.9775 0.0012339 0.28784

p¼3 33.837 5.3218 166.55 5.3217 0.021328 1.5838

p¼4 20.560 6.4872 63.631 6.4871 0.16536 17.165

186.29*** 3.9271** 15.863***

denote statistical significance at the 10%, 5% and 1% levels, respectively.

structural breaks can lead fractional integration tests to find spurious evidence of fractional integration. Financial data, which will normally be high quality and available at high sampling frequency over long time periods, will have less noise. However, macroeconomic and energy time series, while typically available over a long period, is only sampled at monthly or quarterly intervals and, as such, has more noise. Haldrup and Nielsen (2007)

show that fractional integration tests which allow for short-run dynamics are less prone to finding spurious evidence of fractional integration due to non-persistent noise in the data. There are nine series for which we reject the null hypothesis in at least three of the four cases allowing for short-run dynamics. These are Asphalt and Road Oil Consumed by the Industrial Sector; Residual Fuel Oil Consumed by the Industrial Sector; Other

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Table 3 Multivariate test for fractional integration with nonzero mean.

Residential Commercial Industrial Transportation Electric Power * ** ***

, ,

p¼0

p¼1

p¼2

p¼3

p¼4

3604.4*** 4914.8*** 3994.2*** 4674.7*** 3187.1***

172.09*** 45.196*** 281.01*** 52.379 7.0004

0.29599 14.689*** 45.893*** 51.170*** 15.927

10.536 12.705** 27.024*** 44.247*** 11.451***

7.0088 25.669*** 27.183*** 181.49 33.372***

denote statistical significance at the 10%, 5% and 1% levels, respectively.

Petroleum Products Consumed by the Industrial Sector; Distillate Fuel Oil Consumed by the Transportation Sector; Jet Fuel Consumed by the Transportation Sector; Liquefied Petroleum Gases Consumed by the Transportation Sector; Motor Gasoline Consumed by the Transportation Sector; Petroleum Coke Consumed for Electric Power and Residual Fuel Oil Consumed for Electric Power. Most of these series have high means and/or standard deviations. Seven of the nine series with the largest mean consumption and the largest standard deviation in consumption are fractionally integrated (see Table 1). Of those series which are fractionally integrated, the only series which do not have a large mean and standard deviation are Liquefied Petroleum Gases Consumed by the Transportation Sector and Petroleum Coke Consumed for Electric Power. This result is consistent with expectations. Energy consumption is more likely to be fractionally integrated in series with high average consumption because shocks will generate a bigger deviation from the long-run equilibrium path, resulting in a higher level of persistence (Hsu et al., 2008). Series with high volatility in consumption, reflected in the standard deviation, are more likely to be fractionally integrated because the deviations from the longrun equilibrium path, due to shocks that create volatility, will be larger. Thus, departure from the equilibrium path will be more likely to be persistent (see Maslyuk and Smyth, 2009; Mishra et al., 2009; Narayan et al., 2008). Table 3 presents the results of the multivariate LM test for fractional integration based on sector. Because the multivariate LM test for fractional integration takes account of potentially important correlations between the elements of the multiple time series, it could have more power than the univariate LM test for fractional integration (Nielsen, 2005). The null hypothesis is rejected for each of the five sectors when no short-run dynamics are permitted (p ¼ 0). When short-run dynamics are allowed (p40) the findings are mixed. The null hypothesis is clearly rejected for the commercial and industrial sectors. The null is rejected with either p ¼ 2 or 3 for the transportation sector and either p ¼ 3 or 4 for the electric power sector, but only if p ¼ 1 for the residential sector. Thus, overall, allowing for short-run dynamics petroleum consumption in the commercial and industrial sector is fractionally integrated. This result is consistent with both sectors being large consumers of energy. The results for the electric power and transportation sectors are not clear cut, while, petroleum consumption in the residential sector appears to be jointly I(0) with nonzero means.

6. Policy implications In discussing the policy implications we focus on the three sectors for which the results are relatively clear cut—the commercial, industrial and residential sectors. These three sectors together are responsible for almost three quarters of total energy consumption in the United States (Ewing et al., 2007). That petroleum consumption in the commercial and industrial sectors

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is fractionally integrated means that shocks to consumption, caused by disruptions to supply in the Middle East or elsewhere, will have persistent effects on the real economy, such as output and employment, in these sectors. This result is consistent with the findings of previous research suggesting that output and unemployment in the United States is fractionally integrated (GilAlana, 2002b). The results reported here suggest that it would be useful for the commercial and industrial sectors to invest in renewable technologies that would allow firms in these sectors to move away from reliance on petroleum products. Another course of action would be for the commercial and industrial sectors to implement demand management policies that would result in more efficient use of petroleum products. As petroleum consumption in the residential sector appears to be jointly I(0) with nonzero means, disruptions to consumption in this sector would be temporary with no persistent effect on the real economy. The distinction between the commercial/industrial sectors and residential sector in this context makes sense. The commercial and industrial sectors are employers and generate output. Thus, shocks to petroleum consumption in these sectors are more likely to be directly linked to more long-lasting disruptions to the real economy. Depending on the size of the cyclical and secular component of fluctuations, which is contested, if shocks to the real economy in the commercial and industrial sector are persistent, this can be interpreted as providing support for real business cycle theory as well as other theories of the business cycle such as New Keynesian models (see Libanio, 2005 for a survey). If real output in these sectors is persistent, this suggests that following a negative shock automatic return to a equilibrium may not occur, and therefore Keynesian stabilization policies to stimulate demand and move the economy towards full employment have a role to perform (Libanio, 2005). However, a note of caution is needed. If real output is persistent, it is also possible to make a case against sharp contractions to slow the economy in the event it is overheating or in response to currency or fiscal crises (Dutt and Ros, 2003), since the negative effects of such policies will not dissipate in the short run. The results have implications for modelling energy consumption. Non-rejection of the null for petroleum consumption in the residential sector implies standard methods can be employed for conducting, for example, Granger causality, structural vector autoregression, or impulse response analysis. Rejection of the null for petroleum consumption in the commercial and industrial sectors indicates the need to transform the data to make it suitable for such analyses. For example, in Andersen et al. (2003) a fractional difference is taken of the multivariate volatility processes considered there and the resulting multivariate series are modelled by vector autoregressions. There is increased recognition that disaggregated energy consumption should be used when testing for Granger causality, impulse response functions and the like to compare the relative strengths of the relationship between energy consumption and output and/or employment by source (see e.g. Erbaykay, 2008; Ewing et al., 2007; Sari and Soytas, 2004; Sari et al., 2008; Wolde-Rufael, 2004; Yang, 2000). The findings from these studies have important policy implications. For example in Granger causality studies, if unidirectional Granger causality runs from energy consumption to real output, it follows that reducing energy consumption could lead to a fall in income; however if Granger causality runs in the opposite direction this provides strong justification for implementing energy conservation policies because economic growth is not dependent on energy consumption. Drawing the appropriate policy implications from modelling exercises such as these requires correctly identifying the order of integration as part of the preliminary analysis.

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7. Conclusion Previous studies that have tested for a unit root in aggregate energy consumption have potentially reached misleading conclusions because they fail to allow for the possibility that energy consumption might be fractionally integrated and do not distinguish between different types of energy consumption. This study has tested for long memory in disaggregated petroleum consumption in the United States using univariate and multivariate LM tests for fractional integration. The results point strongly to the need to distinguish between different forms of energy consumption and allow for a generalization of the I(0)/I(1) dichotomy when considering the order of integration of energy consumption. The univariate tests suggest that, allowing for shortrun dynamics, nine of the 24 series are fractionally integrated. Consistent with expectations these series tended to have the highest mean and standard deviation. The multivariate tests suggest that petroleum consumption in the commercial and industrial sectors is clearly fractionally integrated when allowing for short-run dynamics while petroleum consumption in the residential sector is jointly I(0) with nonzero means A limitation of the Nielsen (2005) test employed in this study is that it does not allow for the possibility of structural break(s). Previous research has attributed failure to find energy consumption stationary to failure to allow for structural breaks (Chen and Lee, 2007). Fractional integration and structural breaks can be confused (Granger and Hyung, 2004; Diebold and Inoue, 2001). For this reason, some recent studies that have tested for the order of integration of, for example, macroeconomic variables (Gil-Alana, 2002b; Caporale and Gil-Alana, 2008) and international tourist arrivals (Cunado et al., 2008) have started using fractional integration tests that allow for one or more structural break. This would be a useful direction for future research in the energy literature. Another limitation is that the Nielsen (2005) test does not explicitly allow for potential non-linearities in the data. One study that applies a non-linear long memory model to United States unemployment is van Dijk et al. (2002). Applying a test such as this to disaggregated energy consumption or energy production would be another useful path for future research in the energy literature. References Al-Iriani, M., 2006. Energy-GDP relationship revisited: an example from GCC countries using panel causality. Energy Policy 34, 3342–3350. Altinay, G., Karagol, E., 2004. Structural break, unit root and the causality between energy consumption and GDP in Turkey. Energy Economics 26, 985–994. Andersen, T.G., Bollerslev, T., Diebold, F.X., Labys, P., 2003. Modelling and forecasting realized volatility. Econometrica 71, 579–625. Assaf, A., 2007. Fractional integration in the equity markets of the MENA region. Applied Financial Economics 17, 709–723. Baillie, R.T., 1996. Long memory processes and fractional integration in econometrics. Journal of Econometrics 73, 5–59. Baillie, R.T., Chung, C.F., Tieslau, M.A., 1996. Analysing inflation by the fractionally integrated ARFIMA-GARCH model. Journal of Applied Econometrics 11, 23–40. Breitung, J., Hassler, U., 2002. Inference on the cointegration rank in fractionally integrated processes. Journal of Econometrics 110, 167–185. Caporale, G.M., Gil-Alana, L.A., 2008. Modelling the US, UK and Japanese unemployment rates: fractional integration and structural breaks. Computational Statistics and Data Analysis 52, 4998–5013. Chen, P.F., Lee, C-C., 2007. Is energy consumption per capita broken stationary? New evidence from regional based panels. Energy Policy 35, 3526–3540. Cunado, J., Gil-Alana, L., Perez de Gracia, F., 2004. Modelling monthly Spanish tourism: a seasonal fractionally integrated approach. Tourism Economics 10, 79–94. Cunado, J., Gil-Alana, L., Perez de Gracia, F., 2008. Fractional integration and structural breaks: evidence from international monthly arrivals in the USA. Tourism Economics 14, 13–23. Diebold, F.X., Husted, S., Rush, M., 1991. Real exchange rates under the gold standard. Journal of Political Economy 99, 1252–1271. Diebold, F.X., Inoue, A., 2001. Long memory and regime switching. Journal of Econometrics 105, 131–159.

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