Are fluctuations in natural gas consumption per capita transitory? Evidence from time series and panel unit root tests

Energy 78 (2014) 183e195

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Are fluctuations in natural gas consumption per capita transitory? Evidence from time series and panel unit root tests Muhammad Shahbaz a, Naceur Khraief b, c, d, *, Mantu Kumar Mahalik e, Khair Uz Zaman f a

Department of Management Sciences, COMSATS Institute of Information Technology, Lahore, Pakistan Faculty of Economic Science and Management of Sousse, University of Sousse, Tunisia c University of Nice Sophia Antipolis, France d GREDEG (Research Group on Law Economics and Management), France e Amritapuri Campus, Amrita Vishwa Vidyapeetham University, India f COMSATS Institute of Information Technology, Vehari Campus, Vehari, Pakistan b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 May 2014 Received in revised form 26 September 2014 Accepted 29 September 2014 Available online 31 October 2014

The stationary properties of natural gas consumption are essential for predicting the impacts of exogenous shocks on energy demand, which can help modeling the energy-growth nexus. Then, this paper proposes to investigate the panel unit root proprieties of natural gas energy consumption of 48 countries over the period of 1971e2010. We apply the Harvey et al. [69] linearity test in order to determine the type of the unit root tests (the Kruse (2010) nonlinear unit root or LM (Lagrange Multiplier) linear unit root tests). Our results show that the stationarity of natural gas consumption cannot be rejected for more than 60% of countries. In order to provide corroborating evidence, we employed not only the first and second generation panel unit root tests, but also the recent LM panel unit root test developed by Im et al. [28]. This test allows for structural breaks both in intercept and slope. The empirical findings support evidence in favor of stationarity of natural gas consumption for all panels. These results announce that any shock to natural gas consumption has a transitory impact for almost all countries implying that energy consumption will turn back to its time trend. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Natural gas Univariate unit root tests The first and second generation panel data unit root tests

1. Introduction Given the expanding size of economic activities, urbanization, industrialization and the resultant demand for energy use, there has been an increasing tendency in the ‘energy economics literature’ to test the unit root properties of energy consumption series at aggregate and disaggregate levels for managing energyeenvironment and energyegrowth relationships. Supporting the wisdom of this trend, the vast majority of empirical literature on the topic applied various approaches and yielded mixed results [1,5e7,13,21,25,32,34,43,47,49,52,58,59,72]. Moreover, these empirical investigations behind energy consumption stationarity are largely motivated by several factors. First, if energy

* Corresponding author. University of Sousse, Faculty of Economic Sciences and Management, Erriadh City 4023, Sousse, Tunisia. Tel.: þ216 73 301 808; fax: þ216 73 301 888. E-mail addresses: [email protected] (M. Shahbaz), [email protected] (N. Khraief), [email protected] (M.K. Mahalik), [email protected] (K.U. Zaman). http://dx.doi.org/10.1016/j.energy.2014.09.080 0360-5442/© 2014 Elsevier Ltd. All rights reserved.

consumption is stationary at level then shocks to energy consumption will have temporary effects over time and such designed economic policies will have transitory impact. For instance, if energy consumption is stationary, shocks to energy consumption will be fleeting or temporary following major structural changes in energy consumption, the demand for energy consumption will return to its original equilibrium within a short period of time. In this case, disruptions in energy consumption demand will have only a transitory impact on economic activity. In such an environment, the policymakers should not design any adverse policy mechanism breaking the sound relationship between energy consumption and economic growth. Second, if energy consumption contains a unit root then shocks to energy consumption will have permanent or long-term effects. In such environment, shocks to energy consumption will have permanent effects on the level of energy demand. Hence disruptions in energy consumption will have a permanent effect on economic activity and therefore the designed policies will be more effective. In addition, the extent to which the energy sector is linked with others sectors of the economy is also of larger significance as permanent shocks to energy

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Table 1 Survey of literature for stationary properties. Authors

Time period

Unit root tests

Conclusions

Lee and Chang [34] Narayan and Smyth [72] Al-Iriani [1] Soytas and Sari [61] Zachariadis and Pashouritdou [62] Narayan and Smyth [46,72] Chen and Lee [13] Hsu et al. [25] Narayan et al. [49] Mishra et al. [43] Narayan et al. [48]

1954e2003 1954e2003 1979e2000 1971e2000 1973e2008 1971e2003 1973e2008 1971e2003 1973e2007 1980e2005 1973e2007

I(1) I(1) I(0) I(0) I(0) I(1) Miscellaneous results Mixed results I(0) Miscellaneous results I(0)

Apergis et al. [4] Apergis et al. [5] Aslan [6] Aslan and Kum [7] Ozturk and Aslan [52] Hasanov and Telatar [24] Kum [31] Golpe et al. [21] Kula et al. [30] Apergis and Tsoumas [3] Maslyuk and Dharmaratna [40]

1980e2007 1982e2007 1960e2008 1970e2006 1970e2006 1980e2006 1971e2007 1973:1e2010:3 1960e2005 1989e2009 1966e2009

Narayan and Popp [47,73] Congregado et al. [17] Shahbaz et al. [59]

1980e2006 1973e2010 1971e2010

Shahbaz et al. [58] Lean and Smyth [32]

1965e2010 1978e2010

Lean and Smyth [33]

1965e2011

Bolat et al. [11] Bolat et al.[10] Barros et al. [8] Meng et al. [41] Barros et al. [9] Ozcan [51]

1960e2009 1971e2010 1973e2010 1960e2010 1994e2011 1980e2009

Zevot and Andrew [63] structural break test Zevot and Andrew [63] test Univariate and IPS panel tests Carrion-i-Silvestre multiple test [12] LM structural break test Panel seemingly unrelated regressions ADF Long memory test Panel unit root test Lee and Strazicich [36] two structural breaks test LLC, IPS and Maddala and Wu panel tests and CIPS test Lee and Strazicich [36] univariate unit root tests with up to two structural breaks LM structural break test LM structural break test LM structural break test LM structural break test Lee and Strazicich [36] two structural break test Non-Linear Test by Kapitaneous et al. (2003) Lee and Strazicich [35,36]; one structural break test Non-linear specification of an unobserved components model LM structural break test Fractional integration with structural breaks Zevot and Andrew [63] and Clemente et al. [16] univariate unit root tests with structural breaks Pesaran [53] panel unit root test without structural break Non-linear specification of an unobserved components model Lee and Strazicich [35,36] univariate unit root tests with up to two structural breaks LM unit root test with one break and two breaks crash model Lee and Strazicich [35,36] univariate unit root tests with up to two structural breaks LM panel unit root test [55] with no structural breaks and LM unit root test [35] with one and two structural breaks. KwiatkowskiePhillipseSchmidteShin (KPSS) unit root test LM test with two breaks LM test with two breaks LM and RALS-LM unit root tests LM test with two breaks [28,35,36]

consumption may well be transmitted to other sectors of the economy as well as to macroeconomic aggregates. However, the distinction between temporary and permanent shocks to energy consumption has several implications for policymakers, financial investors and producers. For policymakers, the forecasting of energy demand is important because it plays a vital role in formulating energy policies. It is tempting to argue that efficient and timely energy supply for economic growth can be possible after knowing the reliable forecasts of energy consumption in future. For instance, if energy consumption is stationary, then the past behavior of energy consumption enables policymakers in the forecasting process. On other hand, if energy consumption is nonstationary, then the past behavior of this variable can't be used in formulating the forecasts of future demand and one would need to look at other variables explaining energy consumption to generate forecasts of energy demand into the future [5,6,43,58,60]. Furthermore, the issue of whether energy consumption is stationary has important implications for modeling purpose. If unidirectional causality runs from energy consumption to real output, it shows that reducing energy consumption could lead to a fall in income; however, if causation runs in the opposite direction this provides strong justification for implementing energy consumption policies because economic growth is not dependent on energy consumption [43]. Second, the unit root properties of energy prices have important practical implications for financial investors. If energy prices are mean reverting, it reveals that the price level will return to its trend path over time and that enables investors to

I(0) I(0) Miscellaneous results I(0) I(0) Miscellaneous results I(0) Evidence of persistence I(0) Mixed results Mixed evidence of stationarity I(1) Evidence of persistence I(0) I(0) I(0) I(0) I(0) I(0) I(1) I(0) Evidence of persistence I(0)

forecast future movements in energy prices based on its past behavior, but if energy prices follow a random walk process, shocks to energy prices will be permanent and also will be difficult to forecast. Finally, the understanding of temporary and permanent shocks to energy consumption is important for producers to knowing the behavior of energy prices as they use energy as one of the inputs in the process of production [43]. Table 1 provides summary of existing studies investigating whether fluctuations in energy consumption are permanent or transitory. These studies have applied various approaches to test the stationary properties of energy consumption and provided conflicting results. Recently, Apergis et al. [4] investigated the stationary process of natural gas consumption in 50 US states using several panel unit root tests [27,38,39,22]. It is further important to note that the findings of single country can't be generalized to other economies of the world due to the presence of structural breaks and the application of differential methodologies. Keeping this limitation in mind, to date, there has been no empirical attempt of examining the stationary properties of natural gas consumption across numerous countries.1 We address this gap in the literature and make an empirical attempt in investigating the unit root properties of natural gas consumption by applying the recent Lagrange Multiplier (LM) panel unit root test developed by Im et al.

1 The use of a relatively large of countries has the advantage that it is possible to use both a panel and structural breaks [60].

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[28] with testing structural breaks in both the intercept and slope. The empirical findings of this study should enable the policymakers in designing the appropriate policy for macroeconomic stabilization as it is commonly believed that the policymakers are mainly concerned about the consistent and robustness of the results across economies. Natural gas as part of non-renewable energy or fossil fuels is essential the way we live. Similarly, its production is also vital the way we produce and demand in the economy. Hence, natural gas production grew by 1.9%. The US (4.7%) once again recorded the largest volumetric increase and remained the world's largest producer. Norway (12.6%), Qatar (7.8%), and Saudi Arabia (11.1%) also saw significant production increases, while Russia (2.7%) had the worlds' largest decline in volumetric terms (The BP Statistical Review of World Energy, 2013) [77]. Given the rising production of natural gas across the noted sample countries in the world, it appears to be an important input in the production of macroeconomic activities. Rather, the sustainable natural gas production, security and quality are also important in the country's development, prosperity and welfare. In this sense, it is necessary to look at the significance of natural gas production in achieving sustainable economic growth. Thus, the possibility of sustainable economic growth can be achieved if both the growth and natural gas production are cointegrated and moving together at the constant rate in the long run. In this line, the understanding of time series properties of natural gas production is also found to be important because of the effect of disruptions in natural gas production on economic activity. For instance, if natural gas production contains a unit root, gas shocks will have permanent effects on the level of natural gas supplied. Hence disruptions in natural gas production will have a permanent effect on economic activity. However if natural gas production is stationary, shocks to gas production will be temporary following major structural changes in natural gas production, the supply of gas will return to its original equilibrium with the passage of time in the short run. In this case, disruptions in natural gas production will have only a transitory impact on economic activity. From this time series perspective, we believe the importance of natural gas production on economic activity as potential input and further the understanding of sustainable economic growth depending upon the nature of shocks to natural gas production. If shocks to natural gas production permanent, then the sustainable economic growth will be hampered because the speed at which economic growth is expected to increase, the intensity and adequacy of natural gas production are far behind mainly due to structural shocks to gas supply. Moreover, this indicates that a country's welfare and prosperity would necessarily be affected due to the disproportionate relationship between natural gas production and economic growth. In this context, it can be suggested that the energy policy designed for country's development needs to ensure quality, security and sustainable natural gas production for sustaining economic growth in the long run. Non-renewable energy is comprised of coal, crude oil and natural gas. Natural gas is not only an important foundation fuel among fossil fuels but also helping the process of heating and electricity generation. For instance, natural gas is the cleanestburning fossil fuel, with 30% less carbon than oil and as much as 60% less carbon than coal for Canada. Burning natural gas in place of other fuels can reduce emissions and contribute to cleaner air quality. As noted by BP Energy Outlook (2012) [66], natural gas is expected to be the fastest growing of the fossil fuels-with demand rising at an average of 1.9% a year. Non-OECD countries are expected to generate 78% of demand growth. Liquefied Natural Gas (LNG) exports are expected to grow more than twice as fast as gas consumption, at an average of 3.9% per year, and accounting for 29% of the growth in global gas supply to 2035. Although world natural

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gas consumption grew by 2.2%, below the historical average of 2.7%, globally it accounted for 23.9% of primary energy consumption behind oil and coal. According to World Energy Outlook (WEO, 2011) [76], global gas demand was estimated at 3427 billion cubic meters (bcm) in 2012, up 2% from 2011 levels. Gas demand has increased by around 800 bcm over the last decade, or 2.8% per year. For comparison, 50 billion cubic meters (bcm) of natural gas is roughly equivalent to 7% of the US's consumption in 2012. The United States, Russia, Iran and China are world's largest consumers of gas. The largest producers are Russia, the United States, Canada and Iran. Since there has been continued significant worldwide energy demand is expected to double between 2005 and 2050, the natural gas will play a key role in the global energy mix and thus ensure the required supply of fuel which is assumed to be sustainable in the future as it is by far the cleanest and cheaply available fuel, with the lowest CO2 emissions. Such versatility of natural gas makes it an important foundation fuel among other fossil fuels (coal and oil) and that could be another important reason for researchers to study the stationarity of natural gas consumption across economies. The aim of this paper is to investigate the stationary properties of natural gas consumption per capita using data of 48 high, middle and low income countries for 1971e2010 period.2 To examine the stationary properties of natural gas consumption per capita, the first and second generation panel unit root tests along with the recent Lagrange Multiplier (LM) panel unit root test capturing structural breaks in both the intercept and slope have been employed. The contributions of this paper are twofold. First, after testing the cross-section correlation between units, we provide evidence of stationarity of natural gas consumption for more than 40 countries panel by applying panel unit root tests which allow dependence across different units in the panel; the so called “second generation” panel unit root tests. Such issue has been neglected by the previous studies on energy consumption stationarity [4,5,13,25,46] (Narayan et al., 2008; [65,73]). Then, in presence of cross section dependence, this requests to be accounted for by using the second generation tests and gain the high power proprieties of these tests. The second contribution is that we consider a structural break panel unit root test approach. For robustness check, the panel unit root test of Im et al. [28] is performed. Using the ILT [28] test with structural breaks we find robust evidence supporting the stationarity of natural gas consumption for all the panels (high income group countries, middle income countries and low income countries panel) which corroborate the findings of both the first and second generation panel data unit root tests, leading us to conclude the importance of accounting for inter-dependence and structural breaks when testing for unit root in natural gas consumption in all groups of countries. Thus, our results suggest that policies to encourage natural gas use will have temporary positive shocks. The remainder of the paper is organized as follows: Section 2 describes methodology and data. Section 3 presents results and Section 4 concludes the paper. 2. Methodology 2.1. Univariate unit root tests The first step we take into account the possibility of nonlinearity of energy consumption series by testing the null hypothesis of time series linearity against a nonlinear alternative. Therefore, we use the Harvey et al. [69] test which has better size control and offers

2

Availability of data has restricted our analysis to 48 countries.

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M. Shahbaz et al. / Energy 78 (2014) 183e195

substantial power gains over Harvey and Leybourne [68] linearity test. Harvey et al. [69] offer a linearity test which can be applied either to I(0) or I(1) processes. They suggest a weighted average Wald test when the order of integration is unknown which can be written as follows:

Wl ¼ ð1  lÞW0 þ lW1 / c2 ð2Þ where W0 and W1 are Wald tests for the null of linearity when the variable is known to have a unit root and when it is known to be stationary I(0). According to Harvey et al. [69], l converges in probability to 1 when the variable is I(1) and to 0 when the process is I(0). Depending on the whether we reject or accept the null hypothesis, we use the Lagrange Multiplier (LM) unit root test with structural breaks developed by Lee and Strazicich [35,37] for linear series and Kruse [71] test when the linearity hypothesis is rejected. Lee and Strazicich [35,37] offer a minimum LM test with breaks in the level (or intercept) and trend. The LM unit root test not only determines endogenously the time of structural breaks but also avoids the drawback of “spurious rejection” when the null hypothesis is true because Lee and Strazicich [35] allow for structural breaks under both the null and alternative hypotheses. The LM unit root test with one and two structural breaks [35,37]

Intercept

Intercept and trend

Model A Model AA

Model C Model CC

Consider the following DGP (Data Generating Process):

yt ¼ d0 Zt þ et ;

et ¼ bet1 þ 3t

where Zt is a vector of exogenous variables and 3t ~ N(0, s2). The DGP contains break under the null and alternative hypothesis in a consistent process. The one structural break models can be considered as follows. The Model A is described by Zt ¼ [1, t, Dt]0 where Dt ¼ 1 for t _ TB þ 1, and zero otherwise. TB denotes the time period of the structural break. The Model C can be described by Zt ¼ [1, t, Dt, DTt]0 where DTt ¼ t  TBt for t _ TB þ 1, zero otherwise. The two structural breaks can be considered as follows. The Model AA that allows for two shifts in level is described by Zt ¼ [1, t, D1t, D2t]0 where Djt ¼ 1 for t _ TBj þ 1, j ¼ 1,2, and zero otherwise. Finally, the Model CC that contains two changes in level and trend is described by Zt ¼ [1, t, D1t, D2t, DT1t, DT2t]0 where DTjt ¼ t  TBjt for t _ TB þ 1, j ¼ 1, 2, zero otherwise. Depending on value of b, in model AA we have:

Null hypothesis

yt ¼ m0 þ d1 B1t þ d2 B2t þ yt1 þ v1t

Alternative hypothesis

yt ¼ m1 þ g$t þ d1 D1t þ d2 D2t þ d3 DT1t þ d4 DT2t þ v2t

The LM unit root test statistic can be estimated by regression according to the LM (score) principle as follows:

Dyt ¼ d0 DZt þ f~ St1 þ ut

d

One structural break Two structural breaks

Alternative hypothesis

yt ¼ m1 þ g$t þ d1 D1t þ d2 D2t þ v2t

where v1t and v2t are stationary error terms; Bjt ¼ 1 for t ¼ TBj þ 1, j ¼ 1, 2, zero otherwise. For the model CC we have the following null and alternative hypotheses:

~ x  Zt ~ where ~ St1 ¼ yt  j d; t ¼ 2; :::; T; ~d are coefficients in the ~ regression of Dyt on DZt, jx is given by y1  Z1 ~ d. The unit root null hypothesis is described by f ¼ 0 and the LM test statistics are given by:

~ ~ r ¼ T$f ~ t ¼ t­statistic testing null hypothesis f ¼ 0 The minimum LM unit root test determines the break points TBjt endogenously by using a grid search as follows:

rðlÞ LMr ¼ Inf ~ l

tðlÞ LMt ¼ Inf ~ l

where l ¼ TB/T. The break points are determined to be where the test statistic is minimized. In order to eliminate the end points, we use the trimming region (0.15T, 0.85T), where T is a sample size. The critical values for one break and two breaks are given by Lee and Strazicich [35,37]. On the other side, to carry out the unit root test for nonlinear series, we apply the Kruse [71] test. This test is based upon the approach of Kapetanios et al. [70], who propose a unit root test against the alternative of a globally stationary ESTAR (Exponential Smooth Transition Auto-Regression) model.

yt ¼ byt1 þ ∅yt1 Fðq; yt1 Þ þ 3t where 3t is iidð0; s2 Þ and Fðq; yt1 Þ is the transition function which is assumed to be of exponential form:

o n Fðq; yt1 Þ ¼ 1  exp  qðyt1  cÞ2 where it is assumed that q  0. The transition function is bounded between zero and one, and is symmetrically U-shaped around zero. Under the restriction b ¼ 0, Kapetanios et al. [70] show that the ESTAR model is globally stationary if 2 < ∅ < 0 is satisfied despite it is locally nonstationary in yt1 ¼ c. The authors make the restriction c ¼ 0 and consider the following model:

 n o þ 3t Dyt ¼ byt1 þ ∅yt1 1  exp qy2t1 Kapetanios et al. [70] impose b ¼ 0. The null hypothesis H0: q ¼ 0 is tested versus the alternative H1: q > 0. Subsequently, an application of the first-order Taylor approximation of the smooth transition function around q ¼ 0 leads to the following auxiliary regression:

Dyt ¼ d1 y3t1 þ mt Null hypothesis

yt ¼ m0 þ d1 B1t þ d2 B2t þ d3 D1t þ d4 D2t þ yt1 þ v1t

where mt is a noise term depending on 3t. The authors propose a DickeyeFuller type t test, designed as KSS, for unit root hypothesis

M. Shahbaz et al. / Energy 78 (2014) 183e195

against globally stationary ESTAR which correspond to H0: d1 ¼ 0 against the alternative H1: d1 < 0: Panel unit root tests with no breaks

c d1 KSS≡sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   d v ar c d1

Panel unit root with structural breaks

However, Kruse [71] considers that the zero location parameter c in the exponential transition function is too restrictive. Therefore, he relaxed this assumption and suggested an extension to Kapetanios et al. [70] unit root test. Kruse [71] considers the following modified ADF (Augmented DickeyeFuller) regression:

 n o þ 3t yt ¼ byt1 þ ∅yt1 1  exp  qðyt1  cÞ2 The author follows Kapetanios et al. [70] by applying the firstorder Taylor approximation of the smooth transition function around q ¼ 0 and then he proceeds with the following test regression:

187

First generation

Second generation

Levin, Lin and Chu [38] LLC Im, Pesaran and Shin [27] IPS Maddala and Wu [39] MW Choi [14] Im, Lee and Tieslau [28]

Moon and Perron [44] Pesaran [53] Choi [15]

2.2.1. First generation panel unit root tests 2.2.1.1. Levin, Lin and Chu test [38]. The first test is Levin, Lin and Chu [38] test (LLC test) that allow for homogeneity of the first order autoregressive parameters and the cross sectional independence between units as all first generation panel unit root tests. The implementation of LLC test is directly inspired from ADF (Augmented DickeyeFuller) approach in time series. Consequently, three models are considered to test the presence of unit root:

Model 1 : Dyi;t ¼ ryi;t1 þ

pi X

gi;j Dyi;tj þ 3i;t

j¼1

Model 2 : Dyi;t ¼ ai þ ryi;t1 þ Dyt ¼ d1 y3t1 þ d2 y2t1 þ d3 yt1 þ mt In order to improve the power of test, Kruse [71] imposes d3 ¼ 0 and proceeds with:

Dyt ¼

d1 y3t1

þ

d2 y2t1

þ mt

where d1 ¼ q∅ and d2 ¼ 2cq∅. The null hypothesis H0: d1 ¼ d2 ¼ 0 is tested against the alternative H1: d1 < 0, d2 s 0. Kruse [71] proposes to apply the methods of Abadir and Distaso [64] to derive a modify Wald test. This modified Wald test builds upon the one-sided parameter (d1) and the transformed twosided parameter, say d⊥ 2 , that are stochastically independent by definition. 2.2. Panel unit root tests In this section, we briefly present the panel unit root tests needed in our analysis. This review is based on that proposed by Hurlin and Mignon [26]. The interest in such tests has been found recently reinforced by increasingly using panel data with high temporal dimension (typically more than 20). Generally, panel unit root tests can be divided into two classes. The first generation panel unit root tests assume that the cross section units are independent. However, the second generation tests reject this hypothesis and consider the cross sectional interdependence. Beyond the cross sectional dependence problem, it is also necessary to take into account the assumption of the heterogeneity of model's parameters. In this context, our central interest lies on testing whether natural gas energy consumptions are stationary by using first generation, second generation test and panel unit root test based on structural break advanced by Im et al. [28]. Therefore, to offer a robust analysis, it is interesting to make comparison between univariate and panel Lagrange Multiplier (LM) unit root test outcomes with and without a structural break. As a benchmark, we start by reporting the results for Schmidt and Phillips [55] univariate LM unit root test without any structural change. Then, in order to find the structural break points in each country, we apply the univariate test of the minimum LM unit root tests with one and two breaks proposed by Lee and Strazicich [35,37]. After estimating the optimal break-point locations, we use the panel LM unit root test of Im et al. [28].

pi X

gi;s Dyi;tj þ 3i;t

s¼1

Model 3 : Dyi;t ¼ ai þ bi t þ ryi;t1 þ

pi X

gi;j Dyi;tj þ 3i;t

j¼1

The errors 3i,t are iid ð0; s23i Þ across the units i for i ¼ 1, …, N. The hypotheses tests are formulated as follows:

Model 1 : H0 : r ¼ 0 H1 : r < 0 Model 2 : H0 : r ¼ 0 and ai ¼ 0 for i ¼ 1; …; N H1 : r < 0 and ai 2IR for i ¼ 1; …; N Model 3 : H0 : r ¼ 0 and bi ¼ 0 for i ¼ 1; …; N H1 : r < 0 and bi 2IR for i ¼ 1; …; N We find a hypotheses structure close to that proposed by Dickey and Fuller. Then, the LLC testing procedure is implementing in three steps. The independence assumption of individuals' errors terms implies the use of central limit theorem. Therefore, statistical tests are asymptotically normal distributed. Finally Levin et al. [38] propose the following adjusted t statistic:

tr* ¼

b sbr tr  NT b SN * sT b s~23

!

m*T s*T

! (1)

b~23 are respectively the standards deviations of slope where b sbr and s and error term. The mean adjustment m*T and standard deviation adjustment s*T are tabulated by Levin, Lin, and Chu [38, p. 14] for various T. b S N denotes the average of individual ratios of long-run to short-run variances for the individual i. Levin et al. [38] show that t*r converges to a standard normal distribution under the unit root null hypothesis. 2.2.1.2. The Im, Pesaran and Shin test [27]. Unlike the LLC test, the Im, Pesaran and Shin [27] test allows for heterogeneity of the first order autoregressive parameters, but the cross sectional independence assumption still valid. The authors proposed to test the presence of unit root in the following a model (with individual effects and no time trend):

Dyi;t ¼ ai þ ri yi;t1 þ

pi X

bi;j Dyi;tj þ 3i;t

j¼1

The hypothesis test is defined as follows:

(2)

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 H1 :

More specifically, we present three tests [15,44,53] to test the presence of unit root.

H0 : ri ¼ 0 for i ¼ 1; …; N ri < 0 for i ¼ 1; …; N1 ri ¼ 0 for i ¼ N1 þ 1; N1 þ 2; …; N

Under the alternative hypothesis, the individual series yi,t could be divided into subgroups. More specifically, there are N1 stationary series and N  N1 series which admit unit roots. To perform this test, the authors propose two statistics. The first one is the standardized statistics Ztbar(p; b), centered and reduced respectively by the mean and standard deviation of the limiting distribution of individual Augmented DickeyeFuller statistics:

Ztbar ðp; bÞ ¼ with tb arNT

pffiffiffiffi N½tb arNT  EðtiT Þ pffiffiffiffiffiffiffiffiffiffiffiffiffi VðtiT Þ N X ¼ 1=N tiT

(3)

i¼1

where tiT designates the t-statistic associated with the unit root null hypothesis (ri ¼ 0). In a model with individual effects and no time trend, the limiting distribution moments are defined by E(tiT) ¼ 1.533 and V(tiT) ¼ 0.706 [45]. The statistic Ztbar(p;b) sequentially converge to the standard normal distribution when T / ∞ followed by N / ∞. However, if N is small then IPS test show size distortions.3 It is for that reason that Im et al. [27] have proposed (under the null hypothesis ri ¼ 0) an alternative standardized statistic Wtbar(p; b) that have better small sample performance:

i pffiffiffiffih P N tb arNT  N 1 N i¼1 EðtiT ðri ; 0Þjri ¼ 0Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Wtbar ðp; bÞ ¼ P N 1 N i¼1 VðtiT ðri ; 0Þjri ¼ 0Þ

(4)

The authors simulated the values of E(tiT(ri,0)jri ¼ 0) and V(tiT(ri,0)jri ¼ 0) for different values of periods T and lag orders p. However, if N is relative large to T the IPS test shows size distortions (the null hypothesis will be rejected too often).

2.2.2.1. Moon and Perron (MP) [44] test. Moon and Perron [44] are based on factor model to test the presence of a unit root in cross sectional dependent panel. The authors assume an AR(1) model and the presence of common factors in the error term:

yi;t ¼ ð1  li Þmi þ li yi;t þ ui;t ui;t ¼ d0i Ft þ ei;t

For i ¼ 1, …, N and t ¼ 1, …, T. Ft is a (k  1) vector of commons factors, di is the coefficients vector corresponding to the common factors and ei,t is an idiosyncratic error term which is crosssectionally uncorrelated and follows an infinite MA (Moving P j Average) process. So, we have ei;t ¼ ∞ 3 ~ iid(0, j¼0 gi;j L 3i;tj with P i,t j 1). The common factors follow an infinite MA, Ft ¼ ∞ j¼0 ∅j L hi;tj with hi,t ~ iid(0, Ik) Moon and Perron [44] are testing the following unit root null hypothesis H0: li ¼ 1 for i ¼ 1, …, N against the heterogenous alternative hypothesis H1: li < 1 for some i. After, to study the local power proprieties of this test, the authors examine the following local alternative hypothesis:

q li ¼ 1  pffiffiffiffii NT

PMW ¼ 2

N X

lnðpi Þ

(5)

i¼1

has a c2 distribution with 2N degrees of freedom as T / ∞ and N fixed. The statistic proposed by Choi [14] defined as:

ZMW

pffiffiffiffi N N 1 PMW  E½  2 lnðpi Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ V½  2 lnðpi Þ

(6)

Under the null hypothesis as Ti / ∞ and N / ∞, ZMW / N(0, 1). 2.2.2. Second generation panel unit root tests Three second generation tests will be now discussed. These tests allow for cross sectional dependence to define a new statistic tests.

3

Similarly to LLC test.

(8)

where qi is a random variable with mean mq. Then, the hypotheses test become H00 : m0 ¼ 0 against the local alternative hypothesis H10 : m0 > 0. Moreover, the authors proposed for each ei,tP the following 2 short run and long run variances: s2ei ¼ ∞ and j¼0 gi;j P 2 u2ei ¼ ð ∞ g Þ . The sum of positive autocovariance of idiosynj¼0 i;j P P∞ cratic error term is defined as 4ei ¼ ∞ l¼1 j¼0 gi;j gi;jþl . The non-zero averages of these parameters can be written as follows:

s2e ¼ 2.2.1.3. The Maddala and Wu [39] and Choi [14] tests. Maddala and Wu [39] and Choi [14] suggested the use of Fisher [19] type test which is based on the idea of combining the p-values pi from unit root test-statistics for each cross-sectional unit i. Maddala and Wu [39] affirm that when the test-statistics are continuous, the pi are independent uniform (0, 1) variables. Therefore, 2 ln(pi) follows the chi-squared distribution with two degrees of freedom. So, for a set of independent statistics, Maddala and Wu [39] have proposed the following statistics:

(7)

N 1 X s2 ; N i¼1 ei

u2e ¼

N 1 X u2 N i¼1 ei

and

42e ¼

N 1 X 42 N i¼1 ei

(9)

The testing method suggested by Moon and Perron [44] is summarized as follows. First, the authors proposed a pooled Ordinary Least Squares (OLS) estimation of the first order autoregressive coefficient. Next, they use this estimator to build up an b i;t ¼ yi;t  b estimate of the error terms u lyi;t1 via the principal component analysis and then attain an estimate of the (N  k) ^ ¼ ðb matrix D d 1 ; …; b d N Þ. Finally, in order to remove the common factor effects from the original data (de-factoring the data), the ^ is used to construct the following projection matrix: matrix D ^ 1 D ^ 0 . Then, the modified pooled estimator pro^ D ^ 0 DÞ QD^ ¼ IN  Dð posed by Moon and Perron [44] is:

 tr Yt1 QD^ Yt0  NT4e * b

 l ¼ 0 tr Yt1 QD^ Yt1

(10)

where tr($) is the trace operator and Yt ¼ (y1,t, …, yN,t). From this consistent estimator, Moon and Perron [44] suggested the use of the following two t-statistics, denoted as t*a and t*b, for testing the homogenous unit root hypothesis against heterogenous alternative:

 pffiffiffiffi  * NT b l 1 sffiffiffiffiffiffiffi ta* ¼ 4 2b 4e 4 b ue

/ Nð0; 1Þ

T;N/∞

(11)

M. Shahbaz et al. / Energy 78 (2014) 183e195

tb* ¼

 pffiffiffiffi  * NT b l 1

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

 u be 1 tr Yt1 QD^ Y 0t1 2 NT b 2e 4

! / Nð0; 1Þ

T;N/∞

189

Table 3 Descriptive statistics. Countries

Mean

Std. dev.

Skewness

Kurtosis

JarqueeBera (prob. > c2)

High income countries Middle income countries Low income countries

406.2609

255.7349

0.0757

1.7608

0.000

333.6083

196.5695

0.0333

1.8082

0.000

128.0857

75.8450

0.0548

1.7934

0.000

(12) 2.2.2.2. The Choi [15] test. For testing the presence of unit root, Choi [15] proposes to transform the observed series yi,t in order to eliminate the cross-sectional correlations and controlling for deterministic trends. Consequently, Choi [15] discusses the following error component model:

yit ¼ ai þ qt þ yi;t yi;t ¼

pi X

(13)

di;j yi;t1 þ 3i;t

2.2.2.3. The Pesaran [53] test. Under the assumption of no serial correlation in the residuals, Pesaran [53] keeps the same IPS test structure except that he considers an unobserved common factor ft with an individual specific factor loading coefficient gi:

j¼1

where 3i,t is iidð0; s23i Þ. Firstly, to test the presence of unit root in the individual component, it is necessary to orthogonalize the series yi,t the cross-sectional dependence. Therefore, Choi [15] proposes to isolate yi,t by eliminating the individual and time effects ai and qt. The result is a new variable fzi;t gTt¼2 . From this variable, it is then necessary to perform a unit root test without constant and trend since the entire deterministic components have been removed:

Dzi;t ¼ ri zi;t1 þ

pX i 1

Finally Choi [15] suggests combining the p-value pi of DickeyeFuller unit root t-statistics in each cross-sectional unit and using the following three statistics: N 1 X Pm ¼ pffiffiffiffi ½lnðpi Þ þ 1 / Nð0; 1Þ T;N/∞ N i¼1

(15)

N 1 X F1 ðpi Þ / Nð0; 1Þ Z ¼ pffiffiffiffi T;N/∞ N i¼1   N X 1 pi L* ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N ln / Nð0; 1Þ 1  pi T;N/∞ p2 N 3 i¼1

Table 2 Countries in the sample by income.

Low income countries Bangladesh, Egypt, India, Indonesia, Pakistan, Philippines and Vietnam Total countries

"

Number

" þ di ð1=NÞ

N X

#

N X

# yi;t1

i¼1

(19)

Dyi;t þ 3i;t

i¼1

The t-statistic of the OLS estimate of ri is denoted as ti(N, T) which is referred to CADF (Cross Sectionally Augmented DickeyeFuller) statistic for i. Based on the average of individual statistics, it is possible to build the following panel root t-statistic defined as Cross Sectional Augmented IPS: N 1 X t ðN; TÞ N i¼1 i

(16)

CIPSðN; TÞ ¼

(17)

2.2.3. Panel unit root tests with structural break (third generation panel unit root tests) The first and second generation panel unit root tests may suffer from significant loss of power if the data contains structural breaks. In this case, it is complicated to distinguish between unit root and stationary processes with structural breaks. Today, the panel data unit root tests which allow for structural breaks have received considerable attention among econometricians. In this section we discuss the Lagrange Multiplier (LM)-based4 unit-root test developed by Im et al. [28].

where F is the standard cumulative normal distribution function.

Middle income countries Algeria, Argentina, Brazil, Bulgaria, Chile, China, Colombia, Ecuador, Iran, Malaysia, Mexico, Peru, Romania, South Africa, Taiwan, Thailand, Turkey and Venezuela

where 3i;t  iidð0; s2i Þ and E(34i,t) < ∞. To test of the presence of unit root, Pesaran [53] proposes to augment the DickeyeFuller or Augmented DickeyeFuller model by introducing a cross section average of lagged levels and first-differences of the individual series as follows:

(14)

j¼1

High income countries Australia, Austria, Canada, Czech Republic, Finland, France, Germany, Greece, Hungary, Italy, Japan, New Zealand, Norway, Poland, Portugal, Republic of Ireland, Slovakia, South Korea, Spain, Sweden, Switzerland, United States and United Kingdom

(18)

Dyi;t ¼ ai þ ri yi;t1 þ ci ð1=NÞ

bi;j Dzi;tj þ ui;t

Country/income

ui;t ¼ gi qt þ 3i;t

(20)

23

2.2.3.1. Im, Lee and Tieslau [28] structural break unit root test. In order to test the presence of unit root in the presence of structural break, Im et al. [28] consider a data panel model with N crosssectional units and T periods per unit and assume that structural break happened at the time TB,i for unit i: 18

Yi;t ¼ g0i Zi;t þ ui;t

(21)

ui;t ¼ di ui;t1 þ 3i;t

7

48

4 The LM unit root test can be described by the following model: yt ¼ d0 Zt þ ut with ut ¼ but1 þ 3t.. Lee and Strazicich [35,37] develop versions of univariate LM unit-root test with one and two structural breaks (Models: A, AA, C and CC).

190

M. Shahbaz et al. / Energy 78 (2014) 183e195

Table 4 Descriptive statistics for natural gas consumption in each country. Countries

Mean

Std. dev.

Skewness

Kurtosis

JarqueeBera

Probability

Algeria Argentina Australia Austria Bangladesh Brazil Bulgaria Canada Chile China Colombia Czech Republic Ecuador Egypt Finland France Germany Greece Hungary India Indonesia Iran Italy Japan Malaysia Mexico New Zealand Norway Pakistan Peru Philippines Poland Portugal Republic of Ireland Romania Slovakia South Africa South Korea Spain Sweden Switzerland Taiwan Thailand Turkey United Kingdom Us Venezuela Vietnam

0.066340 4.834832 3.277194 7.161914 0.176650 48.45605 0.633411 66.25641 3.192193 43.02184 5.633535 0.462146 1.062511 2.415986 2.832921 14.27649 4.173679 0.801314 0.038055 15.19223 1.331653 1.619362 9.326898 18.51082 0.986688 5.357592 4.822254 23.99119 3.796998 2.639228 1.241085 0.741480 2.188993 0.168387 2.985893 0.740287 0.287911 0.695220 6.783419 14.62379 7.491609 0.999211 1.065237 5.353917 1.004563 64.43097 9.212935 1.998252

0.035754 2.701010 0.336459 1.479000 0.081347 23.22252 0.184313 14.85241 1.601653 39.44045 2.672052 0.129603 0.679268 0.630483 0.392332 1.956305 0.514982 0.288445 0.008680 5.345567 0.872129 0.786045 1.023267 1.649742 0.552886 1.352708 0.838726 4.696381 1.902252 1.138488 0.557144 0.163076 0.644072 0.027635 0.846657 0.302623 0.162181 0.267828 1.623501 1.752036 0.842188 0.202101 0.429078 3.199761 0.134330 7.093890 5.939431 1.984639

0.891810 0.037687 0.545617 0.755330 0.358632 0.017594 1.038918 0.630635 0.358875 1.481449 0.012556 0.498154 0.007524 0.251419 0.065463 0.191778 0.274088 1.112118 0.110286 0.640019 0.084459 1.612668 0.413944 0.034012 0.138396 0.503055 0.483798 0.315498 0.010445 0.249263 0.027607 0.468954 0.609215 0.166934 0.039512 0.267433 0.618959 0.507506 0.427735 0.024724 0.256209 0.050422 0.209437 0.087527 0.337815 0.280109 0.206422 0.830882

3.681533 2.052253 2.173815 2.895703 2.313214 1.951393 5.737773 2.024517 1.844426 4.456700 1.747021 2.705095 1.934831 2.442084 2.797767 2.249344 3.579866 3.783715 4.602014 2.788525 1.457549 6.119422 3.946334 2.506069 2.032155 2.806507 2.167794 2.235437 1.878770 1.774999 1.983386 2.094663 3.168110 2.301997 2.445610 1.482401 2.922348 2.951148 2.392026 1.911419 2.960962 2.548098 1.899287 1.743775 2.173029 3.136601 1.727839 2.487125

6.076317** 1.506509 3.122286 3.821622 1.643571 1.834693 19.68801*** 4.237284 3.084192 18.16789*** 2.617646 1.799328 1.891351 0.940195 0.096733 1.184332 1.061235 9.269056*** 4.358503 2.805363 4.012815 33.55597*** 2.634911 0.414325 1.688896 1.749493 2.714681 1.637854 2.095990 2.915256 1.727589 2.832176 2.521384 0.997794 0.522655 4.315315 2.564116 1.721058 1.835766 1.979090 0.440159 0.357309 2.311709 2.681242 1.900595 0.554172 2.981390 5.040838*

0.047923 0.470832 0.209896 0.147960 0.439646 0.399578 0.000053 0.120195 0.213932 0.000113 0.270138 0.406706 0.388417 0.624941 0.952784 0.553128 0.588242 0.009711 0.113126 0.245937 0.134471 0.000000 0.267816 0.812888 0.429794 0.416968 0.257344 0.440904 0.350640 0.232788 0.421559 0.242661 0.283458 0.607200 0.770029 0.115596 0.277466 0.422938 0.399364 0.371746 0.802455 0.836395 0.314788 0.261683 0.386626 0.757989 0.225216 0.080426

Note: *statistical significance at 10% level. **Statistical significance at 5% level. ***Statistical significance at 1% level.

where the exogenous variables vector Zi,t ¼ (1, t, Di,t) describes the deterministic elements t and a dummy variable Di,t representing the time of structural break,5 defined as follows:

 Di;t ¼

0; t < TB;i t  TB;i ; t  TB;i

(22)

Based on the univariate LM unit root statistic developed by Lee and Strazicich [28], Im et al. [35] suggested a panel LM unit root test statistic. The Lee and Strazicich's model can be considered as follows:

DYi;t ¼

g0i DZi;t

þ di ~ Si;t1 þ 3i;t

where D is the first difference operator, ~ Si;t1 is the detrended variable of Yi,t1 and 3i,t is the error term. The t-statistic (denoted t*i ) for the null hypothesis H0: di ¼ 0 can be calculated for each unit in order to conclude the panel LM test statistic:

(23)

t¼

N 1 X t* N i¼1 i

This in turn can be used to determine the following standardized panel LM test statistic:

 LM t ¼ 5

The analysis can incorporate two structural breaks and the vector of exogenous variables becomes Zit ¼ (1, t, D1i,t, D2i,t) where D1i,t and D2i,t are the dummy variables that denoted first structural break and the second structural beak, respectively.

(24)

pffiffiffiffi

 N tE t qffiffiffiffiffiffiffiffiffiffi

 V t

EðtÞ and VðtÞ are tabulated by Im et al. [28].

(25)

M. Shahbaz et al. / Energy 78 (2014) 183e195

191

Table 5 Linearity test results. Countries

Statistics

Prob. value

Result

Countries

Statistics

Prob. value

Result

US Canada Mexico Argentina Brazil Chile Colombia Ecuador Peru Venezuela Austria Bulgaria Czech Republic Finland France Germany Greece Hungary Rep. of Ireland Italy Norway Poland Portugal Romania

7.856 33.300 24.232 8.407 11.529 42.362 50.268 29.336 23.003 6.304 18.221 22.917 6.136 12.932 2.681 27.476 3.181 12.160 9.242 10.834 8.551 10.855 7.456 11.022

0.097 0.000 0.000 0.078 0.021 0.000 0.000 0.000 0.000 0.178 0.001 0.000 0.189 0.012 0.613 0.000 0.528 0.016 0.055 0.028 0.073 0.028 0.114 0.026

Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Linear Nonlinear Nonlinear Linear Nonlinear Linear Nonlinear Linear Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Linear Nonlinear

Slovakia Spain Sweden Switzerland Turkey United Kingdom Iran Algeria Egypt South Africa Australia Bangladesh China India Indonesia Japan Malaysia New Zealand Pakistan Philippines South Korea Taiwan Thailand Vietnam

19.266 17.801 16.621 24.689 12.982 5.224 13.968 9.367 7.883 14.032 8.569 6.231 15.788 27.166 9.370 26.820 10.519 1.764 17.890 10.642 7.369 1.054 10.466 347.083

0.001 0.001 0.002 0.000 0.011 0.265 0.007 0.053 0.096 0.007 0.073 0.183 0.003 0.000 0.052 0.000 0.033 0.779 0.001 0.031 0.118 0.901 0.033 0.000

Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Linear Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Linear Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear Linear Nonlinear Nonlinear Linear Linear Nonlinear Nonlinear

Note: the 1%, 5%, and 10% critical values for Harvey et al. [69] test are respectively 7.779, 9.488, and 13.277.

3. The data In this study, we use the energy consumption data per capita (expressed in million cubic feet) for 48 countries categorized into three income level classes6 (Table 2). The data is obtained from World Development Indicator data-base (World Bank) and covering the period 1971e2010. Table 3 reports summary statistics for our panel data set. The panel data are significantly normally distributed (with p < 0.05). The High income countries represent about 50% of our sample and they are the largest consumer of natural gas. Table 4 show the descriptive statistics of the energy consumption by country. Canada has the highest average level of energy consumption. On the other side, Hungary has the lowest average level. Natural gas demand tends to be more volatile for China and Brazil. JarqueeBera statistics indicate that we reject the null hypothesis of normal distribution for Bulgaria, China, Greece and Iran (at the 1% significance level), Algeria (at 5%) and Vietnam (at 10%). Skewness and Kurtosis statistics confirm JarqueeBera test results.

4. Empirical results and their discussions 4.1. Univariate unit root tests First, we begin by testing the hypothesis of linearity of natural gas consumption for each country. In order to decide whether to introduce nonlinearities under the alternative hypothesis, we employ the Harvey et al. (2008) [69] linearity test. We presented the linearity test results in Table 5. The hypothesis of linearity is rejected in 38 countries out of 48. Thus, a total of almost 80% of energy consumption time series are nonlinear which implies that nonlinearity is an important property of natural gas consumption in our sample. For the rest of countries, Harvey et al. (2008) [69] test Wl indicates evidence in favor of linear models. Hence, we have

6

According to the World Bank classification.

applied the Lee and Strazicich [35,37] linear unit root tests, along with the Kruse (2011) [71] test. When the linearity hypothesis is rejected, we perform the Kruse [71] unit root test. The unit root tests provide analysis of whether energy consumption tends to turn back to its time trend after a shock. As Table 6 reveals, the unit root null is rejected for 18 countries (Mexico, Argentina, Brazil, Chile, Colombia, Ecuador, Peru, Poland, Romania, Turkey, South-Africa, India, Indonesia, Malaysia, Pakistan, Philippines, Thailand and Vietnam) suggesting that energy price shocks will have a permanent effects on natural gas consumption. However, for the remaining 20 countries, the natural gas consumption is a stationary process. Therefore, any shock to energy demand is likely to be transitory and the energy demand management policies will have a temporary impact.

Table 6 ESTAR unit root test results. Countries

KSS

Result

Countries

KSS

Result

US Canada Mexico Argentina Brazil Chile Colombia Ecuador Peru Austria Bulgaria Finland Germany Hungary Rep. of Ireland Italy Norway Poland Romania

2.683 2.959 2.165 1.319 0.328 2.017 1.178 1.915 0.504 2.724 2.963 3.521 3.683 3.324 2.798

Stationary Stationary Nonstationary Nonstationary Nonstationary Nonstationary Nonstationary Nonstationary Nonstationary Stationary Stationary Stationary Stationary Stationary Stationary

Slovakia Spain Sweden Switzerland Turkey Iran Algeria Egypt South Africa Australia China India Indonesia Japan Malaysia

2.711 2.793 2.829 2.953 1.166 3.684 2.774 2.663 2.417 4.382 3.078 1.147 0.276 3.028 0.234

Stationary Stationary Stationary Stationary Nonstationary Stationary Stationary Stationary Nonstationary Stationary Stationary Nonstationary Nonstationary Stationary Nonstationary

3.146 2.292 2.000 1.629

Stationary Stationary Nonstationary Nonstationary

Pakistan Philippines Thailand Vietnam

1.009 1.665 1.982 0.889

Nonstationary Nonstationary Nonstationary Nonstationary

Note: the 1%, 5%, and 10% critical respectively 3.48, 2.93, and 2.66.

values,

for

Kruse

[71]

test,

are

192

M. Shahbaz et al. / Energy 78 (2014) 183e195

Table 7 LM univariate unit root test results.

Venezuela Czech Republic France Greece Portugal United Kingdom Bangladesh New Zealand South Korea Taiwan LM panel unit root test [28] a

LM univariate test without break [55]

k

LM univariate test with one break (Model C)

k

TB

LM univariate test with two breaks (Model CC)

k

TB1

TB2

Result

0.1755 (2.3473) 0.3875* (2.9396) 0.4834** (3.2047) 0.4644* (2.9780) 0.2855 (1.3937) 1.0145***(5.6003) 0.3974* (2.9144) 0.3929* (2.7816) 0.5145** (3.3730) 0.3916 (2.1136) 12.856***

1 4 0 0 2 0 0 0 0 1

0.7605** (4.7543) 0.5306* (3.5308) 0.8348** (4.7142) 0.9071** (4.8016) 1.0597*** (5.9299) 1.0232*** (5.6927) 0.9633** (4.9368) 1.3029** (4.9443) 0.8897** (4.7494) 1.0901*** (6.2387) 23.766***

3 0 0 1 0 0 1 2 0 0

1989 1988 1981 1986 2007 1984 1994 1995 1990 1999

0.9364* (5.6263) 1.3602** (5.7854) 0.9982* (5.3586) 1.1082** (6.0190) 1.1969*** (6.5952) 2.4575*** (7.2422) 1.5448*** (6.5317) 1.4363** (6.4020) 1.5939** (6.4269) 1.2797*** (7.7052) 38.902***

3 1 0 1 0 4 2 2 1 0

1989 1981 1982 1986 1995 1995 1993 1984 1986 1987

2003 1988 1993 2005 2006 2005 1998 1997 1997 2001

Stationary with break Stationary Stationary Stationary Stationary with break Stationary Stationary Stationary Stationary Stationary with break

Notes: numbers in the parentheses are the optimal number of lagged first-differenced terms included in the unit root test to correct for serial correlation. The 1, 5, and 10% critical values for the LM unit root test with no break are: 3.63, 3.06, and 2.77. The 1%, 5%, and 10% critical values for the minimum LM test with one break are: 4.239, 3.566, and 3.211. The 1%, 5%, and 10% critical values for the minimum LM test with two breaks are: 4.545, 3.842, and 3.504, respectively. The 1%, 5% and 10% critical values for the panel LM unit root tests with structural breaks are 2.326, 1.645 and 1.282 respectively. *Significance at 10% level. **Significance at 5% level. ***Significance at 1% level. a We can find Gauss codes for the Im et al. [28] test on Junsoo Lee's homepage (http://old.cba.ua.edu/~jlee/gauss).

Table 8 Cross sectional dependence test analysis. Cross sectional dependence test

Frees' test of cross sectional independence (p-value) Pesaran's test of cross sectional independence (p-value) Friedman's test of cross sectional independence (p-value)

Panel data form Full panel

High

Low

Medium

30.243 (0.0000) 77.289 (0.0000) 695.905 (0.0000)

1.598 (0.0000) 5.711 (0.0000) 86.524 (0.0000)

1.376 (0.0000) 3.825 (0.0001) 11.969 (0.0627)

3.720 (0.0000) 1.179 (0.283) 40.733 (0.0010)

When the hypothesis of linearity is not rejected, we use the LM unit root test. We begin by examining the behavior of natural gas consumption through applying a unit root test with no break. We choose to use the unit root test of SchmidtePhillips [55] which has a better power than standards tests (DickeyeFuller [18] and PhillipsePerron [54] tests). However, the main limitation of the SchmidtePhillips [55] test that it does not allow for structural breaks which are likely to be the characteristic of energy consumption in many countries due to macroeconomic and political stability. As argued by Amsler and Lee [2]; the SchmidtePhillips test is biased toward accepting the null hypothesis when the alternative is true. To address this limitation we implement the LM unit root test with one and two structural breaks developed by Lee and Strazicich [35,37]. They offer a minimum LM test with breaks in the level (or intercept) and trend. The LM unit root test not only endogenously determines from the data the time of structural breaks but also avoids the drawback of “spurious rejection” when the null hypothesis is true because Lee and Strazicich [35] allow for structural breaks under both the null and alternative hypotheses. Concerning the LM unit root tests with breaks, we choose to conduct the Model C because, according to Sen [56,57]; the model one break in the level and trend performs better than model A in the case of unknown breakpoint dates.7 Moreover, the model AA is nested within Model CC (to Lean and Smyth [33]). In other words, the model which allows for breaks in intercept and trend is more general than the test assuming that the breaks only occur in the intercept. This is why we choose the model CC over the model AA. In Table 7, we display the results of the individual LM unit root tests for 10 countries which show linear behavior. The unit root null is rejected for 7 countries (Bangladesh, Czech Republic, France,

7 Sen [56,57] provides evidence through Monte Carlo simulation that model C performs better than model A in the case of unknown breakpoint dates.

Greece, New Zealand, South Korea and United Kingdom) when structural breaks are ignored. However, when we take into account the LM unit root test with structural breaks, the unit root null is rejected for three more countries (Portugal, Taiwan and Venezuela). These mean that any shock to energy demand will have transitory impacts. These findings overturn the results of early studies tested for a unit root in energy consumption by using conventional tests without structural breaks (ADF, PhillipsePerron -PP- and KPSS). Concerning the break dates, the first breaks generally correspond to 1981e1989 decade for more than two-thirds of countries.8 These incidents include energy crisis of 1979 that was triggered by the Iranian revolution and adversely affected the country's energy sector and global energy industry.9 Besides, the world experienced the oil glut (caused by falling demand) in the early 1980s plus the outbreak of IraneIraq war (in September 1980), which severely affected the global energy outlook [23,50]. The structural breaks of other series correspond to the 1993e1997 period. The second break dates generally coincide with 2001e2006 period. These incidents include the 9/11 in the USA affected world economic activity as well as energy supply. All in all, our results provide evidence in favor of the stationarity hypothesis for 30 of 48 countries. This finding has an important implication that more than 60% of the series are stationary. Hence, the stationarity is an important property of our natural gas consumption series which implies that any shock to natural gas consumption has a transitory impacts for almost two third of the countries in our sample. In that case, the past behavior of energy demand will be of use in formulating forecasts [6].

8 Czech Republic, France, New Zealand, South Korea, Greece, Taiwan, and Venezuela. 9 More than half of the world's gas reserves are in three countries: Russia, Iran and Qatar (OPEC, 2010) [74].

M. Shahbaz et al. / Energy 78 (2014) 183e195 Table 9 Panel data unit root analysis.a Types of test statistic

193

Table 10 Panel unit root test which allow for structural breaks [28]. Test statistic

1% CV

First generation of panel unit root tests: full panel LLC test statistic 8.3744 2.3263 IPS test statistic 11.5931 2.3263 MW test statistic 290.9159 133.4756 Choi test statistic 14.0668 2.3263

5 % CV

10 % CV

1.6449 1.6449 122.1077 1.6449

1.2816 1.2816 116.3152 1.2816

1.6449

1.2816

1.6449

1.2816

2.6077 1.6449 1.6449 1.6449

2.5441 1.2816 1.2816 1.2816

First generation of panel unit root tests: high income LLC test statistic 11.0250 2.3263 IPS test statistic 11.8060 2.3263 MW test statistic 103.068 71.2014 Choi test statistic 10.7137 2.3263

panel 1.6449 1.6449 62.8296 1.6449

1.2816 1.2816 58.6405 1.2816

Second-generation panel unit root tests: high income Moon Perron1 statistic 8.1245 2.3263 (ta_bar statistic) Moon Perron2 statistic 5.7333 2.3263 (tb_bar statistic) Pesaran test [53] 7.773 2.8749 Choi test statistic (Pm) 14.4759 2.3263 Choi test statistic (Z) 8.4181 2.3263 Choi test statistic (Lstar) 10.0702 2.3263

panel 1.6449

1.2816

1.6449

1.2816

2.7148 1.6449 1.6449 1.6449

2.6298 1.2816 1.2816 1.2816

First generation of panel unit root tests: low income panel LLC test statistic 1.4327 2.3263 1.6449 IPS test statistic 1.6069 2.3263 1.6449 MW test statistic 33.8849 29.1412 23.6847 Choi test statistic 3.7579 2.3263 1.6449

1.2816 1.2816 21.0641 1.2816

Second-generation panel unit root tests: full panel Moon Perron1 statistic 2.8608 2.3263 (ta_bar statistic) Moon Perron2 statistic 2.4549 2.3263 (tb_bar statistic) Pesaran test [53] statistic 6.084 2.7260 Choi test statistic (Pm) 13.3044 2.3263 Choi test statistic (Z) 9.6374 2.3263 Choi test statistic (Lstar) 10.3160 2.3263

Second-generation panel unit root tests: low income panel Moon Perron1 statistic 5.2348 2.3263 1.6449 (ta_bar statistic) Moon Perron2 statistic 4.3906 2.3263 1.6449 (tb_bar statistic) Pesaran test [53] 2.243 3.0705 2.8353 Choi test statistic (Pm) 3.5782 2.3263 1.6449 Choi test statistic (Z) 1.6218 2.3263 1.6449 Choi test statistic (Lstar) 2.1255 2.3263 1.6449 LLC test statistic 8.1364 2.3263 1.6449 IPS test statistic 8.5498 2.3263 1.6449 MW test statistic 78.040 56.0609 48.6023 Choi test statistic 8.5170 2.3263 1.6449 Second-generation panel unit root tests: middle income panel Moon Perron1 statistic 9.1880 2.3263 1.6449 (ta_bar statistic) Moon Perron2 statistic 3.3473 2.3263 1.6449 (tb_bar statistic) Pesaran test [53] 4.318 2.9330 2.7534 Choi test statistic (Pm) 4.9544 2.3263 1.6449 Choi test statistic (Z) 3.9529 2.3263 1.6449 Choi test statistic (Lstar) 4.1222 2.3263 1.6449

1.2816 1.2816 2.7264 1.2816 1.2816 1.2816 1.2816 1.2816 44.9031 1.2816

1.2816 1.2816 2.6676 1.2816 1.2816 1.2816

a We can find Matlab codes for the panel unit root test on Christophe Hurlin's homepage (http://www.univ-orleans.fr/deg/masters/ESA/CH/churlin_R.htm).

4.2. Panel data unit root tests To make the analysis robust, the results of panel data unit root tests should be compared with those obtained with univariate unit root tests. In order to check the degree of integration of our series, we have thus carried out a panel data unit root tests for the following panels: the full countries panel (48 countries), high

Panels

No break

One break

Two breaks

Full panel High income panel Middle income panel Low income panel

44.195*** 29.581*** 24.044*** 8.738***

51.699*** 37.055*** 41.075*** 21.171***

105.419*** 47.990*** 44.554*** 26.743***

Note: the 1%, 5% and 10% critical values for the panel LM unit root tests with structural breaks are 2.326, 1.645 and 1.282 respectively. *Significance at 10% level. **Significance at 5% level. ***Significance at 1% level.

income countries panel (23 countries), middle income countries panel (18 countries) and low income countries panel (7 countries). However, before examining the order of integration of our series we have to test the assumption of cross sectional dependence in panels which can arise due to a multiplicity of factors such as unobserved or/and omitted common factors, spatial correlations, economic distance and common unobserved shocks. Three tests for cross section dependence have been used in our study namely, Pesaran's [75] cross sectional dependence test, Friedman's [20] statistic and the test statistic proposed by Frees [67]. Table 8 reveals that the null hypothesis of no cross-sectional dependence is largely rejected at 1% and 10% respectively leading us to conclude the dependence in our data. This finding highlights the importance of taking into account cross-section dependence when investigating the energy consumption stationarity. Despite the presence of cross-sectional dependence we employed a series of panel unit root tests that assume cross sectional independence (the so called first generation panel data unit root tests) and cross-sectional dependence (second generation panel data unit root tests). All unit root tests with no exception suppose no-stationarity under the null hypothesis. However, these tests do not allow for structural breaks. For this reason we completed our analysis by employing the Lagrange Multiplier (LM) panel unit root test with level breaks [28]. The null hypothesis of the LM panel test is that all series contain unit roots, with the alternative that some of the series in the panel are stationary. The results of panel unit root tests reported in Table 9 indicate that null hypothesis of unit root test in natural gas consumption per capita series is rejected by both first and second generation tests for the full panel, high income countries panel, middle income countries and low income countries. The results from the Im, Lee and Tieslau [28] test (Table 10), allowing for structural breaks, corroborate the findings of both the first and second generation panel data unit root tests. The unit root is rejected for each panel in the one and two breaks. The LM panel test provides as well strong evidence in favor of stationarity of natural gas demand. This leads us to conclude that the energy consumption is stationary in each of the four panels. These findings imply that exogenous shocks have a temporary effect in energy demand for the whole countries sample. Finally, for comparison purposes, we applied panel LM unit root test of Im et al. [28] for linear time series. The results are reported at the bottom of Table 7 where we found evidence in support of stationarity for the panel of countries that follow a linear behavior. This finding indicates that natural gas consumption for these countries will return back to its trend path over time and it might be possible to forecast future projections in reference to past energy consumption. 5. Concluding remarks and policy implications The empirical investigation of unit root properties of natural gas consumption is helpful in modeling energy-growth nexus as well as detecting the direction of causality between natural gas

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consumption and economic growth. Before testing the stationarity of the series we use the linearity test in order to determine the type of unit root tests. In this study we employed the linearity test of Harvey et al. [69] which is powerful when the order of integration is unknown. We found more than 80% of time series are nonlinear. For linear series, we have applied the linear LM univariate unit root test with one and two unknown structural breaks to test unit root properties of natural gas consumption per capita. In nonlinear case, we performed the ESTAR unit root test. The empirical findings indicate that the stationarity of natural gas consumption cannot be rejected for more than 60% of countries. For the purpose of robustness analysis, we have applied first and second generation panel unit root tests for testing the stationary properties of natural gas consumption. We found as well strong evidence supporting the stationarity of natural gas consumption for all the panels (high income group countries, middle income countries and low income countries panel) which corroborate the findings of the univariate unit root tests. Ref. [28] is also used to test unit root properties in presence of structural breaks in the series gas consumption at panel level. The empirical findings indicate that the stationarity of natural gas consumption cannot be rejected for all panels. Finally, these results announce that any shock to natural gas consumption has a transitory impact for almost all countries implying that energy consumption will turn back to its time trend. In such situation, changes in natural gas consumption will have only a transitory impact on economic growth. So, policymakers should not design any energy policy mechanism which may have adverse effect on the relationship between natural gas consumption and economic growth. Our results are consistent with Mishra and Smyth [42] who reported that natural gas consumption is stationary at level but Golpe et al. [21] noted that natural gas consumption contains unit root problem. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.energy.2014.09.080. References [1] Al-Iriani M. EnergyeGDP relationship revisited: an example from GCC countries using panel causality. Energy Policy 2006;34:3342e50. [2] Amsler C, Lee J. An LM test for unit root in the presence of a structural change. Econ Theory 1995;11:359e68. [3] Apergis N, Tsoumas C. Long memory and disaggregated energy consumption: evidence from fossils, coal and electricity retail in the U.S. Energy Econ 2012;34(4):1082e7. [4] Apergis N, Loomis D, Payne JE. Are shocks to natural gas consumption is temporary or permanent? Evidence from panel of US states. Energy Policy 2010a;38:4734e6. [5] Apergis N, Loomis D, Payne JE. Are fluctuations in coal consumption transitory or permanent? Evidence from a panel of US states. Appl Energy 2010b;87: 2424e6. [6] Aslan A. Does natural gas consumption follow a non linear path over time? Evidence from 50 states. Renew Sustain Energy Rev 2011;15:4466e9. [7] Aslan A, Kum H. The stationary of energy consumption for Turkish disaggregated data by employing linear and non-linear unit root tests. Energy 2011;36:4256e8. [8] Barros CP, Gil-Alana LA, Payne JE. Evidence of long memory in U.S. nuclear electricity net generation. Energy Syst 2013a;4:99e107. [9] Barros CP, Gil-Alana LA, Payne JE. U.S. disaggregated renewable energy consumption: persistence and long-memory behavior. Energy Econ 2013b;40: 425e32. [10] Bolat S, Belke M, Celik N. Mean reverting behavior of energy consumption: evidence from selected MENA countries. Int J Energy Econ Policy 2013b;4: 315e20. [11] Bolat S, Belke M, Kovachi S. The stationarity of electricity consumption in selected European countries. Eur Sci J 2013a;19:79e87. [12] Carrion-i-Silvestre J, Barrio-Castro TD, Lopez-Bazo E. Breaking the panels: an application of to GDP per capita. Econ J 2005;8:159e75.

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