CC BY
168T. Omay, M. Hasanov, N. Ugar
Energy consumption and economic growth: Evidence from nonlinear panel cointegration and causality tests
In this paper, we examine nonlinear interrelationship between energy consumption and output level for a panel of G7 countries. For this purpose, we propose a nonlinear cointegration test in heterogeneous panels for testing the presence of a cointegrating relationship that follows a globally stationary exponential smooth transition (ESTR) process, and apply our test for investigating long-run relationship between energy use and economic growth in the case of the G7 countries. Our results suggest the presence of a long-run relationship between these two variables whereas adjustment to the equilibrium is inherently nonlinear. After establishing long-run relationship between energy consumption and output, we estimate a Panel Smooth Transition Vector Error Correction Model and apply nonlinear Granger causality tests in order to analyze the direction of the causality between these variables. We find that the causality between energy consumption and output level is dependent on the phases of business cycle. Our results highlight importance of taking account of possible nonlinearities in analyzing output-energy causality nexus and designing energy policies.
Keywords: nonlinear panel cointegration; nonlinear Panel Vector Error Correction Model; cross section dependency. JEL classification: C12; C22.
1. Introduction
The relationship between energy consumption and economic growth has been one of the most investigated yet controversial issues in the energy economics literature since the seminal work (Kraft, Kraft, 1978). The interest of energy economists on this issue gained a new momentum with increasing concerns about global warming, especially after adoption of the Kyoto Protocol in 1997 that entered into force in 2005. Industrialized member countries committed themselves to a reduction of greenhouse gas emission, mainly by restricting fossil fuel consumption. However, since energy is considered as an essential factor of production by many energy economists, e. g., (Stern, 2000; Oh, Lee, 2004; Ghali, El-Sakka, 2004; Beaudreau, 2005; Lee, Chang, 2008), it is argued that reducing energy consumption may hamper economic growth and hence increase unemployment. On the other hand, the proponents of the so-called «conservation hypothesis» argue that the positive relationship between energy consumption and output level stems from positive effects of output growth rate on energy consumption, and hence policies aimed at conserving energy consumption will have only a limited, if any, adverse effect on economic growth. Similarly, supporters of the «neutrality hypothesis» argue that energy consumption and output level are not correlated, and therefore neither energy conservation nor energy promoting policies will affect economic growth of countries (see, for example, (Lee, Chang, 2008; Apergis, Payne, 2009; Ozturk, 2010)). Taking account of these alternative views regarding the relationship
between energy consumption and output level, it is evident that discovering the causal linkages a, between energy consumption and economic growth is vital in designing energy policies for each s-nation. g
(Q
Although the causal relationship between economic growth and energy consumption has been | investigated extensively in the literature, no consensus has been reached yet (see, for instance, ^ a recent literature survey (Ozturk, 2010)). Stern (2000), Oh and Lee (2004), Wolde-Rufael (2004), | Ho and Siu (2007), among others, argue that only energy consumption leads output growth. On ^ the other hand, Zamani (2007), Mehrara (2007), Ang (2008), Zhang and Cheng (2009) argued that causality runs from output to energy consumption, in accordance with the conservation hypothesis. Glasure (2002), Erdal et al. (2008) and Belloumi (2009) found a bi-directional causality between the energy consumption and output level. However, Halicioglu (2009) and Payne (2009) found no causality between energy consumption and output. Soytas and Sari (2003), Lee (2006), Francis et al. (2007), Akinlo (2008), Chiou-Wei et al. (2008) found mixed results for various groups of countries.
Conflicting results in the empirical literature have usually been attributed to use of different time periods, sample countries, econometric methods, and functional forms (e. g., (Soytas, Sari, 2003; Lee, 2006; Ozturk, 2010; Balcilar et al., 2010; Costantini, Martini, 2010)). Modelling possible nonlinear relationships between economic variables has attracted huge interest of economists, and a growing body of empirical work is being devoted to examination of possible nonlinear causal relationships between energy consumption and output level. Recent studies (Hamilton, 2003; Chiou-Wei et al., 2008; Huang et al., 2008; Aloui, Jammazi, 2009; Gabreyohannes, 2010; Rahman, Serletis, 2010), among others, imply that the interrelationship between energy consumption and economic variables might be inherently nonlinear.
Chiou-Wei et al. (2008) examined causality between energy consumption and output in the case of eight Asian countries and the USA using linear and nonlinear causality tests. They found that the implied direction of causality between energy consumption and output in the cases of Taiwan, Singapore, Malaysia and Indonesia is reversed when possible nonlinearity in the interrelationship between the variables is allowed for. However, both the linear and nonlinear causality tests suggest the same direction of causality or non-causality in the cases of Korea, Hong-Kong, Philippines, Thailand and the USA.
Huang et al. (2008) examined nonlinear relationships between energy consumption and economic growth for 82 countries using threshold regression models. Using various candidates for the regime-switching variable they found significant positive relationship between energy consumption and output growth for regimes associated with lower threshold values. However, when the threshold variables are higher than certain threshold levels, they found either no significant relationship or a significant but negative relationship between energy consumption and economic growth.
Hamilton (2003) examined nonlinear relationship between oil price changes and GDP, and found clear evidence of nonlinearity. His results suggest that oil price increases affect GDP much more than oil price decreases. Aloui and Jammazi (2009) examined the relationship between crude oil shocks and stock markets in the case of the UK, Japan, and France using Markov switching EGARCH models. They found that the responses of the real stock market return volatilities to crude oil shocks are regime dependent in all three markets.
Gabreyohannes (2010) examined the effects of price change on electricity consumption using nonlinear smooth transition regression (STR) modelling approach, and found that changes in electricity prices affect residential electricity consumption in Ethiopia asymmetrically. In a simi-
lar framework, Rahman and Serletis (2010) examined asymmetric effects of oil price shocks and monetary shocks on macroeconomic activity using multivariate STR model for the USA. They found that both the oil prices and oil price volatility affect output nonlinearly.
Cheng-Lang et al. (2010) examined causality between sectoral electricity consumption in Taiwan using linear and nonlinear causality tests and found nonlinear bi-directional causality between total electricity consumption and output level, and unidirectional nonlinear causality from output level to residential electricity consumption.
Lee and Chang (2007) and Huang et al. (2008) examined energy consumption output growth causality by separating countries into different groups by level of development and found that the direction of causality varies with level of development. Their results suggest that the causality between energy consumption and output level is not linear, and depends on output level. In addition, Moon and Sonn (1996) argued that economic growth rate rises initially with productive energy expenditures but subsequently declines. In other words, according to Moon and Sonn (1996), there is an inverse U-shaped nonlinear relationship between energy consumption and economic growth.
Our main aim in this paper is to investigate nonlinear causal relationship between energy consumption and out growth rate in the case of G7 (group of seven) countries. The G7 countries are the most industrialized countries that play a crucial role in global economy, and have comparable level of economic development. In addition, these countries' share in total carbon dioxide emission accounted for around 32.2% in 2007 according to calculations of Carbon Dioxide Information Analysis Center (CDIAC) of the US Department of Energy (Boden et al., 2010). In recent years, the G7 countries have followed policies aimed at reducing total greenhouse gas emissions. Therefore, it is important to discover all aspects of the causal relationship between energy consumption and output for these countries.
Soytas and Sari (2003, 2006), Zachariadis (2007), Narayan et al. (2007), Narayan and Smyth (2008), Lee and Chien (2010), among others, have examined the energy consumption and output growth causality for the G7 countries, and found mixed results. Soytas and Sari (2003, 2006), Zachariadis (2007), Lee and Chien (2010) used various multivariate cointegration and causality tests. On the other hand, Narayan et al. (2007), Narayan and Smyth (2008) applied panel cointe-gration techniques. Although we also use panel data techniques, our approach in this paper differs from previous studies in that we allow for possible nonlinearities in interrelationships between energy consumption and output level. This approach allows examination of asymmetric dynamic effects of one variable on another, which is crucial for design of appropriate energy policies.
The main novelty of the paper is that, we propose a nonlinear panel cointegration and causality tests in order to investigate the causal relationship between energy consumption and real output level. Although linear panel cointegration test of Pedroni (2004) indicate no cointegration relationship, we find strong evidence of cointegration after allowing for nonlinearity in the long-run relationship, suggesting that adjustment to the equilibrium level is also nonlinear in nature. This result implies that any shocks to energy consumption in general, and energy policies in particular will affect output level asymmetrically in the long-run. Another contribution of the paper is that we estimate a panel smooth transition vector error correction model that allows for smooth changes between two distinct regimes and examine causal relationship in each regime separately. Estimated model and regime dependent Granger causality tests suggest that the dynamic interrelationship between energy use and output level is dependent on the phases of business cycles. This is an important finding that implies that policy authorities must be careful in designing and implementing energy policies since the effects of one variable on another will not always be the same.
The remaining of the paper is structured as follows. In the next Section 2 we describe our newly &
proposed nonlinear panel cointegration and causality tests as well as panel error correction model. <■
In Section 3 we provide results of the tests, and then Section 4 concludes. |
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2. Econometric Methodology J
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Although several plausible nonlinear models have been used in the empirical economics literature, we prefer smooth transition regression (STR) modelling approach. The STR modelling approach has several advantages over other nonlinear models (see, for example, (Terasvirta, Anderson, 1992; Granger, Terasvirta, 1993)). First, STR models are theoretically more appealing over simple threshold and Markov regime switching models, which impose an abrupt change in coefficients. Instantaneous changes in regimes are possible only if all economic agents act simultaneously and in the same direction. Second, the STR model allows for modelling different types of nonlinear and asymmetric dynamics depending on the type of the transition function. In particular, a STR model with a first-order logistic transition function is more convenient for modelling the interaction between energy consumption and output growth rate if the dynamic interrelationships between the variables depend on the phases of business cycles. On the other hand, a STR model with an exponential or second-order logistic transition function is more convenient if, for example, the interaction between the variables depends not on the sign but on the size of fluctuations in variables. Finally, STR modelling approach allows one to choose both the appropriate switching variable and the type of the transition function unlike other regime switching models that impose both the switching variable and function a priori.
Now we briefly discuss nonlinear panel cointegration and causality tests as well as panel error correction model.
2.1. Nonlinear Panel Cointegration Test
Consider the following panel regression model:
y,,t = a, +b,x,,t + uit for i = 1,..., N, and t = 1,...,T, (1)
where yit and xit denote observable /(1) variables, b = (A,...,bm) are parameters to be estimated, uit is the error term, yit is scalar, and xit =(xlt,x2t,...,xmt) is an (mx1) vector and finally ai is fixed effect (heterogeneous intercept). We assume that an (n x1) vector z'it =(yit,..., xit) is generated as zit = zit-1 +eit, where eit are i. i. d. with mean zero, positive definite variance-covariance matrix S, and E(eit)x < oo for some 5 > 4 .
If the error term u{ t in regression (1) is stationary, then vector zt t is said to be co-integrated, and uit is called equilibrium error (Engle, Granger, 1987). In this paper, we assume that uit can be modelled using following nonlinear model:
ui,t = g u ,t-1 + t-1F ( ,t-1; )+Ci ,t, (2)
where Cit is a zero mean error and F(uit-1; 0J is a smooth transition function of uit. Note that by imposing F (uit-1; 6j ) = 0 or F (uit-1; 6j ) = y,X where mi is vector of level parameters,
one obtains conventional linear cointegration equation (e. g., (Kapetanois et al., 2006)). Following earlier literature on nonlinear cointegration (e. g., (Kapetanois et al., 2003, 2006; Ufar, Omay, 2009; Maki, 2010)) we assume that the transition function F {ui t-1; 6i) is of the exponential form1:
F (uht-i; 6i) = 1- exp {-6ul-i}. (3)
Here it is further assumed that u, t is a mean zero stochastic process and that 6i > 0 . The transition function F (uit-1; 6i) is bounded between zero and one, and is symmetrically U-shaped around zero. The parameter 6i determines the speed of the transition between the two extreme values of the transition function F {ui t-1; 6i )2. The exponential transition function has a nice property in that it allows for adjustment to the long-run equilibrium depending on the size of the disequilibrium.
Substituting (3) in (2) and re-parameterising the resultant equation, we obtain following regression model:
Du,,t = P,u, ,t-i + V U,,t-1 fl - exp {-6,u,2t-i}] + C,- ,t. (4)
If 6i > 0, then it determines the speed of mean reversion. If 6i > 0, this process may exhibit unit root or explosive behaviour for small values of u2t-1. However, if the deviations from the equilibrium are sufficiently large (i. e., for large values of u2t-1), it has stable dynamics, and as a result, is geometrically ergodic provided that pt + V, < 03.
Imposing pi = 0 (implying that u, t follows a unit root process in the middle regime) and further allowing for possible serial correlation of the error term in (4) we obtain the following regression model:
p,
Du,,t = V,u,j-i fl - exp {-6iu5-i}] + 2 jt-j + C,,t. (5)
j=i
Test of cointegration can be based on the specific parameter 6i, which is zero under the null hypothesis of no-cointegration, and positive under the alternative hypothesis. However, direct testing of the null hypothesis is not feasible, since Vi- is not identified under the null. To overcome this problem, following (Luukkonen et al., 1988), one may replace the transition function F {ui t-1; 6,) = 1 - exp {-6iu2it-1} with its first-order Taylor approximation under the null, which
results in the following auxiliary regression model:
p,
Dui ,t=d,uit-i + 2 Pij u>t- J +e-,t, (6)
j=i
where eit comprises the original shocks Cit in equation (5) as well as the error term resulting from Taylor approximation. Note that we allow for different lag order pt for each entity in regression equation (6). Now, the null hypothesis of no cointegration and the alternative can be formulated as:
H0 : d = 0, for all i (no cointegration),
H1 : d <0, for some i (non-linear cointegration).
1 Kapetanois et al. (2003, 2006) show that both second-order logistic and exponential functions give rise to the same auxiliary regression for testing the cointegration.
2 For a thorough discussion of smooth transition regression models and properties of transition functions, see, for example, (Granger, Terasvirta, 1993) and (Terasvirta, 1994).
3 For ergodicity of such nonlinear processes, see (Kapetanois et al., 2003; Ufar, Omay, 2009).
CD =
лТ Y Л-1 Л \
2Г '2 : r t
\ >=1 .7=>+1 /
( Л -1)
(9)
э г!
In empirical application, one may select the number of augmentation terms in the auxiliary regression (6) using any convenient lag selection method. Following (U?ar, Omay, 2009), the cointe-gration test can be constructed by standardising the average of individual cointegration test statis- g
TO
tics across the whole panel. The cointegration test for the 7-th individual is the ¿-statistic for testing | d = 0 (as in (Kapetanois et al., 2003; U?ar, Omay, 2009)) in equation (6) defined by:
•TC
AuMt"3 i ^
t =- 7,1--(7) ^
i,NL " t \3/2 ' ^ '
0i,NL [,- 1Mt"/,-1 )
where o2NL is the consistent estimator such that o2NL = Au\Mt" / (T — 1), Mt = IT — r T [r T r T ) r T
with A" = [A"n ,A"i2,...,A"iT) and rT = (1,1,...,1).
Furthermore, when the invariance property and the existence of moments are satisfied, the usual
normalization of tNL statistic is obtained as follows:
_ [K — e^nl )) (8)
Znl = vV«(w ' (8)
N
where tNL = N-1 ^tiNL, and E(tiNL) and Var(tiNL) are expected value and variance of the tiNL i=1
statistic given in (7).
One of the frequently encountered problems in panel regression models is the presence of cross-section dependency. The cross-section dependency may arise due to spatial correlations, spill-over effects, economic distance, omitted global variables and common unobserved shocks (see, e. g., (Omay, Kan, 2010)). The presence of correlated errors through individuals makes the classical unit root and cointegration testing procedure invalid in panel data models. Banerjee et al. (2004) assess the finite sample performance of the available tests and find that all tests experience severe size distortions when panel members are cointegrated. To overcome this issue, some tests based on the regression equation including the unobserved and/or observed factors as the additional regressors are suggested in recent years (e. g., (Moon, Perron, 2004; Bai, Ng, 2004; Pesaran, 2007; Bai et al., 2009; Omay, Kan, 20104; Kapetanios et. al., 2011)). On the other hand, Maddala and Wu (1999), Chang (2004) and U?ar and Omay (2009) consider the bootstrap based tests to obtain good size properties. Therefore, before the testing procedure is implemented, one must check out the presence of cross section dependency, for example, using the test procedure proposed by Pesaran (2004). It is formulated as:
where p j is the estimated correlation coefficient between error terms for the individuals i and j.
In this paper we followed Uçar and Omay (2009) and applied the Sieve bootstrap method to deal with the cross-section dependency problem5. Once cointegration is found and long-run rela-
4 Omay and Kan (2010) proposed nonlinear CCE estimator as an extension of Pesaran (2007) linear CCE estimator. On the other hand, there are other methods which automatically handle cross-section dependency such as Panel-GARCH methods (Omay, Eruygur, 2012). However, we are not in a position to estimate GARCH effect to use such modeling in our PSTRVEC model.
5 The MATLAB codes of the panel cointegration and unit root test are available upon request.
tionship between the variables is established, one may proceed to estimate panel error correction model. Taking account of the fact that not only adjustment to the long-run equilibrium level, but dynamic interrelationship between the variables might also be inherently nonlinear, we propose and estimate nonlinear Panel Smooth Transition Vector Error Correction (PSTRVEC) model to examine regime-wise interactions between energy consumption and output growth. Now, we turn to discussion of specification and estimation of PSTRVEC models and Granger-causality tests in nonlinear panel regression framework6.
2.2. Specification of PSTRVEC
Following Gonzalez et al. (2005) and Omay and Kan (2010), who also consider a panel smooth transition regression model, a PSTRVEC model can be formulated as:
p, q
Dgdpt t =m +/Vc,>1 j DsdPi ,t - j j Denr j +
■ G( sht; g c)\ßieciM j DgdphH + 1 j j +
Г s,
Denr, ,t =m2 + ß 2eCi ,t-1 2 j D§dP,,t-j 2 j Denr ,t-j + j=1 j=1
+ G (s, ,t; gc) 1ß 2ec, ,t-1 + 2 ^ 2 j DsdP, ,t- j + 2 ^ 2 j Denr ,t - j r+£2
(10)
L j=i J
for i — 1,..., N, and t — 1,...,T, where N and T denote the cross-section and time dimensions of the panel, respectively. Here gdpit denotes the gross output level and enr it is the energy consumption. Furthermore, mi represents fixed individual effects, ecit is the error correction term estimated from the regression (1) (i. e., ecit — uit from equation (1)), and is the error term that is assumed to
be a martingale difference with respect to the history of the vector zi t — (gdpf t, enrt t) up to time
t - 1, that is, E^it |zit_1, zit_2,..., zit_p ,...J — 0, and that the conditional variance of the error term
is constant, i. e., E^2 |zit-1, zit_2,..., zit_p ,...J — o2. Note that we allow for contemporaneous correlation across the errors of the N equations (i. e., cov , ) ^ 0 for l — 1,2 and i j).
Gonzalez et al. (2005) and Omay and Kan (2010) consider the following logistic transition function for the time series STAR models:
G (s, ,t; g c) =
1 + exp|-y^(si,t - cj)!
j=1
-1
with y> 0 and cm > ...> c1 > c0, (11)
where c — (c1,..., cm)' is an m-dimensional vector of location parameters, and the slope parameter y denotes the smoothness of the transition between the regimes. A value of 1 or 2 for m, often meets
6 The RATS codes of PSTRVEC and causality tests are available upon request.
о
the common types of variation. In cases where m = 1, i. e., for first-order logistic transition function, the extreme regimes correspond to low and high values of sit , and the coefficients in regression model (10) change smoothly from bj, fy and ^ to b j + b j, ^ + ^ and ^ + $ j, respectively, as sit increases. When g ^ o, the first-order logistic transition function G(t;g,c) becomes an indicator function I[A], which takes a value of 1 when event A occurs and 0 otherwise. Thus, the PSTR model reduces to Hansen's (1999) two-regime threshold model. J
For m = 2, on the other hand, G(t;g,c) takes a value of 1 for both low and high sjp minimiz-c + c
ing at —-2. In that case, if g ^ o, the PSTR model reduces into a panel three-regime threshold regression model. If g ^ 0, the transition function G(t;g,c) will reduce into constant, and hence, the PSTR model will collapse to a linear panel regression for any value of m7.
The empirical specification procedure for panel smooth transition regression models consists of following steps:
1. Specify an appropriate linear panel model for the data under investigation.
2. Test the null hypothesis of linearity against the alternative of smooth transition type non-linearity. If linearity is rejected, select the appropriate transition variable sit and the form of the transition function.
3. Estimate the parameters in the selected PSTRVEC model.
The linearity tests are complicated by the presence of unidentified nuisance parameters under the null hypothesis. This can be seen by noting that the null hypothesis of linearity may be expressed in different ways. Besides equality of the parameters in the two regimes, H0: bj = Ьj and 9j = 6>j, the alternative null hypothesis H0: g = 0 also gives rise to a linear model. To overcome this problem, one may replace the transition function G(t;g,c) with appropriate Taylor
approximation following the suggestion of Luukkonen et al. (1988). For example, a kth-order Taylor approximation of the (first-order) logistic transition function around g = 0 results in the following auxiliary regression:
Pi k k Pj
,t = l + p0 eciM + 2 p j but- j + 2 p h si ect ,t-i + 22 p * st ^ ,t-j + e, ,t, (12)
j=1 h=1 h=1 j=1
where zit = (gdpit,enrit) and l, p', p, P and p are functions of the parameters ,b, fy, fy, ~b, 0j,Ьj, g, and ci, and eitcomprises the original disturbance terms as well as the error term arising from the Taylor approximation. Now, testing H0: g = 0 in (10) is equivalent to testing the null hypothesis H0: ю1 = ю2 = ю3 = 0 where mi = (pj,pj) in (12). This test can be done by an LM-type test. This test has approximate ^-distribution and defined as follows:
(SSR - SSR1)/kp . , чЧ
LM =-Цг-°-^-г ~ F(kp,TN - N - k(p + 1)), (13)
SSR0 / (TN - N - k (p + 1)) JJ
where SSR0 and SSR1 are the sum of squared residuals under the null and alternative hypotheses, respectively. In order to choose the appropriate transition variable sit, the LM-statistics can be computed for several candidates, and the one for which the P-value of the test statistic is smallest can be selected.
7 For more detailed discussion, see Gonzalez et al. (2005).
When the appropriate transition variable sit has been selected, the next step in specification of a panel STR model is to choose between m = 1 and m = 2. Terasvirta (1994) suggests using a decision rule based on a sequence of tests in Equation 12. Applied to the present situation, this testing sequence is as follows: using the auxiliary regression (12) with k = 3, test the null hypothesis H0: — w2 — w3 — 0. If it is rejected, test H03: w3 — 0, then H02: w2 — 0|w3 — 0 and H01 : — 0|— w3 — 0. These hypotheses are tested by ordinary F-tests, to be denoted as F3, F2, and F1, respectively. The decision rule is as follows: If the F-value corresponding to F2 is the smallest, then exponential transition function should be selected, while in all other cases a first order logistic function should be preferred.
2.3. Estimation of PSTRVEC models and Regime-wise Granger-Causality Tests
Once the transition variable and form of the transition function are selected, the PSTRVEC model can be estimated by using a convenient nonlinear least squares estimator. The optimization algorithm can be disburdened by using good starting values. For fixed values of the parameters in the transition function, y and c, the PSTRVEC model is linear in parameters m, b, fy, fy, b, ^, $ j, and therefore can be estimated by using least squares estimator. Hence, a convenient way to obtain reasonable starting values for the nonlinear least squares is to perform a two-dimensional grid search over y and c, and select those values that minimize the panel sum of squared residuals.
One of the problems encountered in estimation of the panel regression models is the problem of cross-section dependency. Note that in equation (10) we allowed for contemporaneous correlation across the errors of the equations in the system (i. e., cov(^lit,B,ljt) ^ 0 for l = 1, 2 and i ^ j). The cross-section dependency problem might be serious in our case because of strong ties among the sample countries. In order to solve the cross-section dependency problem, we estimate the output and energy equations for all sample countries simultaneously using nonlinear Generalized Least Squares (GLS) estimator iteratively, which gives maximum likelihood (ML) estimates (see, for example, (Greene, 1997, pp. 681-682))8.
After estimation of the coefficients of the PSTRVEC model given in equation (10), one may conduct Granger causality tests in order to examine bidirectional causal relationships between output growth and energy consumption. Since estimated model allows for regime-dependent dynamics between the variables, following Li (2006) we conduct the Granger causality tests separately for each regime. As briefly discussed above, the regimes in the PSTRVEC model are associated with extreme values of the transition function G(sit;g,c). For example, if appropriate transition variable sit in the transition function is output growth rate and the transition function is a first order logistic function, then the regimes will be associated with low growth and high growth episodes, and hence, one may conduct the causality tests separately for low growth and high growth periods.
For instance, assume that the transition variable is indeed output growth rate and that the transition function is first order logistic function. Then, in the framework of the PSTRVEC model given
8 Estimating the system of equations simultaneously remedies the so-called endogeneity bias problem. Moreover, panel regression models with fixed cross-section units (N) and large time span (T), like our sample, does not face with Nickell (1981) bias as stated in Pesaran and Smith (1995). Therefore, our estimation procedure produces unbiased and consistent estimates.
in (10) above, the null hypotheses of no Granger-causality can be formulated for low growth and s, high growth periods as follows: <■
Energy consumption does not Granger cause output growth rate in low growth periods (i. e., when output growth rate is less than some threshold value) in the short run Ho 01 = o
Energy consumption does not Granger cause output growth rate in low growth periods (i. e., when output growth rate is less than some threshold value) in the long run Ho Ho bi bi = o and/or = 01 = o
Energy consumption does not Granger cause output growth rate in high growth periods (i. e., when output growth rate is greater than some threshold value) in the short run Ho 01 = 01 = o
Energy consumption does not Granger cause output growth rate in high growth periods (i. e., when output growth rate is greater than some threshold value) in the long run Ho Ho bi bi == = o and/or = 01 = 0 = o
Output growth does not Granger cause energy consumption in low growth periods (i. e., when output growth rate is less than some threshold value) in the short run Ho 01 = o
Output growth does not Granger cause energy consumption in low growth periods (i. e., when output growth rate is less than some threshold value) in the long run Ho Ho b2 01 = o and/or = o
Output growth does not Granger cause energy consumption in high growth periods (i. e., when output growth rate is greater than some threshold value) in the short run Ho 01 = 01= = o
Output growth does not Granger cause energy consumption in high growth periods (i. e., when output growth rate is greater than some threshold value) in the long run Ho Ho b1 b1 == = o and/or = 01 =^= o
3. Empirical Results
In this section, we provide an empirical evidence for the G7 (group of seven) countries using annual data for the period 1977-2007. Output level ( gdpi t) was proxied by real Gross Domestic Income and was obtained from the Penn World Table Version 6.3 (Heston et al., 2009). Energy consumption was proxied by Total Primary Energy Consumption and was obtained from World Development Indicators (WDI) database. We took natural logarithms of the variables before conducting any test and estimation.
We first test the null hypothesis of unit root for both of the variables. To this end, and for comparison purposes, we applied both conventional IPS linear unit root test (Im et al., 2003) as well as UO nonlinear unit root test of U?ar and Omay (2009). The results of these panel unit tests are provided in Table 1 below.
The results of both linear and nonlinear tests suggest that energy consumption contains a single unit root in levels regardless whether a trend is included or not. Output level, on the other hand, seems to be trend stationary according to the IPS test and non-stationary according to UO test. Considering that conventional linear tests may have low power and size properties against nonlinear processes9, we proceed to test cointegration among these variables. For this purpose, we first estimate panel regression models, results of which are given below:
9 Hasanov and Telatar (2011) have examined stationarity properties of energy consumption across 178 countries and found that newly developed unit root tests that allow for possible nonlinear dynamics outperform conventional linear tests in terms of detection of stationarity. In addition, they found that the energy consumption series of all countries are inherently nonlinear.
gdpi t —1.210 enr,,
(20.141) 1,1
enr.t — 0.545 gdp,.
1,t (20.141) 1,1
Table 1. Linear and nonlinear panel unit root tests
Variables IPS test UO test
Intercept only Intercept and time trend Intercept only Intercept and time trend
W-stat. t-stat. W-stat. t-stat. W-stat. t-stat. W-stat. t-stat.
GDP 2.317 -0.733 -1.778** -2.735** 2.112 -1.018 1.938 -1.742
(0.989) (0.989) (0.037) (0.037)
DGDP -7.039 -3.916 -5.809 -4.012 -6.628* -3.446* -6.124* -3.471*
(0.000) (0.000) (0.000) (0.000)
ENP 1.103 -1.139 -1.171 -2.525 1.149 -1.285 -0.278 -2.217
(0.865) (0.865) (0.120) (0.120)
DENP -11.157 -5.336 -9.976 -5.361 -6.095* -3.298* -4.453* -3.113*
(0.000) (0.000) (0.000) (0.000)
Notes. Figures in parentheses denote P-values of the test statistics. * and ** denote rejection of the null hypothesis of unit root at 1 and 5% significance levels, respectively.
The figures in parentheses below the coefficient estimates are /-statistics of the corresponding coefficient estimates. Then, we collected residuals from these equations and applied nonlinear cointegration test given in equation (8) above as well as linear cointegration test of Pedroni (1999). However, first estimates suggest that the residuals in panel cointegration tests suffer seriously from cross-section dependency problem. Indeed, the cross-section dependency statistic CD of Pesaran (2004) given in equation (9) above was computed to be 13.571 (with P-value = 0.000). Therefore, we used bootstrap method to calculate P-values of both test statistics. The results of these tests that remedy the cross-section dependency problem are provided below in Table 210.
Table 2. Panel cointegration test
Linear cointegration test Nonlinear cointegration test
W-statistic t-statistic W-statistic t-statistic
"и — gdpn - 1.210enr,t 0.208 -1.562 -2.082 -1.564
(0.207) (0.207) (0.027) (0.027)
"it — enr,t - 0.545gdpit 0.893 -1.251 -0.813 -1.891
(0.417) (0.417) (0.059) (0.059)
Notes. Figures in parentheses denote P-values of the test statistics.
Although the linear cointegration test suggests that the variables under investigation are not co-integrated, the non-linear cointegration test suggests that eneigy consumption and output level are co-integrated. Considering the fact the interrelationship between these variables might be inherently nonlinear, we proceed to estimate a nonlinear panel vector error correction model for these variables.
10 The results of both tests without remedying cross-section dependency problem are available from the corresponding author upon request.
The first step in the specification of a nonlinear panel regression model is to estimate appro- s,
priate linear model and conduct linearity tests. For this purpose, we first estimated a panel vector s-
error correction model, results of which are given below: |
<0 ¡8
Dgdp. =«,- 0.155 ec t ,+ 0.527 Dgdp.t ,+ 0.056 Aenrf1, *
s fu r-\ (-1.299) ',t-1 (5.559) ,t-1 (16.163) ',t-1'
IS
Denr.t = m2 - 0.091ect-1 + 0.053Agdp.t-1 + 0.158Denr t_,. J
, 2 (-6.514) , 1 (35.032) ' 1 (3.765) , 1 n
The error correction term has the right sign in both equations, but statistically significant only in the energy equation. In addition, all the remaining coefficients are statistically significant and have the expected sign.
Although the estimated linear model seems to be satisfactory, we proceeded to test linearity of the model using regression model given in (12). For this purpose, we conducted the linearity tests for each equation separately using the lagged output growth rate, the lagged energy consumption, the error correction term and a time trend for three different values of k in equation (12), namely, for k = 1,2,3. These variables, in our opinion, capture all possible sources of nonlinearities in the dynamic interaction between the variables under consideration. For example, use of output growth rate as a transition variable suggests that the nonlinearity in the relationship between the variables might be governed by the phases of business cycle. If error correction term is used as the transition variable, then the nonlinear interactions between energy consumption and output growth will depend on the deviations from the long-run equilibrium level. On the other hand, if the energy consumption is used as the transition variable, then nonlinear dynamics in the interrelationship between the variables will depend on the rate of change of energy consumption. And finally, if time trend is used as the transition variable, then the relationship between the variables will be time varying, but not nonlinear. For this purpose, we use all the variables as a candidate for the transition variable that governs nonlinearities in the dynamic interrelationship between the energy consumption and output growth. As briefly discussed above, unlike other nonlinear regime switching models, the smooth transition regression models allow one to choose the most appropriate transition variable among possible candidates by applying conventional variable addition tests.
The results of the linearity tests are provided in Table 3.
As the results of the tests suggest, the null hypothesis of linearity is rejected at conventional significance levels for all candidate transition variables for both output growth and energy equations. However, the null of linearity is more strongly rejected for both equations when the lagged output growth rate is used as a transition variable. This result indicates that although there might be other sources for the nonlinear interaction between the variables under investigation, such non-linearity primarily depends on phases of the business cycle. Considering the fact that linearity is more convincingly rejected when the output growth rate is used as a candidate transition variable, we choose this variable as the appropriate switching variable and apply sequence of F-tests as suggested by Terasvirta (1994) in order to choose the type of the transition function. The results of these tests are given in Table 4.
As can readily be seen from the table, the smallest P-value of the F-tests correspond to F1, which in turn suggest logistic function as the appropriate transition function. After choosing both the appropriate transition variable and transition function we proceed to estimate the PSTRVEC model. In order to solve possible cross-section dependency problem, we estimated the PSTRVEC model using nonlinear GLS iteratively, which gives maximum likelihood estimates. Estimation results are given below:
Agdp.t = m - 0.064e.t-1 - 0.875 Agdp.t-1 + 0.263 Aenrt-1 +
I,r 1 (-1.580) 1 (-4.449) I,r 1 (1.678) ',t 1
+ (-0.006et t_1 + 0.547 Agdp M - 0.022 Aen; M} • G(Agdp. M; g,c),
[ (-1.716) ',t 1 (6.721) ',t 1 (-1.398) 1,1 1 J ',t 1
Aenrt =m2- 0.151e,.t-1 -0.015 AgdpIt-1 + 0.661 Aenrt-1 +
1 ,Г 2 (-3.276) ',Г 1 (-0.317) ,Г 1 (4.180) h 1
+ ( - 0 .067 e,+ 0 . 1 3 4 Agdp,t-1 + 0.078 Aenr. } • G (Agdp.t_,; g, c),
[ (-1.224) , 1 (2.378) ,Г 1 (2.114) ',t ^ ,Г
G(Agdpt^-;g,c) = 11 + exp[ - 3(.145^Agdp,M + O.Qf)^4
Table 3. Linearity test results
Output equation
Candidate transition variable к = 1 к = 2 к = 3
AgdPit _ 1 29.033 21.634 9.267
(0.000) (0.000) (0.000)
Aenrit _ j 24.558 13.354 9.685
(0.000) (0.000) (0.000)
ecit _ 1 15.488 5.429 6.519
(0.000) (0.000) (0.000)
Time trend (t) 6.976
(0.000)
Energy equation
AgdPit _ 1 33.849 17.115 2.965
(0.000) (0.000) (0.051)
Aenrit _ 1 28.689 15.328 6.668
(0.000) (0.000) (0.001)
eci,t _ 1 18.067 8.705 10.327
(0.000) (0.000) (0.000)
Time trend (t) 8.170
(0.000)
Notes. F-versions of the tests were used. P-values of the test statistics are reported in parenthesis. Table 4. Selection of transition function
F2 F3
Output Equation 2.845 1.515 1.667
(0.038) (0.211) (0.175)
Energy Equation 2.720 0.539 0.573
(0.031) (0.706) (0.682)
Notes. F-versions of the tests were used. P-values of the test statistics are reported in parenthesis.
As briefly discussed above, the regime change in the PSTRVEC model is governed by the transition function G[sjt;g,c). Here, the variables of interest are g that determines the speed oftran-sition between the extreme regimes, and c that determines the midpoint of the transition. The estimated value of c = -0.00124 is very close to zero, which suggests that the extreme regimes in the PSTRVEC model (roughly) correspond to negative and positive values of the GDP growth rate, or to recessionary and expansionary regimes. In fact, the transition function G [sjt; g, c ) takes on values less than 0.01 when lagged output growth rate is less than -1.5 and takes on values greater than 0.99 when the output growth rate is greater than 1.5. Therefore, the regimes identified by the transition function (roughly) correspond to recessionary regimes (i. e., when output growth rate is less than -1.5 percent) and expansionary regimes (i. e., when output growth rate is greater than 1.5 percent). The estimated value of g = 3.145 suggests that the transition between the regimes are rather smooth as can be seen from the Figure 1.
Э
I
1.00
Hh
с
H •о
-2.5 0.0 2.5 5.0
Lagged output growth rate
10.0
Figure 1. Scatter plot of the estimated transition function against transition variable
Before proceeding to formal testing of the regime-wise Granger causality, we discuss the coefficient estimates for both output and energy consumption equations. First, consider the output equation. In the recessionary regime (i. e., when output growth rate is negative and thus, G [sjt ; g, c) ~ 0 ), the estimated coefficient of the error correction term is equal to -0.064, and is statistically insignificant. This result implies that output growth rate does not respond to the deviations from the long-run equilibrium level in recessionary regimes. The estimated coefficient of the lagged energy consumption is equal to 0.263 and is statistically significant only at 10% significance level. This implies that output growth rate increases with energy consumption in recessionary (or low-growth) regimes, although the evidence is (statistically) weak. In expansionary periods (i. e., when output growth rate is positive and thus, G ^ t ; g, c) ~ 1.0 ), the estimated coefficient of the error correction term becomes -0.070 (= - 0.064 - 0.006) and remains statistically insignificant. The estimated coefficient of the lagged energy consumption turns to 0.241 (= 0.263 - 0.022), implying the effect of energy consumption on output growth rate declines slightly in expansionary regimes.
Now, consider the energy equation. The estimated coefficient of the error correction term is equal to - 0.151 and - 0.218 (= - 0.151 - 0.067) in recessionary and expansionary regimes, respec-
tively, and statistically significant in both regimes. This implies that energy consumption adjusts to disequilibrium both in recessionary and expansionary periods, whereas the speed of adjustment increases with output growth rate. The estimated coefficient of the output growth is equal to - 0.015, and statistically insignificant in recessionary regime. In expansionary periods, it turns to 0.119 (= 0.134 - 0.015) and becomes statistically significant, implying that output growth rate has no effect on energy consumption in recessionary regimes but increases it in expansionary regimes.
Now we turn to the regime-wise Granger-causality tests. Vector error correction models provide a framework for testing Granger-causality for the short- and long-run relationships. Short-run Granger-causality test is performed through testing lagged values of explanatory variables, whereas the long-run causality is performed through the significance of the error-correction term. In addition, we also performed so-called stronger form of the Granger-causality, i. e., joint significance of the error correction term and lagged explanatory variables. As briefly discussed above, the PSTRVEC model allows for testing Granger-causality for each regime separately. Therefore, we performed the Granger-causality tests for the recessionary (i. e., when G (sjt; g, c)~ 0) and expansionary (i. e., when G (sjt; g, c)~ 1.0) regimes separately. The results of the regime-wise Granger-causality tests are reported in Table 5.
Table 5. Regime-wise causality tests
Source of causation Dependent variable
(independent variable) DGDP DENR
Recessionary regime Expansionary regime Recessionary regime Expansionary regime
Short-run
DGDP DENR 2.817*** (0.093) 4 973*** (0.083) 0.100 (0.750) 6.556** (0.037)
Long-run
ECT 2.497 (0.114) 2.953 (0.228) 10.732* (0.001) 10.712* (0.004)
Joint (short- and long-run)
ECT/ DGDP ECT/DENR 9.284* (0.009) 11.277** (0.023) 13.634* (0.001) 30.199* (0.000)
Notes. Figures in parentheses denote P-values of the test statistics. *, ** and *** denote rejection of the null hypothesis of unit root at 1, 5 and 10% significance levels, respectively.
The results of the short run Granger causality tests suggest that energy consumption is a Granger cause of the output growth rate both in recessionary and expansionary regimes, although the evidence is statistically weak. Indeed, the null hypotheses that energy consumption does not Granger-cause output growth is rejected for both regimes only at ten percent significance level. The results
of the long-run Granger causality tests, on the other hand, imply that energy consumption does not a, cause output growth rate both in recessionary and expansionary regimes. Stronger (or joint) Grang- ser causality tests suggest that energy consumption is a Granger-cause of output growth rate in both g
TO
regimes. Combined with the results of the short- and long-run causality tests, the joint Granger |
causality test thus suggests that primary effect of the energy consumption on output growth stems ^
from the short-run effects. 1
o
As regards the energy consumption, the Granger causality tests suggest that output growth rate ^ does not Granger-cause energy consumption in recessionary regimes but does Granger-cause it in expansionary regimes in the short-run. On the other hand, the results of the long-run and joint Granger causality tests suggest that output growth Granger causes energy consumption both in the recessionary and expansionary regimes.
4. Conclusion
In this paper, we have examined the causal relationship between total energy consumption and output level for a panel of G7 countries. The novelty of the paper is that we propose a new panel cointegration test in a nonlinear smooth transition regression framework and estimate nonlinear panel smooth transition vector error correction model. This approach allows us to examine possible nonlinear and asymmetric dynamic interactions between energy consumption and output in the sample countries. Our findings can be summarized as follows. First, we find a cointegrating relationship between energy consumption and output level only after allowing for possible asymmetries in the adjustment to the long-run equilibrium level. This result suggests that while small deviations may not be corrected, both energy consumption and output will react to large deviations from the equilibrium and thus bring the economy to the long-run equilibrium level. This result also implies that the shocks in the world energy markets will affect output level asymmetrically depending upon size of the shock.
Second, as the results of the linearity tests suggest, dynamic interrelationship between energy consumption and output growth are highly nonlinear. In fact, we were able to reject the null hypothesis of linearity for all candidate transition variables considered. This finding implies that both the energy economists and policy authorities must be careful and take account of possible nonlinear and asymmetries in examining dynamic interactions between energy use and output growth. The null hypothesis of linearity was rejected more convincingly when lagged output growth rate was used as a candidate transition variable. This result suggests that although there might be different sources of nonlinearities, output fluctuations govern nonlinear interrelationships between energy use and output growth. In addition, estimated PSTRVEC model suggests that that dynamic interrelationship between energy use and output varies over the phases of business cycles.
Third, we conduct regime-wise Granger causality tests and find that the causal relationships between energy consumption and output also vary over phases of the business cycle. In particular, estimated model and nonlinear Granger causality tests suggest that energy consumption increases output in the short-run both in economic recession and expansion periods, although the evidence is statistically weak. On the other hand, we find that energy consumption does not Granger-cause output in the long run irrespective of the initial conditions of the economy. In addition, we find that output growth rate does not cause energy consumption in the short run in economic recession periods. In expansionary or high growth episodes, on the other hand, output growth rate increases
energy consumption. In the long run, output growth increases energy consumption irrespective of initial conditions of the economy.
Our results have several important implications both for researchers and policy authorities. Energy economists must take account of possible nonlinearities in examining causal relationship and dynamic interactions between energy consumption and output growth rate. In particular, we find that conventional linear models might be inappropriate in order to examine both long- and short-run relationships between energy consumption and output growth rate. Our results are important for policy authorities as well. As the results of the Granger-causality tests suggest, energy consumption affects output growth rate only in the short run and does not Granger-cause output in the long run, irrespective of the phases of the business cycles. This finding suggests that the G7 countries can implement energy conversion policies without fear of harming long-run growth paths of the economies. Possible adverse effects of the energy conversion policies on output growth rate shall be limited to only short-run dynamics of the economy and such policies shall not harm the long run growth of the countries. This result also suggests that bad economic conditions (i. e., when the economy is in a recession or output growth rate is low) cannot be considered as a hindrance for implementation of the environmentally friendly policies. In addition, we found that output growth rate does not increase energy consumption in the short run when initial growth rate is relatively low. However, output growth increases energy consumption in the long run irrespective of initial conditions of the economy. These results may be interpreted as evidence of the fact that the technological change (or growth strategies) has been energy-intensive in these countries during the sample period. Therefore, all-in-all, our results also imply that the energy conversion policies must be supplemented by policies aimed at promotion of energy-saving technological progress.
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