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Abstract
This article attempts to test the causal relationship between nuclear energy consumption and real GDP for nine developed countries for the period 1971-2005 by including capital and labour as additional variables. Using a modified version of the Granger causality test developed by Toda and Yamamoto (1995), we found a unidirectional causality running from nuclear energy consumption to economic growth in Japan, Netherlands and Switzerland; the opposite uni-directional causality running from economic growth to nuclear energy consumption in Canada and Sweden; and a bi-directional causality running between economic growth and nuclear energy consumption in France, Spain, the United Kingdom and the United States. In Spain, the United Kingdom and the USA, increases in nuclear energy consumption caused increases in economic growth implying that conservation measures taken that reduce nuclear energy consumption may negatively affect economic growth. In France, Japan, Netherlands and Switzerland increases in nuclear energy consumption caused decreases in economic growth, suggesting that energy conservation measure taken that reduce nuclear energy consumption may help to mitigate the adverse effects of nuclear energy consumption on economic growth. In Canada and Sweden energy conservation measures affecting nuclear energy consumption may not harm economic growth.
1.	Introduction 
The high degree of concentration of energy supply sources where over 68% of oil is concentrated in the volatile region of the Middle East, and where 67% of gas reserves are concentrated in Russia, clearly involves risks in terms of the reliability of the supply of energy needs for many energy-importing countries (World Coal Institute, 2006; Fiore, 2006; Toth and Rogner, 2006; Elliot, 2007; Ferguson, 2007; World Energy Council, 2007; Gnansounou, 2008; Squassoni, 2009; Tol et al., 2009). Since the 1973 oil crisis, supply security has become a primary concern for many oil-importing countries and this insecurity has made the search for alternative sources of cheap domestic energy supply one of the main deriving forces behind the energy policy of many energy importing countries (Toth and Rogner, 2006). Diversifying the sources of energy and finding a stable, safe and clean energy supply have become one of the main priorities of energy policy for many countries (see, Fiore, 2006; Toth and Rogner, 2006; Elliot, 2007; Ferguson, 2007). As part of their strategy of increasing energy security, many countries have built nuclear power plants not only to reduce dependence on imported oil but also to increase the supply of secured energy and also to minimize the price volatility associated with oil imports (Toth and Rogner, 2006; Vaillancourt et al., 2008). The advantage of nuclear energy has also become even more pressing as a result of the Kyoto Agreement that requires signatories to cut back substantially on their emissions of CO2 in order to reduce global warming (Becker and Posner, 2005). Many believe that nuclear energy, as a virtually carbon free source of energy, is one of the solutions to global warming and energy security (Elliot, 2007; Ferguson, 2007). Hence, serious concerns over rising fossil fuel prices, energy security, and greenhouse gas emissions have brought the importance of nuclear energy to the forefront of the wider issue of the energy debate. As the IEA notes, nuclear energy is attracting new interest for increasing the diversity of energy supplies, for improving energy security, and for providing a low-carbon alternative to fossil fuels (International Energy Agency, IEA, 2008). Thus, the importance of nuclear energy as a potential source of energy security and as a virtually carbon free source of energy necessitates not only further research but also the use of alternative testing methodologies to examine the causal relationship between nuclear energy consumption and economic growth. In a recent bivariate study on the causal relationship between nuclear energy consumption and economic growth, Yoo and Ku (2009) suggest that future research should investigate causal relationships using a more generalized multivariate system. In this paper, we do exactly that. Specifically, we examine the casual relationship between nuclear energy consumption and real GDP in nine developed countries for the period 1971-2005 which also includes capital and labor as additional variables. We include capital and labor as additional variables because nuclear energy alone might not be strong enough to spur economic growth. Further, exclusion of a relevant variable(s) makes the estimates not only biased as well as inconsistent but also no-causality in a bivariate system can result from neglected variables (Lütkepohl, 1982). It is possible that the introduction of a third or a fourth variable in the causality framework may not only alter the direction of causality but also the magnitude of the estimates (Loizides and Vamvoukas, 2005). In addition, since a four-variable case incorporates more information than a bivariate case, the causal inference drawn may be more reliable (Loizides and Vamvoukas, 2005). Thus, the previous bivariate causality tests between energy consumption and economic growth may be invalid due to the omission of important variables affecting both energy consumption and economic growth. In this paper the empirical evidence is carried out using the procedure developed by Toda and Yamamoto (1995, hereafter TY) which is valid regardless of whether a series is I(0), I(1) or I(2), noncointegrated or cointegrated of any arbitrary order. Secondly, unlike previous studies, this paper attempts to quantify how much feedback exists from one series to the other using the recently developed generalized forecast error variance decomposition technique proposed by Pesaran and Shin (1998) which is invariant to the ordering of the variables (see Payne, 2002). The rest of the paper is structured as follows. In Section 2 we give a brief account of the role of nuclear energy followed in Section 3 by a short summary of the empirical literature. In Section 4 we present a short description of the methodology used, while the empirical evidence is discussed in Section 5. The summary and the concluding remarks are presented in Section 6
2.	Brief literature review There is now a vast literature that deals with the relationship between energy consumption and economic growth (Chontanawat et al., 2008; Lee et al., 2008; Payne, 2009a, b, 2010; Ozturk, in press). Yet, there seems to be no consensus regarding the direction of causality between energy consumption and economic growth. There is ample evidence to support all the four competing hypotheses. For some countries there is a bi-directional causality while for others there is no causality at all. Still for some countries there is a unidirectional causality running from energy consumption to economic growth while for others there is the opposite causality running Fig. 1. Electricity production from nuclear sources (% of total electricity production). from economic growth to energy consumption. Y. Wolde-Rufael, K. Menyah / Energy Economics 32 (2010) 550–556 551 Similar to the conflicting empirical evidence found regarding the causal relationship between aggregate energy consumption and economic growth, the empirical evidence between nuclear energy consumption and economic growth is also not conclusive. Yoo and Jung (2005), Yoo and Ku (2009) for Korea and Hoe et al. (in press) for India, and Wolde-Rufael (2010) also for India found a unidirectional causality running from nuclear energy consumption to GDP. In contrast, Payne and Taylor (in press) for the United States, Yoo and Ku (2009) for Argentina and Germany; and Wolde-Rufael (forthcoming) for Taiwan found no causality running in any direction. Yoo and Ku (2009) also found bi-directional causality in Switzerland, and unidirectional causality running from economic growth to nuclear energy consumption in France and Pakistan. However, for 14 out of the 20 countries Yoo and Ku (2009) investigated, they did not carry out causality tests, as they could not find their series integrated of the same order, i.e. I(1). In a panel cointegration and panel causality study,Apergis and Payne (2010) found bi-directional causality running between nuclear energy consumption and economic growth providing support for the feedback hypothesis associated with the relationship between nuclear energy consumption and economic growth. The above conflicting evidence has major implications for nuclear energy policy. If there is a unidirectional causality running from nuclear energy consumption to economic growth, reducing nuclear energy consumption could lead to a fall in economic growth. In contrast, if there is a unidirectional causality running from economic growth to nuclear energy consumption, it could imply that policies aimed at reducing nuclear energy consumption may be implemented with little or no adverse effect on economic growth. On the other hand, if there is no causality running in any direction, the neutrality hypothesis is accepted, and reducing nuclear energy consumption may not affect income and nuclear energy conservation policies may not affect economic growth. In contrast, if there is a bi-directional causality running between the two, nuclear energy consumption can stimulate economic growth and in turn economic growth may induce more demand for nuclear energy. In this case, nuclear energy consumption and economic growth complement each other and nuclear energy conservation measures may negatively affect economic growth.
3.	4. Methodology Despite the fact that nuclear energy is considered to be an important source of energy for many countries, there are only few studies that have employed modern advances in times series econometrics of cointegration and causality to test the causal relationship between nuclear energy consumption and economic growth (see, Apergis and Payne, 2010; Heo et al., in press; Payne and Taylor, 2010; Yoo and Jung, 2005; Yoo and Ku, 2009; Wolde-Rufael, 2010, forthcoming). Yoo and Ku (2009) did not find their two series integrated of the same order for 14 out of the 20 countries they studied; consequently they excluded 14 countries or 70% of their sample from testing for non-causality. The validity of their causality test was conditional upon testing for unit root and cointegration among the variables. However, it is well known that pre-tests for unit root and cointegration might suffer from size distortions, which often imply the use of an inaccurate model for the non-causality test (Clarke and Mirza, 2006). Moreover, the need for pre-testing for unit roots and cointegration and the inapplicability when the variables have different orders of integration further adds to the distortions associated with Granger causality from within VAR or vector error correction (VEC) settings. To obviate some of these problems, TY based on augmented VAR modelling, introduced a Wald test statistic that asymptotically has a chi square (χ2 ) distribution irrespective of the order of integration or cointegration properties of the variables. This approach fits a standard vector auto-regression model on levels of the variables (not on their first differences) that give allowances for the long-run information often ignored in systems that require first differencing and pre-whitening (Clarke and Mirza, 2006). The approach developed by TY employs a modified Wald test (MWALD) for restriction on the parameters of the VAR (k) where k is the lag length of the system. The basic idea of the TY approach is to artificially augment the correct order, k, by the maximal order of integration, say dmax. Once this is done, a (k+dmax) th order of VAR is estimated and the coefficients of the last lagged dmax vectors are ignored (see Caporale and Pittis, 1999). Unlike Yoo and Ku (2009) where they have used the traditional Granger causality test or causality from within a VEC, we utilize a causality procedure suggested by TY. The TY procedure requires the estimation of an augmented VAR that guarantees the asymptotic distribution of the Wald statistic. Moreover the procedure does not require pre-testing for the cointegration properties of the VAR system, and thus avoids the potential biases of pre-testing that undermine the traditional causality tests. The test is valid regardless of whether a series is I(0), I(1) or I(2), non-cointegrated or cointegrated of any arbitrary order.1 To undertake the TY version of the Granger non-causality test, for VAR (4), (k= 3 and dmax= 1), we estimate the following system of equations: Where lnYt is the log of real GDP (proxy for economic growth), lnEt is the log of nuclear energy consumption (measured in million tons of oil equivalent), lnKt is the log of real gross fixed capital formation and lnLt is the log of the labour force. All data are annual for 1971-2005. Real GDP and real gross fixed capital formation are in US$ at 2000 constant prices and they were taken from the World Bank, 2008. Nuclear energy consumption is from British Petroleum, 2008. The employment variable is taken from the Conference Board and Groningen Growth and Development Centre, 2008. In line with many researchers, in the absence of capital stock, gross fixed capital formation has been used as proxy for the stock of physical capital (see, Sari and Soytas, 2007; Lee and Chang, 2008; Narayan and Smyth, 2008; Apergis and Payne, 2010; Payne and Taylor, in press; WoldeRufael, 2009). Sari and Soytas (2007) point out that since in the perpetual inventory method (PIM) of estimating the physical capital stock assumes a constant depreciation rate, any variance in capital is mostly related to a change in investment. Thus, it is possible to obtain a fairly reliable measure of the trend in physical capital stock from new fixed investment data (Sari and Soytas, 2007; Lee and Chang, 2008). In Eq. (1), A1…A4 are four 4×4 matrices of coefficients with A0 being the 4 by 1 identity matrix and εs are the disturbance terms. From (1) we can test the hypothesis that nuclear energy consumption (lnEt) does not Granger cause economic growth (lnYt), with the following hypothesis: Ho= a1 12= a2 12= a3 12=0, where ai 12's are the coefficients of the nuclear energy variable in the first equation of the system presented in Eq. (1). Similarly, we can test the opposite non-causality from economic growth (lnYt) to energy consumption (lnEt) with the following hypothesis: Ho= a1 21= a2 21= a3 21=0, where ai 21's are the coefficients of the economic growth variable in the second equation of the system presented in Eq. (1).
4.	6. Concluding 
5.	remarks The aim of this paper was to test the causal relationship between nuclear energy consumption and real GDP for nine developed countries for the period 1971-2005 within a vector autoregressive (VAR) framework by including capital and labour as additional variables to the nuclear energy-economic growth nexus. To do so, we applied two methodologies. First, we used a modified version of the Granger causality test, which is valid regardless of whether a series is I(0), I(1) or I(2), non-cointegrated or cointegrated of any arbitrary order. Secondly, we used the generalized variance decomposition analysis that is invariant to the ordering of the variables in the VAR system. The paper found a unidirectional causality running from nuclear energy consumption to economic growth in Japan, Netherlands and Switzerland while we found the opposite causality running from economic growth to nuclear energy consumption in Canada and Sweden. Unlike Canada, in Sweden nuclear energy consumption was negatively associated with economic growth hence there is a need to make the nuclear energy sector more efficient. In Spain, the UK and the USA, increases in nuclear energy consumption caused an increase in economic growth implying that energy conservation measures taken may negatively affect economic growth. In France, Japan, Netherlands and Switzerland, since increases in nuclear energy consumption caused a fall in economic growth, energy conservation measures may help to mitigate the adverse effects of nuclear energy consumption on economic growth. In Canada and Sweden energy conservation measures taken to reduce nuclear energy consumption may not harm economic growth. In many countries there is a keen interest in developing nuclear energy as a means of ensuring energy security and stabilising and/or reducing greenhouse gas (GHG) emissions; but economic necessity should not outweigh the risks involved. Nuclear safety is a global concern that needs a global solution. The right balance should be struck between the quest for economic growth, nuclear safety, clean energy and the drive towards making these countries relatively energy independent.