Causality between energy consumption and GDP in the U.S.: evidence from wavelet analysis

Abstract

This study investigates the dynamic causal relationship between energy consumption and economic growth in the U.S. at different time scales. The main novelty of the study is that this paper complements the existing studies on the nexus between energy consumption and economic growth by employing the wavelet transformation to obtain different time scales in order to investigate causality between energy consumption and economic growth. This method is first developed by Ramsey and Lampart. Their approach consists of first decomposing the series into time scales by wavelet filters and testing causality of each time scale with the pertinent time scale of the other series separately. The data span from 1973q1 to 2012q1 on a quarterly basis. The main empirical insight is that the causal relationship is stronger at finer time scales, whereas the relationship is less and less apparent at longer time horizons. The results indicate that energy consumption causes economic growth, while the reverse is not true at the original frequency of the data. At the very finest scale the same result arises. However, at coarser scales feedback is observed. In particular, at intermediate time scales the evidence indicates that energy consumption causes economic growth, while the reverse is also true. These empirical findings are expected to be of high importance in terms of the effective design and implementation of energy and environmental policies, especially when a number of countries in the pursuit of high economic growth targets do not pay any serious attention on environmental issues.

Graphical abstract

Keywords

energy consumption / economic growth / wavelet analysis / granger causality

1 Introduction

Over the past period, energy has been one of the fastest growing factors of production used. The causal relationship between energy consumption and economic growth has been a relevant topic in a growing body of empirical literature. Comprehending the actual direction of causality between energy consumption and economic growth has substantial implications for policymakers as well as for the natural environments [1,2].

In terms of the causality methodology, there are two main hypotheses that are expected to be investigated: the energy-led growth hypothesis and the growth-led energy hypothesis, which give rise to the following causality combinations: unidirectional causality from energy consumption to economic growth (the growth hypothesis); unidirectional causality from economic growth to energy consumption (the conservation hypothesis); bi-directional causality from energy consumption to economic growth (the feedback hypothesis); and no causality between energy consumption and economic growth (the neutrality hypothesis).

If energy consumption Granger-causes economic growth, then conservation policies aiming at protecting the environment are expected to deteriorate the current stage of economic growth. In addition, if economic growth Granger-causes energy consumption, energy conservation policies can be implemented to reduce carbon dioxide (CO₂) emissions and global warming without deleterious effects on the process of economic growth. Apparently, comprehending the direction of causality between energy consumption and economic growth is not only important for policymakers to enhance economic growth, but it is also important for them to curtail energy consumption to reduce the emission of CO₂ and global warming. It is hard, however, to document findings of earlier studies that have reached a consensus [3,4].

The objective of this study is to investigate the causality between energy consumption and economic growth in the U.S., for the first time, at different time scales. The main novelty of the study is the employment of a wavelet transformation to obtain different time scales in order to investigate causality between energy consumption and economic growth. Wavelet analysis has become increasingly popular for analyzing economic time series due to its advantages of decomposing a time series into different time scales ([5−7]; among others). In the wavelet decomposition of this paper, multiresolutionary analysis (MRA) for a discrete wavelet transform (DWT) is used to filter the data. Subsequently, Granger causality is tested using wavelet-decomposed series with a wild-bootstrapping procedure.

The empirical findings are expected to be of great importance in terms of the effective design and implementation of energy and environmental policies, especially when a number of countries included in the sample in the pursuit of high economic growth targets do not pay any serious attention to environmental issues.

2 Literature review

Studies on the causal relationship between energy consumption and economic growth have received widespread attention in the economics, energy as well as the environmental literature following the seminal work in the U.S. [8]. However, the causal relationships between energy consumption and economic growth remain yet an unsolved conundrum. Refs. [3] and [4] provide comprehensive surveys for the energy-growth nexus, while Refs. [9−14] report that various sources of energy consumption tend to cause economic growth in the U.S. case. Refs. [15−20] reveal that energy consumption Granger-causes economic growth, while Refs. [21−23] argue that economic growth does not result from energy consumption.

Economic growth is dependent on energy consumption and, thus, any decreases in energy consumption are expected to restrain economic growth [24,25]. By contrast, it is proved that under certain conditions any increases in energy consumption have negative effects on economic growth, a fact that is attributed to a pattern of economic growth that requires a decreasing amount of energy as production shifts towards sectors (i.e., services) that require less energy or to the provision of energy to sectors that suffer from capacity constraints and less efficiencies [26]. The presence, on the other hand, of bi-directional causality indicates that the two variables are interrelated and satisfy a complementarily association, implying that higher energy consumption levels do not have any harmful effect on economic growth [27]. Finally, in terms of the absence of any causality between them, the findings provide support for the neutrality hypothesis, implying that energy conservation policies have no impact on economic growth [28]. Ref. [29] also asserts that the neutrality hypothesis implies that the cost of energy is negligible and it does not affect the economic growth process.

Evidently, it is hard to convince that the Granger causality findings of previous empirical studies have reached a general consensus. These uncertain causality results are rationalized by the heterogeneity in data spans, causality techniques, model specifications, lag order choices, and the characteristics of the country, such as the stages of economic development [3,4,30−32].

With reference to the characteristics of a country, the majority of the studies focus on developed and industrialized countries due to the availability and reliability of data pertaining to the less developed ones [4]. Ref. [33] identifies that energy consumption and economic growth do not influence each other in 22 out of 30 selected OECD countries. By contrast, in only 8 out of 30 selected OECD countries the evidence reveals that Granger causality runs from energy consumption to economic growth. Ref. [34] re-investigates the causal relationship between energy consumption and economic growth of 30 OECD countries and 78 non-OECD countries. In contrast to the result of Ref. [33], it is found that 70% of the selected OECD countries display that energy consumption Granger-causes economic growth, while only 46% of the selected non-OECD countries support this evidence. It is also found that the energy-led growth hypothesis is valid in 69% of the high-development countries, 42% of the middle-development countries and 35% of the low-income countries. Ref. [35] finds that energy consumption and economic growth do not affect each other in the case of low-income countries, while unidirectional causality runs from economic growth to energy consumption in the cases of the middle- and high-income countries.

Another strand of the literature employs panel data to provide further evidence on the investigated relationship. In particular, Ref. [36] shows that, both in the short- and in the long-run, causality runs from energy consumption to GDP. Ref. [37] makes use of a random effect model to examine the impact of renewable energy in Europe on economic growth. The results identify a weak relationship between the two variables under investigation, providing support to the neutrality hypothesis. Refs. [32] and [33], through a panel autoregressive distributed lag model, show that for the case of Eastern European countries the feedback hypothesis seems to hold. By contrast, Ref. [34] support the presence of a non-linear association between the two variables under study and provide evidence in favor of the neutrality hypothesis for a number of Asian countries, while Ref. [35] utilizes disaggregated sectoral data for Greece and documents that a bi-directional causality is present, implying the need for more energy efficiency to reduce the negative impact of energy consumption on economic growth.

Refs. [38−40] attempt to explain the presence of mixed results by emphasizing the differences in certain idiosyncratic characteristics for each country, such as their infrastructure and the different stages of their growth process. In other words, such differences are expected to affect not only the association between energy consumption and economic growth, but also the appropriate design of energy policies aim at preserving both economic growth and the environment. Finally, Ref. [41] argues that countries can hit their economic growth targets without harming the environment only if they adopt certain energy supply restrictions, implying the support of both the neutrality and conservation hypothesis.

3 Methodology

This paper aims at revealing the causal relation among the addressed economic series for various time scales. The causality is not only investigated for the original frequency but also at different frequencies pertinent to the time scale at hand. In order to decompose the series into various time scales, the wavelet analysis is employed. The time scales results obtained via a wavelet transformation correspond to different frequencies. Ref. [42] presents the frequency interpretation of the time scales of a quarterly series as indicated in Table 1.

Wavelets are mathematical tools that can localize data both in time and the frequency domain. With the theoretical foundation completed in the 1980s [43], successful applications were made to economic research including frequency domain analysis, the study of long-memory process, and timescale decompositions. The wavelet decomposition for studying Granger causality between economic variables employed in this paper is decomposing a time series into several layers of translation-invariant sequence at different scales. This method was used in Refs. [5] and [6]. Following their analysis, three major properties of the wavelet analysis which are the handling of nonstationary data, the localization in time, and the resolution of the data at different time scales are the interests in this paper.

The wavelet transformation is an integral transformation which maps an equation from its original domain (which in this case is the time domain) into another domain (in this case is a time scale domain). The wavelet decomposition of a series of observations provides a multi-scale analysis and bears a resemblance to the activity of a camera-lens. Zooming out the lens brings a broad landscape, while zooming in the lens makes it possible to find details which were not observable in the landscape portrait. This dissection of time series into different layers makes the wavelet analysis a very useful tool in economics because most economic time series consist of different layers due to economic agents making decisions with different time horizons. To this end, the original series is considered as a function of time. Next, this function is filtered into its low and high frequency components using wavelet and scaling filters. The resultant wavelet coefficients at each level correspond to the time scale of that level.

In this paper, the maximal overlap discrete wavelet transformation (MODWT) is preferred because it has no constraint on the length of series handled, while it is non-shift invariant. The MODWT is a collection of all wavelet coefficients and the scaling coefficients at the last level: {\tilde{d}}_{\mathrm{1}}, {\tilde{d}}_{\mathrm{2}},..., {\tilde{d}}_J, {\tilde{s}}_J, where {\tilde{d}}_j and {\tilde{s}}_j (j=1,2,…,J) denote a collection of wavelet and scaling coefficients, respectively. The collection of wavelet coefficients corresponds to the time scales. The wavelet and scaling coefficients are obtained by wavelet and scale filters. The wavelet filter of MODWT, {\tilde{h}}_l, has the following properties:

{\displaystyle {\sum }_{\mathrm{0}}^{L-\mathrm{1}}{\tilde{h}}_l}=\mathrm{0},{\displaystyle {\sum }_{\mathrm{0}}^{L-\mathrm{1}}{\tilde{h}}_l^{\mathrm{2}}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}

and

{\displaystyle {\sum }_{\mathrm{0}}^{L-\mathrm{1}}{\tilde{h}}_l{\tilde{h}}_{l+\mathrm{2}n}}={\displaystyle {\sum }_{-\infty }^{\infty }{\tilde{h}}_l{\tilde{h}}_{l+\mathrm{2}n}}=\mathrm{0}

for all nonzero integers n. Similarly, its scaling filter, {\tilde{g}}_l, has the following properties:

{\displaystyle {\sum }_{\mathrm{0}}^{L-\mathrm{1}}{\tilde{g}}_l}=\mathrm{1},{\displaystyle {\sum }_{\mathrm{0}}^{L-\mathrm{1}}{\tilde{g}}_l^{\mathrm{2}}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}

and

{\displaystyle {\sum }_{\mathrm{0}}^{L-\mathrm{1}}{\tilde{g}}_l{\tilde{g}}_{l+\mathrm{2}n}}={\displaystyle {\sum }_{-\infty }^{\infty }{\tilde{g}}_l{\tilde{g}}_{l+\mathrm{2}n}}=\mathrm{0}

for all nonzero integers n. MODWT wavelet, {\tilde{d}}_{j,t}, and scaling, {\tilde{s}}_{j,t}, coefficients at jth level are obtained using the following wavelet and scaling filters:

{\tilde{d}}_{j,t}={\displaystyle {\sum }_{l=\mathrm{0}}^{L-\mathrm{1}}{\tilde{h}}_l}{X}_{t-l\mathrm{mod}N}

{\tilde{s}}_{j,t}={\displaystyle {\sum }_{l=\mathrm{0}}^{L-\mathrm{1}}{\tilde{g}}_l}{X}_{t-l\mathrm{mod}N}

After obtaining the time scales from the wavelet coefficients, an attempt is made to investigate the dynamics of both the original series and the scales. A very important property of the dynamics of the series is the statitonarity. In order to check the stationarity of the series, Augmented Dickey-Fuller (ADF) and KPSS tests are performed.

The ADF test depends on the test first developed in Ref. [44]. In its initial form test could only be used for models with AR (1) process. Later, Ref. [45] improved the test for the cases of AR and MA processes of unknown order which became known as the ADF test. The ADF test is performed for three cases which are depicted in models A, B and C below:

Model A: \mathrm{\Delta }{y}_t=\gamma y_t+{\displaystyle {\sum }_{i=\mathrm{1}}^K{\rho }_i\mathrm{\Delta }{y}_{t-i}+{\epsilon }_t,}

Model B: \mathrm{\Delta }{y}_t=\mu +\gamma y_t+{\displaystyle {\sum }_{i=\mathrm{1}}^K{\rho }_i\mathrm{\Delta }{y}_{t-i}+{\epsilon }_t},

Model C: \mathrm{\Delta }{y}_t=\mu +\beta t+\gamma y_t+{\displaystyle {\sum }_{i=\mathrm{1}}^K{\rho }_i\mathrm{\Delta }{y}_{t-i}+{\epsilon }_t}.

Models A and B are employed when the series has no trend; Model A is preferred when the series moves about zero; Model B is used when the series moves about a constant other than zero. Finally, Model C is employed when the series has a trend as well as a drift term. The test conducted under the null hypothesis \gamma =\mathrm{0} against the alternative hypothesis of . In other words, the coefficient of y _t is tested to see whether it is zero or not. The test statistic is computed as

t_{DF}={\displaystyle \frac{\widehat{\gamma }}{se(\widehat{\gamma })}}.

The KPSS test, on the other hand, tests the null hypothesis of stationarity against the alternative hypothesis of non-stationarity. Ref. [46] assumes that the series can be decomposed into the sum of deterministic trend, a random walk and a stationary error:

y_t=\xi t+r_t+{\epsilon }_t,

where t is the trend, ε _t is the error term. r _t is the random walk, which is explicitly depicted as

r_t=r_{t-\mathrm{1}}+u_t,

where u _t is iid (0, {\sigma }_t^{\mathrm{2}}). In this case since ε _t is already stationary, the null hypothesis of stationarity turns out to be {\sigma }_t^{\mathrm{2}}=0.

Following unit root testing, the empirical analysis is concluded with the Granger causality test. The concept simply states that if a series can be used to forecast the behavior of the other series, then this series Granger causes the other. This statement for two series such as x _t and y _t can be simply tested within the vector autoregression (VAR) framework:

y_t={\beta }_{y\mathrm{0}}+{\displaystyle {\sum }_{i=\mathrm{1}}^L{\beta }_{y,i}{y}_{t-i}+}{\displaystyle {\sum }_{j=\mathrm{1}}^L{\beta }_{y,L+j}{x}_{t-j}+}{\epsilon }_{yt}

x_t={\beta }_{x\mathrm{0}}+{\displaystyle {\sum }_{i=\mathrm{1}}^L{\beta }_{x,i}{x}_{t-i}+}{\displaystyle {\sum }_{j=\mathrm{1}}^L{\beta }_{x,L+j}{y}_{t-j}+}{\epsilon }_{xt}

where L denotes the maximum number of lags, ε _y,t and ε _x,t are the white noise error terms which might be correlated across equations. If the coefficients of the x terms in the first equation are jointly significant, then the null hypothesis that x does not Granger cause y can be rejected. Similarly, if the coefficients of the y terms in the equation, where x _t is the dependent variable, are jointly significant, then the null hypothesis that y does not Granger cause x can be rejected.

4 Data and empirical results

The data employed in this study consist of observations spanning from 1973 to 2012 on a quarterly basis. The data on real GDP (in 2005 prices) and primary energy consumption (Million Kilowatt-hours) for the U.S. are obtained. The primary energy series is obtained from the U.S. Energy Information Administration, while the data on real GDP are obtained from the Bureau of Economic Analysis of the U.S. Department of Commerce.

An energy commodity can be classified as primary if it is acquired from its natural source without any transformation or conversion and, if it is obtained via transformation or conversion of one or more primary energy resources. Ref. [47], based on the definition of the International Energy Agency [48], argues that primary energy is “an energy source that is extracted from a stock of natural resources or captured from a flow of resources and which has not undergone any transformation or conversion other than separation and cleaning.” Thus, the term primary energy consumption refers to the direct use at the source, or supply to users without transformation (For a list of each primary energy source, please see the Appendix).

Natural logarithms of the series, which are depicted in Fig. 1, are used in the analysis. “lpec” indicates the natural logarithm of the primary energy consumption while “lrgdp” indicates the natural logarithm of real GDP.

Next, each series is transformed separately via the s4 wavelet filter. The wavelets decompose both of the series into sets of coefficients, where each set of coefficients is associated with a time scale. The time scales obtained from MODWT of the lrgdp and lpec series are presented in Fig. 2.

Figure 1 depicts the original series and shows that the lpec series has more oscillations than the lrgdp series, while Fig. 2 confirms this fact. Furthermore, it shows that these oscillations are contingent upon only the first two scales. This indicates that up to two years (eight quarters), lpec is relatively animated. However, these fluctuations wane in later scales. Further investigation of the time scales and the original series incorporates the stationarity of the series which is also relevant to causality.

Table 2 lists the results of the ADF and the KPSS unit root tests. In Table 2, the lrgdp and lpec show the original series, while dlrgdp and dlpec show their first differences. In addition, the time scale of each series is displayed by the relevant scale followed by the name of the series after a dot. Both the ADF and the KPSS tests demonstrate that the original series are non-stationary while their first differences are not. This leads to the question whether these series are cointegrated. The concept of cointegration has been introduced in order to deal with multiple series which alone are integrated, while their linear combination has a lower order of integration. Since the empirical findings of the cointegration testing show the absence of any cointegrating relations between the two series under study, the causality test is conducted through VAR model estimation in the first differences of the series.

The time scales on the other are uniformly stationary in cases when there is no deterministic term or only a drift term in the test model is included. Both the ADF and KPSS tests show that the d5 scale of lrgdp is not stationary in the case of a deterministic trend in the model. However, this is not the case in wavelet transformed series because wavelet transform filters away the trend portion into the set of scaling coefficients which is shown as s7 in Fig. 2. Consequently, unlike in unit root tests in the original economic series with time scales, it is rather advisable to focus on the stationarity of the series when no or only a drift term is considered to exist in the data generating process.

The empirical results are tabulated in Table 3. The analysis of the original series indicates that at the 95% confidence interval, energy consumption is caused by economic growth, while the reverse is not true. However at the 90% confidence interval, there is bidirectional causality. The reason for this becomes apparent when time scales are inspected. At the very finest scale, d1, there is a unidirectional causality from economic growth to energy consumption. However, at coarser scales, feedback is observed. Specifically at intermediate time scales, d2 to d4, it is possible to observe that the strength of non-causality from energy consumption to growth wanes. Therefore the reason why there is bidirectional causality in lower confidence interval while only the causality from economic growth to energy consumption prevails is that the non-causality at the frequency related to d1 scale becomes dominant in the original frequency of the data.

5 Conclusions

Wavelets can decompose time series into different time scales, which allows the identification of the influences of energy consumption on economic growth. This influence is not evident when only the observed sampling rate of the data is studied because sampling provides a mixture of the different frequencies and masks differences between short-term and long-term relationships. This is an important distinction in the examination of the above nexus since different factors might influence the association between energy consumption and economic growth in the short-term than in the long-term.

Using quarterly data for the U.S. spanning from 1973 to 2012, this study examined the impact of energy consumption on economic growth over different time scales. The results suggested that this impact varies by time scale: in the short-term, energy consumption is influenced by economic growth, but in the medium and long the reverse is true.

In view of policy implications, the empirical results indicated that if policymakers aim at reducing carbon dioxide emissions to combat global warming, the fact of a bi-directional causal effect between energy consumption and economic growth documents that although energy seems to be a crucial factor for economic growth, energy conservation policies can be also implemented to reduce carbon dioxide (CO₂) emissions and global warming without deleterious effects on the process of economic growth, achieving a simultaneous satisfaction of both economic growth and sustainable economic development. In doing so, both the economic performance and the quality of the environment can be sustained and balanced.

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