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Testing dependence patterns of energy consumption with economic expansion and trade openness through wavelet transformed coherence in top energy-consuming countries

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Economic growth and trade openness are closely linked with energy consumption and hence have environmental consequences. Many studies have investigated the relationship between these variables. Two weaknesses in empirical literature on energy-growth nexus are prominent. First majority of the studies are conducted on different groups of countries; however, no study has focused the top energy-consuming countries despite their immense importance in the context of energy-growth nexus. Second, this literature cannot simultaneously capture time and frequency domains, short- and long-run dependence, and lagging and leading effects among the variables. Furthermore, environmental impacts of increased energy consumption emerging from trade base economic growth are less studied. This study employs wavelet transformed coherence method to examine dependence partners of energy consumption with economic expansion and trade openness in top 10 energy-consuming countries. This methodology avoids the unrealistic assumption of stationarity of the variables due to favorable scaling tool and unveils the time frequency dependence among variables with more reliability as it accounts for the seasonality, cycles, or trends extracted from the transformation change over time. Furthermore, this technique has the novelty to handle data when its transformation from one-dimensional to bi-dimensional time-frequency sphere is allowed. Findings reveal a positive influence of economic growth and trade on energy consumption in many countries. The wavelet transformed coherence indicates short-run coherence among energy consumption and economic growth of all the top 10 energy-consuming countries. Long-run dependence among energy consumption and economic growth exists in case of China, India, Brazil, and South Korea with mostly leading role of energy consumption over economic growth. The findings of the study reiterate the importance of energy consumption in the development of these economies and suggest that energy policies aimed at improving efficiency in the production and consumption of energy will not hurt economic growth.

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  1. Author own calculations. For detail, see Appendix 1 and Appendix 2.

  2. For further explanation of Fourier analysis, see the work of Ransom et al. (2002).

  3. For detail explanation, see work of Tiwari (2012).

  4. For further details of WTC, see Ramsey (1928) and Grinsted et al. (2004).


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The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations



M.I.H. conceived the concept and wrote “Introduction,” “Literature review,” and “Conclusion” sections. N. collected the data and carried out the analysis and wrote the “Research methodology and data” section. M.A.K. wrote the “Results and discussion” section.

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Correspondence to Muhammad Iftikhar ul Husnain.

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Appendix 1


% share in world GDP

% of world population

% share in primary energy consumption

% share in CO2 emission

% share in global exports

% share in global imports

























































South Korea






















Percentage share in world GDP by Worldometer, (2017)

Percentage world population by worldometer, (2017)

Percentage share in primary energy consumption, (2019)

Percentage share in CO2 emission, (2018)

Percentage share in global exports & imports, (2018)

Appendix 2. Wavelet transformed coherence among EC and T

figure a

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Husnain, M.I.u., Nasrullah & Khan, M.A. Testing dependence patterns of energy consumption with economic expansion and trade openness through wavelet transformed coherence in top energy-consuming countries. Environ Sci Pollut Res 28, 49788–49807 (2021).

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