Modeling Vector Error Correction with Exogeneous (VECMX) Variable for Analyzing Nonstationary Variable Energy Used and Gross Domestic Product (GDP)
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Keywords:
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Nonstationary, Cointegration, VECMX Model, Ganger-Causality, Forecasting
Abstract
Analysis of energy used, GDP and population has been carried out in many countries and has become a topic of interest for many researchers and governments. This is because energy used is an important factor for society and industry in a country. In this study, the modeling of the relationship between energy used, GDP and population as an exogenous variable for the cases of Indonesia from 1967-2023 will be discussed. The energy used and GDP data are nonstationary with order one, I(1), and there is cointegration between energy used and GDP. Therefore, the model which will be used is the Vector Error Correction Model with Exogenous variable (VECMX) with population as the exogenous variable. From the results of analysis, the best model is VECMX(3,1) with cointegration rank R=1. Based on this model, the pattern of the relationship among the three variables, Granger-causality between energy used and GDP, exogenous impact on energy used and GDP, and forecasting for the next 10 years will be discussed.
References
Ajmi, A. N. and R. Inglesi-Lotz (2020). Biomass Energy Consumption and Economic Growth Nexus in OECD Countries: A Panel Analysis. Renewable Energy, 162; 1649–1654.
Akarca, A. T. and T. V. Long (1979). Energy and Employment: A Time Series Analysis of the Causal Relationship. Resources and Energy, 2; 151–162.
Al-Mulali, U. and C. N. B. C. Sab (2012). The Impact of Energy Consumption and CO2 Emission on the Economic Growth and Financial Development in the Sub-Saharan African Countries. Energy, 39(1); 180–186.
Altinay, G. and E. Karagol (2004). Structural Break, Unit Root, and the Causality Between Energy Consumption and GDP in Turkey. Energy Economics, 26; 985–994.
Aqeel, A. and M. S. Butt (2001). The Relationship Between Energy Consumption and Economic Growth in Pakistan. Asia-Pacific Development Journal, 8(2); 101–110.
Bekhet, H. A. and N. Y. M. Yusop (2009). Assessing the Relationship Between Oil Prices, Energy Consumption, and Macroeconomic Performance in Malaysia: Cointegration and Vector Error Correction Model (VECM) Approach. International Business Research, 2(3); 152.
Binh, P. T. (2011). Energy Consumption and Economic Growth in Vietnam: Threshold Cointegration and Causality Analysis. International Journal of Energy Economics and Policy, 1(1); 1–17.
Bouyghrissi, S., A. Berjaoui, and M. Khanniba (2021). The Nexus between Renewable Energy Consumption and Economic Growth in Morocco. Environmental Science and Pollution Research, 28; 5693–5703.
Canh, L. Q. (2011). Electricity Consumption and Economic Growth in Vietnam: A Cointegration and Causality Analysis. Journal of Economic Development, 13; 24–36.
Cheng, B. S. (1996). An Investigation of Cointegration and Causality Between Energy Consumption and Economic Growth. Journal of Energy Development, 21; 73–84.
Cheng, B. S. and W. L. Lai (1997). An Investigation of Cointegration and Causality Between Energy Consumption and Economic Activity in Taiwan. Energy Economics, 19; 435–444.
Chontanawat, J., L. C. Hunt, and R. Pierse (2008). Does Energy Consumption Cause Economic Growth? Evidence From a Systematic Study of Over 100 Countries. Journal of Policy Modeling, 30(2); 209–220.
Dickey, D. A. and W. A. Fuller (1979). Distribution of Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, 74; 427–431.
Dickey, D. A. and W. A. Fuller (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica, 49; 1057–1072.
Ebohon, O. J. (1996). Energy, Economic Growth and Causality in Developing Countries: A Case Study of Tanzania and Nigeria. Energy Policy, 24; 447–453.
Erol, U. and E. S. H. Yu (1987). Time Series Analysis of the Causal Relationships Between U.S. Energy and Employment. Resources and Energy, 9; 75–89.
Ghali, K. H. and M. I. T. El-Sakka (2004). Energy Use and Output Growth in Canada: A Multivariate Cointegration Analysis. Energy Economics, 26; 225–238.
Granger, C. W. J. (1988). Some Recent Developments in a Concept of Causality. Journal of Econometrics, 39; 199–211.
Gujarati, D. N. (2003). Basic Econometrics. McGraw-Hill, New York, 4th edition.
Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press, Princeton, New Jersey.
Hannesson, R. (2009). Energy and GDP Growth. International Journal of Energy Sector Management, 3(2); 157–170.
Hoa, T. V. (1993). Effects of Oil on Output Growth and Inflation in Developing Countries: The Case of Thailand From January 1966 to January 1991. International Journal of Energy Research, 17; 29–33.
Hondroyiannis, G., S. Lolos, and E. Papapetrou (2002). Energy Consumption and Economic Growth: Assessing the Evidence From Greece. Energy Economics, 24; 319–336.
Hwang, D. B. K. and B. Gum (1992). The Causal Relationship between Energy and GNP: The Case of Taiwan. Journal of Energy Development, 16; 219–226.
Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3); 231–254.
Kraft, J. and A. Kraft (1978). On the Relationship between Energy and GNP. Journal of Energy Development, 3; 401–403.
Loi, N. D. (2012). Energy Consumption and Economic Development: Granger Causality Analysis for Vietnam. Vietnam Development and Policies Research Centre (DEPOCEN), 14(2012); 1–24.
Magazzino, C. (2015). Energy Consumption and GDP in Italy: Cointegration and Causality Analysis. Environmental Development and Sustainability, 17(1); 137–153.
Mahadevan, R. and J. Asafu-Adjaye (2007). Energy Consumption, Economic Growth and Prices: A Reassessment Using Panel VECM for Developed and Developing Countries. Energy Policy, 35(4); 2481–2490.
Mansoor, A. and B. Sultana (2018). Impact of Population, GDP and Energy Consumption on Carbon Emissions: Evidence From Pakistan Using an Analytic Tool IPAT. Asian Journal of Economics and Empirical Research, 5(2); 183–190.
Oh, W. and K. Lee (2004). Causal Relationship between Energy Consumption and GDP Revisited: The Case of Korea 1970-1999. Energy Economics, 26; 51–59.
Pachiyappan, D., Y. Ansari, M. S. Alam, P. Thoudam, K. Alagirisamy, and P. Manigandan (2021). Short and Long-Run Causal Effects of CO2 Emissions, Energy Used, GDP and Population Growth: Evidence From India Using the ARDL and VECM Approaches. Energies, 14; 8333.
Phillip, P. C. B. and P. Perron (1988). Testing for a Unit Root in Time Series Regression. Biometrika, 75; 335–346.
Pierce, D. and L. Haugh (1977). Causality in Temporal Systems: Characterization and A Survey. Journal of Econometrics, 5(3); 265–293.
Soytas, U. and R. Sari (2003). Energy Consumption and GDP: Causality Relationship in G-7 Countries and Emerging Markets. Energy Economics, 25; 33–37.
Squalli, J. (2007). Electricity Consumption and Economic Growth: Bounds and Causality Analyses of OPEC Members. Energy Economics, 29; 1192–1205.
Tsay, R. S. (2010). Analysis of Financial Time Series. John Wiley & Sons, Inc., New York.
Tsay, R. S. (2014). Multivariate Time Series Analysis. John Wiley and Sons, New York.
Wei, W. W. S. (2006). Time Series Analysis: Univariate and Multivariate Methods. Addison-Wesley Publishing Company, Redwood City, California.
Wei, W. W. S. (2019). Multivariate Time Series Analysis and Application. John Wiley and Sons, New York.
Yang, H. Y. (2000). A Note of the Causal Relationship Between Energy and GDP in Taiwan. Energy Economics, 22; 309–317.
Yu, E. S. H. and J. Y. Choi (1985). The Causal Relationship Between Energy and GNP: An International Comparison. Journal of Energy Development, 10; 249–272.
Yu, E. S. H. and B. K. Hwang (1984). The Relationship Between Energy and GNP, Further Results. Energy Economics, 6; 186–190.
Yu, E. S. H. and J. C. Jin (1992). Cointegration Tests of Energy Consumption, Income, and Employment. Resources and Energy, 14; 259–266.
Akarca, A. T. and T. V. Long (1979). Energy and Employment: A Time Series Analysis of the Causal Relationship. Resources and Energy, 2; 151–162.
Al-Mulali, U. and C. N. B. C. Sab (2012). The Impact of Energy Consumption and CO2 Emission on the Economic Growth and Financial Development in the Sub-Saharan African Countries. Energy, 39(1); 180–186.
Altinay, G. and E. Karagol (2004). Structural Break, Unit Root, and the Causality Between Energy Consumption and GDP in Turkey. Energy Economics, 26; 985–994.
Aqeel, A. and M. S. Butt (2001). The Relationship Between Energy Consumption and Economic Growth in Pakistan. Asia-Pacific Development Journal, 8(2); 101–110.
Bekhet, H. A. and N. Y. M. Yusop (2009). Assessing the Relationship Between Oil Prices, Energy Consumption, and Macroeconomic Performance in Malaysia: Cointegration and Vector Error Correction Model (VECM) Approach. International Business Research, 2(3); 152.
Binh, P. T. (2011). Energy Consumption and Economic Growth in Vietnam: Threshold Cointegration and Causality Analysis. International Journal of Energy Economics and Policy, 1(1); 1–17.
Bouyghrissi, S., A. Berjaoui, and M. Khanniba (2021). The Nexus between Renewable Energy Consumption and Economic Growth in Morocco. Environmental Science and Pollution Research, 28; 5693–5703.
Canh, L. Q. (2011). Electricity Consumption and Economic Growth in Vietnam: A Cointegration and Causality Analysis. Journal of Economic Development, 13; 24–36.
Cheng, B. S. (1996). An Investigation of Cointegration and Causality Between Energy Consumption and Economic Growth. Journal of Energy Development, 21; 73–84.
Cheng, B. S. and W. L. Lai (1997). An Investigation of Cointegration and Causality Between Energy Consumption and Economic Activity in Taiwan. Energy Economics, 19; 435–444.
Chontanawat, J., L. C. Hunt, and R. Pierse (2008). Does Energy Consumption Cause Economic Growth? Evidence From a Systematic Study of Over 100 Countries. Journal of Policy Modeling, 30(2); 209–220.
Dickey, D. A. and W. A. Fuller (1979). Distribution of Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, 74; 427–431.
Dickey, D. A. and W. A. Fuller (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica, 49; 1057–1072.
Ebohon, O. J. (1996). Energy, Economic Growth and Causality in Developing Countries: A Case Study of Tanzania and Nigeria. Energy Policy, 24; 447–453.
Erol, U. and E. S. H. Yu (1987). Time Series Analysis of the Causal Relationships Between U.S. Energy and Employment. Resources and Energy, 9; 75–89.
Ghali, K. H. and M. I. T. El-Sakka (2004). Energy Use and Output Growth in Canada: A Multivariate Cointegration Analysis. Energy Economics, 26; 225–238.
Granger, C. W. J. (1988). Some Recent Developments in a Concept of Causality. Journal of Econometrics, 39; 199–211.
Gujarati, D. N. (2003). Basic Econometrics. McGraw-Hill, New York, 4th edition.
Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press, Princeton, New Jersey.
Hannesson, R. (2009). Energy and GDP Growth. International Journal of Energy Sector Management, 3(2); 157–170.
Hoa, T. V. (1993). Effects of Oil on Output Growth and Inflation in Developing Countries: The Case of Thailand From January 1966 to January 1991. International Journal of Energy Research, 17; 29–33.
Hondroyiannis, G., S. Lolos, and E. Papapetrou (2002). Energy Consumption and Economic Growth: Assessing the Evidence From Greece. Energy Economics, 24; 319–336.
Hwang, D. B. K. and B. Gum (1992). The Causal Relationship between Energy and GNP: The Case of Taiwan. Journal of Energy Development, 16; 219–226.
Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3); 231–254.
Kraft, J. and A. Kraft (1978). On the Relationship between Energy and GNP. Journal of Energy Development, 3; 401–403.
Loi, N. D. (2012). Energy Consumption and Economic Development: Granger Causality Analysis for Vietnam. Vietnam Development and Policies Research Centre (DEPOCEN), 14(2012); 1–24.
Magazzino, C. (2015). Energy Consumption and GDP in Italy: Cointegration and Causality Analysis. Environmental Development and Sustainability, 17(1); 137–153.
Mahadevan, R. and J. Asafu-Adjaye (2007). Energy Consumption, Economic Growth and Prices: A Reassessment Using Panel VECM for Developed and Developing Countries. Energy Policy, 35(4); 2481–2490.
Mansoor, A. and B. Sultana (2018). Impact of Population, GDP and Energy Consumption on Carbon Emissions: Evidence From Pakistan Using an Analytic Tool IPAT. Asian Journal of Economics and Empirical Research, 5(2); 183–190.
Oh, W. and K. Lee (2004). Causal Relationship between Energy Consumption and GDP Revisited: The Case of Korea 1970-1999. Energy Economics, 26; 51–59.
Pachiyappan, D., Y. Ansari, M. S. Alam, P. Thoudam, K. Alagirisamy, and P. Manigandan (2021). Short and Long-Run Causal Effects of CO2 Emissions, Energy Used, GDP and Population Growth: Evidence From India Using the ARDL and VECM Approaches. Energies, 14; 8333.
Phillip, P. C. B. and P. Perron (1988). Testing for a Unit Root in Time Series Regression. Biometrika, 75; 335–346.
Pierce, D. and L. Haugh (1977). Causality in Temporal Systems: Characterization and A Survey. Journal of Econometrics, 5(3); 265–293.
Soytas, U. and R. Sari (2003). Energy Consumption and GDP: Causality Relationship in G-7 Countries and Emerging Markets. Energy Economics, 25; 33–37.
Squalli, J. (2007). Electricity Consumption and Economic Growth: Bounds and Causality Analyses of OPEC Members. Energy Economics, 29; 1192–1205.
Tsay, R. S. (2010). Analysis of Financial Time Series. John Wiley & Sons, Inc., New York.
Tsay, R. S. (2014). Multivariate Time Series Analysis. John Wiley and Sons, New York.
Wei, W. W. S. (2006). Time Series Analysis: Univariate and Multivariate Methods. Addison-Wesley Publishing Company, Redwood City, California.
Wei, W. W. S. (2019). Multivariate Time Series Analysis and Application. John Wiley and Sons, New York.
Yang, H. Y. (2000). A Note of the Causal Relationship Between Energy and GDP in Taiwan. Energy Economics, 22; 309–317.
Yu, E. S. H. and J. Y. Choi (1985). The Causal Relationship Between Energy and GNP: An International Comparison. Journal of Energy Development, 10; 249–272.
Yu, E. S. H. and B. K. Hwang (1984). The Relationship Between Energy and GNP, Further Results. Energy Economics, 6; 186–190.
Yu, E. S. H. and J. C. Jin (1992). Cointegration Tests of Energy Consumption, Income, and Employment. Resources and Energy, 14; 259–266.
Authors
Usman, M., Wamiliana, Russel, E., Kurniasari, D., Widiarti, & Elfaki, F. A. (2025). Modeling Vector Error Correction with Exogeneous (VECMX) Variable for Analyzing Nonstationary Variable Energy Used and Gross Domestic Product (GDP). Science and Technology Indonesia, 10(1), 283–293. https://doi.org/10.26554/sti.2025.10.1.283-293
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