Panel estimation for renewable and non-renewable energy consumption, economic growth, CO₂ emissions, the composite trade intensity, and financial openness of the commonwealth of independent states

Abstract

This article investigates the long-run and causal linkages between economic growth, CO₂ emissions, renewable and non-renewable (fossil fuels) energy consumption, the Composite Trade Intensity (CTI) as a proxy for trade openness, and the Chinn-Ito index as a proxy for financial openness for a panel of the Commonwealth of Independent States (CIS) region including Armenia, Azerbaijan, Belarus, Georgia, Kazakhstan, Kyrgyzstan, Moldova, Russia, Tajikistan, Turkmenistan, Ukraine, and Uzbekistan over the period of 1992–2015. It is the first time that CTI and the Chinn-Ito indexes are used in an economic-pollution model. Employing three panel unit root tests, panel cointegration estimation methods (DOLS and FMOLS), and two panel causality tests, the main empirical results provided evidence for the bidirectional long-run relationship between all the variables in all 12 sampled countries except for economic growth-renewable energy use linkage. The findings of causality tests indicated that there is a unidirectional short-run panel causality running from economic growth, financial openness, and trade openness to CO₂ emissions and from fossil fuel energy consumption to renewable energy use.

Appendices

Appendix 1

Table 8 Studies related to the relationships between CO₂-GDP-non/renewable energy

Table 9 The studies related to the CIS countries

Appendix 2

Pesaran’s residual cross-section dependence (CD) test is based on the pairwise correlation coefficients ${\widehat{\rho}}_{ij}$ as below:

$$ CD=\sqrt{\frac{2}{N\left(N-1\right)}}{\sum}_{i=1}^N{\sum}_{j=i+1}^N\sqrt{T_{ij}}{\widehat{\rho}}_{ij} $$

(1)

The Breusch-Pagan Lagrange multiplier (LM) test statistic for dependence is as follows:

$$ LM={\sum}_{i=1}^{N-1}{\sum}_{j=i+1}^N{T}_{ij}{\widehat{\rho}}_{ij}^2\to {\upchi}_{\frac{N\left(N-1\right)}{2}}^2 $$

(2)

Here, the ${\widehat{\rho}}_{ij}$ denotes the correlation coefficients and the asymptotic χ² distribution is obtained from N fixed for all i and j.

FMOLS and DOLS can be explained as follows:

Considering a simple panel regression equation as

$$ {y}_{it}={\propto}_i+{\beta}_i{X}_{it}+{\varepsilon}_{it} $$

(3)

$$ {x}_{it}={X}_{i,t-1}+{\varepsilon}_{it} $$

(4)

Following Kao and Chiang (2000) who show that FMOLS and DOLS panel cointegration methods are asymptotically normal, the FMOLS estimator’s coefficient can be written as below:

$$ {\beta}_{FMOLS}={\left[{\sum}_{i=1}^N{\sum}_{t=1}^T{\left({x}_{it}-{\overline{x}}_{it}\right)}^{\prime}\right]}^{-1}\left[{\sum}_{i=1}^N\left({\sum}_{i=1}^T\left({x}_{it}-{\overline{x}}_{it}\right)\Big){y}_{it}^{+}+T{y}_i^{\hat{\mkern6mu}}\right)\right] $$

(5)

where ${y}_i^{\hat{\mkern6mu} }$ indicates the serial correlation term and ${y}_{it}^{+}$ denotes the transformation of y_it in order to control the endogeneity problem.

Moreover, the coefficient of DOLS panel cointegration estimator can be obtained as

$$ {\widehat{\beta}}_{DOLS}={\sum}_{i=1}^N{\left[{\sum}_{t=1}^T{z}_{it}{z}_{it}^{\prime}\right]}^{-1}\left[{\sum}_{t=1}^T{z}_{it}{z}_{it}^{\hat{\mkern6mu}}\right] $$

(6)

In Eq. 6, z_it is 2(K + 1)×1 and z_it^{^} equals to (${x}_{it}-{\overline{x}}_{it}$).

The Granger causality test is based on an error correction model (ECM), which in regard to the dependent variable of CO₂ emissions can be formulated as below:

$$ \Delta CO{2}_{it}={c}_{1i}+\sum \limits_p{c}_{11 ip}\Delta CO{2}_{2 it-p}+\sum \limits_p{c}_{12 ip}\Delta {GDP}_{it-p}+\sum \limits_p{c}_{13 ip}\Delta {REU}_{it-p}+\sum \limits_p{c}_{14 ip}\Delta {NREUE}_{it-p}+\sum \limits_p{c}_{15 ip}\Delta {CTI}_{it-p}+\sum \limits_p{c}_{16 ip}\Delta {FIOPEN}_{it-p}+{\sigma}_{1i}{ECT}_{it-1}+{\varepsilon}_{1 it} $$

(7)

In Eq.7, ECT denotes the error connection term. Δ refers to first difference of the variable and p indicates the lag length (we choose it based on Akaike’s information criterion).