Research philosophy and design
This study adopts a positivist research philosophy, assuming that the determinants of renewable energy capacity (REC) can be objectively examined using quantitative panel data analysis. A longitudinal, cross-country comparative research design is employed to investigate the long-run relationships between renewable energy capacity and its determinants across 21 Organization for Economic Co-operation and Development (OECD) countries over the period 2000–2020. Guided by the Kaya Identity, a deductive-analytic approach is used to develop the empirical model and test the hypothesized relationships among renewable energy capacity, ecological policy performance, greenhouse gas (GHG) emissions, eco-friendly technology (EFT), and Green GDP. The analytical framework integrates data collection, diagnostic testing, cointegration analysis, quantile regression, and panel causality analysis to ensure methodological consistency and robust statistical inference.
Data collection and variables
The study utilizes a balanced panel dataset comprising 21 OECD countries observed annually from 2000 to 2020, resulting in 441 country-year observations. Data were obtained from publicly accessible and internationally recognized databases to ensure transparency and reproducibility. Table 1 summarizes the variables, measurement units, data sources, and expected signs. Renewable energy capacity (REC) is used as the dependent variable and is measured as the total installed renewable electricity generation capacity (MW). The explanatory variables include the Ecological Performance Index (EPI), greenhouse gas (GHG) emissions (CO₂-equivalent tonnes), eco-friendly technology (EFT), measured by environment-related patent applications, and Green GDP, measured as gross domestic product adjusted for environmental degradation and natural resource depletion (constant 2015 USD). Renewable energy capacity, EPI, GHG emissions, and EFT were obtained from the OECD Statistics database, whereas Green GDP was obtained from the World Bank database. All variables were transformed into natural logarithms prior to estimation to stabilize variance, reduce heteroscedasticity, and facilitate elasticity interpretation.
Theoretical framework and model specification
The empirical framework is based on the Kaya Identity39, which decomposes carbon dioxide emissions into population, economic activity, energy intensity, and carbon intensity, thereby providing a theoretical basis for understanding the drivers of environmental sustainability:
(1)
where CO2 represents carbon dioxide emissions; CO2/Energy denotes the carbon intensity of energy consumption; Energy/Green GDP represents the energy intensity of environmentally adjusted economic output; Green GDP/Population denotes environmentally adjusted gross domestic product per capita; and Population represents the total population.
The explanatory variables correspond directly to the theoretical components of the Kaya Identity. The Ecological Performance Index represents environmental policy performance aimed at promoting cleaner energy systems. Eco-friendly technology reflects technological innovation that improves energy efficiency and reduces renewable energy costs. Greenhouse gas emissions represent environmental pressure for decarbonization, whereas Green GDP captures environmentally adjusted economic performance. Based on this framework, the following empirical model is estimated39:
(2)
where REC denotes renewable energy capacity; EPI represents the Ecological Performance Index; GHG denotes greenhouse gas emissions; EFT represents eco-friendly technology; Green GDP denotes environmentally adjusted gross domestic product; i indexes countries; t indexes years; τ0 is the intercept; τ1–τ4 are the estimated regression coefficients; εit is the idiosyncratic error term.
Diagnostic tests
Prior to estimating the empirical models, a series of diagnostic tests was conducted to assess the statistical properties of the panel data and to identify appropriate estimation techniques. First, cross-sectional dependence was examined using the Pesaran cross-sectional dependence (CD) test34, as OECD countries are likely to experience common shocks arising from global economic conditions, international energy markets, and coordinated environmental policies:
(3)
where N denotes the number of cross-sectional units; T denotes the number of time periods; i and k index the cross-sectional units (i ≠ k);
represents the estimated pairwise correlation coefficient of the regression residuals between cross-sectional units i and k; j denotes the lag order; E(·) represents the expected value; and V(·) denotes the variance used to standardize the test statistic. Second, slope heterogeneity was assessed using the Pesaran–Yamagata slope heterogeneity test to determine whether the effects of explanatory variables differed across countries40:
(4)
(5)
where Δ̃adj denotes the adjusted slope heterogeneity test statistic; N represents the number of cross-sectional units; T denotes the number of time periods; k is the number of explanatory variables; and S̃ represents the standardized Swamy slope dispersion statistic used to evaluate parameter heterogeneity across panel units. Finally, stationarity was evaluated using the Cross-sectionally Augmented Im–Pesaran–Shin (CIPS) unit root test, which accommodates both cross-sectional dependence and heterogeneous slope coefficients41:
(6)
where CIPS denotes the Cross-sectionally Augmented Im–Pesaran–Shin panel unit root statistic; N represents the number of cross-sectional units; CDFi denotes the cross-sectionally augmented Dickey–Fuller statistic for the ith cross-sectional unit; and i indexes the individual cross-sectional units. The results of these diagnostic tests guided the selection of second-generation panel econometric techniques suitable for heterogeneous panel datasets.
Panel cointegration test
To determine whether a stable long-run equilibrium relationship exists among renewable energy capacity, environmental policy performance, greenhouse gas emissions, eco-friendly technology, and Green GDP, the Panel ARDL bounds cointegration test was employed. Compared with conventional residual-based cointegration tests, the Westerlund approach accommodates cross-sectional dependence, heterogeneous slope coefficients, and small sample sizes. The test produces four statistics: two group-mean statistics (Gt and Ga) and two panel statistics (Pt and Pa). Rejection of the null hypothesis indicates the presence of a long-run equilibrium relationship among the variables36,42:
(7a)
(7b)
(7c)
(7d)
where Gt and Ga denote the group-mean test statistics of the Panel ARDL bounds cointegration test; Pt and Pa denote the panel test statistics; N represents the number of cross-sectional units; T denotes the number of time periods;
is the estimated error-correction coefficient for the ith cross-sectional unit;
represents the pooled error-correction coefficient; SE(
) and SE(
) denote the corresponding standard errors; and i indexes the individual cross-sectional units. The presence of cointegration justifies estimating long-run elasticities and subsequent quantile-based analyses.
Method of moments quantile regression (MMQR)
Because conventional panel estimators provide only average effects, they may conceal substantial heterogeneity across countries operating at different levels of renewable energy deployment. To capture these heterogeneous effects, the Method of Moments Quantile Regression (MMQR) was employed.
MMQR estimates the effects of ecological policy performance, greenhouse gas emissions, eco-friendly technology, and Green GDP across multiple conditional quantiles of renewable energy capacity, thereby allowing the influence of explanatory variables to vary according to the maturity of renewable energy deployment. The method simultaneously accounts for individual fixed effects and unobserved heterogeneity while estimating both location and scale parameters43:
(8)
where Qτ(Yit | Xit) denotes the conditional τth quantile of the dependent variable; Yit represents renewable energy capacity (REC); Xit denotes the vector of explanatory variables (EPI, GHG emissions, EFT, and Green GDP); σ1 is the intercept; ζ is the vector of location parameters; αi represents the country-specific fixed effect; Zit denotes the scale covariates; γ is the vector of scale parameters; Uit is the error term; and i and t index countries and years, respectively. The scale component of the MMQR model is specified as follows43:
(9)
where Zi(X) denotes the scale function of the explanatory variables; Zi represents the vector of scale covariates; X denotes the vector of explanatory variables; i indexes the cross-sectional units (countries); and k denotes the total number of explanatory variables. As a robustness analysis, a conventional panel quantile regression with bootstrapped standard errors was also estimated to verify the consistency of the MMQR findings.
Panel causality test
The direction of causal relationships among renewable energy capacity, ecological policy performance, greenhouse gas emissions, eco-friendly technology, and Green GDP was examined using the Dumitrescu–Hurlin panel Granger non-causality test44. This approach accommodates cross-sectional dependence and heterogeneous panel structures while identifying whether causal relationships are unidirectional or bidirectional.
The panel causality analysis complements the cointegration and MMQR analyses by distinguishing between variables that drive renewable energy capacity and those that respond to changes in renewable energy deployment. Establishing causal direction provides additional evidence to inform policy prioritization and the sequencing of renewable energy interventions.
All statistical analyses were performed using statistical analysis software. The analytical sequence, from diagnostic testing and cointegration analysis to quantile regression and panel causality testing, provides a coherent and reproducible framework for evaluating the determinants of renewable energy capacity across OECD countries.