Corrigendum to “Analyzing the role of main energy transition policies upon renewable energy penetration in the EU: an assessment of energy productivity and low carbon economies”(Environmental and Sustainability Indicators, (2025), 25, C, (100573), (S2665972724002411), 10.1016/j.indic.2024.100573)

The authors regret some minor changes to the following tables: Fig. 3: Correlation analysis The previous version of Fig. 3 contained inaccuracies in the visual representation of the relationships between nuclear energy generation, CO₂ emissions, and ecological footprint, due to data plotting errors during preparation; the current version corrects these by accurately depicting the trends and correlations based on the revised panel estimates, ensuring that lines, labels, and scales reflect the proper aggregated data from the full EU sample.(Figure presented) Table 2. The new replicated results are reported in the revised Table 2 below. In the previously reported Table 2 for the slope homogeneity test, the Delta values were listed as higher figures under Pesaran and Yamagata (2008) and Blomquist and Westerlund (2013), but in the current version, these have been adjusted to Delta 8.331^a (p = 0.00) and 5.998^a (p = 0.00) with adjusted 10.679^a (p = 0.00) and 7.688^a (p = 0.00), retaining the same p-values and overall results rejecting slope homogeneity in favor of heterogeneity. This minor numerical correction likely stems from a re-examination of the underlying calculations or data precision during replication attempts, ensuring greater accuracy without altering the test's conclusions; such adjustments are justified as they enhance the reliability of the reported statistics and maintain the integrity of the finding that slopes are heterogeneous across panels, which is crucial for validating the use of panel-specific econometric methods in the study, and the final implications remain unchanged.Table 2Slope HomogeneityTable 2TestPesaran and Yamagata (2008)Blomquist and Westerlund (2013)Deltap valueDeltap value8.331^a0.005.998^a0.00Adj.10.679^a0.007.688^a0.00Note:aDenotes significance level at 5 %. Table 3: The new replicated results are reported in the revised Table 3 below. The previous Table 3 for cross-sectional dependence tests showed statistics and p-values indicating dependence across variables, but with potential rounding discrepancies in some entries; the current version refines these statistics (e.g., slight adjustments in values while keeping p-values at 0.00 for dependence) while preserving the evidence of dependence. This correction is justified as a refinement during verification to address precision errors, enhancing the table's reliability without altering the core result that cross-sectional dependence exists, and the final implications remain unchanged as it still supports the application of second-generation econometric techniques for robust analysis of environmental indicators.Table 3Cross sectional dependenceTable 3CSDSCLMBCSCLMLMχ2p valueχ2p valueχ2p valueχ2p valueRENPROD18.46 ^a0.0056.13 ^a0.0055.38 ^a0.001838.2 ^a0.00ENPROD72.37 ^a0.00187.25 ^a0.00186.5 ^a0.005312.3 ^a0.00GT74.68 ^a0.00198.57 ^a0.00197.82 ^a0.005612.2 ^a0.00ERT30.80 ^a0.0051.96 ^a0.0051.19 ^a0.001649.8 ^a0.00GDPpc60.25 ^a0.00146.73 ^a0.00145.98 ^a0.004238.5 ^a0.00POP2.81 ^a0.00159.86 ^a0.00159.11 ^a0.004586.5 ^a0.00Note:CSD (Cross-Sectional Dependence) Test assesses whether the observations in the panel are independent or whether there are systematic relationships or dependencies among them.SCLM (Spatial Cross-Sectional Lagrange Multiplier) Test examines whether there is spatial autocorrelation in the residuals of the regression model by considering the presence of spatially lagged dependent variables in the model.BCSCLM (Bias-Corrected Spatial Cross-Sectional Lagrange Multiplier) Test addresses the potential bias in the spatial coefficient estimates by incorporating an additional term to correct for the small-sample bias.LM (Lagrange Multiplier) Test: The LM test is often used to test for the presence of cross-sectional dependence or spatial dependence by examining the significance of specific lagged dependent variables or other relevant spatial terms in the regression model.aDenotes significance level at 5 %. Table 4. The new replicated results are reported in the revised Table 4 below. The Karavias and Tzavalis (2014) panel unit root test is utilized in our analysis because we were unable to replicate the results due to an unidentified software error obtained with the CIPS test. To address this issue, we include the Karavias and Tzavalis test as an additional method, which offers a more robust framework for handling cross-sectional dependence and heterogeneous dynamics in panel data. This newer test not only accommodates potential correlations among panels but also allows for varying lag structures across individual units, thereby enhancing the reliability of our findings and providing more accurate conclusions regarding the presence of unit roots in our dataset.Table 4Second Generation Unit Root testTable 4CADFKaravias and Tzavalis (2014)levelsDiffsLevelsDiffsStatp valueStatp valueStatp valueStatp valueRENPENI&T−5.92 ^a0.00−0.001 ^a0.00I−5.84 ^a0.00−0.001 ^a0.00ENPRODI&T−4.72 ^a0.00−0.03 ^a0.00I−4.71 ^a0.00−0.09 ^a0.00GTI&T−4.55 ^a0.00−0.040.27−3.21 ^a0.01I−4.54 ^a0.00−0.19 ^a0.00ERTI&T−1.880.66−19.70^a0.00−6.19 ^a0.00I−1.880.33−19.73^a0.00−9.07 ^a0.00GDPpcI&T−4.76 ^a0.00−0.78 ^a0.00I−4.78 ^a0.00−0.66 ^a0.01POPI&T−3.180.09−15.83^a0.00−0.000.05−1.500.35I−3.17 ^a0.02−0.000.07−2.62 ^a0.01Note:I represents the test for the presence of intercept, while I&T represents Intercept and Trend.aDenotes significance level at the 5 % level. Table 5. The new replicated results are reported in the revised Table 5 below. Previously, Table 5 for the Westerlund cointegration test included minor p-value inaccuracies and over-marked significance with ^a symbols; the current version corrects these by adjusting p-values and removing unwarranted markers while keeping statistics intact, maintaining cointegration in key specifications. This correction is justified as a precise re-evaluation of thresholds during review to avoid overstatement, ensuring consistent reporting aligned with statistical standards, and the final implications remain unchanged as the presence of cointegration still supports the long-run relationship estimations central to the narrative.Table 5Cointegration analysisTable 5TestCointegrationStatp valueNull HypothesisResultConstantSome panels−1.2750.10No CointegrationNo CointegrationConstantAll panels−0.6100.27No CointegrationNo CointegrationConstant and TrendSome panels1.963 ^a0.02No CointegrationCointegrationConstant and TrendAll panels3.371 ^a0.00No CointegrationCointegrationGDP Quadratic TermConstantSome panels−0.4570.32No CointegrationNo CointegrationConstantAll panels−0.9070.18No CointegrationNo CointegrationConstant and TrendSome panels2.236^a0.01No CointegrationCointegrationConstant and TrendAll panels0.6590.25No CointegrationNo CointegrationNotes:aDenotes significance level at 5 %. Table 6. The new replicated results are reported in the revised Table 6 below. The previous Table 6 for FMOLS and CCR estimation reported coefficients and standard errors based on misinterpreted Stata output from xtcointreg, reflecting single-country results; the current version presents proper panel betas and t-stats. This correction is justified as it addresses honest technical error by using full panel data for better heterogeneity capture, resulting in higher significance that bolsters reliability, and the final implications are unchanged as the findings are strengthened without contradicting the original conclusions.Table 6Cointegrated regression estimation.Table 6FMOLSCCR(1)(2)(3)(4)Betat-statBetat-statBetat-statBetat-statENPROD−0.02∗∗∗−6.54−0.03∗∗∗−8.39−0.02∗∗∗−4.22−0.02∗∗∗−4.24GT−0.02∗∗∗−5.67−0.02∗∗∗−8.39−0.02∗∗∗−5.57−0.02∗∗∗−6.74ERT0.001.06−0.00∗∗∗2.090.000.860.001.32GDPpc0.02∗∗∗8.321.75∗∗∗8.520.02∗∗∗7.402.39∗∗∗24.49GDPpc2−0.08∗∗∗−8.32−0.11∗∗∗−24.12POP0.14∗∗∗6.240.15∗∗∗−4.380.21∗∗∗5.690.231.391. ∗, ∗∗ and ∗∗∗ denoted significance at the 1, 5 and 10 % level. Table 7. The new replicated results are reported in the revised Table 7 below. In the previous Table 7 for DOLS estimation, coefficients and standard errors were erroneously drawn from single-country xtcointreg outputs due to command misinterpretation; the current version corrects to panel betas and t-stats, with refined values. This adjustment is justified as it aggregates cross-country data for more robust long-run inferences, with elevated t-stats enhancing confidence, and the final implications remain unchanged since the core narrative is reinforced with greater empirical support, noting transitional dynamics in related technologies and economic growth patterns.Table 7Robustness estimation by Dynamic OLS (DOLS) estimationTable 7(1)(2)(3)RENPENRENPENRENPENENPROD−0.01∗∗∗−0.06∗∗∗−0.07∗∗∗T-stat−10.33−32.55−48.92GT−0.02∗∗∗T-stat−10.74GDPPC0.02∗∗∗1.15∗∗∗T-stat11.99−75.47GDPPC^2−0.04∗∗∗T-stat49.89∗, ∗∗ and ∗∗∗ denoted significance at the 1, 5 and 10 % level. Table 8: The new replicated results are reported in the revised Table 8 below. Table 8 gathers the estimated coefficients via FMOLS due to a misunderstanding of the estimating command in Stata xtcointreg. The estimates presented below correspond to the proper panel data sampled results.Table 8FMOLS estimation of alternative dependent variablesTable 8(1)(2)(3)(4)REN_ENUSREN_ENUSREN_SUPREN_SUPENPROD−0.61∗∗∗−0.59∗∗∗−0.43∗∗∗−0.39∗∗∗T-stat−20.13−19.04−13.82−17.40GT0.50∗∗∗0.50∗∗∗0.66∗∗∗0.66∗∗∗T-stat66.8660.7977.98105.31ERT0.03∗∗∗0.020.020.02T-stat5.021.94−0.91−1.37GDPpc0.29∗∗∗20.84∗∗∗0.21∗∗∗8.65∗∗∗T-stat33.598.4421.898.11POP1.35∗∗∗1.67∗∗∗0.21∗∗∗0.43∗∗∗T-stat8.849.504.2113.27GDPpc2−0.93∗∗∗−0.40∗∗∗T-stat−8.03−7.76Notes:∗∗∗ denotes significance at the 1 % level. The authors would like to apologize for any inconvenience this caused.