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Summary: The EU countries are facing a burning debate with regard to the nature and amount of decarbonized energy used within the supply mix. This study highlights the role of nuclear power and renewable energy use in achieving economic growth in Europe. Capital, labour, exports, and trade openness series are included within a multivariate framework spanning the 1986 to 2019 period and a two‐step methodology is implemented. First, a panel causality analysis over the top 10 nuclear energy‐consuming EU countries is conducted using the panel non‐causality test from Juodis, Karavias and Sarafidis (2021), robust under large cross‐sectional and time‐series dimensions, as well as heterogeneous coefficients. Second, a sub‐set of three states (Germany, Spain, and France) that are different in terms of long‐run nuclear energy policies is selected and a single‐country time‐series assessment is performed using the vector error correction model, causality tests, as well as impulse response functions. Panel EU results support the "conservation hypothesis" for both nuclear and renewable resources, without feedback effect. The country‐level estimates fail to provide homogeneous results since no causal link is found between economic growth and renewable energy use for Spain and France (confirmation of "neutral hypothesis"). A weak causality from renewable energy use to output growth is observed for Germany, while economic growth enhances the nuclear energy consumption in Spain. [ABSTRACT FROM AUTHOR]

• The Belgium nuclear phase-out plan is analyzed. • A multivariate model through time-series analyses is implemented over the 1974–2019 period. • We develop and apply an innovative partial differential equations (PDE) algorithm. • Time-series and machine learning findings demonstrate suggests that the nuclear phase-out might neither adversely impact the economy's growth nor threaten the emission reduction target in the long-run. By 2025, Belgium will phase-out nuclear power. Unassessed so far, this policy reform may modify the economic and environmental channels through which energy and society interfere in this country. In this paper, we investigate whether this structural energy change may adversely impact the growth of the Belgian economy (i) and its ability to meet its long-term greenhouse gas emission targets (ii). A multivariate model comprising production factors (labor, capital, and exports), nuclear and renewable energy uses, total primary energy supply, economic growth, and CO 2 emissions from the power and heating sector is combined with real time-series data spanning the 1974–2019 period. The analysis consists in sequentially assessing two distinct nexuses (energy-economy and energy-economy-environment) over reduced- and augmented frameworks (excluding and including nuclear energy), and through a two-stage empirical strategy: time-series econometric estimations (Toda-Yamamoto causality test, Impulse Response Functions (IRFs), and the Auto-Regressive Distributed Lags (ARDL) and Machine Learning (ML) experiments with a Partial Differential Equations (PDEs) algorithm. For robustness purposes, we conduct two seminal tests which relate to dynamic predictive processes (T-Mat and Verticality tests). Besides confirming the time-series findings, our ML results highlight the necessity to timely manage the process of nuclear phase-out, along with a progressive deployment of installed renewable energy capacity. This should avoid additional economic costs, energy security threats, and undermining of climate targets. In doing so, this study combines macro-level nexus investigations with the politics and institutional determinants of nuclear energy reliance and seeks to bring inclusive knowledge on this topic. [ABSTRACT FROM AUTHOR]