Forecasting South Africa’s Coal-to-Clean Energy Transition: A Monte Carlo Simulation

Highlights

What are the main findings?

• Under current policies, it is forecasted that coal will lose its majority electricity generation share only around 2053, which is far too slow to meet urgent climate-related targets.
• Policy uncertainty and a very slow baseline decline rate of just 0.75% per year are the main barriers delaying South Africa’s energy transition.

What are the implications of the main findings?

• Credible and stable policy signals are urgently needed because reducing uncertainty could accelerate the coal phase-out by over two decades.
• Ambitious action can shift the transition earlier: a coordinated, multi-instrument policy package could bring the 50% coal-share point into the early–mid 2040s.

Abstract

South Africa remains one of the world’s most coal-dependent electricity systems, with coal accounting for 81.57% of generation in 2023. Despite policy interventions to diversify the energy mix, structural change is slow to emerge. This study provides the first integrated, empirically calibrated forecast of South Africa’s coal-to-clean-energy transition using a unified modelling architecture that combines structural break analysis, Bayesian estimation, and an enhanced Monte Carlo simulation with dynamic volatility (10,000 stochastic pathways). The findings confirm a permanent structural break in 2011 that coincided with the implementation of REIPPPP, following which coal began a statistically significant and sustained decline of approximately 0.7–0.75% points per year. The simulation produced a full probability distribution for the transition year (2053) when coal share falls below 50%. This demonstrated that long-term uncertainty rises faster than linearly and that, under current conditions, deep decarbonisation milestones are unattainable before mid-century. Policy scenario experiments also demonstrated that accelerating the annual decline rate necessitates coordinated, synergistic policy portfolios rather than isolated interventions. These findings provide a transparent, uncertainty-explicit forecast of South Africa’s transition trajectory, as well as a decision-relevant evidence base for planning, regulation, and equitable transition implementation.

1. Introduction

South Africa’s electricity sector is heavily reliant on coal. Coal-fired power plants generate more than 80% of the country’s electricity [1]. This meets approximately 70% to 90% of primary energy needs, making South Africa one of the continent’s largest carbon emitters and most carbon-intensive economies [2]. Eskom, the state-owned utility, generates 95% of the country’s electricity, primarily from coal, and accounts for nearly half of the nation’s carbon dioxide emissions [3]. This entrenched coal dependence has been accelerated by the sector’s importance in jobs, exports, and political alliances. This has historically influenced national policies and slowed the pursuit and development of alternative energy sources [4].

Figure 1 illustrates the mapping sites of power producers in South Africa. This diagram also shows the power output for each type of electricity that is generated. The large grey circles indicate that coal-generated electricity from Eskom is the most dominant. Nonetheless, Eskom faces significant operational and financial challenges. Mismanagement, corruption, and mounting debt at the power utility have resulted in chronic financial instability [5]. Eskom power plants and grid infrastructure are outdated and prone to failure [6]. These issues have resulted in repeated power outages (locally known as load-shedding) for over seventeen years [7]. Despite these issues, Eskom supplies nearly all of South Africa’s electricity and exports to neighbours, accounting for 45% of consumption in some countries [8].

South Africa’s coal-intensive energy sector has significant social and environmental consequences. Klausbruckner et al. [9] highlighted that coal’s dominance also results in significant greenhouse gas emissions. The energy sector accounts for approximately 83% of South Africa’s total emissions, with coal-fired electricity being the largest contributor [2]. The country has seen record-breaking temperatures and severe droughts [10]. These climate changes endanger water supplies and food security [6]. South Africa’s coal reliance produces high emissions per person and per unit of GDP [11]. Consequently, South Africa has Africa’s highest carbon intensity [1]. Historically, economic growth in South Africa has been closely linked to increased pollutant emissions. This pattern suggests a trade-off between development and environmental quality in the coal-dependent model [12].

In addition, Political and institutional factors present additional challenges to South Africa’s energy transition. The domestic coal industry wields significant power and has long been linked to political and economic interests [4]. Centralised governance and institutional bottlenecks have slowed the implementation of transitional initiatives in the pursuit of alternatives energy sources [13].

South Africa faces the dual challenge of meeting rising energy demand while fulfilling its Paris Agreement commitments [14]. Thus, South Africa has already started to take steps to reduce its coal dependence. Over the past decade, the government has implemented two main policy frameworks to promote clean energy. These include the Integrated Resource Plan (IRP) and the South African Renewable Energy Masterplan (SAREM) [15]. Both of these policies aim to increase renewable energy capacity by 2030, generating approximately 29.5 GW of new renewable capacity. Consequently, this gave rise to more targeted programs, such as the Renewable Energy Independent Power Producer Procurement Program (REIPPPP). The REIPPPP has received more than US$20 billion in investment [16]. It has added more than 6 GW of renewable capacity to the grid [2]. The Integrated Resource Plan (IRP) has been updated to reflect the embedded strategies of REIPPPP. The plan calls for decommissioning approximately 11 GW of coal power capacity by 2030. It also aims for renewables to account for approximately 40% of electricity generation by 2030 [17]. As a result, the percentage of low-carbon electricity (renewables plus nuclear) has risen from 4.14% in 1985 to 14.02% in 2022 [16]. Renewables accounted for a record 9.79% of generation in 2022, while nuclear energy has consistently contributed around 3–6% over the years [1].

South Africa’s transition is called a just transition, emphasising social and economic impacts on coal-dependent communities [18]. If not managed properly, phasing out coal could harm workers and regions that depend on the industry [13]. Therefore, this study forecasts South Africa’s shift from coal-fired power generation to clean energy generation. The objective is to predict when coal will lose its dominance (in terms of total percentage in electricity generation) and identify factors that may hinder or slow this transition. We incorporate several theoretical insights into a forecasting model that is specific to South Africa’s data and policy environment. The analysis is based on historical trends in the country (including the impact of the REIPPPP after 2011) and takes into account policy and market uncertainties. By combining multiple methods (such as time-series trend analysis, statistical break detection, and scenario simulations), we forecast when coal will cease to have its dominant role and fall below 50% of total electricity generation.

The problem for South Africa is that the electricity sector remains heavily reliant on coal. Coal-fired power plants produce more than 80% of national electricity while also supporting entrenched socio-technical systems that resist structural change. Despite policy frameworks such as the IRP and SAREM, the transition to clean energy has been hindered by ageing infrastructure, institutional bottlenecks, and policy uncertainty. This continued reliance on coal contributes significantly to greenhouse gas emissions, accounting for approximately 83% of total national emissions, while also contributing to environmental and social vulnerabilities in coal-dependent regions. Political alliances, economic interests, and industry influence all contribute to coal’s dominance. Consequently, this has been slowing the pace and scale of decarbonisation efforts. Although South Africa has committed to a just energy transition, the timing and feasibility of coal’s decline are unknown. This is due to competing socioeconomic pressures, regional vulnerabilities, and uncertainties in renewable deployment. Existing empirical research also reveals significant transition inertia, with high coal retention probabilities and slow renewable uptake. This reveals that the system is not shifting quickly enough to meet decarbonisation goals. As a result, it becomes critical to forecast when coal will lose its dominant position in electricity generation, as well as to identify the factors that may accelerate or impede that transition. This study fills that gap by providing an empirically supported forecast of South Africa’s coal-to-clean energy transition. This provides insights for planning, policy design, and just transition implementation.

In terms of contribution, this paper is the first to provide a unified, fully probabilistic forecast of South Africa’s coal to clean energy transition. The study makes this contribution by combining structural break detection, Bayesian trend estimation, and an enhanced Monte Carlo simulation that generates 10,000 correlated transition pathways. Unlike previous South African studies, which focused on political economy, justice, or qualitative scenario work rather than quantitative transition timelines. This study provides an empirically grounded probability distribution for the year when coal is no longer dominant. It is also the first South African study to model transition uncertainty with dynamic volatility, correlated macro energy shocks, and post-break deterministic decline rates derived directly from historical data. Finally, the paper presents a novel policy scenario engine that incorporates synergistic effects from multiple instruments. This allows for a clear assessment of how ambition and coordination can accelerate the energy transition. Hence, together, these contributions make this the first quantitative study in South Africa that provides a decision-relevant, uncertainty-explicit forecast of coal’s long-term decline.

The remaining sections of this paper are structured as follows: In Section 2, we discuss the theoretical framework as well as the empirical literature that is relevant to the study. Section 3 provided an overview of the methodology and data that were utilised in the research. In Section 4, the findings of the study are presented in an empirical format. The study is concluded in Section 5, which provides recommendations for South Africa’s transition from coal to renewable energy and outlines potential future research directions.

2. Literature Review

This section of the study is divided into two main components. Theoretical literature is exploredin Section 2.1, which provides conceptual frameworks and models for understanding transitional dynamics. Section 2.2 examined the empirical literature that applied and tested theories outlined in Section 2.1.

2.1. Review of Relevant Theoretical Literature

Energy transitions, as shown in Figure 2, are drawn on several interconnected streams of economic theory. This factor demonstrates energy transition’s inherent complexities and multidimensionality.

2.1.1. Path Dependence and Technological Lock-In

Understanding energy transitions requires understanding path dependence and technological lock-in. Path dependence means past decisions limit future options, causing socio-technical systems to stagnate [19,20]. Stagnation arises from sunk costs, returns to scale, network effects, and adaptive expectations [14,21,22,23]. These factors keep certain technologies, behaviours, and policies in place despite better alternatives [24]. The energy system stays on course because history creates momentum [25].

Technological lock-in is path dependence. Lock-in occurs when a dominant technology becomes deeply embedded through sunk investments, economies of scale, network externalities, and supportive regulations [26,27]. Cultural and behavioural factors affect results. Hence, users develop habits and preferences based on familiar technology, while industries develop expertise and norms that favour it [28]. Powerful stakeholders may resist changes that threaten their assets or profits, causing lock-in [19]. Bjørnåvold and Van Passel [29] state that these forces reinforce each other and maintain the system’s trajectory. Lock-in makes new technologies difficult to adopt and makes the system resistant to change [30].

Carbon lock-in occurs in fossil-fuel systems [22]. Cleaner alternatives are hindered by decades of investment in coal mines, oil wells, pipelines, and power plants [24]. The transition to renewables is slow and difficult because infrastructure, markets, and institutions favour coal, oil, and gas [31]. Despite cheaper solar and wind energy, incumbents may resist their adoption at scale in fossil-based systems [29]. Self-reinforcing feedback keeps carbon-intensive technologies in use beyond their lifespan [32].

Policy implications are significant. Even when alternatives are viable, lock-in slows adoption. Incumbents may lobby against change [30]. All of these factors hinder transition. Policymakers should realise that improving technology is not enough. As a result, without interventions, a better option may sit on the shelf while the established system benefits from lock-in [27]. However, exogenous shocks—such as major policy shifts, economic crises, or breakthroughs—can break lock-in [26,33].

2.1.2. Directed Technical Change (DTC) Theory

DTC is an endogenous growth economics innovation theory. It claims innovation is not neutral or automatic [34]. Instead, economic incentives and policies drive innovation [35]. This differs from theories that technology advances without direction [36]. DTC shows how policy can guide innovation toward public goals [37]. It emphasises deliberate efforts to overcome technological lock-in, which hinders new technology adoption [38].

The price effect is a key DTC mechanism. Innovators value cost-effective or high-priced solutions [35]. Energy-saving or alternative technologies will receive more R&D if carbon energy becomes more expensive [37]. Where innovations emerge depends on relative prices [38]. The price effect drives innovation to lower input costs or enter profitable markets [39].

Market-size effect is another. Innovation favours sectors with large markets or abundant inputs [35]. Large markets boost sales and profits, encouraging R&D [38]. Market size can sometimes outweigh price. Innovation favours the larger sector [40]. This bias persists even when other industries charge more for innovation [39]. Historically, fossil fuels dominated energy production. Their massive market contributed to their dominance [35]. DTC acknowledges direct productivity. This reinforces technological change by creating path dependence. Advances in a field make future innovations easier. This enhances the technology’s advantage over competitors [37].

Directed innovation policies must evolve. According to Åhman [41], policies should be adaptable to changing conditions due to unpredictable technology trends. Early support preserves technical diversity and fosters emerging technologies. Avoids prematurely choosing one option. It reduces missed opportunities for better innovations [33]. Pilot projects and subsidies may initially fund several clean energy technologies by governments. Cost reduction and performance improvement can boost support for winners. They should also keep diversifying their options. This adaptability makes the transition policy resilient to uncertainty and new information [42].

2.1.3. Uncertainty, Irreversibility, and the Real Options Theory of Energy Investment

Real Options Theory (ROT) incorporates flexibility and timing into investment analysis. Dixit and Pindyck [43] formalised the approach, showing how investing later can benefit uncertain environments. This theory compares investment opportunities to financial options, surpassing traditional models such as Net Present Value (NPV) [44]. A real options framework gives a company the right but not the obligation to invest in a project later [45]. Management can invest in favourable market conditions and defer or abandon in unfavourable ones, similar to holding a call option [44]. By explicitly valuing managerial flexibility, ROT addresses a major flaw in NPV analysis, which recommends investing as soon as the expected NPV is positive without considering the value of waiting.

Dixit and Pindyck [43] utilised continuous-time dynamic programming and stochastic control techniques to determine optimal investment policies under uncertainty. A classic outcome of their work is a formula for the investment trigger in a simple case (e.g., when the project value follows a geometric Brownian motion). This trigger is often expressed as $V^{*}={\displaystyle \frac{\beta }{\beta -1}}I$, where I is the investment cost and $\beta >1$ is a parameter that increases with uncertainty and project irreversibility [46]. The factor ${\displaystyle \frac{\beta }{\beta -1}}$(greater than 1) inflates the hurdle rate for investment. Evidently, the more volatile the future, the more one stands to lose from a bad irreversible decision. Thus, the longer a company waits and demands a higher upside to justify investing [47]. This approach applies option pricing insights (e.g., Black-Scholes pricing) to real asset decisions, often utilising risk-neutral valuation or contingent claims analysis [44].

Also, uncertainty and irreversibility are key mechanisms in real option theory. Investments with largely irreversible sunk costs have an opportunity cost [48]. By committing today, you avoid waiting for new information. Losing flexibility costs a lot financially [49]. Because future cash flows, prices, and policies are uncertain, flexibility is valuable. ROT models uncertainty by treating energy prices and demand as stochastic processes rather than fixed forecasts [50]. This involves using Ito’s stochastic calculus or dynamic programming to determine how optimal decisions change as uncertainties arise. Since future conditions are hard to predict, waiting for clarity has many benefits. A firm will not make an irreversible investment until the expected benefits outweigh the option to maintain flexibility [45]. In order to proceed optimally, the project must exceed a higher profitability threshold. This optimal trigger point exceeds NPV = 0’s break-even point. This shows how waiting provides information. Consequently, ROT predicts more cautious investment behaviour. Tschulkow et al. [48] highlighted that this method differs from NPV or IRR. So, firms invest later and only after uncertainty is reduced.

ROT has also been widely applied to energy investment scenarios. These scenarios are uncertain and irreversible [51]. Energy projects often have high capital costs that cannot be recovered. These costs are necessary for project completion. Thus, firms face significant uncertainties. These uncertainties include fuel price fluctuations, weather-dependent renewable energy output, new technology development, and energy and climate policy changes [52]. Traditional NPV analysis may recommend investing in a wind farm when expected returns are positive. ROT provides a broader perspective, so firms may rationally delay such investments [49]. Even if the project’s mean NPV is slightly positive, a utility may delay wind farm construction until carbon prices are more certain or technology costs decline [50].

2.2. Review of Relevant Empirical Literature

Table 1. Empirical Studies on Carbon Lock-in and Energy Transition Pathways (Outside South Africa).

Author(s)	Objective of the Study	Methodology	Key Findings
Kokubun [53]	Understand carbon lock-in and transition pathway variation across Japan, Australia, India, and South Africa (1970–2022).	50-year comparative analysis relying on historical energy data and institutional analysis.	A variety of transition pathways exist due to institutional and infrastructural constraints.
Bergougui & Ben-Salha [54]	Assess the impact of environmental governance on global energy transitions; identify drivers of cleaner energy shifts.	Panel data econometrics using fixed-effects and system GMM estimation techniques across a large number of countries.	Environmental policy stringency and governance quality significantly speed up transitions.
Chen [55]	Examine how energy policy uncertainty impacts public–private investment in BRIC countries; test predicted negative correlation.	Panel econometric methods on BRIC country data.	Energy policy uncertainty significantly discourages investment in all four BRIC countries.
Nyiwul et al. [56]	Determine if global economic uncertainty reduces clean energy investment across 93 countries.	Panel data models with fixed effects for country and year.	Economic uncertainty consistently reduces global renewable energy investment.
Raman et al. [57]	Link energy justice and gender equity to connect equity, access, and policy for sustainable development.	Systematic review of the literature as well as policy analysis.	Gender justice must be explicitly integrated; otherwise, transitions may worsen existing inequalities.
Taiwo & Tozer [58]	Investigate origins and convergence of community energy justice frameworks.	Qualitative synthesis of community energy literature.	Procedural power and benefit distribution are critical to just transitions.
Xie et al. [59]	Test how energy-related uncertainty affects corporate investment decisions in China at the firm level.	Panel data models with Chinese firm data.	Energy uncertainty reduces investment, especially in energy-intensive firms.
Bashir et al. [60]	Examine relationships between energy innovation, fossil fuel costs, and environmental compliance in advanced industrial economies.	Panel econometric methods with OECD country data.	Technological innovation and R&D investments significantly boost transition progress.
Ollier et al. [61]	Understand how government policy priorities shift with transition progress, policy sequencing, and credibility effects.	Comparing policies across countries.	Inconsistent or uncertain policies cause investment delays and distort transition pathways.
Shyu [62]	Assess referendums as policy instruments for promoting energy democracy; how democratic tools influence transitional governance.	Case study of Taiwan’s referendums in 2018 and 2021.	Community-oriented instruments improve legitimacy and democratic engagement.
Wyse & Das [63]	Examine the energy democracy concept in transition research; reclaim a unique agenda for equitable energy transitions.	Qualitative literature synthesis.	Balancing procedural power and benefit distribution is essential for social sustainability.
Gao et al. [64]	Examine whether energy transition can reduce the income gap between urban and rural areas in China; assess equity impacts.	Panel data econometrics with Chinese regional data.	Transitions can either narrow or widen socioeconomic disparities.
Kime et al. [65]	Assess equity and justice during low-carbon energy transitions; create metrics for evaluating justice outcomes.	Systematic review of justice frameworks.	Transitions can increase burden on low-income/frontline communities; justice must be explicitly integrated.
Haas et al. [66]	Investigate dealing with deep uncertainty in the electricity and transportation sectors; how uncertainty influences transition investment.	Case studies and real-options analysis.	Uncertainty hinders low-carbon technology adoption; unclear policies increase waiting behavior.
Puttachai et al. [67]	Investigate threshold effects of ESG performance on energy transitions; identify socioeconomic drivers of transition trajectories.	Threshold regression models for country-level data.	ESG factors, unemployment, and school enrolment significantly impact transitions.
Borozan [68]	Identify the structure of European energy transition policy instrument mix; determine which policy combinations effectively drive transitions.	Factor and cluster analysis on EU policy data.	Successful transitions require well-designed policy mixes that incorporate multiple instruments.
Shao & Ma [69]	Evaluate the effectiveness of renewable energy policies and electricity market design for transitions.	Qualitative policy review.	Feed-in tariffs, renewable portfolio standards, and fiscal incentives significantly impact renewable deployment.
Coenen et al. [70]	Investigate regional foundations of energy transitions; how geography influences transition paths.	Conceptual framework and regional case studies.	Transition pathways vary based on institutional and infrastructure lock-ins.
Joshi & Agrawal [71]	Study the uneven distribution of urban energy transitions; understand transitional barriers in Edmonton, Canada.	Qualitative case study analysis.	Significant difference in transition speeds and barriers between urban and rural areas.
Saundry [72]	Examine the United States’ energy system in transition; assess sectoral variations in transition progress.	Qualitative system review.	Electricity generation and transportation sectors exhibit distinct transition characteristics.
Romano & Fumagalli [73]	Examine the impact of uncertainty on greening the power generation sector; understand how uncertainty impacts low-carbon investment.	Systematic literature review	Uncertainty increases waiting behaviour, consistent with real-options logic.
Rogge et al. [74]	Improve conceptual and empirical understanding of policy mixes for transitions; investigate how policy instruments interact.	Mixed-methods approach, including case studies and policy analysis.	Effective policy frameworks must be strategic, stable, and coordinated.
Fouquet [75]	Investigate historical energy transitions focusing on speed, price, and system transformation; identify drivers of successful transitions.	Historical economic analysis of energy data.	Technologies providing cheaper or better services support transition success.
Araújo [76]	Examine the emerging field of energy transitions; evaluate progress, challenges, and opportunities.	Qualitative literature synthesis.	Decarbonisation and replacement of fossil fuels are key transition dynamics.
Gunningham [77]	Evaluate the effectiveness of regulations, economic instruments, and policy tools for sustainable energy transitions.	Comparative policy analysis.	Environmental regulations significantly impact renewable deployment and market transformation.
Tambach et al. [78]	Evaluate Dutch energy transition policy instruments for the existing housing stock; assess sector-specific policy effectiveness.	Policy evaluation framework.	Sector-specific studies reveal distinct transition speeds and barriers.
Dunne & Mu [79]	Test the uncertainty-investment relationship empirically in the petroleum refining industry.	Plant-level data and econometric models.	Uncertainty reduces the likelihood of capacity expansion.

Source: Authors’ own computation.

below provides an empirical review of selected studies conducted outside of South Africa on energy transitions. These studies are arranged chronologically from the most recent to the oldest studies. The studies bring together key studies that look at the drivers, barriers, and justice aspects of energy transitions. With a particular emphasis on the roles of environmental governance, policy uncertainty, investment behaviour, and equity considerations. Each entry summarises the study’s focus, the actual methodology used, and the main findings.

Similarly,

Table 2. Empirical Studies on Carbon Lock-in and Energy Transition Pathways (South Africa).

Author(s) and Year	Objective of the Study	Methodology	Key Findings
Osifeko & Munda [80]	Assess seasonal and diurnal variability of renewable resources in South Africa; provide data-driven insights for hybrid system design.	High-resolution meteorological datasets and spatial mapping techniques.	Northern Cape, Free State, and North West provinces showed significant solar-wind complementarity.
Hastie et al. [81]	Analyse community decision-making at the land-energy nexus; investigate procedural justice and land rights in renewable projects.	Qualitative case study research, participatory mapping, and community focus groups.	Highlighted the possibility of land grabbing and procedural injustices, particularly near the Bolobedu solar plant.
Michael-Ahile et al. [82]	Evaluate community-based energy trading for low-income communities; assess circular energy sharing models for grid reduction.	Agent-based modelling, including energy flow simulations and demand profiling.	Community trading can reduce grid reliance by up to 16%.
Bergougui et al. [83]	Investigate how high-tech research investment promotes green energy transition across countries; evaluate the moderating effect of institutional quality in South Africa.	Panel data econometrics and system GMM estimation across multiple countries.	Institutional quality is critical in facilitating renewable energy adoption.
Miller et al. [84]	Investigate the role of hybrid renewable energy systems in facilitating South Africa’s energy transition; evaluate grid resilience and decentralisation benefits.	Simulation modelling, techno-economic optimisation algorithms, and sensitivity analysis.	Hybrid systems can reduce levelised energy costs by up to 18%.
Xaba [85]	Assess the progress of South Africa’s just energy transition in coal regions; evaluate Komati decommissioning as a representative case study.	Qualitative policy evaluation, including site visits and semi-structured stakeholder interviews.	Highlighted vulnerability of coal regions and the need for integrated socioeconomic planning.
Von Lüpke [86]	Evaluate Just Energy Transition Partnership (JETP) in South Africa; identify key factors influencing international cooperation and funding.	Qualitative policy analysis, process tracing, and document review of JETP agreements.	Eskom’s indebtedness and supply failures create both barriers and political opportunities for reform.
Bothongo & Kinyar [87]	Rethink South Africa’s coal phase-out; determine if renewable energy and eco-innovation promote just transition.	Scenario-based modelling and econometric estimation of environmental and growth outcomes.	Eco-innovation can improve both environmental and economic outcomes during the transition period.
Hussein et al. [88]	Investigate the future of green hydrogen energy technology in South Africa; assess the hydrogen economy’s production viability and export potential.	Techno-economic feasibility analysis, infrastructure gap assessment, and cost modelling.	Green hydrogen has significant economic potential, but infrastructure gaps remain a major impediment.
Mohr [89]	Investigate competing narratives in South Africa’s just energy transition; learn how various actors frame coal, climate, jobs, and transition planning.	Discourse analysis, semi-structured elite interviews, and media content analysis.	Significant narrative divergence among government, labour, industry, and civil society.
O’Connell & Schot [90]	Conduct theoretical and systematic analysis of finance in strategic niche management; investigate how financial mechanisms promote hydrogen innovation.	Case study analysis, document review, and stakeholder interviews in the hydrogen sector.	Further research is needed to understand the dynamics of finance and niche innovation.
Cole et al. [91]	Investigate risk in South Africa’s just transition; determine who is left behind under various transition scenarios.	Quantitative risk profiling, composite indicator construction, and scenario analysis across coal regions.	Identified vulnerable groups for delayed versus accelerated transition timelines.
Essex et al. [92]	Investigate the capacity of South African energy governance to deliver urban sustainable transitions; evaluate governance capacity across several cities.	Qualitative governance assessments, multi-stakeholder workshops, and institutional analysis frameworks.	Fragmented governance structures undermine coordinated transition planning.
Mirzania et al. [93]	Identify barriers to moving beyond coal in South Africa; evaluate implications for a just energy transition across the coal value chain.	Systematic literature review and qualitative synthesis of 150 peer-reviewed studies and policy documents.	Identified gaps in techno-economic modelling and neglected socio-political dimensions.
Msimango et al. [94]	Examine South Africa’s energy policy with emphasis on competition and climate change; evaluate policy coherence and institutional alignment for decarbonisation.	Policy analysis, review of energy white papers, and stakeholder interviews.	Institutional quality is critical to promoting renewable energy adoption.
Hanto et al. [95]	Conduct a thorough political economy analysis of South Africa’s energy transition; understand the causes of policy inertia and coal persistence.	Mixed methods research, including elite interviews, stakeholder mapping, and policy document analysis.	Governance fragmentation and capability inconsistencies impede transition outcomes.
Murombo [96]	Examine regulatory requirements for renewable energy from a South African legal perspective; assess legal and regulatory barriers to renewable deployment.	Doctrinal legal analysis with thorough policy and statute review of energy legislation.	Identified legal and regulatory barriers to renewable deployment.
Müller & Claar [97]	Examine South Africa’s REIPPPP; evaluate auction mechanisms and just transition outcomes.	Policy analysis with contract reviews, tender documents, and stakeholder interviews.	REIPPPP increased renewable capacity but also led to spatial and socio-political tensions.
Nene & Nagy [98]	Investigate legal regulations and policy barriers to renewable energy development; identify policy inconsistencies and regulatory obstacles to green investment.	Qualitative policy analysis and comparative legal assessment across regulatory frameworks.	Policy inconsistency and regulatory misalignment persist.
McEwan [99]	Investigate spatial processes and politics of South Africa’s transition to renewable energy; explore land, zones, and frictions in renewable deployment.	Qualitative spatial analysis and case studies of designated renewable energy development zones.	Land politics and local benefit distribution issues remain unresolved.
Mudziwepasi & Scott [100]	Investigate renewable energy technologies as potential alternatives to grid extension for rural electrification; evaluate the cost-effectiveness of standalone systems.	Techno-economic feasibility analysis, including lifecycle costing and rural demand profiling.	Stand-alone photovoltaic and small wind systems are cost-competitive for rural electrification.
Baker et al. [101]	Investigate the political economy of energy transitions in South Africa; understand how coal-based interests influence policy inertia and transition speed.	Qualitative case study analysis, semi-structured interviews, and historical document review.	South Africa’s minerals-energy complex and coal-favouring actors limit renewable uptake.

Source: Authors’ own computation.

below provides an empirical review of selected studies conducted in South Africa on energy transitions.

South African energy transition literature, as seen in Table 2, has grown significantly over the years. However, significant conceptual and empirical gaps continue to exist in a variety of areas. For example, current research indicates that justice principles are not fully integrated into technical and economic models. As a result, they are less useful for policy design and social planning. Evidence also suggests that local socioeconomic conditions are rarely taken into account in national transition models. Regardless of their significance for understanding community-level impacts in coal-dependent regions. Political economy analyses are still underdeveloped, particularly in terms of how vested interests, state capture, and competing narratives shape transition pathways and policy debates.

Research using primary qualitative methods is limited. Despite the fact that affected communities face disproportionate transition impacts and require greater representation in empirical studies. Scenario modelling is still in its early stages, with little research into future transition pathways, renewable energy mixes, and alternative timelines for accelerated or delayed decarbonisation. Governance and institutional capacity research reveals significant structural flaws. However, existing research does not go into great detail about the interactions between regulatory failure, leadership deficits, and policy misalignment.

Emerging energy sectors such as batteries, electric vehicles, and green hydrogen have significant research gaps. This is evident in market demand, technological viability, financing risks, and institutional readiness. In addition, technical and infrastructure challenges remain. These include, but are not limited to, inadequate solar PV design standards, limited grid integration assessments, and insufficient attention to geological opportunities for carbon storage. Equity and vulnerability metrics are still evolving, with gaps in data availability, integration, and standardisation impeding robust distributional assessments during transition planning.

Furthermore, media and discourse analysis receive little attention. Despite evidence that public narratives about the coal phase-out are incomplete and dominated by technological or crisis framing rather than structural transformation. Comparative research across regions and industries is equally lacking. However, such studies may reveal common constraints or policy lessons that support more coherent national transition strategies. Therefore, these gaps highlight the need for interdisciplinary, community-engaged, and policy-relevant research to support a more just, coherent, and analytically rigorous energy transition in South Africa.

3. Methodology

This study applied several methods to predict how long it will take South Africa to reduce its reliance on coal for electricity generation from 81.57% in 2023 to 50%. For South Africa, reaching the 50% coal share threshold is a significant step toward meaningful decarbonisation of the country’s energy sector. The study used four main types of analysis. These include reviewing past developments in the energy sector through historical structural analysis, identifying moments of significant change using structural break detection, applying Bayesian inference, running Monte Carlo simulations to explore a range of possible future outcomes, and developing policy scenarios to assess how different choices could shape the sector.

3.1. Theoretical Justification for the Applied Methodology

The Bayesian forecasting model presented in this chapter is based on a unified theoretical framework that incorporates path dependence, Real Options Theory (ROT), and Directed Technical Change (DTC). These perspectives agree that technological and energy system evolution is not instantaneous or completely flexible. It unfolds through sequential, uncertain, and path-conditioned choices made by diverse actors.

The integration of these theories allows for a forecasting framework that can, firstly, represent historical constraints (path dependence) encoded through priors. This includes transition structures that reflect existing infrastructure, technological capabilities, and institutional commitments. Secondly, Bayesian updating is used to model adaptive decision-making under uncertainty (ROT). This is used to simulate the flexibility of real-world options. Thus, reflecting decisions that evolve in response to new information. Finally, policy-driven technological evolution (DTC) is incorporated using likelihood functions and transition probabilities. These are generally responsive to incentive environments, innovation rates, and knowledge accumulation.

3.2. Research Design Workflow

Figure 3 illustrates the sequential research design applied in this study. This figure demonstrates how each analytical component leads to the next.

The methodology proceeds in hierarchical order. That is, it begins with data collection and descriptive analysis. It then progresses to structural break testing and model selection, which are integrated using Bayesian estimation. The methodology progresses to a Monte Carlo simulation model that captures stochastic behaviour. The simulation results are fed into several parallel analytical streams, including transition probability and policy scenario analysis. These are then integrated using sensitivity analysis, resulting in final forecasts and policy insights.

3.3. Data Preparation and Pre-Processing

This study utilised yearly data from 1985 to 2023. The analysis begins in 1985, as this is the first year in which reliable and consistent disaggregated data on key renewable energy sources became available. Also, starting from 1985 provides enough historical depth to capture long-term variability and structural changes in renewable energy trends. This then makes it appropriate for robust temporal analyses. The final year, 2023, represents the most recent year with complete and validated data across all variables. This aligns with best practices that emphasise data completeness and accuracy when defining the temporal scope of a study. As a result,

Table 3. Key variables of interest that are used.

Variables	Denoted As	Measurement	* Source
Gross electricity generation
Total electricity generation	EG	Terawatt-hours (TWh), or a trillion watt-hours.	Energy Institute-Statistical Review of World Energy–with major processing by World in Data
Electricity generated using fossil fuels
Electricity generated from coal	CE	Terawatt-hours (TWh), or a trillion watt-hours.	Energy Institute-Statistical Review of World Energy–with major processing by Our World in Data
Electricity generated from gas	GE	Terawatt-hours (TWh), or a trillion watt-hours.
Electricity generated from oil	OE	Terawatt-hours (TWh), or a trillion watt-hours.
Nuclear energy
Electricity generated from nuclear	NE	Terawatt-hours (TWh), or a trillion watt-hours.	Energy Institute-Statistical Review of World Energy–with major processing by Our World in Data
Renewable energy sources
Electricity generated from wind power	WP	Terawatt-hours (TWh), or a trillion watt-hours.	Energy Institute-Statistical Review of World Energy–with major processing by Our World in Data
Electricity generated from solar power	SP	Terawatt-hours (TWh), or a trillion watt-hours.
Electricity generated from Hydropower	HP	Terawatt-hours (TWh), or a trillion watt-hours.
Economic related variables
Trade	TR	Trade as a share of GDP (%)	World Bank and OECD national accounts–processed by World in Data
Gross domestic product	GDP	% annual growth rates	SARB
Carbon intensity of energy production	CI	measured in kilograms of CO2 per kilowatt-hour.	Energy Institute-Statistical Review of World Energy–with major processing by World in Data
Political Corruption Index	PCI	Index (Central estimate of the extent to which a country is affected by political corruption)–a proxy measure for public sector governance.	V-Dem–processed by World in Data

Notes: * Secondary data that is publicly available. Source: Authors’ own computation.

highlights and describes the key variables of interest used in this study.

For the purposes of this study, it is important to clarify the energy terms used throughout the paper. For instance, electricity generated by wind, solar, and hydropower is considered renewable energy. Renewable and nuclear energy combined are examples of low-carbon energy sources. The term “clean energy” refers to low-carbon energy and technologies with near-zero emissions, such as green hydrogen and carbon capture. Coal is neither renewable nor low-carbon nor clean. Natural gas is treated separately as a fossil fuel.

3.3.1. Core Transition Metrics and Threshold Identification

The proportion of electricity generated from coal is an important metric for assessing the progress of the energy transition. Hence, following Ducoli et al. [102], this is calculated as the percentage of total electricity generated by coal, which can be expressed by Equation (1) below:

$$C{S}_t={\displaystyle \frac{C{E}_t}{E{G}_t}}\times 100$$

(1)

The transition away from coal-dominated electricity generation is then detected by monitoring when this share falls below a certain threshold. Specifically, when coal contributes less than 50% of total electricity generation. This is expressed in Equation (2) below:

$${\delta }_t=\mathbb{I}({\mathit{CS}}_t<50\%)=\{\begin{array}{cc}1,& \mathit{if} {\mathit{CS}}_t<50\%\\ 0,& \mathit{otherwise}\end{array}$$

(2)

where $\mathbb{I}\left(\cdot \right)$ is the indicator function that equals 1 if the condition is true and 0 otherwise. For instance, when the indicator function takes the value of 1 ${(\delta }_t=1)$ in a given year ($t)$, the share of coal drops below 50%. This signifies that coal is no longer the dominant energy source for electricity. However, when the indicator function equals zero (${\delta }_t=0$), indicates that coal remains at or above 50%. This reflects that the transition event has not yet occurred. In this way, the indicator variable marks the point in time when the shift away from coal dominance happens.

Next, to extend the analysis, we developed several indicators that measure the scale of renewable energy generation and its effect on displacing fossil fuels. Empirical evidence consistently shows that renewable energy indicators are usually formed by summing electricity from individual technologies, especially wind, solar and hydro [103]. For example, the Lancet Countdown indicator tracks electricity from all low-carbon sources and separately reports renewable power from wind, solar and hydro [103]. Also, other empirical studies [104,105,106,107] applied composite measures that combine wind, solar and hydro to assess renewable energy penetration and system impacts.

Consequently, Equation (3) uses this standard method by defining total renewable electricity as the sum of wind, solar, and hydropower. This formulation corresponds to how the literature views key renewable technologies. It also provides a solid foundation for evaluating how renewables reduce reliance on coal-generated electricity. Hence, by combining these major renewable sources into a single indicator, the measure captures the technologies most closely related to ongoing fossil-fuel displacement. Thus, this approach reflects the realities of today’s power systems.

$${\mathit{RE}}_t={\mathit{WP}}_t+{\mathit{SP}}_t+{\mathit{HP}}_t$$

(3)

Equation (3) shows an aggregate value of renewable energy ($R{E}_t$). This represents the absolute contribution of these zero-carbon sources to the electricity grid in a given period. However, while this is the absolute indicator (${\mathit{RE}}_t$) reflects the scale of zero-carbon generation, it does not fully demonstrate renewables’ relative importance in the evolving electricity system. As a result, to address this limitation, we developed a second indicator that measures the proportion of renewables in total electricity generation. This formulation is displayed in Equation (4) and is well supported by the literature. That is, several studies [108,109,110] define renewable electricity shares as the proportion of renewable sources to total generation, which is typically expressed as a percentage. These studies demonstrated that a relative measure is a useful and widely used indicator of renewable energy’s systemic significance. Then, Equation (4) thus closely follows this established practice. This equation illustrates more clearly how renewable energy contributes to the long-term transformation of the electricity mix.

$${\mathit{RE}\text{\_}\mathit{share}}_t=\left({\displaystyle \frac{{\mathit{RE}}_t}{{\mathit{EG}}_t}}\right)\times 100\%$$

(4)

This percentage, $RE\text{\_}shar{e}_t$, directly quantifies the contribution of renewable technologies in generating electricity. By constructing and tracking this share variable (${\mathit{RE}\text{\_}\mathit{share}}_t$) in parallel with a similar coal share indicator ($C{S}_t$), we can model the displacement process. For instance, a rising $RE\text{\_}shar{e}_t$ necessarily implies a reduction in the share of other sources of electricity generation (i.e., coal). This provides a clear metric to assess the progress and scale of the transition away from fossil fuel dominance in the energy sector.

3.3.2. Descriptive Statistical Characterisation

Following Pan et al. [111], we estimate standard descriptive statistics in order to contextualise the historical data employed in this study and lay the groundwork for stochastic modelling. These metrics summarise the overall trend, volatility, and year-to-year dynamics of coal’s contribution to national electricity supply. As a result, these include, but are not limited to, the sample mean (${\mu }_{CS}$), standard deviation (${\sigma }_{CS}$), mean annual change (${\mu }_{\Delta }$), and the standard deviation of annual changes (${\sigma }_{\Delta }$). The parameter ${\sigma }_{\Delta }$ (expressed in percentage points per year) serves as the foundation for calibrating the GARCH volatility process, with the unconditional variance component set as $\omega =0.1\cdot {\sigma }_{\Delta }^2$.

Therefore, by employing these parameters, the study ensures methodological consistency with the larger empirical literature. These parameters provide a statistically rigorous foundation for modelling coal-share dynamics, which can reflect the documented behaviour of coal in volatile and evolving energy systems.

3.3.3. Addressing Model Over-Parameterisation

The sample size of this study is limited. It contains only 39 annual observations from 1985 to 2023. This includes approximately fifteen calibrated parameters. Consequently, this may raise concerns about potential overparameterisation. This issue is critical in energy-market modelling, as empirical studies [112,113], may show high volatility and complex structural behaviours in coal and carbon markets. For this reason, in order to ensure statistical credibility despite the small sample size, the study employed three complementary mitigation strategies. Firstly, Bayesian priors (see Section 3.4.2) help to keep parameter estimates within empirically plausible bounds. This method is consistent with evidence that volatility processes in energy assets demonstrate well-defined persistence [114]. Secondly, historical back-testing (see Section 4.9) provides an empirical check on the model’s validity. This is consistent with previous research that has used diagnostic tests to ensure the robustness of energy market models [112]. Lastly, theoretical foundations support parameter selection in established energy-transition frameworks. This is consistent with previous research that has linked statistical structures to documented changes in coal demand and socioeconomic dynamics [115].

Therefore, these strategies keep the model simple and empirically sound. As a result, this approach mitigates the practical risks of overparameterisation while preserving critical system behaviours.

3.3.4. Nomenclature of Mathematical Notation

The nomenclature of mathematical notation that is used in this study is presented in

Table 4. Nomenclature of Mathematical Notation.

Symbol	Description	Unit Measurement	First Appearance
$C{S}_t$	Coal share of electricity generation	%	Equation (1)
$R{E}_t$	Renewable energy generation	TWh	Equation (3)
$RE\text{\_}shar{e}_t$	Renewable energy share of generation	%	Equation (4)
${\mu }_{CS}$	Mean coal share over sample period	%	Section 3.3.2
${\sigma }_{CS}$	Standard deviation of coal share	%	Section 3.3.2
${\mu }_{\Delta }$	Mean annual change in coal share	pp/year	Section 3.3.2
${\sigma }_{\Delta }$	Standard deviation of annual changes	pp/year	Section 3.3.2
${\delta }_{\mathrm{base}}$	Baseline annual coal decline rate	pp/year	Equation (11)
${\beta }_{\mathrm{pre}}$	Pre-break trend slope	pp/year	Equation (7)
${\beta }_{\mathrm{post}}$	Post-break trend slope	pp/year	Equation (8)
$\omega$	GARCH base volatility	–	Equation (38)
$\alpha$ (GARCH)	GARCH shock sensitivity	–	Equation (38)
$\beta$ (GARCH)	GARCH volatility persistence	–	Equation (38)
${\lambda }_{\mathrm{renew}}$	Renewable feedback strength	–	Equation (40)
${\varphi }_{\mathrm{econ}}$	Economic feedback sensitivity	–	Equation (40)
${\tau }_i$	Transition year for simulation $i$	year	Equation (43)
$\stackrel{-}{\tau }$	Mean transition year across simulations	year	Equation (45)
$s_{\tau }$	Standard deviation of transition years	year	Equation (46)
$F\left(y\right)$	Cumulative probability of transition by year $y$	%	Equation (48)
$m$	Policy multiplier	–	Equation (50)
$\Delta \delta$	Total policy-induced acceleration	pp/year	Equation (50)
$ϵ$	Arc elasticity	–	Equation (62)
MAPE	Mean absolute percentage error	%	Equation (63)

Notes: pp/year refers to percentage points per year. Source: Authors’ own computation.

.

3.4. Applied Structural Break Test and Trend Evolution

This study employed a formal structural break analysis to empirically test for significant shifts in South Africa’s coal phase-out over time. A key hypothesised turnaround point is the year 2011. A breakpoint year previously identified by Majenge et al. [116]. This marks the start of the Renewable Energy Independent Power Producer Procurement Programme (REIPPPP). A government policy intervention intended to speed up the diversification of the electricity mix.

3.4.1. Chow Test for Pre-Specified Structural Break

Chow’s Test was used to statistically determine whether the coal share trend changed as a result of this event. The Chow test determines whether a time series shows a significant change in its underlying trend structure at a given breakpoint. Thus, we test the null hypothesis:

$$H_0:{\beta }_{\mathit{pre}}={\beta }_{\mathit{post}}$$

(5)

against the alternative:

$$H_1:{\beta }_{\mathit{pre}}\ne {\beta }_{\mathit{post}}$$

(6)

where $\beta$ represents regression coefficient vectors before and after the hypothesised breakpoint (2011, the REIPPPP launch year).

The methodology involves partitioning the time series data into two distinct regimes: a pre-policy period (1986–2010) and a post-policy period (2011–2023). For each regime, a simple linear trend model is estimated. Let $t$ represent a continuous time index (e.g., $t=1$ for 1986, $t=2$ for 1987, etc.). The models are specified as:

Pre-break Regime (1985–2010):

$${\mathit{CS}}_{t_{pre}}={\alpha }_{\mathit{pre}}+{\beta }_{\mathit{pre}}\cdot t+{ϵ}_{\mathit{pre},t}, t=1,\dots ,T_{\mathit{pre}}$$

(7)

Post-break Regime (2011–2023):

$${\mathit{CS}}_{t_{post}}={\alpha }_{\mathit{post}}+{\beta }_{\mathit{post}}\cdot t+{ϵ}_{\mathit{post},t}, t=T_{\mathit{pre}}+1,\dots ,T$$

(8)

Equations (12) and (13), $\alpha$ represents the model intercept, $\beta$ denotes the slope coefficient (the annual trend rate of change in the coal share). ${\epsilon }_t$ is a white-noise error term. For comparison, a pooled model that assumes no structural break is also estimated over the entire sample:

Pooled model (1985–2023):

$${\mathit{CS}}_{t_{pool}}={\alpha }_{\mathrm{pool}}+{\beta }_{\mathrm{pool}}\cdot t+{ϵ}_{\mathrm{pool},t}, t=1,\dots ,T$$

(9)

The core logic of Chow’s test is to determine whether allowing separate trend parameters (${\alpha }_{\mathrm{pre}},{\beta }_{\mathrm{pre}}$) and (${\alpha }_{\mathrm{post}},{\beta }_{\mathrm{post}}$) significantly improves the model’s fit compared to the restricted, single-trend model. This is quantified by an F-statistic that compares the residual sums of squares (RSS) from the different models. Let ${\mathrm{RSS}}_{\mathrm{pool}}$ be the RSS from the pooled model, and ${\mathrm{RSS}}_{\mathrm{pre}}$ and ${\mathrm{RSS}}_{\mathrm{post}}$ be the RSS from the segmented models (7) and (8), respectively. Let $k=2$ be the number of estimated parameters in each segmented model (intercept and slope), and $T$ be the total number of observations. The Chow test statistic evaluates whether separate regressions for the two periods significantly improve model fit:

$$F_{\mathit{chow}}={\displaystyle \frac{\left({\mathit{RSS}}_{\mathit{pool}}-({\mathit{RSS}}_{\mathit{pre}}+{\mathit{RSS}}_{\mathit{post}})\right)/k}{({\mathit{RSS}}_{\mathit{pre}}+{\mathit{RSS}}_{\mathit{post}})/(T-2k)}}$$

(10)

Equation (10) above measures the improvement in fit (reduction in unexplained variance) gained by estimating separate regressions for the two periods, normalised by the number of additional parameters ($k$). The denominator is the best estimate of the common error variance from the segmented models.

Given the null hypothesis (i.e., no structural break), the statistic $F_{\mathit{chow}}$ follows an F-distribution with $k$ and $T-2k$ degrees of freedom. If the calculated $F_{\mathit{chow}}$ exceeds the critical value at the 0.05 significance level, we reject $H_0$ and conclude that a statistically significant structural break occurred in 2011.

Following the identification of a structural break, we concentrate on the regression model for the period after that breakpoint (the period following the REIPPPP launch). This model produces a coefficient ${\beta }_{\mathit{post}}$. This represents the average annual change in the coal share variable under this new regime. We transform this coefficient to make the result more understandable for our analysis. We define the fundamental baseline transition speed (${\delta }_{\mathit{base}}$) as the negative value of the post-break regression coefficient:

$${\delta }_{\mathit{base}}=-{\beta }_{\mathit{post}}$$

(11)

This transformation is performed for direct interpretation. Since ${\beta }_{\mathrm{post}}$ from a model of coal’s declining share is typically a negative number, then applying the negative sign renders ${\delta }_{\mathrm{base}}$ a positive value. Consequently, ${\delta }_{\mathrm{base}}$ represents the estimated annual percentage point decline in coal’s share of electricity generation that characterised the post-policy period. This extracted parameter, ${\delta }_{\mathrm{base}}$, it is not merely a historical observation. It serves as the foundation for all subsequent modelling in this study. In other words, it provides the empirically grounded baseline rate of change from which we develop forward-looking projections and construct alternative policy or market scenarios.

3.4.2. Rolling Regression for Trend Detection

Following Wang et al. [117], we used the rolling regression technique to track how the rate of energy transition has increased over time without imposing a fixed breakpoint. This technique enabled us to identify data-driven variations in the underlying energy transition trend. We accomplish this by using a 10-year moving window (1995–2023). Then, we fit a linear regression model using only the data from the previous nine years and year t, as shown in Equation (12) below:

$$C{S}_s={\alpha }_{\mathrm{rolling}}\left(t\right)+{\beta }_{\mathrm{rolling}}\left(t\right)\cdot s+{ϵ}_s, where s=t-9,t-8,\dots ,t$$

(12)

In this equation, $C{S}_s$ is the coal share in year $s$, ${\alpha }_{\mathrm{rolling}}\left(t\right)$ is the estimated intercept, and ${\beta }_{\mathrm{rolling}}\left(t\right)$ is the key output. This is the estimated slope coefficient for the window ending in the year $t$. ${\beta }_{\mathrm{rolling}}\left(t\right)$ represents the local short-term trend speed (the average annual change in coal share) observed over a 10-year moving window. By repeating this process for each year $t$, we generate a time series of these estimated trend speeds (${\beta }_{\mathrm{rolling}}\left(t\right)$). This shows how the pace of transition has varied.

In order to distinguish meaningful regime shifts from statistical noise, we applied a two-part significance criterion. This has been done to identify a potential shift in the trend for the year t only if both of the following conditions are satisfied. The first condition relates to statistical significance, which requires absolute value of the estimated slope for that window must be more than twice its standard error [118]. This can be expressed as:

$$\mid {\beta }_{\mathit{rolling}}\left(t\right)\mid >2\cdot SE\left({\beta }_{\mathit{rolling}}\right(t\left)\right)$$

(13)

This condition, expressed in Equation (13), ensures that the detected trend is robust and unlikely to be a random fluctuation.

The second condition is directional change, which means that the sign of the current slope must differ from the sign of the slope calculated for the previous window (ending in year $t-1$) [119]. This can be expressed as:

$$\mathrm{sign}\left({\beta }_{\mathrm{rolling}}\right(t\left)\right)\ne \mathrm{sign}\left({\beta }_{\mathrm{rolling}}\right(t-1\left)\right)$$

(14)

This criterion, expressed in Equation (14), captures a true reversal or inflection point, such as a shift from a period of stagnation (a near-zero or positive $\beta$) to a period of clear decline (a significantly negative $\beta$). Therefore, only when both conditions are satisfied do we classify the year $t$ as marking a statistically significant change in the transition regime. This allows us to identify inflection points directly from the data.

3.5. Model Comparison and Selection

Following the identification of a structural break, three competing parametric models are specified and estimated. The objective is to determine the functional form that captures the underlying data-generating process in the most effective and efficient manner. This is done to maintain a balance between the model’s complexity and its fit. For this reason, different hypotheses regarding the nature of the transition are represented by the candidate models. These models include a constant linear decline, a curvilinear path (either accelerating or decelerating), and an asymptotic decay towards a long-run floor.

Equation (15) expresses the first model (a linear trend), which represents a hypothesis of a continuous, absolute annual decrease in the coal share:

$${\mathit{CS}}_{t_{lin}}={\alpha }_{\mathrm{lin}}+{\beta }_{\mathrm{lin}}\cdot t+{ϵ}_{\mathrm{lin},t}$$

(15)

where ${\alpha }_{\mathrm{lin}}$ denotes the intercept, ${\beta }_{\mathrm{lin}}$ denotes the constant slope (change in coal share per year) and ${\epsilon }_t$ is a white-noise error term. This model serves as a baseline for our analysis.

Equation (16) expressed the second model that included a quadratic trend. This enabled us to capture the acceleration or deceleration in the coal share percentage change:

$${\mathit{CS}}_{t_{quad}}={\alpha }_{\mathit{quad}}+{\beta }_{\mathit{quad}}\cdot t+{\gamma }_{\mathit{quad}}\cdot t^2+{ϵ}_{\mathrm{quad},t}$$

(16)

In this equation, ${\gamma }_{\mathrm{quad}}$ is the quadratic coefficient. A statistically significant negative ${\gamma }_{\mathrm{quad}}$ would indicate a concave (downward-accelerating) decline, suggesting the transition is gaining pace over time.

Equation (17) describes the third model, which illustrates an exponential decay process with an asymptote. This equation captures a hypothesis that the coal share declines proportionally to its distance from a long-run equilibrium level:

$${\mathit{CS}}_{t_{exp}}=A\cdot exp[-\lambda \cdot (t-t_0\left)\right]+C+{ϵ}_{\mathit{exp},t}$$

(17)

where $t_0=1985$ is a baseline year index for normalisation. The parameter $A$ represents the initial amplitude of the decay component above the asymptote. $\lambda >0$ is the decay rate constant, and $C$ is the long-run asymptotic floor toward which the time series converges. As a result, this model is suitable for describing the dynamics of a saturating transition.

Next, model selection is then performed using established information criteria, which penalise model likelihoods based on the number of estimated parameters in order to prevent overfitting. For each model, the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are computed. According to Majenge et al. [120], the use of AIC and BIC criteria is standard practice for objectively comparing models and guiding the selection of the most appropriate one for the given data.

As a result, let $k$ denote the number of model parameters (e.g., $k=2$ for linear, $k=3$ for quadratic, $k=3$ for exponential decay) and $T$ the number of observations. RSS the model’s residual sum of squares. AIC and BIC criteria are calculated as follows:

$$\mathit{AIC}=2k+T\cdot ln\left({\displaystyle \frac{\mathit{RSS}}{T}}\right)$$

(18)

$$\mathit{BIC}=k\cdot ln\left(T\right)+T\cdot ln\left({\displaystyle \frac{\mathit{RSS}}{T}}\right)$$

(19)

In both Equations (18) and (19), the first term penalises model complexity ($k$), while the second term rewards goodness-of-fit (lower RSS). ${\displaystyle \frac{\mathrm{RSS}}{T}}$ is proportional to the log-likelihood under a Gaussian error assumption, which is what these criteria are estimating. Therefore, the model with the lowest value for a given criterion is preferred. This indicates the best trade-off between goodness of fit and parsimony (simplicity) [121].

3.6. Applied Empirical Estimation Procedure

3.6.1. Estimation Procedure for Multivariate Correlation

For this analysis, we applied Pearson’s correlation coefficient to determine the strength and direction of the linear relationship between each pair of variables. This measure provided a consistent way to determine both the strength and direction of associations observed across the period for each variable pair.

Following Wang et al. [122], for any two variables ($x_i$ and $x_j$) measured over time ($t=1,\dots ,T$) their correlation coefficient $\left({\rho }_{ij}\right)$ is calculated as:

$${\rho }_{ij}={\displaystyle \frac{{\displaystyle {\sum }_{t=1}^T}(x_{i,t}-{\stackrel{-}{x}}_i\left)\right(x_{j,t}-{\stackrel{-}{x}}_j)}{\sqrt{{\displaystyle {\sum }_{t=1}^T}(x_{i,t}-{\stackrel{-}{x}}_i{)}^2{\displaystyle {\sum }_{t=1}^T}(x_{j,t}-{\stackrel{-}{x}}_j{)}^2}}}$$

(20)

where ${\stackrel{-}{x}}_i$ and ${\stackrel{-}{x}}_j$ are the respective sample means. This coefficient ranges from −1 (perfect negative correlation) to +1 (perfect positive correlation). All the calculated correlations are then organised into a symmetric matrix $\left(R\right)$. This matrix offers a coherent map of the system’s interdependent behaviour and structure. Equationally, the symmetric matrix can be generally expressed as follows:

$$R=\left[\begin{array}{ccccc}1& {\rho }_{12}& {\rho }_{13}& {\rho }_{14}& {\rho }_{15}\\ {\rho }_{21}& 1& {\rho }_{23}& {\rho }_{24}& {\rho }_{25}\\ {\rho }_{31}& {\rho }_{32}& 1& {\rho }_{34}& {\rho }_{35}\\ {\rho }_{41}& {\rho }_{42}& {\rho }_{43}& 1& {\rho }_{45}\\ {\rho }_{51}& {\rho }_{52}& {\rho }_{53}& {\rho }_{54}& 1\end{array}\right].$$

(21)

Note that ${\rho }_{ij}={\rho }_{ji}$ and the diagonal elements are 1, as each variable is perfectly correlated with itself. For the purposes of stochastic simulations and scenario analysis, it became essential to generate random shocks that replicate the empirical correlation structure observed in $R$. Hence, a direct draw from a standard multivariate normal distribution would produce independent shocks.

In other words, integrating these values into a matrix provided the essential statistical foundation for later simulation that required accurate modelling of joint variability patterns across variables. Hence, directly drawing shocks from a standard multivariate normal distribution would otherwise have produced independent disturbances, which would not reflect the underlying correlation structure observed in the empirical data. Consequently, the constructed correlation matrix allowed the subsequent scenario analysis to generate stochastic shocks that correctly preserved the system’s interconnected dynamics.

Next, following Liu et al. [123], we applied the Cholesky decomposition to ensure that the desired dependency structure is correctly imposed. This approach is appropriate because the correlation matrix is symmetric and positive-definite. Hence, allowing it to be factorised into the product of a lower-triangular matrix and its transpose. Specifically, using this method, the positive-definite correlation matrix (R) is factorised into the product of a lower triangular matrix (L) and its transpose:

$$R=L{L}^{\top }$$

(22)

The matrix $\left(L\right)$ serves as the transformation key. This transformation enables the generation of correlated random variables or fields by mapping independent standard normal vectors through (L). Thus, guaranteeing that the simulated samples inherit the correlation encoded in (R).

Then, to generate a vector of correlated shocks (z) (with mean zero and unit variance), we first draw a vector $\left(u\right)$ of independent standard normal variables:

$$u\sim \mathcal{N}\left(0,I_5\right),$$

(23)

where $0$ is a 5 × 1 vector of zeros and ${\mathrm{I}}_5$ is the 5 × 5 identity matrix. The correlated shock vector is then obtained through the linear transformation:

$$z=Lu.$$

(24)

The resulting vector $z$ preserves the zero mean and unit variance of the inputs, but its elements now exhibit the correlation structure defined by $R$, such that $\mathit{Cov}\left(z\right)=R$.

3.6.2. Estimating Procedure for Bayesian Parameter

A Bayesian approach has been adopted to estimate the parameters of a selected model by AIC and BIC. This method was chosen considering the research conducted by Kojima et al. [124]. The Bayesian approach combines prior knowledge with observed data to generate a complete probability distribution (the posterior distribution) for all model parameters. Consequently, this quantifies the uncertainty of estimation. In other words, the Bayesian approach treats unknown parameters as random variables and expresses all forms of uncertainty in terms of probability distributions [124].

The observed data likelihood is specified as a normal distribution around a function of time:

$$C{S}_t\sim \mathcal{N}\left({\mu }_t,{\sigma }^2\right), \mathit{for} t=1,\dots ,T,$$

(25)

where the mean ${\mu }_t$ is defined by the model:

$${\mu }_t=\alpha +\beta \cdot t+\gamma \cdot t^2.$$

(26)

In this Equation (26) $\alpha$ represents the baseline intercept, $\beta$ captures the linear time trend (average annual change), and $\gamma$ captures the curvature (acceleration or deceleration of the trend). The parameter ${\sigma }^2$ is the variance of the normally distributed errors.

We specified prior distributions to encode plausible assumptions before observing the data. That is, for the coefficient vector $\theta =(\alpha ,\beta ,\gamma {)}^{\mathrm{\top }}$, we assume a multivariate normal prior:

$$\theta \sim \mathcal{N}({\mu }_0,{\mathsf{\Sigma }}_0),$$

(27)

with prior mean ${\mu }_0=({\mu }_{CS},\mathrm{0,0}{)}^{\top }$ and a diagonal prior covariance matrix ${\Sigma }_0=\mathit{diag}({100}^2,1^2,{0.1}^2)$. This centres the intercept near the historical average coal share (${\mu }_{CS}$). This expresses weak prior beliefs of no significant linear or quadratic trend, with different degrees of uncertainty for each parameter.

For the error variance ${\sigma }^2$, we employed a conjugate Inverse-Gamma prior:

$${\sigma }^2\sim \mathit{Inv}\text{-}\mathit{Gamma}\left({\alpha }_0,{\beta }_0\right), \mathit{with} {\alpha }_0=3 \mathit{and} {\beta }_0=2$$

(28)

This choice centres the prior for the residual variance on a reasonable value, while maintaining a proper but weakly informative distribution.

Next, Posterior inference proceeds through Gibbs Sampling Algorithm. The joint posterior distribution $p(\theta ,{\sigma }^2\mid CS)$ it is analytically seemingly impossible to estimate. We therefore use a Gibbs sampler, a Markov Chain Monte Carlo (MCMC) technique, to draw sequential samples from the conditional posterior distributions of each parameter block.

Thus, let $X$ be the $T\times 3$ design matrix containing a constant column, a column of time indices $t$, and a column of squared time indices $t^2$. Also, let $\mathrm{C}\mathrm{S}$ be the $T\times 1$ vector of observed coal share values.

The first step in the process is to take a sample of the coefficients $\theta$. This means that the posterior distribution for the coefficients is multivariate normal, which is conditional on the current state of the variance $\left({\sigma }^2\right)$ and the data:

$$\theta \mid {\sigma }^2,CS\sim \mathcal{N}({\mu }_n,{\Sigma }_n),$$

(29)

where the posterior precision matrix ${\Sigma }_n^{-1}$ and mean ${\mu }_n$ are updated from the prior using the data:

$${\Sigma }_n^{-1}={\Sigma }_0^{-1}+{\sigma }^{-2}{X}^{\top }X,{\mu }_n={\Sigma }_n({\Sigma }_0^{-1}{\mu }_0+{\sigma }^{-2}{X}^{\top }CS)$$

(30)

The second step involves sampling the variance ${\sigma }^2$. Based on the current coefficients $\theta$ and data, the posterior distribution for variance is Inverse-Gamma:

$${\sigma }^2\mid \theta ,CS\sim \mathit{Inv}\text{-}\mathit{Gamma}({\alpha }_n,{\beta }_n),$$

(31)

with updated shape and scale parameters:

$${\alpha }_n={\alpha }_0+{\displaystyle \frac{T}{2}},{\beta }_n={\beta }_0+{\displaystyle \frac{1}{2}}{\displaystyle \sum _{t=1}^T}{(C{S}_t-\alpha -\beta t-\gamma t^2)}^2$$

(32)

The algorithm iterates between Step 1 and Step 2, producing a correlated sequence of draws from the joint posterior. Then we run the Gibbs sampler for 15,000 iterations. The initial 5000 iterations are discarded as a burn-in period to allow the chain to converge to the target posterior distribution. We retain the subsequent $N=\mathrm{10,000}$ samples, denoted ${\{{\theta }^{\left(i\right)},{\left({\sigma }^2\right)}^{\left(i\right)}\}}_{i=1}^N$, for inference.

Posterior summaries are calculated directly from these samples. The sample average approximates the posterior mean of the coefficients, which serves as our central estimate:

$$\mathbb{E}[\theta \mid CS]\approx \stackrel{-}{\theta }={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{\theta }^{\left(i\right)}.$$

(33)

The sample covariance, expressed in Equation (34), approximates the posterior covariance matrix, which quantifies the uncertainty and correlations between coefficient estimates.

$$\mathit{Var}[\theta \mid CS]\approx {\displaystyle \frac{1}{N-1}}{\displaystyle \sum _{i=1}^N}({\theta }^{(i)}-\stackrel{-}{\theta })({\theta }^{(i)}-\stackrel{-}{\theta }{)}^{\top }.$$

(34)

Additionally, credible intervals (i.e., the 95% highest posterior density interval) for any parameter or derived quantity are calculated using the retained samples’ empirical quantiles. This provides a complete probabilistic description of the estimated transition dynamics.

3.6.3. Estimating Procedure for Monte Carlo Simulation with Dynamic Volatility

In order to characterise the full spectrum of potential future pathways for South Africa’s coal phase-out, we employed an enhanced Monte Carlo simulation framework (10,000 stochastic trajectories are generated). Monte Carlo Simulation with Dynamic Volatility was chosen based on the study conducted by Zhai et al. [125]. In this study, this method produces a large number of stochastic predictions for the coal share. It models the inherent volatility and structural uncertainty of the transition process. Consequently, each simulated path demonstrates a plausible future that includes dynamic volatility and economic dependencies. This enabled us to generate a probability distribution for the crucial transition year where the share of coal will fall below 50%.

The core of the simulation, as shown in Equation (35), is a discrete-time stochastic process for the annual coal share ${\mathit{CS}}_t$. The evolution from year $t$ to $t+1$ is determined by its current value plus the annual change ${∆\mathrm{CS}}_t$:

$${\mathit{CS}}_{t+1}={\mathit{CS}}_t+{\Delta }_t$$

(35)

The annual change (${\Delta }_t$) is decomposed into a deterministic trend and a stochastic shock. It is modelled in Equation (36) as the sum of the negative baseline transition speed ($-{\delta }_{\mathit{base}}$). This represents the systematic, expected annual decline and a composite stochastic disturbance term ${\eta }_t$ that captures all unpredictable fluctuations. This can be expressed as follows:

$${\Delta CS}_t=-{\delta }_{\mathit{base}}+{\eta }_t$$

(36)

where $-{\delta }_{\mathit{base}}$ is the deterministic annual decline rate, calibrated from the post-2011 trend identified in the structural break analysis (Equation (8)), representing the central tendency of the phase-out. The term ${\eta }_t$ is critical, as it aggregates uncertainties from multiple sources, including macroeconomic conditions, policy shifts, and technological breakthroughs.

Additionally, to realistically model the time-varying nature of market and policy uncertainty, the volatility of the stochastic component (${\eta }_t$) is governed by a Generalized Autoregressive Conditional Heteroskedasticity (GARCH(1,1)) process. This allows the magnitude of shocks to cluster over time, reflecting periods of high and low instability. The shock is defined as follows:

$${\eta }_t={\sigma }_t\cdot z_{1,t},$$

(37)

where $z_{1,t}$ is a standard normal shock specific to the coal share process, and ${\sigma }_t$ is its time-dependent conditional standard deviation. The evolution of the conditional variance ${\sigma }_t^2$ is given by:

$${\sigma }_t^2=\omega +\alpha \cdot {\epsilon }_{t-1}^2+\beta \cdot {\sigma }_{t-1}^2$$

(38)

where ${\epsilon }_{t-1}={\Delta }_{t-1}+{\delta }_{\mathit{base}}={\sigma }_{t-1}\cdot z_{t-1}$ is the previous period’s realised shock. The parameter $\omega >0$ is the base volatility, $\alpha \ge 0$ measures the sensitivity to recent shock magnitude, and $\beta \ge 0$ captures the persistence of volatility. The parameters are economically calibrated: $\omega =0.1\cdot {\sigma }_{\Delta }^2$, anchoring the long-run variance; $\alpha =0.1$, assigning moderate weight to recent shocks; and $\beta =0.8$, ensuring high persistence in volatility regimes, consistent with energy policy and investment cycles.

Nonetheless, it is important to note that the parameters are empirically calibrated as summarised in Table 3. As a result, using these calibrated parameters, the enhanced composite shock incorporates interdependencies as shown in Equation (39).

To extend the justification highlighted in

Table 5. Calibrated Model Parameters and Justification.

Parameter	Symbol	Value	Justification
Baseline coal decline rate	${\delta }_{\mathit{base}}$	0.754% per year	Post-2011 trend from Chow test (Equation (8)). Represents the empirical annual decline in coal’s share of electricity generation following the REIPPPP policy intervention.
GARCH base volatility	$\omega$	$0.1\cdot {\sigma }_{\Delta }^2$	Anchors long-run variance to historical volatility (${\sigma }_{\Delta })$. Standard GARCH specification ensures unconditional variance consistency with observed data.
GARCH shock sensitivity	$\alpha$	0.1	Moderate weight assigned to recent shocks. Falls within the literature range of 0.05–0.15 for energy price and policy volatility models [125].
GARCH volatility persistence	$\beta$	0.8	High persistence parameter reflecting the tendency of volatility to cluster over time. Consistent with energy policy and investment cycles where uncertainty propagates across multiple periods (literature range: 0.7–0.9).
Renewable feedback strength	${\lambda }_{\mathrm{renew}}$	0.8	Calibrated from historical displacement elasticity between coal and renewable energy (−0.93 from Figure 4A). Sensitivity sweep over 0.5–1.2 showed stability of transition year within ±2 years.
Economic feedback sensitivity	${\varphi }_{\mathrm{econ}}$	0.05	Derived from the GDP–coal correlation (0.18 from Figure 4A). Each one percentage point positive GDP shock temporarily slows coal decline by 0.05 percentage points. This value was validated through sensitivity analysis (Section 4.9).

Source: Authors’ own computation.

, empirical work in energy-related studies consistently shows that ARCH parameters are small, whereas GARCH parameters are large and persistent. This pattern supports choosing values such as α = 0.1 and β = 0.8. For example, crude oil volatility estimates for WTI show an ARCH coefficient of 0.133 and a GARCH coefficient of 0.861 [126]. These values are very similar to the proposed pair. Studies of international fossil fuel equity indices also show low ARCH effects below 0.25 and high GARCH effects above 0.57 [127]. The sum of α and β typically ranges from 0.77 to 0.99, with α = 0.1 and β = 0.8 being typical empirical behaviour [127]. Similar values around 0.9 are found in clean energy ETF volatility studies [125]. Gilli [128] recommends that α be less than 0.1 and β be at least 0.85. This confirms that the chosen parameters are consistent with standard modelling practice. According to Chan and Grant [129], energy price modelling guidelines require α + β < 1 for stationarity, which is met by α = 0.1 and β = 0.8. Applied studies and modelling criteria indicate that α = 0.1 and β = 0.8 are reasonable and realistic values. Therefore, this pair corresponds well to observed energy market volatility dynamics.

In addition, the composite stochastic term ${\eta }_t$ is enhanced to incorporate interdependencies and feedback effects from the broader economic-energy system. It integrates correlated shocks from the five key variables defined earlier (${\mathrm{z}}_t=[z_{1,t},z_{2,t},z_{3,t},z_{4,t},z_{5,t}{]}^{\mathrm{\top }}$), representing shocks to coal share, GDP growth, renewable energy share, governance (Political corruption index), and carbon intensity, respectively. Thus, Equation (42) can be expanded and expressed as follows:

$${\eta }_t={\sigma }_t{z}_{1,t}+{\psi }_1{z}_{2,t}+{\psi }_2{z}_{3,t}+{\psi }_3{z}_{4,t}-{\lambda }_{\mathrm{renew}}\cdot \mid z_{3,t}\mid \cdot (1-{\displaystyle \frac{C{S}_t}{100}})+{\varphi }_{\mathrm{econ}}\cdot z_{2,t}\cdot \left({\displaystyle \frac{C{S}_t}{100}}\right)$$

(39)

The terms ${\psi }_i{z}_{j,t}$ capture direct linear impacts from GDP ($z_2$), renewable energy share ($z_3$), and governance ($z_4$) shocks. The renewable displacement feedback is modelled by $-{\lambda }_{\mathrm{renew}}\cdot \mid z_{3,t}\mid \cdot (1-C{S}_t/100)$, where ${\lambda }_{\mathrm{renew}}=0.8$. The absolute value $\mid z_{3,t}\mid$ ensures a positive renewable energy shock always reduces coal share. Also, the opposite is true, where a negative renewable energy shock increases the share of coal. The term $(1-C{S}_t/100)$ makes the displacement effect more potent when there is a larger remaining non-coal share of the market to replace. The economic feedback sensitivity is modelled by $+{\varphi }_{\mathrm{econ}}\cdot z_{2,t}\cdot (C{S}_t/100)$, where ${\varphi }_{\mathrm{econ}}=0.05$. This creates a pro-cyclical link, whereby positive GDP shocks ($z_{2,t}>0$) can temporarily slow the coal decline, with an effect proportional to coal’s current market share ($C{S}_t/100$).

Additionally, it is to quantify the renewable share co-evolution. The renewable energy share (${\mathrm{RE}\text{\_}\mathrm{share}}_t$) evolves in parallel, driven primarily by its own positive shocks but also influenced by economic conditions:

$${\mathrm{RE}\text{\_}\mathrm{share}}_{t+1}={\mathrm{RE}\text{\_}\mathrm{share}}_t+0.5\mid z_{3,t}\mid +0.1\mid z_{2,t}\mid$$

(40)

Equation (45) indicates that positive shocks to renewables ($z_3$) and, to a lesser extent, positive economic shocks ($z_2$), lead to annual increases in renewable penetration in total generation of electricity. A physical system constraint is enforced as follows:

$${\mathrm{RE}\text{\_}\mathrm{share}}_t\le 100-C{S}_t,$$

(41)

which ensures the combined share of coal and renewables does not logically exceed 100% of the electricity generation mix.

Lastly, it is to quantify the dynamics of carbon intensity as the environmental outcome, which is improved through two channels:

$$C{I}_{t+1}=C{I}_t\cdot (1-0.01\mid z_{5,t}\mid )-0.05\Delta C{S}_t$$

(42)

The first term represents autonomous technological improvement and policy-driven decarbonisation. This is modelled as a percentage reduction triggered by positive carbon intensity shocks ($z_5$). The second term directly links environmental gains to energy transition. This stipulates that each percentage point decline in coal share ($\Delta C{S}_t$) reduces the carbon intensity of the economy by 0.05 units.

3.6.4. Estimating Procedure for Transition Statistics and Assessing Probabilities

The core output of the Monte Carlo simulation is an ensemble of 10,000 plausible future pathways for the coal share. So, from each simulated pathway, indexed by $i$, we extract a key metric, the transition year (${\tau }_i$). This is defined as the first year in which the coal share in that particular pathway falls to or below the 50% threshold. This marks the point in time where coal ceases to be the dominant source of electricity. Therefore, $i-th$ simulation can be expressed as follows:

$${\tau }_i=min\{t:C{S}_t^{\left(i\right)}\le 50\%\}$$

(43)

The complete set ${\left\{{\tau }_i\right\}}_{i=1}^N$, where $N=\mathrm{10,000}$, forms an empirical probability distribution of possible transition dates. This captures the full range of uncertainty that is inherent in the process.

Following Raju [130], key statistical measures are taken into consideration. We use standard statistical moments to summarise the empirical distribution. These include the median transition year, the mean (average) transition year, and the standard deviation.

Firstly, the median transition year captures the central value at which 50% of simulations transition earlier (pre) and 50% transition later (post). It represents the distribution’s 0.5 quantile:

$$\mathit{Median}=Q_{0.5}\left(\right\{{\tau }_i\left\}\right)$$

(44)

Secondly, we measure the mean (average) transition year, which captures the arithmetic average of all simulated transition years:

$$\stackrel{-}{\tau }={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{\tau }_i$$

(45)

Lastly, we computed a standard deviation, which captures the dispersion or uncertainty around the mean transition year:

$$s_{\tau }=\sqrt{{\displaystyle \frac{1}{N-1}}{\displaystyle \sum _{i=1}^N}{({\tau }_i-\stackrel{-}{\tau })}^2}$$

(46)

Next, to communicate the range of likely outcomes, we construct confidence intervals directly from the empirical quantiles of the simulated transition years. A $(1-\alpha )$ confidence interval, which contains the central $(1-\alpha )\times 100\mathrm{\%}$ of the distribution, is expressed as follows:

$${\mathit{CI}}_{1-\alpha }=\left[Q_{\alpha /2}\left(\right\{{\tau }_i\left\}\right), Q_{1-\alpha /2}\left(\right\{{\tau }_i\left\}\right)\right]$$

(47)

For example, a 90% confidence interval ($\alpha =0.10$) is calculated using the 5th percentile ($Q_{0.05}$) as the lower bound and the 95th percentile ($Q_{0.95}$) as the upper bound. This interval indicates the range of years within which the transition is expected to occur with 90% probability, according to the model.

Then, to assess the likelihood of completing the transition by specific target years, we estimate the empirical cumulative distribution function (CDF), denoted $F\left(y\right)$. For any given future year $y$, $F\left(y\right)$ estimates the probability that the transition occurs on or before that year. It is calculated as the proportion of simulated pathways that have transitioned by year $y$:

$$F(y)={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}\mathbb{I}({\tau }_i\le y),$$

(48)

where $\mathbb{I}(\cdot )$ is the indicator function, which equals 1 if the condition (${\tau }_i\le y$) is true and 0 otherwise. This allows us to report key policy-relevant probabilities, such as:

$$\begin{gathered} F\left(2030\right)\mathit{\text{: Probability of transition by 2030.}} \\ F\left(2040\right)\mathit{\text{: Probability of transition by 2040.}} \\ F\left(2050\right)\mathit{\text{: Probability of transition by 2050.}} \\ F\left(2060\right)\mathit{\text{: Probability of transition by 2060.}} \end{gathered}$$

(49)

These metrics collectively provide a probabilistic assessment of the energy transition timeline. This evaluation quantifies both the central expectation and the risks of delay throughout the transition.

3.6.5. Estimating Procedure for Policy Scenario Analysis with Synergistic Effects

Pallaske [131] provided us with a methodology that we followed to evaluate the potential of coordinated approaches to climate change. The methodology models the impact of a portfolio of $P=6$ distinct policy instruments. Each instrument $i$ is assigned a base impact coefficient, denoted $p_i$. This quantifies its standalone effectiveness in accelerating the annual decline of the coal share (measured in percentage points per year). A key advantage of this analysis is the modelling of policy synergies. This refers to the super-additive effects that take place when policies are implemented together.

The total additional decline rate ($\Delta \delta$) induced by the policy portfolio is therefore modelled with two components. These components are Linear Additive Impact (LAI) and Synergistic Impact (SI). Shui et al. [132] noted that LAI measures the sum of the base effects of all implemented policies that are scaled by an overall policy multiplier $m$. SI measures the sum of all pairwise interaction effects between policies. The strength of the interaction between policy $i$ and policy $j$ is governed by a synergy coefficient $s_{ij}$. This tends to amplify the product of their base impacts. Therefore, the total policy impact is expressed in Equation (50) below:

$$\Delta \delta =m\cdot {\displaystyle \sum _{i=1}^P}{p}_i+{\displaystyle \sum _{i=1}^p}{\displaystyle \sum _{j=i+1}^p}{s}_{ij}·m^2·p_i{p}_j$$

(50)

where the policy multiplier $m$ defines the ambition level of the scenario, taking values such as 0 (no new policy), 0.5 (moderate implementation), 1.0 (full implementation), and 1.5 (aggressive implementation).

For any given policy scenario, expressed in Equation (51), the effective annual decline rate in the coal share (${\delta }_{\mathrm{scenario}}$) is calculated by adding the total policy-induced acceleration ($\Delta \delta$) to the empirically estimated baseline decline rate (${\delta }_{\mathrm{base}}$) derived from historical data:

$${\delta }_{\mathit{scenario}}={\delta }_{\mathit{base}}+\Delta \delta$$

(51)

This increased rate (${\delta }_{\mathrm{scenario}}$) is the anticipated rate at which the energy transition will occur in accordance with the particular policy framework that is being examined.

Therefore, to provide a clear, first-order estimate of the policy portfolio’s effect on the transition timeline, we calculated a deterministic transition year (${\tau }_{\mathit{scenario}}$). This calculation assumed the enhanced decline rate (${\delta }_{\mathrm{scenario}}$) remains constant from the base year (2023) onward, with no stochastic shocks. The formula shown in Equation (52) projected how many years it would take, at this constant speed, for the coal share to fall from its observed level in 2023 ($C{S}_{2023}$) to the 50% dominance threshold:

$${\tau }_{\mathit{scenario}}=2023+{\displaystyle \frac{C{S}_{2023}-50\%}{{\delta }_{\mathit{scenario}}}}$$

(52)

The outcome of this analysis offers a straightforward and comparative metric that can be utilised to evaluate the impact of various policy ambition levels ($m$) and synergy assumptions ($s_{ij}$) on the anticipated midpoint of the energy transition. This is done within a simplified context that does not involve any level of uncertainty. Thus, Equation (52) is utilised prior to the incorporation of the complete complexity of stochastic simulations.

3.6.6. Estimating Procedure for the Acceleration Pathway for Climate Targets

Similar to the study conducted by Song et al. [133], which interpolated the ambition pathway between the baseline year and the target year (climate target years), this analysis begins by establishing a benchmark. This benchmark is the constant annual rate of decline in coal share required to achieve the transition (reducing coal share to 50% or below) by a specified target year $T_{\mathrm{target}}$ (e.g., 2040, 2050, 2060, 2070, 2080 and 2090). Assuming a uniform, linear decline from the base year (2023), this minimum required rate ${\delta }_{\mathrm{target}}$ is calculated as the total percentage points that must be eliminated, divided by the number of years available:

$${\delta }_{\mathit{target}}={\displaystyle \frac{C{S}_{2023}-50\%}{T_{\mathit{target}}-2023}}$$

(53)

This value (${\delta }_{\mathrm{target}}$) represents a constant speed that, if maintained from 2023 onward, would result in crossing the 50% threshold exactly in the target year.

In reality, we make an assumption that the current historical decline rate (${\delta }_{\mathrm{base}}$) is lower than the required rate (${\delta }_{\mathrm{target}}$) for most ambitious targets. Therefore, the transition must accelerate over time. Consequently, we model four distinct mathematical trajectories (Linear, Exponential, Step-change and Logistic) for how the annual decline rate $\left({\delta }_t\right)$ could increase from ${\delta }_{\mathrm{base}}$ at $t=0$ (2023) to ${\delta }_{\mathrm{target}}$ at $t=T_{\mathrm{target}}-2023$, where $t$ is the number of years since 2023.

Firstly, Linear Acceleration (LA) captures the decline rate increases by a constant amount each year and is expressed as follows:

$${\delta }_t={\delta }_{\mathit{base}}+({\delta }_{\mathit{target}}-{\delta }_{\mathit{base}})\cdot {\displaystyle \frac{t}{T_{\mathit{target}}-2023}}$$

(54)

Secondly, Exponential Acceleration (EA) captures the decline rate that grows at a constant percentage rate (compounded annually). That is, the constant growth rate $\lambda$ is derived from the required doubling and/or halving time:

$$\lambda ={\displaystyle \frac{ln({\delta }_{\mathit{target}}/{\delta }_{\mathit{base}})}{T_{\mathit{target}}-2023}}$$

(55)

The trajectory is then expressed as:

$${\delta }_t={\delta }_{\mathit{base}}\cdot exp(\lambda \cdot t)$$

(56)

Thirdly, Step-Change Acceleration (SCA) describes how the system operates at the current (slower) rate for half of the period before instantly shifting to the higher required rate for the duration. This model represents a delayed but decisive policy intervention that can be expressed as follows:

$${\delta }_t=\{\begin{array}{cc}{\delta }_{\mathit{base}},& \mathit{if} t<{\displaystyle \frac{T_{\mathit{target}}-2023}{2}},\\ {\delta }_{\mathit{target}},& \mathit{otherwise}.\end{array}$$

(57)

Lastly, Logistic (S-Curve) Acceleration (LSA) captures the acceleration that follows a sigmoidal path. This can be visualised as an S-Curve with a slow initial ramp-up, a period of rapid mid-term acceleration, and a final tapering as it approaches the target rate. As a result, this model often reflects real-world adoption and scaling dynamics and can be expressed as follows:

$${\delta }_t={\delta }_{\mathit{base}}+{\displaystyle \frac{{\delta }_{\mathit{target}}-{\delta }_{\mathit{base}}}{1+exp[-k(t-t_{\mathit{mid}}\left)\right]}}$$

(58)

where $k=0.15$ controls the steepness of the acceleration phase, and $t_{\mathrm{mid}}=(T_{\mathrm{target}}-2023)/2$ sets the midpoint of the acceleration curve at the halfway point of the timeline.

3.6.7. Estimating Procedure for Global Sensitivity Analysis

The study used a global sensitivity analysis (GSA) to determine the robustness of the model’s projections. This technique is similar to the one used in the study by Gao et al. [134]. GSA examines how uncertainty in key variables influences the transition timeline [135]. It varies all parameters simultaneously over a wide range and thus captures complex interactions within the model. This feature distinguishes GSA from local methods that change a single variable at a time. According to Li et al. [136], GSA provides a more in-depth understanding of the applied model’s uncertainty drivers.

The study tested three foundational parameters. These included the Base Decline Rate, the Volatility Level, and the Transition Threshold. These parameters were chosen because they reflect the structural, stochastic, and definitional kinds of uncertainties [137].

Firstly, Base Decline Rate ($\delta$) captured the assumed rate of coal reduction. The tested range spans from fifty percent below to fifty percent above the baseline, as shown in Equation (64) below:

$${\delta }_{\mathrm{test}}\in \left[ 0.5\times {\delta }_{\mathrm{base}}, 1.5\times {\delta }_{\mathrm{base}} \right]$$

(59)

Secondly, Volatility Level ($\sigma$) captures the magnitude of annual stochastic fluctuations. We do this by testing values from half to double the historically observed volatility of coal share changes:

$${\sigma }_{\mathrm{test}}\in \left[ 0.5\times {\sigma }_{\Delta }, 2.0\times {\sigma }_{\Delta } \right]$$

(60)

where ${\sigma }_{\Delta }$ is the historical standard deviation of annual changes. Lastly, Transition Threshold ($\theta$) captures the target coal share. This defines the coal-share level as “transition”. This threshold is tested between forty-five and fifty-five percent as shown in Equation (61):

$${\theta }_{\mathrm{test}}\in [45\mathrm{\%},55\mathrm{\%}]$$

(61)

For each parameter combination, the model runs a full simulation to produce a new transition year distribution.

Next, to quantify and compare the sensitivity of the results to each parameter, we calculated an arc elasticity ($ϵ$). Arc elasticity measures how sensitive the transition year is to parameter changes [138]. In other words, Arc elasticity calculates the percentage change in the average transition year caused by a one percent change in the input parameter over the tested range. Thus, the elasticity of the mean transition year $\stackrel{-}{\tau }$ with respect to a given parameter is calculated as:

$${ϵ}_{\mathit{parameter}}={\displaystyle \frac{\left(\frac{{\tau }_{\mathit{max}}-{\tau }_{\mathit{min}}}{\stackrel{-}{\tau }}\right)}{\left(\frac{{\mathit{parameter}}_{\mathit{max}}-{\mathit{parameter}}_{\mathit{min}}}{\stackrel{-}{\mathit{parameter}}}\right)}}$$

(62)

Equation (62) expresses both the numerator and denominator. That is, the numerator calculates the percentage difference in the average transition year ($\stackrel{-}{\tau }$) between the simulations based on the parameter’s maximum value (${\tau }_{\max }$) and its minimum value (${\tau }_{\min }$). The denominator calculates the percentage difference between the tested maximum and minimum values of the parameter itself, relative to its central value ($\stackrel{\mathrm{‾}}{\mathrm{parameter}}$).

As a result, an elasticity of $\mid ϵ\mid >1$ indicates the model output (transition timing) is highly sensitive to that parameter (i.e., elastic). That is, a percentage change in the parameter leads to a larger percentage change in the result. In other words, this reflects a high absolute elasticity value that indicates heightened sensitivity [139]. Consequently, parameters with elasticity values greater than one are thought to have a strong influence on the model output. Thus, small changes in these parameters can cause amplified changes in the results [140]. In contrast, an elasticity of $\mid ϵ\mid <1$ indicates the model is inelastic, or relatively robust, to variations in that parameter. In other words, elasticity values less than one indicate stable projections under parameter uncertainty. Therefore, in this case, parameters are less influential, and uncertainties in their values have a lower impact on the model output [141]. Subsequently, the elasticity ranking system facilitates determining which assumptions have the greatest influence on model uncertainty in the study forecasts.

3.7. Applied Diagnostic Tests and Methodology Validation

The study’s applied methodology was validated using historical back-testing (HBT), Markov Chain Monte Carlo (MCMC) convergence diagnostics, and cross-system consistency checks. These techniques aimed to evaluate reliability, detect structural weaknesses and confirm the model’s robustness.

Firstly, we used an HBT procedure to assess our simulation model’s predictive accuracy. HBT measured how well model forecasts matched actual results over a given period. The process began with establishing a threshold date and segmenting the dataset into training and testing groups [142]. The training data calibrated the model without subjecting it to additional observations. As a result, Li et al. [136] highlighted that this method tends to detect model overfitting and weaknesses in dynamic forecasting.

Secondly, the accuracy of these out-of-sample forecasts is quantified using the Mean Absolute Percentage Error (MAPE). MAPE calculates the average magnitude of the prediction errors relative to the actual values, expressed as a percentage [143]. For a test period containing $T_{\mathrm{test}}$ years, the MAPE is computed as:

$$\mathrm{MAPE}={\displaystyle \frac{100\mathrm{\%}}{T_{\mathrm{test}}}} \sum _{t\in \mathit{test} \mathit{period}}\mid {\displaystyle \frac{C{S}_t^{\mathit{actual}}-C{S}_t^{\mathit{predicted}}}{C{S}_t^{\mathit{actual}}}}\mid$$

(63)

As a result, for interpretation purposes, following Alsini et al. [144], a MAPE value of 0% indicates perfect prediction and maximum confidence in the forecast model. Values below 10% indicate excellent accuracy and high reliability for future forecasts. Values ranging from ten to twenty percent indicate good to moderate accuracy, which may require minor improvement in the forecast model. Values greater than 20% represent suboptimal accuracy and indicate the need for model refinement. Therefore, when MAPE exceeds 50%, the model underperforms and is unreliable for projections [145].

Thirdly, MCMC convergence diagnostics are critical for assessing the reliability of Bayesian analyses [146]. These diagnostics determine whether the MCMC algorithm adequately explored the posterior distribution. This ensures that the statistical inferences drawn from the samples are valid and not influenced by initial values or chain mixing difficulties [147]. As a result, Geweke diagnostic test has been utilised to assess the convergence of MCMC simulations. This test compares the mean of an early segment of the Markov chain (e.g., the first 10%) to the mean of a late segment (e.g., the last 50%) for a specific parameter $\theta$. It is used to determine whether the chain has reached a stationary distribution and thus convergence [148].

Consequently, the test calculates a Z-score:

$$Z={\displaystyle \frac{{\stackrel{-}{\theta }}_{\mathit{early}}-{\stackrel{-}{\theta }}_{\mathit{late}}}{\sqrt{{\widehat{\sigma }}_{\mathit{early}}^2/n_{\mathit{early}}+{\widehat{\sigma }}_{\mathit{late}}^2/n_{\mathit{late}}}}}$$

(64)

where $\stackrel{-}{\theta }$ denotes the segment mean, ${\widehat{\sigma }}^2$ the spectral variance estimate (adjusting for autocorrelation in the chain), and $n$ the segment length. Given the null hypothesis of convergence, the test statistic has a standard normal distribution [149]. If the Z-score falls within a specified range (commonly ±1.96 for a 95% confidence interval or a Bonferroni-corrected range such as [−2.87, 2.87]), the chain is considered to have converged. If the z-score is outside of this range, as Li et al. [149] affirmed, it indicates non-convergence.

Lastly, accounting consistency is a necessary component of any energy system model. Thus, we carried out cross-system consistency checks. Our framework enforces this by ensuring that, for each simulated year (t), all electricity generation sources account for 100% of the total energy mix. This can be expressed as follows:

$$C{S}_t+{\mathit{RE}\text{\_}\mathit{share}}_t+{\mathit{Other}\text{\_}\mathit{share}}_t=100\% \forall t$$

(65)

Here, ${\mathit{Other}\text{\_}\mathit{share}}_t$ represents the combined share of all non-coal, non-renewable sources (e.g., oil, nuclear). This test is done to prevent outcomes that are illogical and to guarantee that any displacement of coal is allocated to an increase in the share of renewables or other sources of electricity generation. This constraint is coded into the logic of the simulation of this study. Therefore, maintaining this internal consistency is absolutely necessary in order to generate transition pathways that are both physically plausible and interpretable.

3.8. Method Comparison and Justification

Table 6. Comparison of Forecasting Methods for Energy Transition Analysis.

Criterion	ARIMA/ SARIMA	VAR/ VECM	System Dynamics	Machine Learning (LSTM/RF)	Our Integrated Monte Carlo
Handles non-linear trends	No	Limited	Yes	Yes	Yes
Captures stochastic volatility	No	No	Limited	Yes	Yes (GARCH)
Incorporates policy shocks	No	Weak	Yes	No	Yes (structural break)
Accounts for parameter uncertainty	No	Weak	Limited	No	Yes (Bayesian priors)
Multi-variable correlation structure	No	Yes	Yes	Limited	Yes (Cholesky)
Policy scenario simulation	No	Limited	Yes	No	Yes (synergy multiplier)
Interpretability for policymakers	High	Medium	Medium	Low	High
Data requirements (annual)	Low	Medium	High	Very high	Medium

Source: Authors’own computation.

below compares the integrated Monte Carlo approach employed in this study against alternative forecasting methods commonly applied to energy transition analysis.

As a result, the study adopted an integrated Monte Carlo framework because it is the best tool for dealing with the various types of uncertainty in the current problem. The authors emphasise that the analysis must account for both stochastic uncertainty (random year-to-year fluctuations) and epistemic uncertainty (imperfect knowledge or imprecise parameters). Monte Carlo methods are specifically designed to deal with both types of uncertainty effectively. Another reason for using this approach is the presence of a structural break in 2011. This change in the underlying data generation process necessitates a model transition between regimes. Hence, traditional time series approaches, such as ARIMA or VAR, struggle with regime switching behaviour unless additional external indicators (i.e., dummy variables) are included. This limitation reduces their suitability for the task at hand.

The approach was also chosen because the analysis entails simulating policy portfolios, which include potential interactions and combined effects. These complex and potentially synergistic policy implications necessitate a framework that is modular and adaptable. Machine learning models, while powerful, typically operate as black boxes. These models may not be well-suited to investigate how various policies interact and influence one another within the system. Likewise, while system dynamics modelling could theoretically represent feedback loops in the energy system, such models frequently necessitate lengthy and demanding calibration procedures. In other words, they are not naturally designed to generate probability distributions for the potential years in which transition outcomes can occur. Thus, limiting their usefulness for the study’s objectives.

Overall, these limitations highlight why an integrated Monte Carlo approach is more appropriate. The model is capable of combining scenario-based reasoning with explicit uncertainty treatment, naturally accommodating regime changes, and transparently representing both stochastic variation and imperfect knowledge.

4. Results and Discussion

To begin this section of the study, it is important to first highlight the key policy takeaway based on the empirical analysis. Under current policies, coal is unlikely to account for less than 50% of electricity generation in South Africa until the mid-2050s. With the central estimate clustering around 2053. This slow pace is fuelled by a very modest baseline decline rate of about 0.7–0.75% annually. Policy uncertainty remains a significant impediment to progress, and modelling indicates that clearer, more credible long-term signals could accelerate the transition by more than two decades. As a result, coordinated and ambitious policy action (particularly full or aggressive implementation of a multi-instrument package) may accelerate the transition to the early or mid-2040s.

4.1. Descriptive Statistics Assessment

Table 7. Descriptive statistics outcome.

Parameter of Interest	Value	Unit of Measurement
Number of years (T)	39	years
Mean coal share (${\mu }_{CS}$)	91.83	%
Standard deviation of coal share (${\sigma }_{CS}$)	2.83	%
Coefficient of variation (${\sigma }_{CS}$/${\mu }_{CS}$)	0.03	coefficient
Minimum coal share	81.57	%
Maximum coal share	94.99	%
Range	13.42	%
Median coal share	92.92	%
Interquartile range of CS	3.12	%
Mean annual change (${\mu }_{\Delta }$)	−0.34	pp/year
Standard deviation of annual changes (${\sigma }_{\Delta }$)	1.34	pp/year
Signal-to-noise ratio ($\left|{\mu }_{\Delta }\right|$/${\sigma }_{\Delta }$)	0.25	ratio
Interquartile range of (ΔCS)	1.53	pp/year
Current Coal share (2023)	81.57	%
Distance to 50% threshold	31.57	%

Notes: pp/year refers to percentage point per year. Source: Authors’ own computation.

below displays the results received from conducting the descriptive statistics assessment.

The findings paint a clear picture of an electricity system that has remained heavily reliant on coal for nearly four decades. Coal has an average share of 91.83% over 39 years, with a very small standard deviation of 2.83% and a coefficient of variation of only 0.03. This demonstrates remarkable stability in the generation mix, with little evidence of structural change over time. Even in 2023, coal accounted for 81.57% of total electricity generation. This appears to highlight the persistence of this dependency and thus implies that efforts to diversify the energy mix have had little impact.

Further statistical indicators support the conclusion that change has been minimal. For instance, the narrow range of 13.42% and a similarly constrained interquartile range of 3.12 indicate that fluctuations were small and mostly contained within a predictable band. However, this appears to point toward system rigidity rather than progressive transition. Coal’s share has been decreasing, but at a slow and inconsistent pace, with a mean annual decline of only −0.34% and a large standard deviation of 1.34. The low signal-to-noise ratio of 0.25 supports this conclusion and thus demonstrates that any downward trend is overshadowed by short-term variability. This could be due to policy reversals, inconsistency in planning, or economic pressures that periodically reinforce coal reliance.

Finally, the discovery that coal remains 31.57% above the 50% threshold that would signal the end of its majority status emphasises the magnitude of the transition still required. This significant gap indicates that, despite global decarbonisation efforts, the system in question has yet to make significant progress toward energy diversification or emissions reduction. Hence, collectively, these results indicate a slow and fragile transition, with insufficient momentum to drive long-term and meaningful structural change.

4.2. Structural Break Test and Trend Evolution Analysis

4.2.1. Structural Break Test Assessment

The analysis demonstrates a clear structural shift in South Africa’s coal share following 2011, with the findings consistently confirming a statistically significant trend reversal. Prior to 2011, coal’s share increased gradually, as shown by the blue regression line in Figure 4A. This line indicates an annual rise of approximately 0.08% over the 1985–2010 period. This modest increase is further supported by the low pre-break R-squared value of 0.22, which suggests that annual variations often outweighed the slow upward trend. Although coal remained highly dominant at the beginning of the sample period, the evidence indicates that the pre 2011 trajectory lacked strong, sustained momentum.

A clear departure from this pattern appears after 2011, where the post-break trend demonstrates a decisive and consistent decline. The red line in Figure 4A shows that coal’s share decreased by approximately 0.75% annually, marking a substantial reversal of the earlier trajectory. The post-break regression also reveals a markedly higher R-squared value of 0.80. Thus, indicating that the declining trend explains about 80% of the observed variation and therefore fits the data significantly better than the earlier pattern. This steep improvement in model fit strongly suggests that the downward trend has been sustained and stable following the structural break.

The Chow test results presented in Figure 4C offer statistical confirmation of this shift. The F statistic of 47.8, which substantially exceeds the critical value of 3.27, indicates that the pre-break and post-break slopes differ significantly. This has led to a clear rejection of the null hypothesis. Consequently, this confirms that 2011 represents a meaningful turning point rather than a continuation of prior fluctuations. The magnitude of the shift is further evidenced by the contrast between the pre-break and post-break intercepts. That is, this is reflected by substantially different baseline levels of coal dependence across the two periods.

Figure 4F strengthens this conclusion by comparing the fit of the pooled model with that of the two-regime model. The latter provided a far more accurate representation of long-term coal share behaviour. The pooled model’s RSS of 204.9 indicates a relatively poor fit when assuming a single long run trend. Whereas the two-regime specification reduces this value to 54.9, representing a notable 73% decline in total error. The large difference between the pre-2011 error (29.37) and the post-2011 error (25.53) suggests improved explanatory power when recognising the break’s existence. Hence, together, these results demonstrate that coal followed distinct trends before and after 2011 and thus confirm that the identified policy shift permanently altered the sector’s trajectory.

Figure 4E provides further insight into the practical implications of this change by illustrating the expected pace of the coal phase-out. Although the post 2011 decline rate of around 0.75% per year is meaningful, it remains slow enough to imply continued coal dominance for several decades if maintained. On this basis, coal could remain at 50% of total electricity generation until approximately 2065. This then reflects a deeper or more ambitious intervention that may be required to accelerate decarbonisation. Therefore, the comparison between pre-break and post-break trends highlights the importance of the REIPPPP. Since, without such intervention, coal’s share would likely have remained stable or even increased over time.

4.2.2. Evolution Trend Analysis

The results presented in Figure 5A–E demonstrate a clear structural shift within the coal share trend. Before the turning point in 2011, the rolling slopes in Figure 5A consistently hovered near zero and failed to reach statistical significance at the 95 percent level. This indicates a long period of stagnant behaviour within the system. This pattern also implies that coal’s dominance remained largely unchallenged, as short-term fluctuations generated noise but no sustained directional change over time. The rolling regression, therefore, portrays an energy system operating in a stable equilibrium, where deviations lacked sufficient strength to accumulate into a long-term decline.

The distribution of slopes displayed in Figure 5B reinforces this interpretation. Most slope estimates cluster around zero, with a mean of approximately minus 0.14 and a standard deviation of 0.34. Thus, suggesting limited movement across earlier years. The minimum slope of minus 0.88 and the maximum of 0.38 further demonstrate that while variation existed, it did not translate into a systematic trend before 2011. These combined patterns confirm that the system lacked directional momentum and remained structurally unchanged for an extended period.

A significant change becomes evident in 2011, which emerges as the only year meeting both statistical conditions required to classify a genuine structural break in the rolling regression series. During this year, the rolling slope exceeded two standard errors and shifted decisively from non-negative to clearly negative. This then provided strong evidence of a new downward trajectory in the coal share trend. Following 2011, the slopes remain consistently negative and statistically significant. Hence, supporting the conclusion that a persistent and structurally meaningful decline took hold during the subsequent decade.

Figure 5D strengthens this interpretation by showing a steady cumulative decline across each ten-year rolling window after 2011. This consisted of an annual average reduction estimated at approximately negative 0.7%. Although the downward shift progresses gradually, its consistency across overlapping windows suggests a robust and durable transformation rather than a temporary deviation or isolated event. This behaviour indicates that the system has entered a new equilibrium characterised by sustained decline and thus replacing the previous static pattern that dominated earlier decades.

Additional insight is provided by Figure 5B,E, which show the probability distribution of rolling slopes and the associated R-squared values, respectively. The probability density appears approximately normal with a mean close to zero. For this reason, this then reinforced the absence of strong pre-break trends, while the average R-squared value of about 0.49 suggests moderate explanatory power across the rolling windows. These findings demonstrate that model fit varies over time as structural conditions evolve, and that earlier periods lacked the coherence observed in post-break years.

4.3. Results from Model Comparison and Selection

A comparison of three models (linear, quadratic, and exponential decay), as shown in

Table 8. Model comparison and selection results.

Model of Interest	k	T	RSS	AIC	BIC	AIC Selected (Yes/No)	BIC Selected (Yes/No)
Linear	2	13	25.53	12.77	13.90	No	No
Quadratic	3	13	13.84	6.81	8.51	Yes	Yes
Exponential Decay	3	13	101.95	32.77	34.47	No	No

Source: Authors’ own computation.

, revealed that a quadratic model best describes the decline in South Africa’s coal share of electricity. The quadratic model has the lowest AIC (6.81) and BIC (8.51) values, which are significantly better than the linear (AIC: 2.77 and BIC: 13.90) and exponential (AIC: 32.77 and BIC: 34.47) alternative models.

In other words, across all metrics used, the quadratic model emerged as the best representation of the dataset’s underlying pattern. The significantly lower RSS indicates that it captures the variation in the data far more effectively than the linear model (which assumes a constant rate of change) and the exponential decay model (which assumes a rapid early decline). Both the AIC and the BIC support this conclusion. These criteria explicitly account for the fact that the quadratic and exponential models have an additional parameter beyond the linear model. Despite its increased complexity, the quadratic model still has the lowest information criterion scores. This means that the improvement in fit more than compensates for the penalty of having an extra parameter. In contrast, the exponential model not only does not outperform the others after penalisation, but it also performs significantly worse in its raw fit. Hence, the quadratic model is chosen by both AIC and BIC. This implies that its superiority is resistant to various types of complexity penalisation. Whereas AIC prefers models with higher predictive accuracy, BIC prefers parsimony. In this case, both agree that the quadratic model provides the best balance of overfitting and explanatory performance.

4.4. Multivariate Correlation Analysis

Figure 6 below illustrates the Pearson correlation matrix and the coal share variable distribution of the correlated shock. The correlation analysis, as shown in Figure 6a, revealed a clear and consistent set of relationships that contribute to understanding broader energy transition dynamics. The nearly perfect negative correlation (−0.93) between coal share and renewable energy share indicates that increases in renewable energy penetration are directly proportional to decreases in coal’s contribution to the electricity mix. This magnitude indicates not only a parallel trend but a high likelihood of substitution, with renewables actively displacing coal. The positive correlation between coal share and carbon intensity (0.47) emphasises coal’s role as a major source of emissions. Whereas the moderately negative correlation between renewable energy share and carbon intensity (0.50) confirms that renewable deployment leads to cleaner energy outcomes. Hence, collectively, these findings highlight the dual environmental and structural importance of shifting the energy balance to renewables.

Institutional quality is also recognised as an important factor. For instance, the political corruption index (PCI), which measures governance effectiveness, is negatively correlated with coal share (0.34) and positively correlated with renewable energy share (0.39). This suggests that better governance is associated with less reliance on coal and more use of renewable energy. Hence, governance improvements could help strengthen regulatory enforcement, attract investment, and support the development of clean energy infrastructure. Likewise, GDP growth appears to be only weakly correlated with changes in energy mix (0.18 for coal, 0.19 for renewables). This suggests that short-term economic fluctuations have little influence on structural energy transitions. However, longer-term institutional and policy conditions appear to play a more important role.

Figure 4B illustrates the coal share shock distribution that appears to be perfectly centred at zero. This suggests no systematic bias towards positive or negative shocks. That is, the shock distribution is roughly symmetrical, with only a slight negative skewness (−0.26). This means that slightly larger than expected declines were more common than unexpected increases. In other words, coal phase-out has accelerated on occasion, but not to the point where overall stability is jeopardised. The kurtosis value of 2.64, which is less than the normal benchmark of 3, indicates that the distribution tails are lighter and there are fewer severe shocks than would be expected with a standard Gaussian process. This further indicates a controlled and predictable transition.

The extremes of the distribution, with the largest negative shock of 3.13% and the largest positive shock of 2.31, are within 2–3 standard deviations of the mean. This demonstrates that while outliers exist, they are not excessive. The majority of shocks fall within ±1–2%, indicating that coal share dynamics are moderately volatile but stable. The mean shock is nearly zero (0.01). This indicates that the model used to estimate expected coal share trends is well calibrated and does not have a systematic bias toward overly optimistic or pessimistic projections. This balanced distribution confirms that upward and downward deviations typically offset over time. Thus, indicating an adaptive but stable transition pathway.

Next,

Table 9. Cholesky decomposition results.

Row	Coal_Share	GDP_Growth	RE_Share	PCI	Carbon_Intensity
Coal_share	1.00	0.00	0.00	0.00	0.00
GDP_growth	0.18	0.98	0.00	0.00	0.00
RE_share	−0.93	−0.02	0.36	0.00	0.00
PCI	−0.34	0.01	0.20	0.92	0.00
Carbon_intensity	0.47	0.09	−0.17	−0.09	0.86

Source: Authors’ own computation.

shows cholesky decomposition is used to investigate shock transmission across variables. the resulting lower-triangular matrix. The matrix quantifies how shocks are transmitted through the system. Each coefficient represents the immediate effect of one variable on another. The order is as follows: coal_share, GDP_growth, RE_share, PCI, and carbon_intensity. This structure reflects the assumed causal priority of the variables. Coal_Share is considered the most exogenous variable in the system. Shocks to coal share affect economic and environmental indicators. GDP_Growth responds to coal share innovations. The share of renewable energy varies in response to output fluctuations. Institutional quality responds with additional lag. Carbon intensity adjusts last, reflecting cumulative system effects.

As a result, a shock to the coal share has a single immediate effect (1.00). Because it is listed first, coal use is regarded as the most exogenous variable in the system. This assumes that short-run changes in coal dependence occur independently of other variables. A coal-share shock has a positive impact on GDP growth (0.18), indicating that increased coal use leads to short-term economic growth. This could reflect entrenched energy structures that continue to rely on fossil fuels for production. The strong own response (0.98) suggests that GDP growth is primarily influenced by its own innovations, rather than external shocks.

Coal-intensive system shocks have a significant negative impact on renewable energy share (−0.93), indicating that they hinder the current growth of renewables. This is consistent with a typical substitution dynamic. That is, as coal dominates marginal generation, renewable deployment slows. The weak negative response to GDP growth (−0.02) suggests that short-run economic expansions do not significantly affect renewable uptake concurrently. Renewable deployment has a modest positive response to its own shock (0.36), indicating that it is only partially self-driven in the short run, which reflects structural constraints.

Rising coal dependence is linked to a deterioration in governance indicators, as evidenced by the negative response of PCI to coal-share shocks (−0.34). It responds positively to renewable energy shocks (0.20), indicating that shifts towards renewables may coincide with institutional improvements. The high own-shock coefficient (0.92) suggests that corruption is largely self-perpetuating in the short term. Carbon intensity increases after shocks to coal share (0.47) and GDP growth (0.09). Thus, indicating that an economy driven by fossil fuels increases emissions per unit of output. Renewable energy shocks reduce carbon intensity (−0.17), indicating a displacement effect on fossil generation. PCI shocks reduce carbon intensity marginally (−0.09), indicating that improved institutional quality may reduce carbon-intensive activities. The high own-response (0.86) indicates that carbon intensity is significantly path-dependent in the short run.

Consequently, the Cholesky decomposition results show a system in which coal shocks dominate the energy-economy-governance-emissions nexus. This appears to be in line with South Africa’s entrenched coal lock-in and political economy literature. Renewables reduce emissions and strengthen governance signals, but their short-term impact is less than coal’s. Therefore, until structural change occurs, economic growth and fossil-fuel use will continue to increase carbon intensity.

4.5. Bayesian Parameter Analysis

4.5.1. Bayesian Parameter Estimation

Bayesian posterior results, as shown in

Table 10. Bayesian Parameter Estimation Results.

Parameter Coefficient	Posterior Mean	Posterior Std	Confidence Interval (Lower) 95%	Confidence Interval (Upper) 95%	Sample Size	Period
Intercept (α)	90,459	0.752	88,982	91,962	10,000	1985–2023
Linear (β)	0.474	0.086	0.303	0.644	10,000	1985–2023
Quadratic (γ)	−0.015	0.002	−0.020	−0.011	10,000	1985–2023
Error Variance (σ2)	2.221	0.501	1.450	3.405	10,000	1985–2023

Source: Authors’ own computation.

, demonstrate a clearly defined quadratic trend in the decline of coal share.

The intercept term has a high posterior mean of 90,459 and a fairly narrow confidence interval. This indicates a high level of certainty about the outcome variable’s baseline level when the explanatory components are zero. The posterior standard deviation of 0.752 indicates that the estimate is very stable throughout the posterior distribution. This indicates strong convergence with minimal parameter uncertainty.

The linear coefficient (β) has a posterior mean of 0.474, with a 95% confidence interval of 0.303–0.644. This positive value indicates that the predictor had a consistent upward marginal effect on the outcome. As a result, this implies that increases in the explanatory variable are associated with an overall upward trend in the dependent variable. The moderate posterior standard deviation (0.086) indicates a reasonable level of certainty. Importantly, because the confidence interval is entirely above zero, the positive linear effect is statistically credible in the Bayesian framework.

The quadratic term (γ) has a posterior mean of −0.015 with a small standard deviation, and the confidence interval ranges from −0.020 to −0.011. This unambiguously negative estimate indicates curvature in the estimated relationship. In other words, it shows that the initially positive linear trend gradually fades. In practice, this suggests that marginal effects decrease over time or across predictor space. In simple terms, this means that the relationship begins on an upward slope but eventually flattens or bends downward. The extremely narrow interval also suggests that the quadratic component is estimated with a high degree of certainty.

Finally, an error variance (σ²) estimate of 2.221 with a credible interval of 1.450 to 3.405 indicates moderate volatility in the model’s unexplained component. The posterior standard deviation of 0.501 indicates that variance estimation remains stable across sampling draws. This residual variance scale indicates that, while the model effectively captures the main structural pattern, there is still some natural variability or noise that the included parameters do not account for.

As a result, the Bayesian estimates show a robustly estimated nonlinear trend with a strong baseline effect, a significant positive growth component, and a slight but systematic deceleration in growth over the observation period. Therefore, the precision of the estimates indicates a well-behaved posterior distribution and high model reliability.

4.5.2. Bayesian Quadratic Model Forecasting

Bayesian quadratic model fit and a forecast to the year 2060 are shown in Figure 7 below.

Figure 7A demonstrated that the model fits historical coal share data exceptionally well. Between 1985 and 2023, the red fitted line almost aligns with the blue dotted observations. The strong historical fit boosts confidence in the model’s structure. The red line slopes downward over the forecast period of 2024 to 2060. The decline follows a concave curve. This means that coal’s share in the electricity generation mix starts slowly but accelerates over time. Figure 7B illustrates the probability of coal’s share falling below 50% over time. Figure 7C shows forecast coal share distributions for four milestone years. Each year’s forecast is presented as a kernel density curve with a mean marker. Figure 7D summarises the forecast with four key decadal observations. Each decade shows the average projected coal share, the 95% credible interval, and the probability that coal will fall below 50%.

As a result, the concave, downward-sloping trajectory, as shown in Figure 7A, implied by the posterior mean is particularly significant. It indicates that the decline in coal’s share is unlikely to proceed at a constant rate. Instead, reductions appear gradual in the early decades before becoming more pronounced after mid-century. This non-linear dynamic is consistent with the broader understanding that energy systems often demonstrate substantial inertia. This is where established infrastructures, regulatory regimes, and market conditions slow the pace of early transition.

Short-term projections reveal a high degree of certainty. The narrow credible intervals in the early forecast horizon demonstrated that coal is expected to maintain a dominant role in electricity generation through the 2020s and into the 2030s (see Figure 7D). The model consistently places coal’s share well above 50% during this period, and no simulated pathways indicate the possibility of a majority coal transition before 2040. This finding underscores the persistence of structural dependence on coal in the short-term. Consequently, this suggests that the rapid decarbonisation will remain challenging without significant and disruptive policy interventions.

As the projection horizon extends into the middle of the century, uncertainty begins to widen. By 2050, the distribution of projected coal shares spans values both above and below the 50% threshold (see Figure 7C). This represents a diverging potential pathway for the energy system. Although probabilities, as shown in Figure 7B, still favour coal remaining above half of total generation at this point, the emergence of a meaningful minority of trajectories falling below 50% signals the beginning of a plausible transition era. The identification of approximately 2053 as the most likely year in which coal becomes a minority source represents a critical insight. This estimated tipping point is supported by both the mean trajectory and the balance of probabilities. Thus, providing a coherent narrative for interpreting mid-century structural change.

Beyond the 2050s, the projections show increasingly strong indications of sustained decline. By 2060, coal’s expected share decreases substantially, and the probability of its remaining above 50% becomes very small. Although credible intervals widen significantly at this horizon (reflecting the inherent uncertainty embedded in long-range forecasting), the direction of change is clear. For this reason, the energy system is highly likely to have transitioned away from the majority of coal by this time, even under conservative assumptions.

4.5.3. Bayesian Quadratic Model Long-Term Forecast and Uncertainty

The results presented across Figure 8A–D offer a detailed view of how uncertainty evolves within the Bayesian quadratic model used to forecast coal’s share over the coming decades. These figures together show a transition from short-term stability to long-term unpredictability, driven largely by the growing influence of parameter uncertainty. In the early years of the forecast, uncertainty is dominated by short-term, year-to-year fluctuations in coal use, known as stochastic uncertainty. These random shocks explain nearly all variation in the first decade, demonstrating that the model captures a period where coal share remains relatively stable and predictable.

However, as the forecast horizon extends beyond 10 to 15 years, parameter uncertainty becomes increasingly important. This form of uncertainty reflects imprecision in estimating the underlying trend that drives the long-term decline in coal. By mid-century, parameter uncertainty contributes between 80% and 90% of total variance. This means that long range projections are constrained primarily by uncertainty in the model’s underlying structural path rather than by short-term randomness. This shift is consistent with the sharply rising total variance over time, which grows approximately with the fourth power of the forecast horizon.

The coefficient of variation (CV), as shown in Figure 8B, offers further insight into how reliable these forecasts remain as coal’s expected share declines. Initially, the forecast is highly precise, with CV values well below 10%, reflecting low uncertainty relative to a large mean share. As the coal share begins to decrease, however, the CV increases. Once coal is projected to fall below 50%, the relative uncertainty escalates sharply. By the late 2050s, CV values of 20% to 30% indicate that possible outcomes span a wide range around the mean, thus reducing the precision of long-term estimates. This pattern highlights an important asymmetry. That is, even if absolute uncertainty rises steadily, its impact becomes more significant as the expected coal share diminishes.

The widening of the 50%, 80% and 95% credible intervals reinforces this interpretation (see Figure 8C). These ranges expand approximately quadratically over time. Hence, confirming that uncertainty increases faster than linearly as the forecast progresses. Short-term credible intervals remain narrow, indicating strong confidence in short-term predictions. By contrast, the much wider 95% interval by 2060 (spanning roughly around 40% to 60%) shows that long-term scenarios diverge substantially. Even though the underlying distribution remains well behaved and close to normal. This widening has clear implications for planning: narrow intervals support focused, central case decision-making in the short term. Whereas long-term strategies must be flexible enough to accommodate a wide range of plausible outcomes.

Finally, the probability surface in Figure 8D provides a dynamic view of when coal is likely to cross specific thresholds. The black dotted line, indicating the 50% probability contour, aligns with earlier panels in projecting that coal’s share will reach 50% around 2053. In the early years, the probability of coal falling below high thresholds (such as 80% or 90%) is close to zero, reflecting stability in the short term. The steep gradients observed during the 2030s and 2040s suggest that the model produces relatively tight forecasts as the transition begins to accelerate. However, by 2060, these gradients flatten significantly. For this reason, this illustrates growing divergence in possible future paths and a moderate probability that coal could fall below 20%. This shift demonstrates how, once structural change gains momentum, the likelihood of lower coal shares increases significantly, even though substantial uncertainty remains.

4.6. Monte Carlo Simulation Results with Dynamic Volatility

4.6.1. Analysis of Monte Carlo Simulation with Dynamic Volatility

Figure 9 displays the results of the Monte Carlo simulation with dynamic volatility. The simulation highlights the uncertainty surrounding South Africa’s coal transition. Figure 9A provides detailed visual evidence of the Monte Carlo simulation, showing 37 distinct coal share trajectories that diverge substantially over time. The figure clearly demonstrates close alignment between the mean and median paths, with an average difference of only 0.071%. This indicates a minimal central bias in the distribution. As illustrated, the 95% credible interval expands noticeably from 6.7 points in 2024 to 31.9 points in 2060. This reflects a nearly tenfold increase in long-run uncertainty. This widening uncertainty underscores how future coal transition outcomes become progressively less predictable. Even though the ensemble mean shows a steady decline of 35.3% across the projection period.

Figure 9B reinforces this growing uncertainty by highlighting substantial variation in the final 2060 values. This uncertainty ranges from 48.5% to 78.8%, thus revealing large disparities in potential outcomes. The figure demonstrates that only 72.5% of simulations fall below the 50% threshold. Hence, confirming that coal dominance is likely to decline but may persist under slower transition pathways. The distribution shown in the figure, therefore, emphasises how transition timing remains deeply uncertain, with few trajectories achieving a sustained decrease below half before the 2050s.

Figure 9C deepens this understanding by charting the evolving probability of coal’s share falling below 50 percent across the forecast horizon. The figure shows a probability of zero through 2030, demonstrating a limited scope for early transition under current structural conditions. Probability growth remains subdued until the 2040s, reaching only 0.2% in 2040 and increasing gradually to 17.4% by mid-century. As shown in the figure, a steeper probability rise occurs after 2050, culminating in a transition probability of 71.5% by 2060, even though it does not reach absolute certainty. The key turning points illustrated in 2052 and 2056 highlight significant increases in transition likelihood. This marks an important inflection point in the energy system’s long-term transition.

Figure 9D presents the trajectory of renewable energy shares. This figure shows a rise from 12.8% in 2024 to 30.0% by 2060, thus representing an overall increase of 17.2%. The figure illustrates a clear co-movement between rising renewables and falling coal use. Yet, the displacement ratio of 48.7% indicates that renewables replace slightly less than half of coal’s decline. The widening credible interval from 1.2 to 7.6 points mirrors the uncertainties highlighted in earlier figures and signals increasing long-run variability in renewable deployment outcomes. The figure, therefore, illustrates the crucial but insufficient role of renewables in meeting South Africa’s broader electricity demand without additional generation sources.

Figure 9E shows a steep and sustained reduction in carbon intensity, falling from 273.6 kg CO₂/MWh in 2024 to 20.6 kg by 2060, representing a 92.5% decline overall. The figure highlights important milestones, including reductions of 34.1% by 2030, 50% by 2034, and 80% by 2047. This aligns closely with the system’s projected shift away from coal-based generation. Despite the broadening credible interval shown in the figure, the long-term downward trajectory remains clear and consistent with the coal transition patterns displayed in Figure 9A,D.

Figure 9F provides insight into volatility dynamics using the GARCH(1,1) model. The model showed a modest but persistent variation in projected volatility across the forecasted period. The figure illustrates volatility values fluctuating within a narrow range, with a maximum of 1.38% and a minimum of 1.32%. This then indicates only limited variability across the years. The underlying parameters displayed in the figure, including a strong persistence term of 0.80, indicate that past volatility heavily influences future patterns, even as new shocks gradually diminish over time. The figure therefore supports the interpretation that forecast uncertainty becomes structurally embedded and thus influences credible interval width and the reliability of long-run projections.

4.6.2. Analysis of Uncertainty Decomposition and Sensitivity Results

Figure 10 shows an analysis of the uncertainty decomposition and sensitivity, following a Monte Carlo simulation with dynamic volatility. These results highlight the evolving influence of different uncertainty sources across the forecast horizon. Figure 10A demonstrates that stochastic uncertainty dominates the early years, contributing 62.7% of total variance in 2025. This suggests substantial vulnerability to short-term shocks and policy or economic volatility. As the projection advances, parameter uncertainty becomes increasingly influential, accounting for 90.1% of variance by 2035 and reaching 97.2% by 2060. This indicates that long-term forecasts are chiefly constrained by imprecise estimates of decline rates and feedback effects. The sustained minimal contribution of model uncertainty across all years suggests that the structural specification of the model remains robust despite growing overall variance. Total variance rising from 2.87 in 2025 to 64.55 by 2060 further underscores the compounding influence of long-term parameter uncertainty on forecast dispersion.

Sensitivity results in Figure 10B indicate that baseline decline rates $\left({\delta }_{base}\right)$ apply the strongest influence on transition timing, where a faster decline accelerates the transition by approximately ten years. Stronger renewable feedback mechanisms $\left({\lambda }_{renew}\right)$ also accelerate coal reduction, thus advancing the transition by around five years. In contrast, economic mechanisms $\left({\phi }_{econ}\right)$ challenges and persistent GARCH volatility $\left({\beta }_{GARCH}\right)$ act as delaying forces, adding three and two years, respectively, to the transition timeline. This highlights the potential for structural constraints to offset progress generated by favourable energy trends. These findings illustrate that both technological and economic parameters shape transition dynamics, with certain uncertainties capable of materially slowing decarbonisation efforts over several decades.

Figure 10C reinforces this pattern by displaying widening fan chart confidence bands, where the 50%, 80% and 95% intervals steadily expand over time. Their widths multiply by factors of 4.59, 4.70 and 4.76, respectively, between 2024 and 2060. This widening confirms that long term projections experience faster than linear uncertainty growth. This is driven predominantly by the dominance of parameter sensitivity rather than random shocks. The close alignment of the mean and median paths suggests a largely symmetric outcome distribution. Even as dispersion increases substantially in later years.

Therefore, these outcomes collectively suggest that without significant changes in policy ambition, investment patterns or structural energy system conditions, long-term reductions in coal use are unlikely to meet internationally aligned climate expectations.

4.7. Transition Statistics and Probabilities Analysis

The results presented in Figure 11A–F offer a detailed picture of the uncertainty surrounding the expected timing of coal’s decline to below a 50% share of electricity generation. Figure 11A demonstrates that the most probable transition year clusters around 2045, with both the mean and median falling very close to this estimation. This appears to suggest strong central convergence across simulations. The simulations also reveal wide dispersion, as the earliest transition occurs in 2019 and the latest extends to 2079. Thus, indicating the sensitivity of coal decline to differing underlying conditions and external shocks.

Figure 11B provides additional insight by illustrating the empirical cumulative distribution function. This shows that only 3.6% of simulations reach the transition threshold by 2030, thus indicating that early transition scenarios remain highly improbable under existing conditions. The probability rises meaningfully by mid-century, reaching 72.5% by 2050 and nearly 96% by 2060. This then signals a strong long-term tendency towards coal decline despite early-phase uncertainty. Figure 11C highlights the decade-level clustering of transition probabilities. This shows that only 3.5% of outcomes occur during the 2020s, while the 2030s account for 24.1% and the 2040s for 44.7%, clearly identifying the 2040s as the most likely transition decade. These decade-level distributions demonstrate that mid-century remains the most plausible horizon for coal’s structural decline, with earlier or later outcomes becoming progressively less likely.

Figure 11D further shows that the standard deviation of 8.3 years highlights substantial uncertainty associated with predicting the precise transition year, demonstrating that long-term structural change remains highly variable under current trajectories. The confidence intervals reinforce this variability, since the 50% interval from 2039.4 to 2050.6 spans more than a decade. Whereas the 90% interval from 2031.4 to 2059.1 expands to nearly three decades, indicating substantial tail risks at both ends of the transition window. Figure 11E,F visually illustrate how uncertainty broadens as the forecast horizon extends. These figures illustrate how small early differences across simulations later compound into substantially divergent trajectories. The widening spread of simulated lines in Figure 11F shows how random shocks can either accelerate or delay coal reduction. Thereby affecting when the 50% threshold is crossed relative to the deterministic baseline year of 2063. The median pathway reflects a central estimate. Yet, the dispersion of individual trajectories underscores how sensitive transition timing remains to external fluctuations.

4.8. Analysis of Policy Scenarios: Synergies and Accelerated Pathways for Climate Targets

4.8.1. Policy Scenario with Synergistic Effects Discussion

The policy scenario analysis, as highlighted in

Table 11. Results of Policy Scenario with Synergistic Effects.

Scenario	Scenario: No New Policy (m = 0.0)	Scenario: Moderate Implementation (m = 0.5)	Scenario: Full Implementation (m = 1.0)	Scenario: Aggressive Implementation (m = 1.5)
Linear impact	0.0000 pp/year	0.3050 pp/year	0.6100 pp/year	0.9150 pp/year
Synergistic impact	0.0000 pp/year	0.0044 pp/year	0.0174 pp/year	0.0392 pp/year
Total policy impact (Δδ)	0.0000 pp/year	0.3094 pp/year	0.6274 pp/year	0.9542 pp/year
Effective decline rate (δ_scenario)	0.5000 pp/year	0.8094 pp/year	1.1274 pp/year	1.4542 pp/year
Deterministic transition year	2084	2060	2050	2044
Synergy contribution	0% of total impact	1.4% of total impact	2.8% of total impact	4.1% of total impact
Acceleration factor vs. baseline	1.00×	1.62×	2.25×	2.91×
Years saved vs. no new policy	-	23.5 years	34.2 years	40.3 years

Source: Authors own computation.

, illustrates how progressively stronger climate policy ambition significantly accelerates South Africa’s coal transition by altering the annual decline in coal’s energy share. The scenarios vary through a policy multiplier that consistently influences the pace of decline. Consequently, demonstrating that policy design directly shapes transition speed. The results also indicate that policy instruments generate predominantly linear effects. Although modest synergistic interactions begin to emerge when ambition is increased across the full policy package.

The baseline scenario reflects a slow and prolonged transition, with coal declining by only 0.5% per year and the system not fully transitioning until 2084. This highlights the insufficiency of current trajectories. Moderate ambition strengthens the annual decline to 0.81%, bringing the transition forward to 2060. This demonstrates the substantial effect of coordinated but still modest interventions. The full implementation scenario further increases the decline to 1.13%, enabling a transition by 2050. Thereby revealing how comprehensive policy adoption can generate meaningful acceleration in transition. The aggressive policy scenario results in the most rapid shift, pushing the decline rate to 1.45% and advancing the transition to 2044. Thus, demonstrating the transformative potential of high ambition strategies.

Therefore, across all scenarios, linear policy effects remain the strongest drivers of change. But synergistic gains grow as ambition intensifies, rising from 1.4% under moderate ambition to 4.1% in the aggressive case. These findings indicate that while individual policy measures contribute to change, integrated policy packages generate enhanced outcomes, particularly when deployed at scale. The results, therefore, emphasise the importance of coherent, ambitious, and mutually reinforcing climate policies capable of accelerating the coal transition by nearly threefold compared with the baseline trajectory.

4.8.2. Acceleration Pathways for Climate Targets Analysis

The results presented in Figure 12 reveals how different acceleration pathways shape the long-term decline of coal’s share within the energy system. The four pathways illustrate linear, exponential, step change, and logistic dynamics. Each pathway reflects contrasting assumptions about policy strength and market transformation. The figure is divided into two sections, with the upper panels showing required decline rates for specified policy targets and the lower panels demonstrating how coal’s share evolves under each dynamic pattern.

The analysis of the upper section (Figure 12A–D) indicates that the annual decline rates required for the 2040, 2050, and 2060 targets significantly exceed the capabilities of all four acceleration patterns. For example, the 2040 scenario demands an annual decline of 1.18%, which is more than twice the historical baseline trend. Even the more adaptive exponential and step change patterns fail to reach this threshold, thus highlighting the scale of acceleration required. Similarly, the 2050 and 2060 targets require annual reductions of 0.74% and 0.54%, respectively. These outcomes also lie beyond the achievable range of these dynamics. As a result, these findings suggest that earlier decarbonisation goals rely on deep and early structural interventions rather than modified trajectory shapes.

The bottom section (Figure 12(Aa–Dd)) presents how coal’s share would evolve under each dynamic pathway when aiming for the 2070 target. This target requires a more moderate annual decline of 0.43%. All four patterns reach this threshold by approximately 2066, showing that the target is feasible under current transition dynamics. The convergence of the pathways around this date demonstrates that altering the decline pattern alone cannot compensate for insufficient overall reduction rates. Instead, the results emphasise that reaching ambitious interim targets requires accelerated action well beyond baseline trends.

Therefore, shifting the shape of the transition is insufficient without substantial increases in the pace of decline. Ambitious early objectives such as the 2040 and 2050 targets require bold, sustained commitments that exceed historical patterns, whereas the more distant 2070 target remains broadly attainable under a wide range of future dynamics.

4.9. Global Sensitivity Analysis

The findings from the sensitivity analysis revealed how uncertainty in key parameters influences the projected timing of the global coal transition. Figure 4 shows that the model’s behaviour is shaped primarily by three parameters. Namely the base decline rate (δ), the volatility (σ) in annual coal share changes, and the transition threshold (θ) that marks the shift point. The results indicate that each parameter contributes differently to the model’s sensitivity, thereby affecting the stability and reliability of long-term transition forecasts. Figure 13A demonstrates that the base decline rate put forth the strongest influence on the timing of the transition. This is because its elasticity value of 1.200 indicates a highly responsive model. This suggests that even minor changes in the assumed decline rate can significantly shift the projected timing. The importance of this parameter implies that achieving clarity on long-term structural decline trends is essential for producing credible forecasts, particularly in policy contexts that rely on long-horizon planning.

Figure 13B highlights the impact of volatility, which captures unpredictable fluctuations resulting from economic shocks, policy changes, or energy market disruptions. With an elasticity of 0.80, volatility introduces moderate sensitivity, widening the range of possible transition years. This broadening reduces the precision of forecasts, thereby lowering confidence in central estimates. Hence, improving the management or understanding of volatility could therefore enhance the predictability of transitional outcomes. Figure 13C shows that the transition threshold contributes the least influence, demonstrated by its elasticity value of 0.50. Although adjustments to the threshold slightly alter the projected transition year, the overall effect remains limited when compared with the other parameters. This indicates that the precise definition of the transition point is important but not decisive for long-term modelling.

Figure 13D uses a spider plot to visually compare the elasticities. This affirms the dominant role of the base decline rate in shaping model outputs. The figure clearly illustrates that the model responds most strongly to structural decline speed, followed by volatility, and finally the threshold level. This visual evidence reinforces the interpretation that improving empirical accuracy about decline rates would significantly reduce uncertainty. Figure 13E ranks the parameters by influence, again placing the decline rate first, volatility second, and threshold third. The ranking helps identify priority areas for empirical research, suggesting that better estimates of decline rates would offer the greatest improvements in model reliability. For this reason, efforts to reduce volatility could also produce more stable and interpretable projections. Finally, Figure 13F provides an overall robustness assessment. This figure shows that the model maintains moderate sensitivity through its highest elasticity value of 1.200. This means that although the model responds noticeably to parameter changes, it does not behave in an excessively fragile manner. Therefore, continuous monitoring of parameter evolution remains important for maintaining confidence in long-term forecasts, particularly for policy making and strategic planning.

4.10. Diagnostics Test Analysis

This section discusses the results of historical back-testing (HBT), Markov Chain Monte Carlo (MCMC) convergence diagnostics, and cross-system consistency checks for our forecasting model.

The combined evidence from the back-testing assessment and predictive performance evaluation indicates that the forecasting model performs robustly across multiple diagnostic measures. The historical back testing (see Figure 14A) results revealed how the model behaves when confronted with previously observed data. These findings are reinforced by the convergence diagnostics, which suggest that the Markov Chain Monte Carlo (MCMC) procedure functioned reliably throughout the estimation process. Thus, ensuring that subsequent inferences remained stable and appropriately representative of the underlying parameter space.

The predictive accuracy metrics further demonstrate the model’s strong alignment between predicted and actual coal shares (see Figure 14C). They offer clear evidence of dependable performance during the test period. The mean absolute percentage error (MAPE) of 4.40% suggests that the forecasts remained consistently close to observed values (see Figure 14B). Thereby, validating the model’s capacity to track short-term fluctuations with reasonable precision. The supporting statistics, including the mean absolute error of 2.99% and the root mean square error of 3.69, highlight similarly small deviations. Observed together, these collectively confirm the credibility of the model’s numerical outputs across the assessment window.

The forecast bias of −2.99% indicates a slight but manageable tendency to underestimate outcomes. This suggests that future refinements may aim to reduce this small directional skew while preserving overall accuracy. Importantly, the behaviour of the prediction intervals demonstrates that the model’s uncertainty quantification is well calibrated. Thereby enhancing trustworthiness in long-term projections and risk assessments. The 90% interval successfully captured 92.3% of actual results, while the 50% interval captured 53.8%. Thus, illustrating a close correspondence between nominal and empirical coverage levels. These proportions indicate that the uncertainty bands meaningfully reflect real-world variation, which provides valuable guidance for interpreting the stability of future coal share trajectories.

Therefore, the combined diagnostics in Figure 14 from HBT, MCMC convergence evaluation, and predictive performance metrics illustrate a model that not only fits past data effectively but also generalises well within the assessment period. This convergence of evidence demonstrates reliable construction, sound uncertainty calibration, and credible forward-looking behaviour. Thus, making the model suitable for applications requiring dependable projections of coal sector dynamics.

In addition,

Table 12. Geweke Parameter Estimation Convergence Results.

Parameter	Z-Score	Early Mean	Late Mean	Converged? (Yes/No)
Drift (δ)	−0.199	−0.4942	−0.4896	Yes
Volatility (σ)	0.379	1.1989	1.1927	Yes
Mean Reversion (α)	−2.978	0.134	0.2994	No *
Long-term Mean (μ)	−1.178	49.0193	49.8879	Yes
Jump Intensity (λ)	−1.365	0.0473	0.0486	Yes

Notes: * Z-score > |1.96| suggests lack of convergence at 95% confidence. Source: Authors’ own computation.

summarises the convergence diagnostics for the MCMC estimation of five key parameters in the stochastic coal transition model.

As a result, the convergence diagnostics provide important insights into the reliability of the parameter estimates generated by the stochastic coal transition model. Geweke test was applied to compare the early and late portions of each MCMC chain. This has allowed the assessment of whether the sampling process achieved a stable representation of the posterior distribution. As a result, four of the five estimated parameters demonstrated satisfactory convergence, indicating that their chains mixed well and provided credible posterior estimates suitable for model interpretation. The drift, volatility, long-term mean, and jump intensity parameters all displayed Z scores that remained within the accepted range. Thus, suggesting that their early and late sample means were sufficiently similar to meet the diagnostic threshold. These results strengthen confidence in the stability of most model components, thereby supporting their use in forecasting and scenario analysis within the transition modelling framework.

However, the mean reversion parameter did not satisfy the Geweke criterion. This is evident by a Z score that exceeded the established cut-off used to judge convergence reliability. This outcome implies that the chain associated with mean reversion may have suffered from inadequate mixing or insufficient sampling length, which ultimately prevented it from settling into a stable posterior distribution. We acknowledged that the lack of convergence for this parameter introduces some level of uncertainty into the interpretation results. Because these results discussed in this study relied to a certain extent on the mean reversion mechanism, which may affect the robustness of specific model dynamics. Future research may address this issue by methodological adjustments, such as extending the chain length or refining the sampling procedure. This may possibly allow the model to better capture the behaviour of this parameter. Despite this limitation, the overall diagnostic results indicate that most model elements were estimated successfully, providing a generally strong foundation for analysing the coal transition pathway represented by the stochastic framework.

5. Conclusions and Policy Recommendations

This study sought to forecast when coal would lose its dominance in South Africa’s electricity generation. The study bridged a critical gap in understanding the rate and timing of coal’s decline. South Africa’s energy economy is still heavily reliant on coal and emits high levels of carbon dioxide. Coal currently dominates electricity production, significantly increasing national carbon emissions and climate vulnerability. The study sought to predict when coal’s share of electricity generation would drop below 50%. This threshold represents a symbolic and practical shift towards a cleaner, more sustainable energy system. The study used historical trend analysis, structural break detection, Bayesian inference, and Monte Carlo simulations. It also used policy scenario modelling to determine how various interventions affect transition speed. The findings show that coal’s share has decreased since the REIPPPP’s launch in 2011. However, the decline is slow and insufficient to meet South Africa’s climate and development targets. Under current trends, coal will remain dominant well beyond 2040, delaying meaningful decarbonisation.

5.1. Key Summary Findings

This study has shown that South Africa’s energy transition is shaped by interconnected theoretical, institutional, and empirical dynamics that influence how coal reliance evolves over time. The analysis demonstrated that energy transitions unfold through sequential and uncertain decisions shaped by historical constraints, technological change, and policy incentives, which were operationalised through a unified Bayesian forecasting framework. This model allowed the study to embed path dependence, adaptive decision-making, and policy-responsive technological evolution in order to understand transition trajectories more realistically. The empirical findings established a clear structural break in 2011. This marks the moment when coal dependence shifted from slow growth to steady decline due to major policy intervention. This shift confirmed that policy action plays a decisive role in redirecting long-term energy pathways, particularly in systems characterised by infrastructure lock-in and powerful incumbents.

The study’s empirical metrics further revealed that coal’s share has declined at an average annual pace too slow to meet climate goals within required timeframes. The descriptive statistics and volatility measures demonstrated that the transition process is neither linear nor stable, with year-to-year variations reflecting economic shocks, governance conditions, and renewable energy dynamics. Stochastic modelling showed that volatility clusters over time, increasing uncertainty and complicating long-term planning for policymakers and investors. These dynamics underline the importance of recognising path dependence, which continues to slow the transition despite falling renewable costs and technological advancements.

The study also highlighted that renewable energy expansion and economic factors interact strongly with coal use. Thus, confirming that increases in renewables are consistently associated with reductions in coal consumption. Correlations between governance quality and coal reliance further emphasised that stronger institutions support cleaner energy investments and more effective policy delivery. This is consistent with broader literature showing that governance capacity, stable regulation, and multi-level coordination substantially reduce transition volatility and improve investor confidence.

The study’s scenario and policy synergy modelling showed that coordinated policy portfolios can significantly accelerate the annual decline of coal’s share when implemented comprehensively rather than individually. This finding aligns with evidence that coherent policy mixes that can combine renewable support, carbon pricing, regulatory constraints, and innovation incentives generate more rapid decarbonisation than isolated instruments. The integrated modelling framework also confirmed that advanced forecasting approaches, including stochastic simulations and scenario analysis, provide more reliable guidance for planning by explicitly representing uncertainty and identifying transition inflection points.

Overall, this study concludes that South Africa’s coal to clean energy transition can accelerate only through a combination of strong policy signals, technological scaling, institutional strengthening, and socially inclusive strategies. The evidence indicates that no single mechanism is sufficient, and that sustained progress depends on aligning governance capacity, economic conditions, and coordinated policy action to shift long-term energy trajectories more decisively. The analytical results demonstrated that reducing coal reliance is possible but requires ambitious, early, and coordinated measures. These combined measures can address both technical uncertainties and deeply embedded structural barriers.

5.2. Policy Recommendations

The policy recommendations proposed in this study collectively underline the urgent need for a more coherent and ambitious framework that can accelerate South Africa’s energy transition while reducing long-standing uncertainties.

The analysis emphasises that clear and consistent long-term policy signals are essential, because these signals directly influence investor expectations and help lower perceived political risks associated with large scale renewable projects. Hence, as the first policy recommendation, publishing an updated Integrated Resource Plan with binding coal decommissioning schedules and explicit post 2030 procurement targets would therefore provide a stable foundation for planning and investment decisions. Legislated commitments are especially important, since statutory obligations can reduce the likelihood of policy reversals during future political cycles and thereby support sustained investor confidence.

A second recommendation relates to institutional reform. That is, the creation of an independent energy transition regulator with responsibility for overseeing implementation across multiple administrations. Such a regulator would help ensure continuity, improve transparency, and reinforce accountability. Thereby enabling a more predictable environment for private sector participation over the long term. Hence, enhancing regional cooperation is also identified as a strategic priority. Because regional power pool integration and cross-border transmission investment can strengthen system reliability while lowering overall system costs. This regional approach could allow South Africa to export surplus renewable electricity and import power during shortages, and thus supports a more flexible and resilient energy system.

Domestically, the third recommendation calls for urgent electricity market reform to allow competitive procurement of flexible services. This includes demand response and battery storage, which support the integration of variable renewable generation. A flexible grid reduces dependence on ageing coal infrastructure. Thereby facilitating a smoother and more economically efficient transition. The study further argues that South Africa’s current trajectory is incompatible with the Paris Agreement, making the establishment of a formal commitment to end coal use by 2040 both necessary and feasible under the proposed policy scenario. Therefore, achieving this target requires a tripling of the annual coal decline rate, coupled with full implementation of all recommended measures.

As the last policy recommendation, governance reform is highlighted through the proposed creation of a Climate Action Committee within the Office of the Presidency. This committee should be mandated to track progress and provide annual public reporting on the 2040 roadmap. This mechanism would help maintain political focus, strengthen public trust, and ensure consistent monitoring of transition outcomes.

5.3. Limitations and Future Research

While the modelling framework applied in this study accounts for policy uncertainty, economic shocks, governance effects, and the stochastic dynamics of coal displacement. It ignores several real-world physical and operational constraints found in actual electricity systems. As previously stated, the model implicitly assumes that renewable energy is perfectly dispatchable and seamlessly integrated into the electricity grid. Thus, replacing coal on an annual basis with no system balancing, operational reserves, or curtailment. In practice, wind and solar output are highly variable. For instance, hydropower is limited by rainfall and drought cycles. The system relies on firm capacity, storage technologies, and demand side flexibility to ensure reliability.

Similarly, the model does not account for transmission bottlenecks or spatial grid constraints. Despite the fact that South Africa’s best renewable resources are geographically separated from existing coal-based transmission infrastructure. Hence, excluding these constraints risks overstates the transition’s speed and smoothness. This happens if grid and storage investments lag behind renewable energy growth. For these reasons, future research should formally link the stochastic Monte Carlo framework to a technologically detailed capacity expansion or power system model that operates at hourly or sub-hourly resolution. Such an integrated approach would enable future studies to take into account dispatchability constraints, grid congestion, locational resource quality, storage requirements, and operational feasibility. This will result in transition timelines that better reflect the physical realities of South Africa’s electricity system.