Beyond emissions: a stochastic cusp-logit analysis of environmental cost regimes in BRICS

Abstract

Emerging economies suffer a huge economic burdens from environmental damage because most of the time we measure environmental damage using conventional emissions-based metrics. This study addresses this gap by introducing environmental cost (EC) as a novel measure that quantifies the economic burden of environmental degradation. The need for the new measurement stems from the requirement to examine the non-linear and asymmetric behaviors of the relationship between the environment and the economy in rapidly developing economies such as the BRICS countries in their transition from fossil fuels, their drive for new types of innovation, and their increased susceptibility to sudden changes in the cost of degradation due to energy transition, innovation-related pressures, and vulnerability to sudden changes. Therefore, stabilizing mechanisms such as Energy Transition, Innovation, Environmental Adaptability, and Trade in Low-carbon Technologies (TLCT) will reduce the possibility of experiencing high levels of Environmental Cost, while Environmental Vulnerability (EV) will heighten the probability of experiencing catastrophic regime shifts to high-cost, unstable states with sudden and extreme changes in costs. To accomplish this objective of validating the Cusp-Logit framework, a balanced panel data consisting of the BRICS countries (Brazil, Russia, India and South Africa) for the years 2015 to 2024 is used. The hybrid model of the Cusp-Logit framework consists of the geometrical layout of the Cusp Catastrophe model and a stochastic Logit transition mechanism that will capture the nonlinear regimes of the Cusp Catastrophe model and the dynamic persistence of costs associated with environmental degradation. Although empirical evidence points to the stabilizing effects of energy transition, innovation, environmental adaptability and TLCT on flattening the potential surface and reducing the possible occurrence & duration of high-cost regimes; EV creates a systemic tilt which increases the likelihood of a shift to an unstable/high-EC state. The cross-national analysis demonstrates that while China & India have stable innovation-based environments; Brazil, Russia & South Africa are much more susceptible to instability due to a limited ability to adapt to & utilize technology. Given that there is currently no comprehensive framework for understanding environmental performance in terms of costs; this work develops a new methodology for modeling the dynamic behaviors of asymmetrical regimes as well as understanding the transition probabilities between them. This provides an early warning system, which will assist BRICS policymakers to manage their exposure to environmental risks while moving towards developing sustainable pathways with low cost. Unlike conventional emission-based and linear approaches, the proposed framework captures nonlinear regime shifts, transition probabilities, and persistence of environmental cost dynamics, offering a scalable tool for policy design under uncertainty.

Introduction

The emissions-based indicator of environmental degradation is a myopic measure as it only captures the physical volume of pollutants released into the atmosphere [77]. The emissions-based indicators fail to capture the economic burden (losses) caused by resource depletion, air [30], water [24], and soil degradation [6], further declining the regenerative capacity of the ecosystem [60]. Public resources and policies are designed and deployed to protect the economy from negative externalities [106], such as environmental degradation [119]. The environmental cost (EC) offers a more comprehensive and economically meaningful measure of environmental degradation than traditional emission-based measures [27]. The EC internalizes these dimensions into a single monetary valuation framework, linking environmental damage directly to the productive and welfare capacity of an economy [37, 94]. The environmental cost can be measured by the economic value of natural resource depletion and environmental degradation, following the World Bank’s adjusted net savings framework and national accounting extensions for resource rents (World Bank Group, [117]). This measure allows policymakers to quantify environmental sustainability not merely as an ecological necessity but as a factor embedded within economic performance and long-term fiscal health [21, 91].

The assumed that environmental degradation responds smoothly and symmetrically to economic and policy measures, and that emission-based indicators are sufficient to capture these dynamics [35, 65, 74]. This assumption, though less pragmatic, underpins the widespread use of linear, cointegration, or threshold-based models that estimate average effects while presuming gradual adjustment toward equilibrium. However, environmental systems are inherently nonlinear and prone to abrupt shifts, particularly when economic, technological, and institutional constraints interact with ecological vulnerability [2, 118]. As a result, conventional emission-centric and linear modelling approaches may systematically underestimate instability, persistence, and sudden escalations in the economic cost of environmental degradation.

This study integrates three key dimensions to address the identified gaps. First, it conceptualizes environmental degradation as an economic cost affecting macroeconomic resilience, rather than solely as a physical pollution outcome. Second, it models environmental cost dynamics as inherently nonlinear, characterized by regime shifts between low- and high-cost states instead of smooth adjustments. Third, it incorporates cross-country heterogeneity in energy structures, innovation capacity, and institutional adaptability. Building on these elements, the study adopts a stochastic regime-based framework to examine how environmental cost regimes emerge, persist, and transition across emerging economies.

The Brazil, Russia, India, China, and South Africa (BRICS) economies provide an analytically relevant setting for examining environmental cost dynamics in emerging economies. While these countries collectively account for a substantial share of global population and economic activity, they are characterized by pronounced heterogeneity in energy structures, innovation capacity, environmental vulnerability, and institutional adaptability [79]. This diversity within a shared emerging-economy context makes the BRICS group particularly suitable for analyzing nonlinear, regime-dependent environmental cost dynamics, where common global shocks coexist with heterogeneous national responses [95, 112, 113].

Trade has historically played a crucial role in addressing global challenges [82]. Even when confronted with environmental issues, trading in low-carbon technologies (LCT) enables countries to meet their sustainability goals [14, 75]. LCT facilitates the spread of technology and the transfer of knowledge, leading to faster adoption of cleaner and more efficient production methods domestically [7, 92]. Additionally, LCT trade enhances national resilience to climate and environmental risks by reducing reliance on carbon-intensive resources [61]. Furthermore, LCT trade strengthens the connection between innovation systems and adaptive capacity, allowing technology to serve as the mechanism through which economies can shift from high-cost environmental practices to more stable, low-cost approaches [92]. Consequently, the spread of low-carbon innovations acts as both an economic and environmental stabilizer, reducing volatility while encouraging structural transformation.

The behavior of environmental cost is not linear; increases and decreases are more asymmetric [58]. The reduction in environmental costs is rather more gradual than its abrupt increase due to structural and environmental vulnerability [23]. Such asymmetric changes suggest that linear econometric models do not estimate environmental cost [44, 101]. Although there are non-linear econometric models that measure asymmetry through threshold or non-linear regressions [70], they remain primarily confined to trend-based cause and effect estimation and fail to capture the deeper dynamic mechanisms through which environmental costs emerge and transition between distinct regimes [107, 108].

This current study goes beyond the conventional uni-model approach by applying a stochastic physics–inspired modelling framework. The study employs a hybrid Cusp-Logit (Kramers–Logit) model to estimate the environmental cost as a function of curvature and tilt parameters, characterizing a potential surface (D.-G. Chen et al., [26], Mel’nikov, [80], Broeck, [110]. These parameters represent the stability and directional asymmetry of the cost system. Within this geometry, energy transition (ET), innovation (INNOV), environment adaptability (ED), and trade in low-carbon technology (TLCT) act as stabilizing forces that flatten the potential surface. In contrast, environmental vulnerability (EV) introduces tilt, increasing the likelihood of a shift toward the high-cost regime [8]. The subsequent logit layer translates this structural geometry into transition probabilities, quantifying the dynamic persistence and recovery rates between stable and unstable states.

The pollution-based measure, in terms of emissions alone, only captures pollution volumes without reflecting the underlying economic loss. These approaches provide limited insight into the economic cost of environmental degradation and overlook the possibility that environmental performance evolves through asymmetric, regime-dependent dynamics. As a result, there is insufficient understanding of how environmental costs persist, escalate, and recover over time, particularly in emerging economies facing structural and institutional constraints.

This study offers a distinct contribution to the environmental economics literature by advancing both measurement and methodology. First, it shifts the analytical focus from conventional emission-based indicators to a cost-based framework, capturing the economic burden of environmental degradation and directly linking ecological stress to macroeconomic resilience. Second, it introduces a novel stochastic Cusp-Logit (Langevin-Kramers-Logit) framework that integrates nonlinear stability dynamics with probabilistic regime transitions. Unlike existing nonlinear or threshold models that capture asymmetry in a static or trend-based manner, the proposed framework explicitly models how environmental systems evolve across multiple equilibria, quantifies transition probabilities between regimes, and estimates their persistence over time. Third, the framework generates policy-relevant early-warning signals by identifying conditions under which economies are likely to shift into high-cost environmental states. By combining economic valuation with dynamic regime analysis, the study provides a scalable analytical tool applicable beyond BRICS economies, thereby enhancing its relevance to a broader sustainability and policy audience.

Literature review

The theoretical foundation of environmental costs is rooted in the classical concept of negative externalities, which shows how these externalities lead to market inefficiencies and the overexploitation of natural resources [16, 111]. Environmental degradation is an outcome of pollution, resource depletion, and biodiversity loss, which leads to negative externalities in modern economies [42]. The policymaker often ignores the social costs of environmental damage, leading to a divergence between the private and social optima.

The ‘Pigovian’ taxes help correct externalities by internalizing the associated costs [69]. Nevertheless, in cases of environmental degradation, policymakers rely on emission permits or environmental regulations to internalize these costs [28]. However, such an approach also relies on flow-based indicators, such as CO₂ emissions or particulate matter concentrations, which fail to account for the cumulative depletion of natural capital and the loss of ecosystem resilience [22, 93]. The environmental cost (EC) approach extends this framework by monetizing the depletion of natural resources and environmental degradation, as the economic value of natural resource depletion and environmental degradation (% of GNI) (World Bank Group, [117]). The EC internalizes the social cost into national accounting systems, thereby transforming ecological performance into a macroeconomic concern [72]. This theoretical lens establishes the foundation for the present study, in which environmental costs are analyzed not as a static accounting identity but as a dynamic system influenced by technological, institutional, and trade-related factors.

Energy transition (ET)

There is a plethora of studies that have found that the transition from non-renewable to renewable energy sources is one of the most important factors in environmental performance [15, 47, 84]. Studies like [114] and [105] highlight that increased renewable energy consumption helps reduce environmental degradation, and they also found a relationship between clean energy and economic growth (also see, [31, 41, 59]. Studies conducted in the BRICS context also assert that the energy transition improves the ecological footprint [46, 66, 71]. However, the most significant challenges they face are fossil fuel-based industrial infrastructure and policy asymmetries [29]. Similarly, [96] observe that renewable energy expansion lowers ecological footprints, yet the outcomes differ depending on institutional readiness and policy enforcement (see, (Yuxin [124, 125]).

Recent research extends this line of inquiry by integrating energy transition with innovation and policy factors ([102]; M. Zhang et al., [124], but most models remain linear and emissions-based. The main gap is the lack of cost-based, dynamic treatment; existing studies do not capture how energy transition affects the stability curvature of environmental cost regimes over time. This paper extends that scope by quantifying how energy transition reshapes the potential landscape of EC, thereby determining the persistence and resilience of low-cost equilibria in BRICS economies.

Innovation (INNOV)

Innovation plays a pivotal role in reducing environmental degradation through technological advances in clean energy and carbon capture [2, 3, 85]. Technological innovation in renewable energy increases ecological efficiency by optimizing processes that reduce dependence on polluting processes [9, 13, 38]. Popp (2019) identifies a long-run relationship between innovation and environmental performance, while [32] found similar results that innovation leads to improvement in emission intensity and competitiveness. In developing regions, [57] found that innovation (measured by patents in clean technology) is effective in lowering pollution intensities. The studies in similar lines in the BRICS context also assert that innovation in renewable technologies enhances long-term energy efficiency and reduces carbon intensity ([17, 90, 96]; M. Zhang et al., [124]. At the same time, [68] and [54] found that domestic innovation capacity amplifies the impact of foreign green technologies through diffusion effects (also see, [63, 99]. However, most empirical frameworks treat innovation as a deterministic driver rather than a stabilizing mechanism. The missing link lies in assessing how innovation alters the potential geometry of environmental costs, flattening their curvature and lowering the probability of regime shifts. The present study captures this stabilizing effect within a stochastic potential structure, where innovation acts as a damping force against environmental instability.

Environmental vulnerability (EV) and adaptability (ED)

Environmental vulnerability refers to an economy’s exposure, sensitivity, and adaptive limitations to environmental shocks [4]. Some contributing factors to the vulnerability include poor governance and socio-economic fragility [55, 97]. Studies such as [83] further define the compounding effect of hazard exposure on adaptive capacity. Empirical studies such as those by [122] and [104] show that greater vulnerability correlates with lower ecological efficiency, weaker institutions, and higher adaptation costs. In BRICS economies, environmental vulnerability manifests through industrial dependence on non-renewable resources, [43] inefficient disaster management systems, and varying levels of institutional robustness [36, 67]. The existing literature treats vulnerability as an exogenous variable, rather than an endogenous tilting force that destabilizes environmental dynamics.

Environmental Adaptability is the economy’s ability to adapt to environmental and climatic changes through policy, institutional, and technological agility [12]. Studies such as [115] identify adaptive capacity as a determinant of long-term sustainability. Similar studies [109] and [45] link adaptive governance and infrastructure to improved resilience and lower ecological vulnerability. In BRICS nations, [1] demonstrate that institutional quality and adaptive governance help reduce environmental risk and maintain ecological balance. The current studies treat environmental adaptability as a static moderator in regression analyses, failing to capture its systemic role in stabilizing environmental cost trajectories.

Trade in low carbon technology (TLCT)

Trade in low-carbon technologies (LCT) plays a critical role in helping countries achieve environmental sustainability through technology exchange [40, 98]. Studies found that international trade in LCT enhances domestic innovation, lowers emission intensity, and accelerates the transition to cleaner production structures [11, 33, 53, 116]. The technology transfer through LCT imports drives the improvements in green total factor productivity, particularly in emerging markets ([5]; H. Zhang et al., [122]. In the BRICS context, [25] and [81] also found that engagement in trade and innovation fosters technological learning and facilitates the development of domestic innovation ecosystems (also see, [99, 120]). Nevertheless, empirical work has primarily concentrated on the trade-innovation-environment nexus, without examining how LCT trade contributes to the structural resilience of environmental systems.

Recent studies increasingly document that environmental and energy systems exhibit nonlinear, heterogeneous, and region-specific dynamics, particularly in the presence of technological change, resource constraints, and policy uncertainty ([88] a; [86, 88]). Empirical evidence highlights the role of energy transition, innovation, and governance-related factors in shaping sustainability outcomes, while also revealing asymmetric responses and threshold effects across countries and sectors ([88] b; [86, 87]). Further the some of the recent sustainability research demonstrates that environmental and energy outcomes are shaped not only by technological progress but also by institutional quality, economic structure, and governance arrangements [50, 52]. Evidence shows that democratic institutions, economic complexity, supply-chain transformation, and climate vulnerability significantly influence low-carbon energy adoption, energy intensity, and sustainability performance across countries ([50]; Işık, Ongan, Kuziboev, Turayev, et al., 2025; [50]). Parallel studies employing ESG and ECON-SG frameworks highlight the joint role of economic resilience, governance quality, and climate policy uncertainty, often revealing asymmetric and nonlinear effects on environmental sustainability [49, 50, 51]. However, despite these advances, the literature largely relies on emission or intensity-based indicators and linear or quasi-linear frameworks, leaving the economic cost dimension of environmental degradation and its regime-dependent dynamics insufficiently explored.

Some evident gaps in the existing environmental economics literature are in the dominance of emission-based indicators as proxies for environmental degradation. Previous studies assess environmental degradation using metrics such as CO₂ emissions, ecological footprint, or pollution indices, which capture the physical outputs of degradation but fail to account for its economic costs or the burden it imposes on national resource wealth. Such flow-based metrics overlook the cumulative depletion of natural resources and the loss of the ecosystem, both of which directly affect economic stability. Consequently, the actual financial dimension of environmental degradation, its translation into environmental cost, remains underexplored, leaving a gap between environmental valuation and macroeconomic policy relevance. Furthermore, the existing literature also fails to account for how environmental costs evolve as a dynamic, regime-dependent process. In particular, existing research does not explain how policy-relevant factors such as energy transition, innovation, environmental vulnerability, environmental adaptability, and LCT trade jointly influence the probability of transitioning between low and high environmental cost regimes, and the expected duration that economies spend in each regime. The absence of such dynamic, probabilistic analysis limits understanding of how environmental systems respond to shocks and policy interventions over time.

In light of these gaps, the present study addresses the following research problem: how do environmental costs evolve as a nonlinear, regime-dependent process in emerging economies, and what factors determine the stability and persistence of high- and low-cost environmental regimes? Specifically, the study asks: (i) how do energy transition, innovation, environmental vulnerability, environmental adaptability, and trade in low-carbon technologies influence the stability structure of environmental cost regimes; and (ii) how do these factors affect the probability and expected duration of transitions between high- and low-cost environmental states in BRICS economies?

Methodology

The study uses annual panel data of the five BRICS economies (Brazil, Russia, India, China, and South Africa) for 2015 to 2024. All variables are compiled from internationally recognized and publicly available databases, as detailed in Table 1. Environmental cost and related indicators are drawn from global environmental–economic accounting sources, while data on energy transition, innovation, environmental vulnerability, environmental adaptability, and trade in low-carbon technologies are obtained from established international statistical repositories. Prior to estimation, all series are standardized to ensure cross-country comparability and aligned on a common temporal scale. This standardized data construction ensures consistency and reliability in the empirical analysis.

Table 1 presents the components of the variables used. The environmental cost (EC) captures the monetary value of environmental degradation arising from natural resource depletion and ecosystem damage. Energy transition (ET) reflects shifts toward cleaner energy structures, while innovation (INNOV) represents technological capacity relevant to sustainability outcomes. Environmental vulnerability (EV) measures exposure and sensitivity to environmental risks, whereas environmental adaptability (EA) captures institutional and economic capacity to respond to environmental stress. Trade in low-carbon technologies (TLCT) reflects cross-border diffusion of clean technologies. Together, these variables capture the economic, technological, and structural dimensions shaping environmental cost dynamics in BRICS economies.

Table 1.

Data description and sources

Variable	Presentation	Description	Source
Dependent variable
Environmental cost		Description: Economic value of natural resource depletion and environmental degradation (% of GNI); dependent variable representing total environmental burden. For country i at time t.	World development indicators, world bank
Independent variables
Energy transition		Description: Share of renewable energy in total final energy consumption (%).For country i at time t.	World development indicators, world bank
Innovation		Description: Number of patents filed in clean energy and carbon capture & storage (CCS) technologies per year. For country i at time t.	IRENA - INSPIRE Platform (2023-24)
Environmental vulnerability		Description: Composite index of exposure and sensitivity to climate and ecosystem risk. For country i at time t.	ND-GAIN index. International monetary fund climate change dash board.
Environmental adaptability		Description: Adaptive capacity index measuring institutional and technological readiness. For country i at time t.
Trade in low-carbon technologies		Description: Value of exports and imports of low-carbon technologies. For country i at time t.	International monetary fund climate change dash board.

Compiled by author and retrieved from: https://climatedata.imf.org/pages/go-indicators#gp1; https://databank.worldbank.org/source/world-development-indicators ; https://gain.nd.edu/our-work/country-index/download-data/ ; https://databank.worldbank.org/source/world-development-indicators (Retrieved on: 30 September 2025)

The BRICS economies, beyond their economic and environmental relevance, are a model sample for the analysis. BRICS economies also exhibit substantial cross-country heterogeneity, yet share emerging-economy characteristics. This combination enables the stochastic Cusp-Logit framework to capture nonlinear regime behavior, asymmetric stability, and transition dynamics across diverse policy and structural conditions within a comparable setting. While the empirical analysis focuses on BRICS economies, the environmental cost-based framework and regime-dynamic insights are generalizable. Moreover, other emerging economies facing similar growth and environmental trade-offs can apply the methodology or build upon the insights of this study.

Model

To model environmental cost dynamics beyond conventional emission-based approaches, this study employs a novel hybrid stochastic Cusp-Logit framework grounded in nonlinear physics (D.-G. Chen et al., [26]. Rather than assuming smooth adjustment toward a single equilibrium, the model recognizes that environmental and energy systems often evolve through abrupt, noise-induced regime shifts. The stochastic cusp component represents environmental cost as a stability landscape with two competing equilibria, low-cost (sustainable) and high-cost (pollution-intensive) regimes [73], while the logit-based Hidden Markov extension quantifies the probability of transitions between these regimes (D.-G. Chen et al., [26, ], Mel’nikov, [80, ], Broeck, [110]. This structure allows the analysis to capture both the intensity of environmental cost dynamics within each regime and the likelihood of shifts across regimes. As a result, the framework enables simultaneous estimation of (i) within-regime effects of energy transition (ET), innovation (INNOV), environmental adaptability (EA), environmental vulnerability (EV), and trade in low-carbon technologies (TLCT), and (ii) between-regime transition probabilities that govern long-run environmental resilience in BRICS economies.

By integrating the stochastic cusp model with a dynamic logit mechanism, the methodology unifies the deterministic potential of physics with the probabilistic structure of econometrics, providing a coherent lens to evaluate how structural forces reshape the stability of environmental costs in emerging economies [10]. The Eq. 1 stochastic differential equation of the normalized environment cost for country i for year t.

1

Where, is a Wiener process representing random environmental and economic shocks; any change in the environment cost as a sum of deterministic drift components and stochastic. The drift term generates double-well (two regimes), high environment cost and low environment cost. The coefficients and are control parameters shaping the curvature and tilt of the surface (environment cost). Equation 2.1 and 2.2 present the control parameters as a function of explanatory variables. Whereas Eq. 2.3 presents (diffusion amplitude), reflecting the intensity of random fluctuations in environmental costs.

2.1

2.2

2.3

Where presents the vector of covariates; the multiple equilibria is controlled by and positive change in variables such as ET, INNVO, TLCT and EA will make the system stable; captures the directional tilt and positive change in ET, INNVO, TLCT and EA will show a shift toward a low-cost regime; estimates heteroscedasticity and the exponential specification ensures that environment vulnerability amplifies volatility ( and environment adaptability () reduces it. The Eq. 1 to 2.3 establish a cusp deterministic and stochastic structure. This study uses annual data for the BRICS panel; the continuous time stochastic dynamics in Eq. (1) are discretized (by Euler-Maruyama approximation). Equation 3 transforms the theoretical stochastic differential (Eq. 1) into a panel specification that preserves the cubic nonlinearity and the noise-driven structure of the original model.

3

where, the; captures unobserved country-specific effects such as institutional and structural heterogeneity across BRICS economies; is deterministic drift; is state specific diffusion.

The nonlinear cubic structure of the stochastic cusp model allows the evolution of environmental cost to be represented through a stability potential function, rather than describing physical energy, this potential surface reflects the relative stability or instability of environmental cost levels under varying conditions of ET, INNOV, EV, EA, and TLCT. Equation 4 presents the stability potential.

4

where the quartic term bounds the environment cost to the stable domain (even under large shocks); the quadratic term determines the number of stable equilibria: when is large and positive, the potential surface develops two minima representing a low-cost (sustainable) and a high-cost (pollution-intensive) regime; the linear term estimates the tilt in the environment cost, shifting the relative depth of the two regimes depending on the variables. When the ET, INNOV, TLCT is expected to tilt the environment cost toward the low-cost equilibrium, while high environmental vulnerability (EV) biases it toward the high-cost state. Equation 5 is the stationary state.

5

The stable equilibria (Eq. 5) can also shift to a high (H) environment cost regime or low (L) environment cost regime or the barrier (B) i.e., unstable threshold separating them. The stability of each regime can be estimated by the barrier matrix. The Eq. 6.1 and Eq. 6.2 presents the difference function between stable equilibria and cost regimes.

6.1

6.2

where is the stability threshold, indicates that the low-cost regime is resilient to shocks and unlikely to collapse into a high-cost state, whereas a smaller implies that the high-cost regime is fragile and can easily transition toward sustainability; the presents the stochastic variance (noise intensity).

Study further grounds the novel stochastic cusp approach of regime change by using the Logit-regression model for regime change. To model how countries shift between the low (L) environment cost and high (H) environment cost regimes, the cusp framework is extended through a Kramers consistent logit formulation [103]. Here, the transition probability depends on the barrier height () and noise intensity (), where larger barriers or lower volatility make regime switches less likely, Eq. 7.1 and Eq. 7.2 presents the probabilistic Logit equation for low-cost and high-cost regimes .

7.1

7.2

where, and are the barriers from Eq. 6.1 and Eq. 6.2 respectively, is the stochastic variance, and includes the covariates [ET, INNOV, EV, EA, TLCT]. Furthermore, the change in ET, INNOV, and TLCT is expected to increase the probability of shifting from high-cost to low-cost regimes, while environmental vulnerability raises the opposite risk. This dynamic logit layer thus links the structural stability derived from the cusp model to the probabilistic regime switching observed across the BRICS economies. Figure 1 summarizes the causal structure of the stochastic Cusp-Logit model, illustrating how the explanatory variables jointly shape stability, asymmetry, and volatility in environmental cost dynamics.

Fig. 1.

Variable Interconnections and Causal Pathways in the Stochastic Cusp-Logit Environmental Cost Framework. Source: Authors’ own conceptualization based on the stochastic Cusp-Logit (Kramers-Logit) framework. The figure depicts how energy transition (ET_it), innovation (INNOV_it), environmental vulnerability (EV_it), environmental adaptability (EA_it), and low-carbon technology trade (TLCT_it) affect environmental cost dynamics through the stability (a_it), asymmetry (b_it), and volatility (σ_it) channels of the stochastic cusp model

Results and discussion

Table 2 presents the descriptive statistics for the BRICS panel data. The average EC from 2025 to 2024 is 23.47 per cent of GNI, with moderate variation (SD = 2.11), indicating notable but stable ecological pressure across BRICS economies. The average ET and INNOV are 48.62% and 3.85, respectively, for the BRICS. Furthermore, the average EV and EA are 0.56 and 0.64, respectively, suggesting moderate risk exposure but improving institutional responsiveness. Trade in low-carbon technologies (TLCT) maintains a mean of 17.75, indicating growing technology diffusion and the integration of low-carbon goods into BRICS trade structures. The Jarque-Bera test indicates that the data follows a normal distribution.

Table 2.

Descriptive statistics Source: Authors’ calculations from Eviews

Mean
	23.472	48.621	3.846	0.562	0.637	17.745
Median	23.300	48.950	3.770	0.570	0.640	17.635
Std. Dev.	2.108	2.445	0.741	0.092	0.081	1.206
Skewness	0.284	-0.231	0.134	0.118	-0.205	0.197
Kurtosis	2.991	2.451	2.732	2.082	2.148	3.066
Jarque Bera	1.083	2.907	1.455	2.998	3.120	0.635
Probability	0.582	0.234	0.482	0.224	0.209	0.728
Observations	96	96	96	96	96	96

The correlation estimates among the variables are presented in Table 3, indicating that environmental cost (EC) is negatively correlated with energy transition (ET), innovation (INNOV), environmental adaptability (EA), and trade in low-carbon technologies (TLCT), confirming that higher technological and institutional progress reduces ecological burden. The EC shows a positive relationship with environmental vulnerability (EV), asserting that environmental risks increase the cost of environmental degradation. These significant correlations justify the inclusion of all variables in the model and highlight potential interdependencies across BRICS economies.

Table 3.

Correlation matrix

	--	-0.5621***	-0.3987***	0.6342***	-0.4214**	-0.4856***
	-0.5621***	--	0.4720***	-0.5337***	0.3598**	0.4053***
	-0.3987***	0.4720***	--	-0.3225**	0.4361***	0.3124**
	0.6342***	-0.5337***	-0.3225**	--	-0.3785***	-0.4167***
	-0.4214**	0.3598**	0.4361***	-0.3785***	--	0.3342**
	-0.4856***	0.4053***	0.3124**	-0.4167***	0.3342**	--

***, and ** indicates significant at 1%, and 5% level of significance, respectively

Source: Authors’ calculations from Eviews

The study utilized a panel unit root test to determine the stationarity of the panel data for the specified variables (see, [19, 48, 62, 76]. Given these interconnected dynamics among the BRICS group, it is essential to check the cross-sectional dependence of the panel data before nonlinear estimation [20, 78, 89]. Cross-sectional dependence (CSD) presents challenges in panel data analysis, particularly when observations from different countries are influenced by shared economic characteristics [39, 100].

The unit root estimates in Table 4 show that the data are stationary at the I(1) level of integration (at difference). The cross-sectional dependence estimates in Table 4 indicate that BRICS economies exhibit cross-sectional dependence reflecting shared shocks, policy diffusion, and regional linkages. These results justify the adoption of second-generation panel estimators and a stochastic nonlinear framework that explicitly accounts for interdependence and dynamic regime shifts. Further, the presence of cross-sectional dependence indicates that BRICS economies are jointly affected by common global shocks. The fixed effect models are used to control for time-invariant structural heterogeneity across countries, while time-varying common stocks such as global energy price movements and the pandemic are captured through the stochastic diffusion term (Wiener process, see Eq. 1) [121]. Estimation is carried out using Quasi-Maximum Likelihood Estimation (QMLE), which provides consistent inference in nonlinear stochastic models even under heteroscedasticity and distributional misspecification [18]. Together, these features ensure reliable estimation of environmental cost dynamics despite strong cross-sectional dependence.

Table 4.

Panel unit root and cross sectional dependency estimates

Variable	Panel unit root test				Cross sectional dependency test
	CADF (Level)	CADF (Δ)	CIPS (Level)	CIPS (Δ)	LM (Breusch–Pagan)	LM (Pesaran scaled)	CD (Pesaran)
	-2.148	-5.932***	-2.084	-6.144***	128.44***	34.52***	10.83***
	-2.671**	-5.876***	-2.554**	-5.921***	141.62***	37.94***	11.67***
	-1.845	-4.782***	-1.803	-4.936***	132.11***	32.67***	9.42***
	-1.732	-3.955***	-1.688	-4.011***	117.32***	28.05***	8.13***
	-2.284*	-5.488***	-2.205*	-5.552***	124.08***	30.46***	8.76***
	-3.552***	-6.457***	-3.686***	-7.743***	109.77***	26.38***	7.52***

***, **, and * indicates significant at 1%, 5% and 10% level of significance, respectively

Source: Authors’ calculations using Eviews

Stochastic cusp estimates

Table 5 presents the stochastic cusp model using Quasi Maximum Likelihood Estimation (QMLE), which provides consistent parameter estimates under non-Gaussian disturbances [56] and allows for country-specific heteroscedasticity [34]. The panel QMLE captures structural and environmental factors jointly influence the curvature (and tilt of the environmental cost surface. To control for heterogeneity across BRICS panel the fixed effects were included.

Table 5.

Estimated stochastic cusp parameters (panel QMLE) Source: authors’ calculations using python

Variables	Curvature	Tilt	Variance
	-0.1423**	-0.2034**	-0.0721**
	-0.1152*	-0.1604**	-0.413*
	0.1861***	0.2143***	0.1384**
	-0.0734*	-0.0892**	-0.0521**
	-0.1271**	-0.1982***	-0.0662*
Constant	0.0384*	0.0543*	--

***, **, and * indicates significant at 1%, 5% and 10% level of significance, respectively

The estimates confirm the nonlinear structure of environmental costs for the BRICS countries. The curvature and tilt of energy transition (ET) indicates that ET reduces the environment cost. A higher transition rate will flatten the environment cost surface and shift the cost system to a low cost equilibrium. The INNOV also exerts a negative effect (with and) indicating that technology advancement in carbon capture and storage reduces the cost and enhances the cost stability. Conversely, Environmental Vulnerability (EV) has a higher impact on increasing environment cost by raising the cost surface by 0.186 times, tilting the cost to hight cost regime by 0.214 times and amplifying the volatility by 0.138. The environment adaptability (AD) offsets this pressure = −0.073, −0.089, η = −0.052), highlighting the importance of responsive institutions in dampening shocks. Finally, Trade in Low-Carbon Technologies (TLCT) strengthens resilience (=−0.127, =−0.198), confirming that international openness to clean technology reduces systemic asymmetry in environmental costs. The small positive constants (+0.038, +0.054) capture the average baseline curvature and tilt when policy drivers are at mean levels indicating a mild intrinsic tendency toward equilibrium that can be reshaped through transition and innovation efforts. Table 6 presents the estimates of the average barrier metrics derived based on stochastic cusp model coefficients to visualize country-wise relative stability of low- and high-cost regimes across BRICS.

The estimates reveal distinct patterns of environmental-cost stability across the BRICS countries, where countries like China and Russia exhibit the deepest low-cost wells and the highest stability indices (2.5832 and 2.1753), suggesting a strong low environmental cost regime due to sustained equilibria and a lesser probability for a high cost regime. Whereas countries like India and Brazil are moderate, with a stability index of approximately 1.6, but have some volatility due to fluctuating transition intensity. Conversely, South Africa indicates shallow wells and a higher likelihood of oscillating between regimes (stability ≈ 1.10). Overall, higher energy-transition intensity, innovation, and low-carbon trade correspond to deeper, more asymmetric potentials that favor the low-cost equilibrium, while environmental vulnerability flattens these basins, increasing susceptibility to cost surges.

Further, the estimates in Table 6 also highlight cross-country differences consistent with country-specific policy trajectories during the 2015 to 2024 period. High stability index of China reflects its sustained policy initiatives under its ‘Dual Carbon’ goals, which prioritize peak carbon emissions before 2030 and carbon neutrality by 2060, alongside large-scale investments in renewable energy [126], green finance [64], and clean technology innovation (Yu [123]). These policies deepen the potential for low-cost energy by strengthening innovation capacity and accelerating the energy transition. Russia’s comparatively high barrier height (between 2015 and 2024), despite its fossil fuel-intensive structure, partly explains the strategic shifts in energy exports and efficiency improvements following geopolitical and trade realignments, which have reinforced short-term cost stability. In contrast, South Africa’s lower barrier height and prolonged residence in the high-cost regime reflect structural dependence on coal, slower renewable deployment, and persistent institutional and fiscal constraints that weaken adaptive capacity. These policy and structural differences help explain the persistence of asymmetric stability patterns across BRICS economies.

Table 6.

Average barrier metrics and stability indices by country Source: authors’ calculations using python

Country			Stability index
Brazil	0.3478	0.2149	1.6085
Russia	0.4206	0.1928	2.1753
India	0.3817	0.2336	1.6279
China	0.4439	0.1718	2.5832
South Africa	0.2971	0.2690	1.0996

Further, Table 7 estimates the dynamic regime-transition probabilities using the Kramers-consistent logit model that determines how likely BRICS economies are to move between low- and high-cost regimes over time. The potential geometry stability index between the regimes in Table 7 fails to highlight the likelihood of a country switching between regimes over time. The Kramer-consistent logit estimates the probability of these transitions (low cost to high cost ( and High cost to low cost . This probability is based on the normalized stability index and the structural variables identified earlier.

Table 7.

Logit estimates of regime transitions (Kramers-Consistent). source: authors’ calculations using python

Variables	High cost entry	Low cost recovery
	-0.6308***	0.7124***
	-0.2487**	0.3065**
	-0.1914**	0.2258**
	0.2142**	-0.1710*
	-0.1651**	0.1492**
	-0.1976**	0.2119**
Constant	-0.0139	-0.0197

***, and ** indicates significant at 1%, and 5% level of significance, respectively

The estimated transition probabilities of the stability index shows a strong and significant impact on environment cost regimes, one unit increase will lower the likelihood of an upward shift by 0.6308 times and one unit increase in stability index will help to recover by 0.7124 times, confirming the Kramers principle (that deeper potential wells slow escape but accelerate return). The risk of entering the high environment cost regime reduces by 0.248 times due to energy transition (ET) and 0.191 times because of innovation (INNOV) in carbon capture and storage technology. Further ET and INNOV increases probability of recovery by 0.30 times and 0.22 time respectively, highlighting the importance of energy transition policy and technological enhancement. Whereas, the risk of high-cost regime increases by 0. 2142 time due to environment vulnerability (EV) and also reduces recovery probability by 0.171 times. The factors such as trade in low carbon technology (TLCT) and environment adaptability (EA) have very mirror-image effects, lowering exposure and promoting resilience.

Insights from stochastic cups and Kramer-Logit models

The estimates of stochastic cusp and Kramers-consistent logit models show the asymmetric impact of ET, EV, ED, INNOV and TLCT and how they shape both the form and the motion of environmental-cost regimes in the BRICS economies. The cusp estimation captures the geometry of stability, where curvature ( determines the depth of the potential wells (environment cost) and tilt ( reflects directional asymmetry between low- and high-cost equilibria. In this structure, energy transition (ET), innovation (INNOV), adaptability (ED), and low-carbon trade (TLCT) lower curvature and reduce tilt, flattening the potential surface and anchoring the system in a stable, low-cost state (see Fig. 2). Conversely, environmental vulnerability (EV) increases both parameters, creating a steeper slope toward the high-cost basin and magnifying stochastic noise.

Fig. 2.

Cusp stability landscape of environmental cost.

Source: Authors’ calculations using Python

The logit extension of the stochastic cups structural geometry into dynamic probabilities of movement between regimes shows a strong and significant effect of the stability index. The estimates confirm that deeper potential wells are associated with lower chances of cost escalation and faster recovery after shocks. ET, INNOV, and TLCT reduce the probability of high-cost entry and enhance recovery speed, whereas EV increases upward transition risk and weakens resilience (see Fig. 2). Together, these layers illustrate that policy design should not only deepen the low-cost basin (through structural transformation) but also accelerate the recovery path (through adaptive and trade mechanisms). In essence, the cusp model defines the shape of environmental resilience, and the logit model defines its speed.

Regime probabilities and expected durations

The time-based regime probability for smooth dynamic change is estimated for and based on the Kramers-consistent logit model. This estimates two aspects: it captures the frequency (i.e., how often) each BRICS economy occupies a high environment cost or low environment cost regime, and also the expected durations and of each regime before the transition occurs. Table 8 presents the country-wise averages regime probabilities and durations over the study period (2015 to 2024).

Table 8.

Average regime probabilities and expected durations (Years). Source: authors’ calculations using python

Country			Expected duration (in years) for high-cost	Expected duration (in years) for low-cost
Brazil	0.43	0.57	2.3	3.1
Russia	0.35	0.65	1.8	3.5
India	0.47	0.53	2.5	2.9
China	0.29	0.71	1.5	3.8
South Africa	0.58	0.42	2.9	2.1

The regime probabilities show that the stability gradient across the BRICS group. Countries like China and Russia exhibit the most resilient structures, spending over two-thirds of the time in the low-cost regime and recovering quickly after the shocks. Further, countries like Brazil and India display intermediate resilience, alternating more frequently between cost states, in contrast to South Africa, which remains in a high-cost regime for around 60% of the observed period, highlighting vulnerability and weaker adaptive dynamics. The expected duration estimates are in line with cups geometry, asserting that (downward) transition from high cost to low cost regime takes less time for the countries with strong ET, INNOV and TCLT. Whereas, the transition takes a longer time for vulnerable environment dominated countries. This persistence structure demonstrates that stability in environmental cost is not only structural (depth of potential) but also temporal linked to how long economies can resist reverting to high-cost states. Figure 3 presents the BRICS heat-map of the probability of maintaining the low environmental cost from 2015 to 2034. The vertical black line marks the start of the projection period. The pixelated structure emphasizes year-to-year probability variation, revealing China and India’s faster stabilization, while Brazil, Russia, and South Africa show more persistent volatility in projection till the year 2034.

Fig. 3.

Projected transition probabilities of low-cost environmental regime across BRICS (2015 to 2034).

source: authors’ calculations using python

Policy sensitivity of regime transition probabilities

Table 9 presents estimates of sensitivity to regime change, where the regime change probability is measured from the regime probability following a ± 1 standard deviation shock in each variable. Whereas, the change in duration and its sensitivity is measured by the average expected change in regime persistence (duration) under the stochastic transition model. The estimates suggest that innovation, energy transition, and environmental adaptation are the most crucial stabilizers of environmental costs in BRICS economies. A one-standard-deviation increase in innovation intensity reduces the likelihood of entering a high-cost regime by nearly 10%, extending the expected duration of the low-cost state by about 1.8 years. Similarly, innovations in renewable energy transition and adaptive capacity significantly increase environmental resilience.

Table 9.

Policy sensitivity of regime transition probabilities.

Source: authors’ calculations using python

Variable	¹	¹	Expected duration change (Years) ²
	-7.2%	7.2%	1.4 years
	-9.8%	9.8%	1.8 years
	14.6%	-14.6%	-2.1 years
	-6.4%	6.4%	1.2 years
	-5.9%	5.9%	1.0 years

¹ Change in regime probability following a ± 1 standard-deviation shock in each variable

² Average expected change in regime persistence (duration) under the stochastic transition model

The estimates also reveal that environmental vulnerability is a major destabilizing factor in the environmental cost regime. Any increase in EV will increase the probability of a high-cost state by 14.6% and shorten the regime duration by 2 years. The increase in TLCT leads moderately to stability by flattening regime asymmetry and supporting the diffusion of resilient production systems. Overall, the results highlight that technological progress, institutional adaptivity, and Trade in LCT jointly anchor the BRICS economies within sustainable, low-cost equilibria, mitigating the risk of abrupt environmental deterioration.

Model diagnostic and robustness

Table 10 presents the model diagnostic and forecasting accuracy test estimates to assess model robustness. The estimates confirm that the Cusp-Logit stochastic hybrid model is statistically robust and has predictive consistency. The relatively low AIC (1.932) and BIC (2.104) values, along with a high log-likelihood (-487.31) and a pseudo-R² of 0.63, indicate that the model effectively captures the structural and stochastic determinants of environmental cost dynamics. The mean VIF below five and non-significant Breusch Pagan (p = 0.216) and Ljung Box (p = 0.178) results verify the absence of multicollinearity, heteroskedasticity, and residual autocorrelation, ensuring parameter stability.

Table 10.

Model robustness and forecast accuracy statistics.

source: authors’ calculations using python

Diagnostic criterion	Statistic value
Akaike Information Criterion (AIC)	1.932
Bayesian Information Criterion (BIC)	2.104
Log-Likelihood	-487.31
Pseudo-R² (McFadden)	0.63
Mean VIF	< 5.0
Breusch Pagan (p-value)	0.216
Ljung Box Q (p-value)	0.178
Mean Absolute Percentage Error (MAPE)	3.27%
Root Mean Square Error (RMSE)	0.048
Mean Squared Prediction Error (MSPE Ratio)	0.76
Brier Score	0.082
Correlation (Predicted vs. Actual)	0.91

The estimates also show that the low MAPE (3.27%) and RMSE (0.048) assert the model replicates observed environmental-cost behavior with high precision. The MSPE ratio of 0.76 shows that the hybrid framework outperforms a standard linear Logit benchmark, while the Brier Score (0.082) and correlation between predicted and actual regime probabilities (0.91) confirm its superior classification and forecasting accuracy. Collectively, these results validate the model’s robustness, suggesting that the stochastic potential structure reliably explains both the magnitude and timing of regime transitions in environmental cost across the BRICS economies.

The empirical results and robustness estimates indicate that environmental cost dynamics in BRICS economies are governed by nonlinear regime behavior characterized by asymmetric stability and persistence. The estimated regime probabilities, expected durations, and barrier height measures collectively demonstrate how stability and transition risks vary across policy and structural conditions. In addition, the country-specific marginal effects of energy transition, innovation, environmental vulnerability, environmental adaptability, and low-carbon technology trade reveal the channels through which policy-relevant factors influence regime outcomes. These analytical insights provide a coherent empirical basis for the conceptual, methodological, and applied guidance synthesized in the concluding section. Figure 4 synthesizes the main empirical findings by jointly presenting country level environmental cost regime stability, key drivers of regime transitions, persistence effects, and their associated policy implications.

Fig. 4.

Summary of empirical findings of environmental cost regime dynamics in BRICS.

source: authors’ own visualization based on the empirical estimates.

Conclusion and policy takeaways

The key significance of this study lies in bridging environmental valuation with nonlinear regime dynamics, enabling a deeper understanding of how environmental costs evolve, persist, and transition under structural and policy forces. This study uses the environmental cost approach to measure environmental degradation in place of traditional emission or pollution measures for the BRICS group of countries. The cost-based approach of measuring environmental degradation empowers analysis to capture the actual economic burden of resource depletion. Furthermore, the study enhances the analysis by measuring the dynamics of environmental costs as a function of energy transition, innovation, environmental vulnerability, environmental adaptability, and trade in low-carbon technology, using a novel hybrid methodology based on the Cusp-Logit approach. The Cusp-Logit (Kramers Logit) model integrates physics-inspired potential geometry with probabilistic econometric estimation, allowing environmental cost to emerge as a dynamic system that shifts between high- and low-environment-cost regimes.

The findings reveal that environmental cost behavior is far from linear or symmetric. The estimates also reveal that innovation (INNOV) and energy transition (ET) significantly reduce both the probability and duration of high-cost regimes. At the same time, environmental vulnerability (EV) tilts the system toward instability. And environmental adaptability (EA) acts as a resilience enhancer, lengthening the persistence of low-cost equilibria, and trade in low-carbon technologies (TLCT) diffuses stabilizing effects through technological spillovers. Collectively, these results demonstrate that the BRICS environmental economic system is susceptible to nonlinear responses, where small policy shifts can lead to disproportionately large impacts on sustainability outcomes. The policy takeaways based on the findings are as follows:

1. Regime contingent policy design beyond incremental adjustments: The stochastic Cusp-Logit results indicate that policy effectiveness is inherently regime-dependent. Economies operating near persistent high environmental-cost regimes, such as South Africa and Brazil, are unlikely to achieve durable improvements through either incremental or fragmented interventions. Instead, coordinated and sufficiently strong policy actions in energy transition and low-carbon technology trade are required to overcome stability barriers and flatten the potential surface that sustains high-cost equilibria. Policy design should therefore focus not only on marginal improvements in environmental indicators, but on pushing key drivers beyond regime-critical thresholds that enable structural transitions toward low-cost environmental states.

2. Adaptive environmental policy under macroeconomic and geopolitical uncertainty: Environmental cost dynamics unfold under pervasive uncertainty arising from climate policy volatility, geopolitical conflict, pandemics, and macro-financial instability, etc. Although the study does not explicitly estimate policy uncertainty indices, uncertainty is captured through regime probabilities, expected durations, and transition risks embedded in the stochastic framework. These measures provide policymakers with early-warning signals that indicate when an economy is approaching unstable regions of the environmental cost landscape. In such periods, adaptive and counter-cyclical environmental policies are more effective than fixed or linear targets in preventing transitions into persistent high-cost regimes.

3. Strategic takeaway for local firms facing regime transition risks: For local firms, the regime-based framework offers actionable signals for strategic planning. Rising probabilities and longer expected durations of high-cost environmental regimes indicate elevated regulatory, compliance, and transition risks. Firms operating under such conditions should prioritize innovation lead adjustments, energy efficiency improvements, and alignment with low-carbon production methods to reduce exposure to regime-related cost escalation. Conversely, stable low-cost regimes signal favorable conditions for scaling clean technologies and long-term sustainable investments.

4. Investment signals from regime persistence and transition probabilities: For investors, regime persistence and transition probabilities provide indicators of environmental and policy risk. Persistent high-cost regimes imply higher uncertainty and long-term exposure to transition risks, warranting cautious portfolio allocation. In contrast, stable low-cost regimes reflect stronger environmental resilience and institutional readiness, supporting investment in low-carbon technologies and innovation-oriented sectors. Integrating regime signals into investment decisions can therefore enhance portfolio resilience under environmental and policy uncertainty.

The robustness of these policy implications is reinforced by alternative model specifications, which confirm that the identified regime dynamics, persistence patterns, and marginal effects are not sensitive to variable substitutions. This consistency strengthens confidence that the regime-based guidance derived from the model reflects structural characteristics of environmental cost dynamics rather than specification-driven outcomes, thereby enhancing its credibility for policy formulation and strategic decision-making. By explicitly linking variable implementation, nonlinear economic theory, and country-specific policy relevance, this study provides an integrated framework for understanding and managing environmental cost dynamics in emerging economies. It contributes to the environmental economics literature by operationalizing environmental degradation as a cost-based measure that quantifies negative externalities in economic terms, thereby moving beyond emission-centric metrics. Furthermore, the application of a stochastic Cusp-Logit framework enables the analysis of nonlinear regime transitions and the probability of persistence between high- and low-environmental-cost states.

Taken together, the study provides a clear roadmap for scholarship and practice: (i) The conceptual contribution: Advances environmental economics by reframing environmental degradation as a cost-based, nonlinear, and regime-dependent economic process, encouraging future research to move beyond emission-centric and linear modeling approaches. (ii) The methodological contribution: The study offers a transferable stochastic Cusp-Logit framework for analyzing stability, persistence, and transition dynamics in sustainability outcomes, which can be applied to other environmental and economic systems. And (iii) The applied contribution (Policy and Practice): Provides policymakers with a practical tool to identify regime-specific vulnerabilities, anticipate shifts toward high-cost environmental states, and design targeted interventions to sustain low-cost environmental trajectories in emerging economies.

Author contributions

Dhyani Mehta: Conceptualization, Data curation, Software, Validation, Formal analysis, Writing - original draft, Writing - review & editing. Nikunj Patel: Data collection and Data curation, Formal analysis, Validation, Writing - original draft, Writing - review & editing. Abdikafi Hassan Abdi: Data curation, Software Validation, Writing - original draft, Writing - review & editing.

Funding

There is no funding for this research.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent to publication

Not applicable.

Competing interests

The authors declare no competing interests.