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Open Access 08.01.2025

On the resiliency of post-crisis decoupling in higher-order economy-energy-environment nexus in high-inflation developing economies

verfasst von: Soumya Basu, Keiichi Ishihara

Erschienen in: Quality & Quantity

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Abstract

Macroeconomic pathways of enabling decoupling of emissions from economic growth in a post-crisis period is analyzed in this study for the high-inflation developing economy of India. A novel control system internalizing the inherent stochasticity of economy-energy-environment (3E) nexus extends the interpretation of Environmental Kuznets Curve hypothesis, where this study finds that decoupling is an emergent phenomenon of a 3E system. Using Zivot-Andrews unit root test, adaptive error correction modelling and robustness analysis through information theory-based approximate entropy method, the stochastic model is found to reproduce real-world higher order phenomena more accurately than previously theorized systems. With high entropy (information content) in long-run and short-run coefficients, the stochastic model can replicate the resiliency speed in a post-crisis period, without new information input. Some key findings of policy/macroeconomic linkages include: (a) decoupling progress lies in capital building and inhibited by inflationary growth; (b) fossil fuel imports, inflation and energy-use have a whiplash effect on carbon emissions in post-crisis periods; (c) electricity and non-electric-energy have differential effect on trade, with decoupling prevalent in electricity sector only; (d) inflation opposes GDP-emission causality during business cycle movements; (e) decoupling policies should be discretized to growth and recession phases of business cycle, with inflationary fossil fuel rebounds actively disincentivized in recession periods.
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1 Introduction

The discourse of human-caused climate change (HCCC) science is to enable decoupling of emissions from economic growth, achievable by emission intensity reduction (renewable energy incorporation) and energy intensity reduction (energy conservation measures) (Basu et al. 2022). Intermittency of renewables and inability to economically store renewable energy poses difficulty in energy transition from fossil fuels (FF) to renewable energy (RE) (IEA 2020b). Moreover, FFs being integrated into economic processes, a rapid structural change can lead to drastic short-term socioeconomic shocks, making decoupling and energy transition not straightforward solutions (Basu et al. 2022). FF penetration is largely dependent on the stage of economic maturity, as denoted by the environmental Kuznet’s curve (EKC) hypothesis (Tiwari et al. 2013). Even though the EKC has been validated for multiple studies (Basu et al. 2022; Dong et al. 2019; Marques et al. 2018; Mikayilov et al. 2018; Pao and Chen 2019; Piłatowska and Włodarczyk 2018), several studies have found no evidence for its support (Basu et al. 2022; Ben Jebli and Ben Youssef 2017; Işik et al. 2017; Lee and Chang 2007). Moreover, an important factor which has been ignored is the pace of economic growth, which can be entirely powered by FFs (Basu and Ishihara 2023), as in the case of fast-growing developing economies like India and China. Therefore, the basis for existence of the EKC may not be a simple measurement of the relative change of CO2 emissions to gross domestic product (GDP), but a complex interplay of macroeconomic factors within a macroeconomic system.
EKC and decoupling are two sides of the same coin, being affected by macroeconomic dynamics. It may be a natural question to ask how decoupling status changes with economic events specifically after the 1997 Kyoto Protocol and the 2015 Paris Agreement targets. It is imperative to study the interrelations among energy, economy and environment, herein termed as 3E nexus, specifically focusing on the 3E nexus as a control system being affected by stochasticity (Simionescu 2022). Nexus analysis via basic control system mechanisms have been studied for socioeconomic systems which have focused on how social factors (such as employment, education, etc.) impact energy-economy systems (Ghali and El-Sakka 2004; Ghosh 2009; Narayan and Smyth 2005; Shahbaz et al. 2013a, b, c; Yu and Hwang 1984; Yu and Jin 1992). However, existing literature shows diverging opinions in establishing causalities within the 3E nexus in attempts to prove the EKC hypothesis, ranging from emissions- > GDP (Marques et al. 2018; Mikayilov et al. 2018; Yu and Hwang 1984), GDP- > emissions (Shahbaz and Feridun 2012; Shahbaz and Lean 2012; Tiwari et al. 2013) and bi-directional dependencies (Bunnag 2023; Gyamerah and Gil-Alana 2023; Zuhal and Göcen 2024). The first issue in these past studies is that the directional dependencies are considered as evidence of the EKC, where in fact these dependencies are variable in magnitude and direction based on the variables considered within the 3E control system model (Mikayilov et al. 2018). Each model is based on an established economic theory, or a leading hypothesis of the respective study, wherein the inclusion of a macroeconomic determinant can change the state of the modelled system. GDP, capital and even international trade are not independent variables, but part of a dynamic feedback system (s) (Işik et al. 2017; Nepal et al. 2021; Shahbaz et al. 2013a, b, c). This paper attempts to create several control systems to approximate the real-world behavior of the Indian 3E system, to exactly gauge the level of decoupling across the time period of modern HCCC action policies.
The second issue this paper attempts to tackle is the reconciliation of decoupling with higher-order economic phenomena. While GDP growth is treated in existing literature as linear or exponential, money supply, GDP, inflation and interest rates are related to each other via business cycles (King and Watson 1996). Any transaction of goods is ultimately energy consumption, and thus, in the peak of a business cycle interest rates are minimum, which increases both energy-use and GDP, but reduces money-value, leading to inflation. This, in turn, leads to rising interest rates, which slowly creates deflation, but also tends to reduce GDP growth and energy-use (King and Watson 1996; Neumeyer and Perri 2005). This change in money-value increases prices, leading to other higher order macro-behavior such change in employment growth and consumer propensities (Cingano 2014). Previous studies have tried to derive causal relations in the 3E nexus, but have focused on leading hypotheses deriving the Granger-cause within 3E systems (K. R. Abbasi et al. 2021; Ho and Siu 2007; Narayan and Smyth 2005; Nepal et al. 2021; Shahbaz et al. 2013a, b, c; Tiwari et al. 2013). To the best of our knowledge, existing research has not addressed the status of decoupling during growth and recession phases and whether that has an impact on emissions at the macro-level. The second target of this paper is to empirically analyze various 3E control systems to identify the dynamics of CO2 emissions in such systems and its relation to macroeconomic variables. As a result, several statistical techniques are employed to estimate which system approximates higher-order behavior of the Indian 3E nexus the best. For achieving decoupling in a developing economy, it is imperative to identify how the status of decarbonization changes with higher-order behavior of economic variables during these phases (Dong et al. 2019; Mikayilov et al. 2018).
The third issue that this paper tackles lies in the concept of resilience of macroeconomic systems. Hollnagel and Woods 2005, posited that artefacts are ‘value neutral’, and their inclusion into a system has the intended or no unintended effects (Hollnagel and Woods 2005). Resilience is the ability to recover from a disturbance, but the earlier an adjustment is made, the more resilient a system can be. Similarly, in macroeconomic systems exogenous ‘disturbances’ come in the form of economic shocks like the 2008 global financial crisis and the 2019 COVID-19 pandemic (recent global crises) (Heffron and Sheehan 2020; Mirzaei and Al-Khouri 2016; Zhang et al. 2023). In our experience, economic growth, capital, inflation and even emissions have all rebounded after every historical crisis, displaying an intrinsic resiliency (Zhang et al. 2023). Thus, to accurately assess the status of decoupling and validate the EKC in a developing economy, the 3E control system has to exhibit the ‘early adjustment’ behavior proposed by Hollnagel and Woods 2005, in response to an exogenous disturbance (Hollnagel and Woods 2005). Such an adjustment (or rebound) has to be potentially close to the attributes of the real-world phenomenon (Basu et al. 2022; Hollnagel and Woods 2005). Within these economic complexity contexts, the main argument has to be that macro-level emissions are not directly linked to economic growth, specifically under conditions of high-inflation (Aydin and Pata 2020; Basu et al. 2022; Lean and Smyth 2010; Tiwari et al. 2013; Zuhal and Göcen 2024). This is because regime shifts can change money supply (in other words, GDP growth) instantaneously, whereas emissions arise from industrial processes of utilizing available energy sources (Basu et al. 2022). The third layer is that many of these energy sources are imported as FF in a fast-growing developing economy, like India and China (S.Basu and Ishihara 2023; Basu et al. 2023). As a result, the key position of this research is to simultaneously detect ‘early adjustments’ signs in a macroeconomic 3E nexus and to shed light on the feedback pathway of the nexus that creates the delay from GDP to emissions, within higher-order behavior and shocks. This paper attempts to propose a novel 3E control system that mirrors the real-world 3E dynamics of the Indian energy sector during the 2008 financial and the COVID-19 crises. Furthermore, the principal aim of this study is to uncover key feedback linkages (multi-chain causality) that is responsible for approximating the resiliency of the 3E system.
India is an interesting macroeconomic case for decoupling analysis, specifically because of the pace of its economic growth being largely fueled by FF penetration in power generation (a 375% increase in thermal power generation from 1990 to 2020 despite a RE capacity increase from 1.8GW to 138.3GW in the same period (International Energy Agency 2021). On the socioeconomic front, India’s unemployment has risen from 5.6 to 8.0% (World Bank 2023b), whereas poverty has decreased from 39 to 19.8% (Author’s estimation) from 2000 to 2020 (World Bank 2023a), which is still significantly at more than 300 million people living below poverty-line. In order to alleviate poverty and sustain an exponentially growing population, economic growth is crucial, which existing research has not addressed whether this economic growth results in innovation of decarbonization (Mohamed et al. 2022). Economic growth has been noticeable with GDP increasing by 550% in this period (World Bank, n.d.-a), notwithstanding that inflation has increased by 5.8% (World Bank, n.d.-b) and cumulative emissions by 250% (Worldometer 2023) from 2000 to 2020. However, inflation in India rapidly switches between 4 and 6%, creating significant changes in consumerism, and hence, energy demand (Ang 2011). Accounting the issue of business cycles’ impact on decarbonization policies, the third highest global emitter does pose the perfect litmus to test existing pathways, and propose novel directions in the aftermath of COVID-19, which is seeing unprecedented inflation-levels.
Moreover, unlike other fast-growing developing economies like China, the 2008 crisis did not significantly contract GDP or cumulative emissions in India (Li et al. 2012), while CO2 emissions decreased by 6% in the year following COVID-19 (IEA 2020a). This has drastic impacts on the 3E nexus’ de-carbonization efforts, which previous research has only addressed from the viewpoint of GDP growth (Basu et al. 2022; Pao and Chen 2019; Piłatowska and Włodarczyk 2018). Secondly, India is a much larger net importer of oil products than China (Basu et al. 2021), which raises the question as to how macro-level emissions have changed in relation to Trade Openness (TROP) during business cycle movements and before and after economic shocks. The aforementioned effect of resiliency of 3E control systems is most-imperative for India, since an economic shock creates major volatility of energy import purchases. In fact, this creates a shock in oil prices to countries exporting oil/coal to India (Deheri and Ramachandran 2023). A system that can simultaneously stabilize and determine the relation between demand, imports and emissions, will be essential to both climate policy makers in India and energy product exporting economies to India.
The target of this study is to investigate the set of factors in a control system, that is capable of representing the higher order phenomena in the 3E nexus system of India. Based on the high-inflation context of India, this study investigates the novel critical links that exist among energy imports, inflation and CO2 emissions, which have not been uncovered in literature within the contexts of a macroeconomic decoupling framework. To answer the question of resiliency of macroeconomic systems, we treat the 2008 financial crisis as a case-study. The novelty that this study contributes to the field of energy economics is to combine econometrics with information theory to extract the behavior of the long-run components of a vector error correction model (VECM). In our novel proposed model, we find a long-run feedback loop between capital, inflation and energy imports, with GDP and total primary energy supply (TPES) as inputs. This paper builds a framework for analyzing effective energy transition policies that can be enacted post-crises for any developing nation by training VECM models within specific economic regimes for said economies. This has the potential to involve stakeholders across the board, with policymakers enacting necessary adjustment to the Indian decoupling contexts, energy products exporters to India diversifying macro-supply chains against volatility, like economic shocks, and academicians to dive into newer avenues of econo-environmental causalities for high-inflation economies.
In the literature review, a set of theories guiding 3E nexus control systems is extracted from the viewpoint of macroeconomic variables. In the results, the reproducibility of higher order phenomena and robustness against economic shocks is compared for theoretical models and our novel proposed model from the perspective of information theory. In the discussion, the reasons of higher order reproduction of the novel model are analyzed through a feedback view of long-run cointegration models.

2 Determining macroeconomic frameworks of decoupling

3E nexus studies have majorly focused on causality analysis in control systems by constructing differential equations using vector auto regression (VAR), VECM models and autoregressive distributed lag (ARDL) systems. Most factors considered within these EKC systems can be divided into four strands. The first branch deals with the dynamic relationships among GDP, emissions and energy-use, where the direction of causality is generally tested as unidirectional from energy to GDP or vice-versa or bidirectional (Apergis and Payne 2009; Jamel and Derbali 2016; Kraft and Kraft 1978; Lean and Smyth 2010; Mikayilov et al. 2018; Paul and Bhattacharya 2004; Yu and Hwang 1984; Yu and Jin 1992). One particular recent study confirmed that both economic growth and energy-use significantly degraded the environment in 8 developing Asian nations, including India (Jamel and Derbali 2016). This is of interest to us, since we want to model the socioeconomics of energy transition in India. However, the question of the extent of environmental impact was inconsequential in this modelling for several studies (Apergis and Payne 2009; Jamel and Derbali 2016; Lean and Smyth 2010).
The second branch associates Cobb–Douglas production theory (that suggests GDP is a result of capital formation, labor and productivity (Cobb and Douglas 1928), within the 3E nexus. Since, productivity is ultimately a result of the efficiency of energy conversion, the energy-use acts as a proxy for factor productivity (Abokyi et al. 2018; Apergis and Payne 2009; Ghali and El-Sakka 2004; Lean and Smyth 2010; Lee and Chang 2007; Shahbaz et al. 2012; Stern 1993, 2000; Tiwari et al. 2013). Labor is often proxied by employment (Ghali and El-Sakka 2004; Yu and Jin 1992), wherein one study tried to evaluate the dynamic relationship between electricity-use and employment for India (Raza Abbasi et al. 2021). Even with employment being a highly stochastic indicator, the stochastic phenomena of the 3E nexus has not been captured by existing studies.
The third branch treats international trade and CO2 emissions as an important nexus analysis indicator (Cerdeira Bento and Moutinho 2016; Tiwari et al. 2013). Trade openness (TROP) is an important economic indicator, since it is the part of macroeconomics that is not completely internal to a nation. While considering a control system, multiple studies found that increased trade has a beneficial effect on decoupling in the long-run, reducing emissions (Kasman and Duman 2015; Shahbaz et al. 2014; Sultan and Alkhateeb 2019). However, in terms of energy transition, increased imports can be a sign of a lack of energy security. Energy security concerns have to be internalized into a control system to fully address the concept of decoupling under higher-order phenomena.
The final macroeconomic group of studies is neoclassical, where financial development is theorized to influence energy consumption and thereby, emissions (F. Abbasi and Riaz 2016; K. R. Abbasi et al. 2021; Adedoyin and Zakari 2020; Asafu-Adjaye 2000; Shahbaz et al. 2013a, b, c; Yuan et al. 2008). While financial development can be a proxy for investment (Nepal et al. 2021), it is quite difficult to relate social behavior with it. Developing countries, including India, have an extensive middle-class and also suffer from poverty. From socioeconomic perspectives, social behavior is tied to inflation (King and Watson 1996; Neumeyer and Perri 2005). While a particular study focused on omitted variables in system considerations (Glasure 2002), social behavior was not considered. The only indicator that can simultaneously proxy social behavior due to inflation and financial development, is Consumer Price Index (CPI).
There are a few studies that have combined the production and trade theories (Abokyi et al. 2018; Ben Jebli and Ben Youssef 2017; Lean and Smyth 2010; Shahbaz et al. 2013a, b, c), as well as trade and financial development theories (Acaravci and Ozturk 2010; Nepal et al. 2021; Rafindadi 2016; Shahbaz et al. 2013a, b, c). For the purposes of financial impulse analysis (economic crises), causality analysis in past studies have been more fruitful when theories are combined. This implies that macroeconomic interlinkages cannot be delineated by a single leading theoretical basis. In fact, for the purposes of estimating resiliency post an economic crisis, non-linear and higher-order behavior has to be considered. Table 1 highlights the indicators for nexus analysis of previous studies.
Table 1
Summary of Literature on 3E nexus analysis from different theoretical perspectives
Theory
Region
Factors
Refs.
Linear economic growth
U.S.A
E, GNP
Yu and Hwang (1984)
U.S.A
E, GNP, Emp
Yu and Jin (1992)
Australia
El, GNI, Emp
Narayan and Smyth (2005)
India
GDP, E-El, Emp
Ghosh (2009)
Hong Kong
GDP, E-El
Ho and Siu (2007)
U.S.A
E, GNP
Kraft and Kraft (1978)
E.U. (12)
GDP, C
Mikayilov et al. (2018)
Australia
GDP, C
Marques et al. (2018)
India
GDP, E
Paul and Bhattacharya (2004)
Central America (6)
GDP, E, C
Apergis and Payne (2009)
Malaysia
GDP, E-El
Lean and Smyth (2010)
Asia (8)
GDP, E, C
Jamel and Derbali (2016)
U.K
GDP, E, C, Economic uncertainty
Adedoyin and Zakari (2020)
Production
Pakistan
GDP, NG, K, Emp, Exp
Shahbaz et al. (2013a, b, c)
U.S.A
GDP, K, L, E
Stern (1993)
India
GDP, K, L, E
Cheng (1999)
O.E.C.D (all)
GDP, K, L, E
Lee et al. (2008)
Pakistan
GDP, K, L, E (RE/NRE)
Shahbaz et al. (2012)
Canada
GDP, E, K, Emp
Ghali and El-Sakka (2004)
Trade
Turkey
E, Exp
Erkan et al. (2010)
India
GDP, Coal, C, TROP
Tiwari et al. (2013)
Tunisia
GDP, E, C, TROP
Shahbaz et al. (2014)
E.U. (12)
GDP, E, C, TROP, Urb
Kasman and Duman (2015)
Italy
GDP, E-El (RE/NRE), TROP, C
Cerdeira Bento and Moutinho (2016)
Production + Trade
Tunisia
GDP, E (RE/NRE), TROP, K, C
Ben Jebli and Ben Youssef (2017)
Ghana
K, E-El, Ind. Value, TROP, L
Abokyi et al. (2018)
Taiwan
GDP, K, L, E, Exp
Lee and Chang (2007)
Finance
Pakistan
GDP, E-El, E-El Price
Raza Abbasi et al. (2021)
Asia (4)
GNI, E, Price of Goods
Asafu-Adjaye (2000)
South Korea
GDP, E, Govt. Spend, Money, OP
Glasure (2002)
China
GDP, E, E-El, Oil, Coal, Ind. Value, Emp
Yuan et al. (2008)
Pakistan
GDP, FDI, Cred, Stock Market, C
Abbasi and Riaz (2016)
Global (69)
GDP, E, Ind. Value, C
Liu and Hao (2018)
Trade + Finance
India
GDP, E, FDI, C, TROP
Nepal et al. (2021)
Greece
GDP, Cred, TROP, Tourism, C
Işik et al. (2017)
India
Tech. Innovation, FDI, TROP, E, C
Zameer et al. (2020)
Turkey
GDP, E, TROP, C, Cred
Acaravci and Ozturk (2010)
Nigeria
GDP, E, C, Cred., TROP
Rafindadi (2016)
Production + Trade + Finance
China
GDP, E, Cred, TROP, K, Exp, Imp
Shahbaz et al. (2013a, b, c)
While existing frameworks have several deficiencies for accounting the status of decoupling across cyclic and economic-shock phenomena, key indicators are built through hypotheses of the study. The first key novelty in the framework established in this study is the consideration of TPES. TPES energy can be broadly divided into electricity and non-electric use, since much of the renewable energy is driven into the electricity sector. Rapid electrification of most sectors is happening, primarily industry and transport (Basu et al. 2022; IEA 2020b). In fact, energy transition for 2030 Paris Agreement goals pits electricity as a necessary replacement for FFs (International Renewable Energy Agency 2020). While several studies have investigated electricity and non-electric energy separately, only a few studies have considered their interactions in the same system ( Abbasi et al. 2021; Yuan et al. 2008). However, the effect of electricity and non-electricity being differentially affected by macroeconomic complexity has not been elucidated. Neither has the level of decoupling in different economic regimes with these energy-supply sectors been identified separately, Moreover, in India power generation is largely dependent on imported FFs like coal and oil, significantly contributing to business cycle movements (Jahan and Serletis 2019). With different dependencies on consumer-need (hence, GDP) and energy imports, decoupling effects have to be quantified separately for the two, and more importantly, the economic interactions between the variables have to be uncovered per regime change.
Hypothesis I: Electricity and non-electricity energy-use differently affects trade openness, providing variable impacts on decoupling.
Secondly, inflation is a key factor in higher-order business cycle movements. While there have been few studies on the dynamics of electricity production and GDP in India (Ghosh 2009; Paul and Bhattacharya 2004), no previous research has addressed how inflation affects the dynamics of macro-CO2 emissions. As business cycles change inflation along with GDP, it is imperative to also answer what the causality of CO2 emissions and inflation is, and how it changes with growth and recession phases. Existing models have mostly used a GDP-deflator, ignoring how inflation specifically plays a part in decarbonization (Cerdeira Bento and Moutinho 2016; Marques et al. 2018; Mikayilov et al. 2018; Ozturk 2010; Shahbaz et al. 2014). With the rebound effect of the COVID-19 crisis, inflation has increased significantly in India (Basu and Ishihara 2023; Lee et al. 2023), the effect of which on emissions has not previously been hypothesized in terms of EKC. This is a key contribution of the paper to show the dynamic links between inflation and emissions, affected by the 2008 financial and COVID-19 crises in the Indian 3E nexus.
Hypothesis II: Consumer price index (CPI) (or inflation) will oppose causality of GDP and CO2 emissions in high inflation developing countries.
The third factorial deficiency in existing models is the non-consideration of energy security as part of decoupling assessment. During economic shocks while TROP may be maintained, the ramifications on energy imports may be manifold, as seen in the economic sanctions during the Ukraine-Russia crisis (Gaur et al. 2023; Nguyen et al. 2023). This creates a ripple-effect in the 3E nexus, which is often considered as exogenous in existing studies (Narayan and Smyth 2005; Ozturk 2010; Shahbaz et al. 2013a, b, c). However, geopolitical implications are quite different among economies, specifically with India continuing to import Russian oil, despite sanctions (Verma 2024). To estimate the resiliency in 3E macroeconomic systems and account energy security endogenously in decoupling assessment across economic shocks, energy imports should be looked at as an independent variable in control system constructions, and the interplay with 3E variables have to be quantified.
Hypothesis III: Energy imports are causal effects of GDP and energy-use in 3E macroeconomic systems, and are vital to resiliency of such systems.
In order to test the validity of the above three hypothesis, this study explores six modeled systems, wherein the novel model extends the boundaries of previous 3E nexus systems and is tested for resiliency against the 2008 financial crisis shock (Fig. 1). The higher-order reproduction is also tested for assessing the dynamics of decoupling more accurately in India.

3 Data and methodology

3.1 Modelling specifications

The 3E nexus models are built upon the framework of Fig. 1, with specified long-term behavior from cointegration approach, and short-run behavior determined by VECM technique. To measure the higher-order and economic shock effects on decoupling, macro-CO2 emissions are the independent variables in each of the models. It has to be noted that these are vector models, wherein all variables are interdependent, making each variable capable of being independent, which is reliant on the purpose of the modelling. To account for the higher-order effects and integrating the economic shock resilience endogenously into the 3E nexus systems, quarterly data is used from 1996 to 2020, encompassing both the 2008 financial crisis and the pre-crisis period for COVID-19. It has to be noted, the Indian macro data is properly reported from 1996 onwards, as well. All the series are first normalized to base year 2015 = 100 and then transformed into logarithmic form to eliminate heteroskedasticity in time-series modelling (Abbasi et al. 2021). VECM incorporating long-run cointegration are quite prevalent in econometric studies (Abokyi et al. 2018; Mohamed et al. 2022), allowing the three hypotheses to be testable. Over short samples, such as in this macroeconomic analysis, VECM has been shown to have complex dynamic issues, such as multiple lags, difference lags, etc. (Basu and Ishihara 2023; Ghosh 2009; Johansen 1991; Jordan and Philips 2018; Shahbaz et al. 2013a, b, c). This issue is dealt in the robustness analysis, where approximate entropy method is used (Delgado-Bonal and Marshak 2019), to account for the amount of information present in the explanatory variables (and in the simulated results). Moreover, VECM is compartmentalized against overfitting to achieve a dynamic equilibrium. Both these are novel approaches to econometric VECM modelling. The 6 models to assess the decoupling situations are given in Eqs. 16.
$$\begin{aligned}{ln\Delta C}_{t}=f ({ln\Delta GDP}_{t},{ln\Delta E}_{t}) \end{aligned}$$
(1)
$$\begin{aligned}{ln\Delta C}_{t}=f ({ln\Delta GDP}_{t},{ln\Delta K}_{t}{,ln\Delta E}_{t}) \end{aligned}$$
(2)
$$\begin{aligned}{ln\Delta C}_{t}=f ({ln\Delta GDP}_{t},{lnTROP}_{t},{ln\Delta E}_{t}) \end{aligned}$$
(3)
$$\begin{aligned}{ln\Delta C}_{t}=f ({ln\Delta GDP}_{t},{{{ln\Delta CPI}_{t},ln\Delta TROP}_{t},ln\Delta E}_{t})\end{aligned}$$
(4)
$$\begin{aligned}{ln\Delta C}_{t}=f ({ln\Delta K}_{t},{{ln\Delta CPI}_{t},{ln\Delta TROP}_{t},ln\Delta E}_{t})\end{aligned}$$
(5)
$$\begin{aligned}{ln\Delta C}_{t}=f ({{ln\Delta GDP}_{t},ln\Delta K}_{t},{{ln\Delta CPI}_{t},{ln\Delta TROP}_{t},ln\Delta E}_{t},{ln\Delta El}_{t},{ln\Delta EImp}_{t})\end{aligned}$$
(6)
Each of the models (Eqs. 16) are trained over growth and recession periods from 1996Q2 to 2008Q4, and thereafter an impulse is exogenously applied to GDP and K (where applicable) in 2009Q1 replicating the 2008 financial crisis. Such an impulse is more than the 2x standard deviation, which will allow to test the resiliency effects of each of the systems. Based on several criteria presented later, the most resilient system out of the 6 models, against the 2008 financial crisis, is retrained from 1996Q1 to 2020Q3 to estimate the level of decoupling against several macroeconomic indicators over multiple business cycles. The resilient model is capable of reduce errors simultaneously from growth to recession phases, and thereby provides a clearer picture of macroeconomic decoupling, not explored in previous studies. The time period allows to capture the pre-COVID and COVID-19 impacts on the 3E nexus. The key contribution of such a 3E nexus model is to guide net-zero policies in an increasingly recession-dominant, post-COVID-19 global economy.

3.2 Data specifications

Quarterly data for GDP, Capital (K), Import Value (Imp) and Export Value (Exp), Electric Energy-use (E-El) and CPI is collected from the Federal Reserve Bank of St. Louis (FRED) from 1996Q2 to 2020Q4. E and Non-electric Energy-use (E-NEl) are taken from British Petroleum database 2020, while Carbon emissions (C) and Energy Imports (E-Imp) are from IEA World Energy Outlook 2020 (IEA 2020b). E-El, E-NEl, E-Imp and C are available as annual data, and were converted to quarterly data by the Denton-Cholette method (Sax and Steiner, 2013). Table 2 gives the units and the sources of all the time series data.
Table 2
Modelling variables and abbreviations, data sources, and units
Variable
Units of measurement
Data source
GDP
Constant 2015 US$
Federal Bank of St. Louis (FRED) (n.d.)
K (capital)
Constant 2015 US$
Federal Bank of St. Louis (FRED) (n.d.)
E (TPES)E-NEl (Non-electric energy)
Exa Joules (EJ)
British Petroleum (2023)
 
Exa Joules (EJ)
British Petroleum (2023)
E-El (electricity-generation)
Exa Joules (EJ)
British Petroleum (2023)
E-Imp (Energy Imports)
Exa Joules (EJ)
British Petroleum (2023)
TROP (trade openness)
Quarterly (%)
Federal Bank of St. Louis (FRED) (n.d.)
CPI (consumer price index)
Ratio
(Federal Bank of St. Louis (FRED) (n.d.)
C (CO2 emissions)
Mega Tons (MT)
British Petroleum (2023)
Trade Openness (TROP) is calculated as the ratio of total trade (imports + exports) to GDP for each quarter. GDP, K, C, CPI and E-Imp emissions are scaled by indexing 2015Q3 = 100. The data is in logarithm (except TROP) and represented in Fig. 2. From Fig. 2, it can be clearly delineated that there exist distinct higher order phenomena in the data, even after normalizing and taking logarithms, specifically for GDP, K (capital), CPI (inflation) and C (CO2 emissions). It is seen GDP and K have suffered a significant negative shock in 2009Q1 for the 2008 financial crisis. However, the negative shock from COVID-19 in 2020Q2-Q3 is much larger than that of the 2008 financial crisis. It can be inferred from the GDP, CPI and K movements that India entered recession periods from 2000Q1 to 2003Q3 and from 2012Q1 to 017Q2. Table 3 presents the associated statistics of the variables. Both electric and non-electric energy, and CPI are positively skewed, implying that there is an absence of absolute decoupling in the Indian 3E nexus when considering inflation. The kurtosis of the first differenced GDP and K are unusually high, with a higher negative skew, which shows a significant business cycle movement, underscoring the importance of exploring the dynamics of decoupling from the standpoint of such higher-order phenomena.
Table 3
Descriptive statistics of the modelled variables from Fig. 2
Variable
Mean
Median
S.D.
Skewness
Kurtosis
Ln GDP
1.611
1.602
0.379
− 0.001
− 1.396
Ln K
1.765
1.833
0.264
− 0.268
− 1.371
Ln CPI
1.776
1.743
0.206
0.135
− 1.400
TROP
0.395
0.409
0.109
− 0.119
− 1.083
Ln E-El
1.258
1.245
0.172
0.116
− 1.214
Ln E-NEl
1.990
1.997
0.153
0.015
− 1.413
Ln C
1.821
1.818
0.160
0.049
− 1.430
Ln E-Imp
1.705
1.700
0.247
− 0.028
− 1.373
ΔLn GDP
0.012
0.013
0.019
− 3.873
42.97
ΔLn K
0.008
0.010
0.037
− 1.847
39.68
ΔLn CPI
0.007
0.008
0.007
0.065
2.091
ΔTROP
0.001
0.002
0.023
− 0.191
2.266
ΔLn E-El
0.006
0.006
0.005
0.670
6.865
ΔLn E-NEl
0.005
0.005
0.003
− 0.104
2.542
ΔLn C
0.005
0.005
0.006
− 0.246
1.468
ΔLn E-Imp
0.009
0.008
0.010
0.071
0.290
Δ represents the first differences

3.3 Unit root tests

Before performing the econometric modelling and specifying the model, unit root tests need to be performed on each time series to assess the stationarity and integration order of the variables. Stationarity is absolutely required to remove the statistical uncertainty of spurious regressions (Dickey and Fuller 1979). The Augmented Dickey-Fuller (ADF) has been used in form (Eq. 7), (ii) a form with intercept (Eq. 8), and (iii) a form with intercept and trend (Eq. 9). However, ADF has been reported to give biased results [46], wherein Kwiatkowski’s KPSS test (reverse hypothesis of the ADF) is used (Kwiatkowski et al. 1992). The non-inclusion of structural breaks in time-series unit root testing by ADF and KPSS has been argued to be spurious by econometricians (Shahbaz et al. 2013a, b, c; Tiwari et al. 2013). As a result, the Zivot-Andrews structural break unit root test is used in this paper (Zivot and Andrews 2002), to account for the changes in time-series regime and approximate the resiliency of the modelled variables against the exogenous shock. The Zivot Andrews is built in three forms in this paper: (i) one-time break in variables at level form (Eq. 10), (ii) one-time break in the slope of the trend component (Eq. 11) and (iii) one-time break both in intercept and trend function of the variables to be used for empirical analysis (Eq. 12) (Raza Abbasi et al. 2021; Zivot and Andrews 22).
$${\Delta Y}_{{\text{t}}} = {\mu Y}_{{{\text{t}} - 1}} + \mathop \sum \limits_{i = 1}^{k} {\updelta }_{{\text{i}}} {\Delta Y}_{{{\text{t}} - {\text{i}}}} + {\upvarepsilon }_{{\text{t}}} .$$
(7)
$${\Delta Y}_{{\text{t}}} = {\upalpha }_{0} + {\mu Y}_{{{\text{t}} - 1}} + \mathop \sum \limits_{i = 1}^{k} {\updelta }_{{\text{i}}} {\Delta Y}_{{{\text{t}} - {\text{i}}}} + {\upvarepsilon }_{{\text{t}}}$$
(8)
$${\Delta Y}_{{\text{t}}} = {\upalpha }_{0} + {\upbeta }_{0} {\text{t}} + {\mu Y}_{{{\text{t}} - 1}} + \mathop \sum \limits_{i = 1}^{k} {\updelta }_{{\text{i}}} {\Delta Y}_{{{\text{t}} - {\text{i}}}} + {\upvarepsilon }_{{\text{t}}}$$
(9)
where Y represents a time series, t is time period sampling interval, \({\upalpha }_{0}\) is the intercept, \({\upbeta }_{0}\) is the coefficient for time trend, µ is the coefficient of lagged value of time series at level, \({\updelta }\) is the coefficient of the lagged value of time series at first difference, k is the optimal lag length and \({\upvarepsilon }_{{\text{t}}}\) is the random walk error term. The null hypothesis \({\upmu } = 0\), is agreed when there is no unit root, against the alternate hypothesis of \({\upmu } < 0\), when there is a unit root present.
$${\Delta Y}_{{\text{t}}} = {\text{a}}_{0} + {\text{b}}_{0} {\text{t}} + {\text{a}}_{0} {\text{Y}}_{{{\text{t}} - 1}} + {\text{b}}_{0} DU_{t} + \mathop \sum \limits_{i = 1}^{k} {\updelta }_{{\text{i}}} {\Delta Y}_{{{\text{t}} - {\text{i}}}} + {\upvarepsilon }_{{\text{t}}}$$
(10)
$${\Delta Y}_{{\text{t}}} = {\text{b}}_{0} + {\text{c}}_{0} {\text{t}} + b_{0} {\text{Y}}_{{{\text{t}} - 1}} + {\text{c}}_{0} DT_{t} + \mathop \sum \limits_{i = 1}^{k} {\updelta }_{{\text{i}}} {\Delta Y}_{{{\text{t}} - {\text{i}}}} + {\upvarepsilon }_{{\text{t}}}$$
(11)
$${\Delta Y}_{{\text{t}}} = {\text{c}}_{0} + {\text{c}}_{0} {\text{t}} + {\text{c}}_{0} {\text{Y}}_{{{\text{t}} - 1}} + {\text{d}}_{0} DU_{t} + {\text{d}}_{0} DT_{t} + \mathop \sum \limits_{i = 1}^{k} {\updelta }_{{\text{i}}} {\Delta Y}_{{{\text{t}} - {\text{i}}}} + {\upvarepsilon }_{{\text{t}}}$$
(12)
where \(DU_{t}\) is a dummy variable representing that there is a mean shift with the time break, while \(DT_{t}\) shows that there is a trend shift with the time break. Equation 13 shows the conditions for hypothesis confirmation of unit root presence.
$$DU_{t} = \left\{ {\begin{array}{*{20}l} {1~ if~ t > TB} \\ {0~ if ~t < TB} \\ \end{array} } \right.\ and\ DT_{t} = \left\{ {\begin{array}{*{20}l} {t - TB~ if~ t > TB} \\ {0~ if ~t < TB} \\ \end{array} } \right.$$
(13)
The null hypothesis of unit root break date is \({\text{c}}_{0}=0\) which indicates that series is not stationary with a trend not having information about structural break point, while \({\text{c}}_{0}<0\) hypothesis implies that the variable is found to be trend-stationary with one unknown time break. Zivot–Andrews unit root tests all points as a potential break-point and estimates through regression for all possible break points successively.
For both the unit root tests and modelling the 3E control systems, the optimum lag order is selected based on the established Akaike Information Criterion (AIC) in Eq. 14 (Akaike 1969) and Bayesian Information Criterion (BIC) in Eq. 15 (Schwarz 1978).
$${\text{AIC}} = \ln \left| {\left[ {{\text{Cov}}} \right]} \right| + \frac{2}{{\text{T}}} \cdot {\text{K}}$$
(14)
$${\text{BIC}} = \ln \left| {\left[ {{\text{Cov}}} \right]} \right| + \frac{{\ln {\text{T}}}}{{\text{T}}} \cdot {\text{K}}$$
(15)
where [Cov] represents the estimated covariance matrix, T is the number of samples used in training the model and K is the number of parameters estimated by the model. The lowest value for AIC and BIC shows optimality for the control system.

3.4 VECM dynamic cointegration modelling

An adaptive Vector Error Correction Model (a-VECM) is introduced in this paper, which performs a least error-path Monte Carlo simulation on the unrestricted VAR (uVAR) of the models, where the adaptive nature is to freely switch between the 5 Johansen cointegration methods (Table 4) (Johansen 1991) according to the least error of the subsequent stage. Equation 16 shows the uVAR.
$${\text{Y}}_{{{\text{k}},{\text{t}}}} = \sum\limits_{{i = 1}}^{p} {{\text{V}}_{{\text{i}}} } {\text{Y}}_{{{\text{k}},{\text{t}} - {\text{i}}}} + \varepsilon _{{\text{t}}}$$
(16)
where Yk,t is an n-dimensional time series, such that k = 1, 2, 3, …n is integrated at the same order, p is the optimal lag length of the model, V is a matrix of VAR coefficients.
Table 4
Types of Johansen Cointegration models (Johansen 1991)
Model
Error correction form
Cointegrated series
Data
H2
AB′yt−1
No intercept, no trend
No trend
H1*
A (B′yt−1 + c0)
Intercept, no trend
No trend
H1
A (B′yt−1 + c0) + c1
Intercept, no trend
Linear trend
H*
A (B′yt−1 + c0 + d0t) + c1
Intercept, linear trend
Linear trend
H
A (B′yt−1 + c0 + d0t) + c1 + d1t
Intercept, linear trend
Quadratic trend
Yk,t is said to be cointegrated if a linear combination (cointegrating relation) β1Y1t +  + βn.Ynt of the components is stationary, wherein β = 1, …, βn) is a cointegrating vector. The deviation from the stationary mean, at time t-1 of the linear combination of the n-dimensional time series, is the error correction term (Eq. 17).
$$\text{error}={\upbeta ^{\prime}}{\text{Y}}_{\text{k},\text{t}-1}$$
(17)
The rate at which the time series can correct the error is called adjustment speed (α), where α =  (α1, …, αn) is the vector of adjustment speeds for the n-time series of the model. With multiple cointegrating relations, α and β become matrices A and B  (Eq. 18).
$$\text{AB}^{\prime}{\text{Y}}_{\text{k},\text{t}-1}={\text{CY}}_{\text{k},\text{t}-1}$$
(18)
where C is known as the impact matrix, the rank of which determines the long-term stochastic trends and relationships among variables (the cointegrating models are shown in Table 4).
Equations 1924 show the a-VECM form for the 6 models of Eqs. 16.
$$\begin{aligned}\Delta {\text{ C}}_{{\text{t}}} &= \alpha _{0} + {\text{ect}}_{{{\text{GDP}}}} {\text{GDP}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{E}}} {\text{E}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{C}}} {\text{C}}_{{{\text{t}} - 1}} {\text{ }} \\ &\quad+ \sum\limits_{{{\text{j}} = 1}}^{{\text{n}}} {\alpha _{{\text{j}}} } \Delta {\text{ GDP}}_{{{\text{t}} - {\text{j}}}} + \sum\limits_{{{\text{k}} = 1}}^{{\text{n}}} {\alpha _{{\text{k}}} } \Delta {\text{ E}}_{{{\text{t}} - {\text{k}}}} + \sum\limits_{{{\text{i}} = 1}}^{{\text{n}}} {\alpha _{{\text{i}}} } \Delta {\text{ C}}_{{{\text{t}} - {\text{i}}}} + \varepsilon _{{\text{t}}}\end{aligned}$$
(19)
$$\begin{aligned} \Delta {\text{ C}}_{{\text{t}}} &= \alpha _{0} + {\text{ect}}_{{{\text{GDP}}}} {\text{GDP}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{K}}} {\text{K}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{E}}} {\text{E}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{C}}} {\text{C}}_{{{\text{t}} - 1}} {\text{ }} \\ &\quad+ \sum\limits_{{{\text{j}} = 1}}^{{\text{n}}} {\alpha _{{\text{j}}} } \Delta {\text{ GDP}}_{{{\text{t}} - {\text{j}}}} + \sum\limits_{{{\text{k}} = 1}}^{{\text{n}}} {\alpha _{{\text{k}}} } \Delta {\text{ K}}_{{{\text{t}} - {\text{k}}}} + \sum\limits_{{{\text{l}} = 1}}^{{\text{n}}} {\alpha _{{\text{l}}} } \Delta {\text{ E}}_{{{\text{t}} - {\text{l}}}} + \sum\limits_{{{\text{i}} = 1}}^{{\text{n}}} {\alpha _{{\text{i}}} } \Delta {\text{ C}}_{{{\text{t}} - {\text{i}}}} + \varepsilon _{{\text{t}}}\end{aligned}$$
( 20)
$$\begin{aligned} \Delta {\text{C}}_{{\text{t}}} & = \upalpha _{0} + {\text{ect}}_{{{\text{GDP}}}} {\text{GDP}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{TROP}}}} {\text{TROP}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{E}}} {\text{E}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{C}}} {\text{C}}_{{{\text{t}} - 1}} \\ & \quad + \mathop \sum \limits_{{{\text{j}} = 1}}^{{\text{n}}} \upalpha _{{\text{j}}} \Delta {\text{GDP}}_{{{\text{t}} - {\text{j}}}} + \mathop \sum \limits_{{{\text{k}} = 1}}^{{\text{n}}} \upalpha _{{\text{k}}} \Delta {\text{TROP}}_{{{\text{t}} - {\text{k}}}} + \mathop \sum \limits_{{{\text{l}} = 1}}^{{\text{n}}} \upalpha _{{\text{l}}} \Delta {\text{E}}_{{{\text{t}} - {\text{l}}}} + \mathop \sum \limits_{{{\text{i}} = 1}}^{{\text{n}}} \upalpha _{{\text{i}}} \Delta {\text{C}}_{{{\text{t}} - {\text{i}}}} + \upvarepsilon _{{\text{t}}} \\ \end{aligned}$$
( 21)
$$\begin{aligned} \Delta {\text{C}}_{{\text{t}}} & = \upalpha _{0} + {\text{ect}}_{{{\text{GDP}}}} {\text{GDP}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{CPI}}}} {\text{CPI}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{TROP}}}} {\text{TROP}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{E}}} {\text{E}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{C}}} {\text{C}}_{{{\text{t}} - 1}} + \mathop \sum \limits_{{{\text{j}} = 1}}^{{\text{n}}} \upalpha _{{\text{j}}} \Delta {\text{GDP}}_{{{\text{t}} - {\text{j}}}} \\ & \quad + \mathop \sum \limits_{{{\text{l}} = 1}}^{{\text{n}}} \upalpha _{{\text{l}}} \Delta {\text{CPI}}_{{{\text{t}} - {\text{l}}}} + \mathop \sum \limits_{{{\text{k}} = 1}}^{{\text{n}}} \upalpha _{{\text{k}}} \Delta {\text{TROP}}_{{{\text{t}} - {\text{k}}}} + \mathop \sum \limits_{{{\text{m}} = 1}}^{{\text{n}}} \upalpha _{{\text{m}}} \Delta {\text{E}}_{{{\text{t}} - {\text{m}}}} + \mathop \sum \limits_{{{\text{i}} = 1}}^{{\text{n}}} \upalpha _{{\text{i}}} \Delta {\text{C}}_{{{\text{t}} - {\text{i}}}} + \upvarepsilon _{{\text{t}}} \\ \end{aligned}$$
( 22)
$$\begin{aligned} \Delta {\text{C}}_{{\text{t}}} & = \upalpha _{0} + {\text{ect}}_{{\text{K}}} {\text{K}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{CPI}}}} {\text{CPI}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{TROP}}}} {\text{TROP}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{E}}} {\text{E}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{C}}} {\text{C}}_{{{\text{t}} - 1}} + \mathop \sum \limits_{{{\text{j}} = 1}}^{{\text{n}}} \upalpha _{{\text{j}}} \Delta {\text{K}}_{{{\text{t}} - {\text{j}}}} \\ & \quad + \mathop \sum \limits_{{{\text{l}} = 1}}^{{\text{n}}} \upalpha _{{\text{l}}} \Delta {\text{CPI}}_{{{\text{t}} - {\text{l}}}} + \mathop \sum \limits_{{{\text{k}} = 1}}^{{\text{n}}} \upalpha _{{\text{k}}} \Delta {\text{TROP}}_{{{\text{t}} - {\text{k}}}} + \mathop \sum \limits_{{{\text{m}} = 1}}^{{\text{n}}} \upalpha _{{\text{m}}} \Delta {\text{E}}_{{{\text{t}} - {\text{m}}}} + \mathop \sum \limits_{{{\text{i}} = 1}}^{{\text{n}}} \upalpha _{{\text{i}}} \Delta {\text{C}}_{{{\text{t}} - {\text{i}}}} + \upvarepsilon _{{\text{t}}} \\ \end{aligned}$$
( 23)
$$\begin{aligned} \Delta {\text{C}}_{t} & = {\upalpha }_{0} + {\text{ect}}_{{{\text{GDP}}}} {\text{GDP}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{K}}} {\text{K}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{CPI}}}} {\text{CPI}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{TROP}}}} {\text{TROP}}_{{{\text{t}} - 1}} \\ & \quad + {\text{ect}}_{{{\text{El}}}} {\text{El}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{NEl}}}} {\text{NEl}}_{{{\text{t}} - 1}} + {\text{ect}}_{{\text{C}}} {\text{C}}_{{{\text{t}} - 1}} + {\text{ect}}_{{{\text{EImp}}}} {\text{EImp}}_{{{\text{t}} - 1}} + \mathop \sum \limits_{{{\text{j}} = 1}}^{{\text{n}}} {\upalpha}_{{\text{j}}} \Delta {\text{GDP}}_{{{\text{t}} - {\text{j}}}} \\ & \quad + \mathop \sum \limits_{{{\text{k}} = 1}}^{{\text{n}}} {\upalpha}_{{\text{k}}} \Delta {\text{K}}_{{{\text{t}} - {\text{k}}}} + \mathop \sum \limits_{{{\text{l}} = 1}}^{{\text{n}}} {\upalpha}_{{\text{l}}} \Delta {\text{CPI}}_{{{\text{t}} - {\text{l}}}} + \mathop \sum \limits_{{{\text{m}} = 1}}^{{\text{n}}} {\upalpha }_{{\text{m}}} \Delta {\text{TROP}}_{{{\text{t}} - {\text{m}}}} + \mathop \sum \limits_{{{\text{o}} = 1}}^{{\text{n}}} {\upalpha}_{{\text{o}}} \Delta {\text{El}}_{{{\text{t}} - {\text{o}}}} \\ & \quad + \mathop \sum \limits_{{{\text{p}} = 1}}^{{\text{n}}} {\upalpha}_{{\text{p}}} \Delta {\text{NEl}}_{{{\text{t}} - {\text{p}}}} + \mathop \sum \limits_{{{\text{q}} = 1}}^{{\text{n}}} {\upalpha}_{{\text{q}}} \Delta {\text{C}}_{{{\text{t}} - {\text{q}}}} + \mathop \sum \limits_{{{\text{r}} = 1}}^{{\text{n}}} {\upalpha}_{{\text{r}}} \Delta {\text{EImp}}_{{{\text{t}} - {\text{r}}}} + {\upvarepsilon }_{{\text{t}}} \\ \end{aligned}$$
( 24)
The ARDL bounds cointegration has been used extensively in the past studies to identify the causalities in macroeconomic nexuses (Acaravci and Ozturk 2010; Marques et al. 2018; Ozturk 2010). While a distributed lag-model has numerous advantages of information preservation, it has the potential of breakdown when an impulse of greater than 2x standard deviation is applied (analogy for an economic shock). In the traditional VECM (Mohamed et al. 2022; Shahbaz et al. 2012), long-run dependencies are not controllable since the regime-dependent switching of the Johansen form cannot be adapted. Therefore, this study requires a model that can not only maintain the long-run dynamics of a 3E nexus, but also approximate the resiliency of the modelled 3E nexus from the economic shock. The advantage of a-VECM over previous approaches is that long-run cointegration will follow the non-linear path of least error during the training of the control system.

3.5 Resiliency determination against economic shocks

The final part introduces several novel methodological frameworks in VECM analysis, and is associated with checking the robustness of estimations of Eqs. 1924 (the 6 models) pre- and post-2008 crisis. In previous literature, established 3E nexus systems have not been checked for their resiliency against economic shocks or capability to reproduce higher-order phenomena (Bunnag 2023; Mirzaei and Al-Khouri 2016; Shahbaz et al. 2014; Tiwari et al. 2013; Zuhal and Göcen 2024). While past models have generalized the causality directions over the entire training period, in higher-order phenomena residuals are often not normally distributed, and follows a wave-like pattern. This paper develops a framework that could be used to account for these factors in EKC and decoupling verification internalizing the real-world business cycle phenomena. Mean percentage accuracies of reproduction and forecasting are evaluated for the 6 models, with the innovation being that the forecasting errors are after the 2008 shock, testing the resiliency of the 3E nexus models. Also, the R-factors during the economic phases of growth and recession from 1996 to 2012 are checked for each model (as defined in Eq. 25).
$$R = \frac{{\sum \left| {\left| {Y_{real} } \right| - \left| {Y_{est} } \right|} \right|}}{{\sum \left| {Y_{real} } \right|}}$$
(25)
where Yreal and Yest are the real recorded and model estimate values for the dependent factor. This R-factor enables to test the not only the overall robustness of the models, but also segment the residuals and check the significance in segregated training periods, adding a significant improvement error-correction models’ robustness analysis.
Apart from the above, the information contained in the estimated models have to be measured to understand which model can most resemble the real world. For this, the principle of entropy is applied to the estimated data of each model (Zhao and Lin 2011). Entropy is a measure of disorder in a system (chaos), and the more chaotic or unpredictable the measurements of a system is, the more information it contains (Olbrys and Majewska 2022). Thus, chaos in a system (time series) proves to reveal more information about the energy-economy-emission nexus, which can be seen as the closest application of Occam’s Razor (the simplest explanation is the best one, but it should be complete) (Gill 2022). The measure of chaos of the estimated time-series data by the models is provided by calculating the approximate entropy of each of the estimates. Each of the estimated time series data in each model is equally spaced in time as follows:
$$\text{U}\left(1\right),\text{ U}\left(2\right), \dots ,\text{ U}\left(\text{N}\right)$$
(26)
Where N are the raw data values. We define m as a length of run-time data (0 ≤ m ≤ N) and r as a real, positive number specifying a filtering level tolerance for accepting matches. The following sequence of vectors is then formed:
$$X\left( 1 \right), X\left( 2 \right), \ldots , X \left( {N - m - 1} \right)$$
(27)
which in an m-dimensional real space defined by:
$${\text{X}}\left( {\text{i}} \right) = \left[ {{\text{x}}\left( {\text{i}} \right),{\text{ x}}\left( {{\text{i}} + 1} \right), \ldots ,{\text{ x}}\left( {{\text{i}} + {\text{m}} - 1} \right)} \right]$$
(28)
the above vector sequence is used for each magnitude of i as:
$${\text{C}}_{{\text{i}}}^{{\text{m}}} \left( {\text{r}} \right) = \frac{{{ }\left( {{\text{r}} - {\text{ d}}\left| {{\text{X}}\left( {\text{i}} \right),{\text{X}}\left( {\text{j}} \right)} \right|} \right)}}{{{\text{N}} - {\text{m}} + 1}}$$
(29)
The functional magnitude of the m-dimensional space is defined as
$${\uppsi }^{{\text{m}}} { }\left( {\text{r}} \right) = \frac{1}{{{\text{N}} - {\text{m}} + 1}}{ }\mathop \sum \limits_{{{\text{i}} = 1}}^{{{\text{N}} - {\text{m}} + 1}} {\text{log }}\left( {{\text{C}}_{{\text{i}}}^{{\text{m}}} \left( {\text{r}} \right)} \right)$$
(30)
In the final step, Eq. 23 represents the final expression for Approximate Entropy (ApEn) calculation.
$${\text{ApEn }}\left( {{\text{m}},{\text{r}},{\text{N}}} \right) = {\uppsi }^{{\text{m}}} \left( {\text{r}} \right) - {\uppsi }^{{{\text{m}} + 1}} { }\left( {\text{r}} \right)$$
(31)
where m ≥ 1 and ApEn (0, r, N) (u) =  − C1 (r). While the principle of maximum entropy is usually applied to statistical thermodynamics, mechanics, physiology (Olbrys and Majewska 2022), etc., this is unique to macro-economic VECM analysis is subject to it. Only one previous study applied ApEn to the VECM analysis of the Indian electricity sector (Basu et al. 2024), which provided a very unique perspective to the modelling results and fitting. In fact, this is the most novel methodological intervention in this paper, as till now in literature only residual diagnostics have been applied for testing vector models’ robustness. The ApEn measurement relies on the Shannon’s entropy of the model coefficients itself (Shannon 1948), providing economic modelling robustness that could show the actual information content in the system.

4 Results

4.1 Unit root results

Table 5 reveals the results of the unit root tests of ADF and KPSS for every time-series parameter, while Table 6 shows the Zivot-Andrews structural break test results.
Table 5
Results of the Unit Root Tests shows that the variables are stationary at the first differences, thus integrated at order I (1)—ADF and KPSS
Variable
At level
At first difference
ADF statistic
KPSS statistic
ADF statistic
KPSS statistic
ln GDP
− 3.326 (2)c
1.284
− 82.12 (0)a*
0.279
ln K
− 3.093 (2)c
1.454
− 90.95 (0)a*
0.187
ln CPI
− 3.041 (1)c
1.562
− 78.69 (0)a*
0.171
TROP
− 3.742 (1)c
1.681
− 96.20 (0)b*
0.214
ln E-El
− 13.31 (1)c
1.629
− 115.7 (0)a*
0.053
ln E-NEl
− 3.672 (0)c
1.116
− 56.74 (0)a*
0.205
ln C
− 7.081 (0)c
1.183
− 185.4 (1)b*
0.099
ln E-Imp
− 5.955 (0)c
0.675
− 90.72 (0)a*
0.181
(): optimum lags for the ADF test
*Significant at 1% level
aIntercept and trend are 0
bOnly trend is zero;
cIntercept and trend are non-zero
Table 6
Results of the Zivot-Andrews structural break test shows that the variables are stationary at the first differences, thus integrated at order I (1)
Variable
At level
At first difference
t-statistic
Break
t-statistic
Break
ln GDP
− 2.456 (2)
2004Q2
− 12.12 (0)*
2009Q1
ln K
− 4.012 (2)
2005Q1
− 13.82 (0)*
2009Q1
ln CPI
− 2.785 (1)
2008Q3
− 12.58 (0)*
2009Q2
TROP
− 3.247 (1)
2020Q2
− 11.74 (0)*
2010Q2
ln E-El
− 4.831 (1)
2009Q2
− 17.65 (0)*
2009Q3
ln E-NEl
− 3.868 (1)
2020Q3
− 14.64 (0)*
2009Q3
ln C
− 4.858 (0)
2004Q4
− 16.25 (1)*
2009Q1
ln E-Imp
− 4.667 (0)
2014Q2
− 15.35 (1)*
2010Q1
(): optimum lags for the ZA test
*Significant at 1% level
All the variables are non-stationary at their levels but stationary at their first differences, confirmed by both ADF and KPSS tests. Therefore, all the variables are integrated at order I (1). However, to mitigate the bias of ADF, Zivot-Andrews test is performed.
The structural breaks are scattered across the time intervals at level among the variables, while at first differences, the breaks are consistent with the 2008 financial crisis, eliminating the edge-effects of COVID-19. TROP and E-Imp being stochastic in nature, show minor deviation from the 2008 crisis for the breaks at first differences. All variables are integrated at I (1) and thus, a dynamic control system can be constructed at first differencing with all the indicators.

4.2 Optimal lag order and cointegrations

The optimal lag for each of the systems of Eqs. 1924 are checked using AIC and BIC from 1996Q2 to 2008Q4 (pre-financial crisis), displayed in Table 7, It has been argued in literature that AIC and BIC are quite reliable for small samples, compared to other lag-length criteria (Shan et al. 2024). With the trade model having the maximum lag-length, it can be inferred that such modelled structure is unstable, while the 3E nexus stochastic model having a lag length of 4, shows the seasonal and annual dependencies are captured, which is absent in other 3E systems. This is counterintuitive to existing literature results (Nepal et al. 2021; Zameer et al. 2020).
Table 7
System Lag length for the 3E systems of Eqs. 1924 based on AIC and BIC
Lags
Models
C = f (GDP, N-El)
C = f (GDP, K, N-El)
C = f (GDP, TROP, N-El)
C = f (GDP, CPI, TROP, N-El)
C = f (K, CPI, TROP, N-El)
C = f (GDP, K, CPI, TROP, El, N-El, E-Imp)
AIC
BIC
AIC
BIC
AIC
BIC
AIC
BIC
AIC
BIC
AIC
BIC
0
− 831.65
− 825.86
− 1078.4
− 1070.6
− 1058.7
− 1051.0
− 1382.4
− 1372.8
− 1320.8
− 1311.2
− 2368.9
− 2353.5
1
− 1254.1
− 1231.1
− 1600.3
− 1562.0
− 1508.8
1470.5
− 1952.4
− 1895.0
1862.4
− 1805.1
− 3048.9
− 2911.2
2
− 1291.5*
− 1251.5*
− 1594.2
− 1556.1
− 1534.5
− 1466.4
− 2033.2
− 1929.1
− 1910.8*
− 1806.8*
− 3144.2
− 2886.9
3
− 1271.8
− 1215.7
− 1624.0*
− 1596.7*
− 1503.9
− 1406.6
− 2047.2*
− 1957.6*
− 1866.0
− 1716.3
− 3167.4
− 2793.1
4
  
− 1538.0
− 1412.1
− 1452.6
1326.8
− 1996.1
− 1801.8
  
− 3317.1*
− 2943.7*
5
    
− 1439.0
− 1285.4
      
6
    
− 1539.0*
− 1412.0*
      
*Denotes selection of the lag order
Table 8 shows the long-run Johansen cointegration test results, wherein the novel a-VECM method allows regime switching from the types of models in Table 4, allowing the detection of dynamic higher-order behavior. Model 6 has the maximum number of cointegrated indicators, pre-indicating the existence of several linkages among the parameters. The non-significance of lower-ranks for trade-model show that such a system, without control variables (like E-Imp), is prone to overfitting. The lack of cointegration in finance-trade model 5 (not including GDP) shows GDP, as a parameter, is necessary to construct an Indian 3E nexus model.
Table 8
The Johansen cointegration for the 3E systems of Eqs. 1924 based on Table 4
Rank
Models
C = f (GDP, N-El)
C = f (GDP, K, N-El)
C = f (GDP, TROP, N-El)
C = f (GDP, CPI, TROP, N-El)
C = f (K, CPI, TROP, N-El)
C = f (GDP, K, CPI, TROP, El, N-El, E-Imp)
Trace
Max. Eigen
Trace
Max. Eigen
Trace
Max. Eigen
Trace
Max. Eigen
Trace
Max. Eigen
Trace
Max. Eigen
R = 0
60.09*
37.37*
64.40*
37.45*
87.68*
45.53*
87.15*
31.22***
118.1*
51.17*
474.6*
145.0*
R ≤ 1
22.72*
17.37**
26.97***
16.73
42.15*
26.61*
55.93*
25.31***
66.93*
32.73*
329.7*
112.6*
R ≤ 2
5.345**
5.345**
10.23
9.943
15.54**
11.63***
30.62**
14.91
34.20**
24.32**
217.0*
67.18*
R ≤ 3
  
0.287
0.287
3.914**
3.913**
15.71**
10.95
9.880
7.338***
149.9*
56.22*
R ≤ 4
      
4.753**
4.753**
2.547
2.547
93.64*
41.84*
R ≤ 5
          
51.79*
25.93*
R ≤ 6
          
25.86*
16.53**
R ≤ 7
          
9.335*
9.335*
*Significant at 1% level
**Significant at 5% level
***Significant at 10% level

4.3 a-VECM dynamic cointegration results

The 3E nexus models are trained from 1996Q2 to 2008Q4 (51 samples). With the financial crisis effect at 2009Q1, a conditional impulse is applied to GDP and K at 2009Q1 and 2009Q2 to induce the negative effect of the Lehman shock, and the models are forecasted for further 12 periods till 2011Q4. The adaptive nature of the a-VECM enables the change in the cointegration model type from pre-2008 crisis to post-2008 crisis, which gives a distinct advantage over ARDL, wherein the robustness of the modelling control systems can be checked across growth and recession phases and the rebound from the 2008 financial crisis in the forecasting. Table 9 shows the long-run and short-run results for the dependencies of emissions on corresponding economic factors for each model. For models 1–5, the E-NEl and E-El are cumulatively viewed as total primary energy supply (TPES) and is treated as a single variable. Figure 3 shows the CUSUM test and Fig. 4 shows the CUSUMsq test plots for the 6 models.
Table 9
The a-VECM long and short-run analysis for the 6 models from 1996Q2 to 2008Q3
Independent Variables
Models
C = f (GDP, TPES)
C = f (GDP, K, TPES)
C = f (GDP, TROP, TPES)
C = f (GDP, CPI, TROP, TPES)
C = f (K, CPI, TROP, TPES)
C = f (GDP, K, CPI, TROP, E-El, E-NEl, E-Imp)
Long-run Results
Constant
0.151
− 0.282
0.819*
0.152
0.098
0.595
lnGDPt-1
0.047
− 0.093
0.227*
0.045
 
0.663**
lnKt-1
 
− 0.010
  
0.036
− 0.703*
lnCPIt-1
   
− 0.114
0.059
0.805*
TROPt-1
  
0.110*
0.030
0.005
0.120
lnE-Elt-1
0.409**
0.205
0.009
0.374***
− 0.087
0.120
lnE-NElt-1
     
0.054
lnCt-1
− 0.538*
0.043
− 0.684*
− 0.397**
− 0.060
0.281
lnE-Impt-1
     
0.706*
Short-run Results
ΔlnGDPt-1
0.117
− 0.268
− 0.818*
− 0.094
 
− 0.330**
ΔlnKt-1
 
0.147***
  
0.072
− 0.684*
ΔlnCPIt-1
   
− 0.224
− 0.130
0.643**
ΔTROPt-1
  
− 0.088**
0.063***
0.096**
0.057
ΔlnE-Elt-1
0.679**
1.638*
2.143*
0.845**
0.654**
− 0.151**
ΔlnE-NElt-1
     
1.253**
ΔlnCt-1
0.210
− 0.143
0.283***
0.485
0.122
− 0.592
ΔlnE-Impt-1
     
0.156
Diagnostic Tests
LL
664.01
835.95
833.67
1081.2
993.32
1917.9
AIC
− 1280.2
− 1583.9
− 1451.4
− 1972.5
− 1886.6
− 3211.8
BIC
− 1234.8
− 1501.6
− 1256.2
− 1794.7
− 1792.0
− 2634.5
χ2 Normal (JB)
48.97*
10.96**
2.027#
0.041#
22.18*
23.77*
χ2 Corr (LBQ)
28.97b, #
14.14a, #
25.62a, #
13.27a, #
71.62a, *
18.29a, ***
χ2 ARCH
0.159#
1.319#
2.161#
6.546**
0.995#
2.553#
*Significant at the 1% level
**Significant at the 5% level
***Significant at the 10% level
#Significant above the 10% level.
a20 lags involved in the Monte-Carlo Auto-correlation test.
b45 lags involved in the Monte-Carlo Auto-correlation test.
The diagnostic tests show that residuals of models 1–4 are serially autocorrelated, while models 3–4 are also not normally distributed. Moreover, model 4 contains heteroskedasticity. However, more serious concerns are in finance-trade-production hybrid model 5, where Fig. 4e shows that the CUSUMsq plot lies outside the critical bounds. Hence, model 5 is not considered to accurately represent the 3E nexus in the pre-financial crisis period. The elimination of model 5 shows that GDP is a key factor for constructing 3E systems, mirroring the outcomes of past literature (Işik et al. 2017; Ozturk 2010; Paul and Bhattacharya 2004).
The long-run dependencies of emissions present key macroeconomic linkages leading up to the 2008 financial crisis. While in growth and trade-production-finance models TPES is coupled to emissions, the 3E nexus stochastic model reveals that electricity is actually decoupled from emissions (− 0.151). Simultaneously, a 1% increase in short-run non-electricity-use increases emissions by 1.253%, which proves aforementioned hypothesis I. It can be inferred that RE penetration into electricity has structurally changed the energy dynamics of India, shifting emissions to other energy sectors, which is non-evidenced by existing macroeconomic models (Ghosh 2009; Paul and Bhattacharya 2004). Another important advantage of stochastic model 6 over trade model 3 is that TROP is seen to be coupled in model 3, whereas TROP is non-significant in model 6. A major inhibiting factor of decoupling is FF imports (0.706), which gives evidence that E-Imp is an important control variable to estimate the real macroeconomic dynamics of TROP on emissions, contrary to existing models (Nasreen and Anwar 2014; Nepal et al. 2021; Nguyen et al. 2023). Finally, GDP is seen to be non-significant in the long-run in most models, with model 6 evidencing that inflation (CPI) is the most decoupling-inhibiting long-run factor (0.805% increase in emissions for 1% increase in inflation). We can partially prove aforementioned hypothesis II when comparing the recommendation of previous literature on inflation dynamics of macro-decoupling (Mohamed et al. 2022; Nguyen et al. 2023). In fact, the key policy takeaway is that long-run capital formation is the highest contributing decoupling factor (-0.703), when K is within a 3E stochastic framework.
The short-run dynamics have three major implications on economic shock rebound and business cycle recessions for Indian net-zero targets. In all the models, TPES had a coupling effect on short-term emissions, with capital and trade models being especially pronounced. However, electricity-use persisted with a decoupling effect even in the short-run, as opposed to non-electric energy-use. Secondly, it can be ascertained that CPI exaggerates emissions for short-term GDP gains, as short-term GDP increase causes a significant decoupling (-0.330), but CPI again couples in the short-run (0.643). Thirdly, we can confirm hypothesis II, as inflation and GDP both have pronounced decoupling effects in both trade model 3 and stochastic model 6. From a policy perspective, short-run economic recovery is boosted by emission-intensive production, which shows short-run decoupling with economic growth. However, this is uneconomic, as in both short- and long-run inflation majorly inhibits decoupling opportunities (Basu et al. 2022; Piłatowska and Włodarczyk 2018).

4.4 Robustness analysis of 3E models

The most significant result of the aforementioned systems is their ability to internalize the resiliency of macroeconomic 3E systems, against the economic shock of 2008. Figures 5, 6, 7, 8 and 9 show models’ 1–4 and 6 reproduction from 1996Q2 to 2008Q3 (training period) and forecasts from 2009Q1 to 2011Q4 (testing period). The exogenous shock is applied to GDP and K in the 2008Q4 period. The detailed coefficients of all the a-VECM models are given in appendices A-F, along with the residual diagnostic tests for all the variables. Table 10 shows the mean aggregated per-centage reproduction accuracy (MAPRA), mean aggregated percentage forecasting accuracy (MAPFA) and approximate entropy (ApEn) for the 5 models, which are the key robustness tests of this study. Specifically, ApEn is a measure of the amount of information contained in the modelled values, giving an indication of total information in the considered 3E nexuses.
Table 10
The MAPRA, MAPFA and ApEn for models 1–6 (Eqs. 19)–(24) for training data of 1996Q2 to 2008Q4 and forecasting data from 2009Q1 to 2011Q4
Model
MAPRA (%)*
MAPFA (%)*
ApEn
1 (GDP, TPES, C)
88.1
84.0
0.129
2 (GDP, K, TPES, C)
80.5
68.3
0.038
3 (GDP, TROP, TPES, C)
74.5
80.7
0.193
4 (GDP, CPI, TROP, TPES, C)
73.6
78.9
0.206
5 (K, CPI, TROP, TPES, C)
69.6
83.7
0.061
6 (GDP, K, CPI, TROP, E-El, E-NEl, C, E-Imp)
96.2
85.2
0.430
*The values are derived by averaging the Residual-Sum-of-Squares from the residuals of all indicators, in the training and testing time intervals
Reflecting the diagnostic tests of a-VECM, model 5 has the lowest MAPRA, while the other trade models 3 and 4 also show quite low MAPRA and MAPFA. A visual inspection of Figs. 5, 6, 7, 8 and 9 show that models 2, 3 and 4 fail to reproduce the business cycle (higher-order) movements significantly. In fact, production model 2 has the lowest forecasting accuracy showing that these systems are not robust representations of 3E systems in view of higher-order phenomena and economic shocks. 3E stochastic model 6 reveals the most accurate factors of all the models.
Growth model 1 has relatively high MAPRA and MAPFA, but a much lower information content (ApEn of 0.129) shows that such a model is a linear approximation of higher-order movements, rather than a reconstruction of the same. Higher information content in models 3 and 4 show the merit of such systems of previous analyses (Abokyi et al. 2018; Cerdeira Bento and Moutinho 2016), but TROP alone cannot detect the resiliency pathway in post-crisis macroeconomic recovery. However, with an ApEn of 0.43, a 3E stochastic model shows the capability to accurately capture the higher-order movements and be resilient to exogenous shocks. The application of ApEn is highly significant in the context of this macroeconomic study because resiliency is a function of the amount of known information in the system (Delgado-Bonal and Marshak 2019; Hollnagel and Woods 2005). The dynamics of decoupling policies can only be stable if the system’s breaking point and dynamic stabilities can be uncovered, and therefore, this paper proposes the ApEn and R-factor framework for resiliency determination.
Figure 9 shows model 6 is the only control system that holds robustness post impulse (2008 crisis), with highly accurate directionality of GDP, E-NEl, E-El and C. Moreover, the training period also shows much better MAPRA with a-VECM coefficients, with models 1 and 3 following. The R-factor for time blocks are shown in Table 11, for the variables of GDP, E (E-NEl and TPES) and C for models 1, 3 and 6, with respective observed economic phases.
Table 11
Summary of R-factors (normalized) in two growth and one recession phases and recovery phase post-2008 financial crisis of GDP, E and C for Models 1, 3 and 6 (Eq. 25)
Phase
Model
GDP
E
C
Growth Phase 1 (1996Q1–2000Q1)
1 (GDP, TPES, C)
0.003
0.002
0.003
3 (GDP, TROP, TPES, C)
0.010
0.011
0.006
6 (GDP, K, CPI, TROP, E-El, E-NEl, C, E-Imp)
0.001
0.000
0.001
Recession Phase 1 (2000Q2–2003Q3)
1 (GDP, TPES, C)
0.034
0.012
0.012
3 (GDP, TROP, TPES, C)
0.021
0.008
0.008
6 (GDP, K, CPI, TROP, E-El, E-NEl, C, E-Imp)
0.007
0.003
0.002
Growth Phase 2 (2003Q4–2008Q4)
1 (GDP, TPES, C)
0.023
0.008
0.008
3 (GDP, TROP, TPES, C)
0.015
0.004
0.004
6 (GDP, K, CPI, TROP, E-El, E-NEl, C, E-Imp)
0.005
0.001
0.002
Post-crisis Recovery (2008Q2–2011Q4)
1 (GDP, TPES, C)
0.017
0.011
0.016
3 (GDP, TROP, TPES, C)
0.021
0.010
0.010
6 (GDP, K, CPI, TROP, E-El, E-NEl, C, E-Imp)
0.005
0.006
0.007
R factor higher than 0.1 shows insignificance, and less than 0.01 shows high significance
R-factors not only reveal the dynamics of decoupling within 3E systems, but also validate the inferences of the a-VECM coefficients towards approximating high-order macroeconomic phenomena by the control systems. It can be seen that the simplest model (growth model 1) shows minimal errors at the beginning of the training period, with the trade model 3 being not so accurate. Hence, the growth model can be assumed to be a linear approximation of a 3E system, which shows the linear causality between GDP and C (Acaravci and Ozturk 2010; Kraft and Kraft 1978; Shahbaz et al. 2013a, b, c), without higher-order effecting linkages. The merits of the trade decoupling hypothesis (Işik et al. 2017; Shahbaz et al. 2013a, b, c; Zameer et al. 2020) is seen in the recession phase, since the stochasticity of TROP is higher than GDP (3rd and 4th order behavior).
However, TROP is not directly linked to emissions, as the 3E stochastic model shows that the overall macroeconomic behavior can be approximated to complete mean-reverting trends in the recession phase. E-Imp is a control factor to TROP-GDP interactions, which affect emissions (as seen in long-run of Table 9). In line with the interpretations of ‘early adjustment’ in resilient macroeconomic systems (Hollnagel and Woods 2005; Mirzaei and Al-Khouri 2016), the differential effect of growth- CPI coupling and GDP decoupling in short-run- is supposedly what represents an economic adjustment. Seeing that model 6 is able to predict the recession and post-crisis GDP rebound an order of magnitude better than other models, shows that the real-world resiliency is internalized. Hypothesis II of GDP and CPI having opposing behavior being only limited to short-run, exemplifies the post-crisis resilience.
With long-run and short-run decoupling only seen with respect to capital growth, the Indian pathway to net-zero emissions around economic uncertainty is surely in the form of policies that ensure stable RE infrastructure and asset growth. The rebound of emissions after economic shocks is mainly due to coupling with CPI, which is ignored by HCCC mitigation policies due to the short-run momentary decoupling provided by money-supply-aided inflation. The R-factors and a-VECM coefficients of model 6 indicate that decoupling is not a fixed measurement scale, and hence, neither should be the EKC hypothesis. In a high-inflation developing economy, decoupling is an emergent phenomenon of the momentary demand for innovation in HCCC mitigation or demand in economic recovery, whichever is prioritized by policy instruments.

5 Discussion: novel feedback pathways for decoupling

This section deliberates the major findings against existing literature to extract new decoupling pathways within economic complexities. Now that 3E stochastic model 6 has been proved to be the most robust in detecting higher-order macroeconomic behavior and economic shock rebound, what exactly causes it? This section analyzes the feedback loops that lead to resiliency, which can be adopted into existing energy transition policy frameworks.
To examine the feedback pathways, model 6 is re-trained from 1996Q2 to 2020Q3 time-period, along with the dependencies of every variable, as per Eq. 24, shown in Table 12.
Table 12
The a-VECM long and short-run analysis for model 6 from 1996Q2 to 2020Q3
Independent variables
Dependent variables
GDP
K
CPI
TROP
E-El
E-NEl
C
E-Imp
Long-run Results
Constant
− 0.319
1.130
− 0.020
2.462***
0.463
0.142
0.595
0.515
lnGDPt-1
− 0.001
1.789*
0.570***
0.108
0.260
− 0.009
0.663**
− 0.137
lnKt-1
− 0.241**
− 1.137*
− 0.894*
1.860*
− 0.081
− 0.004
− 0.703*
1.071*
lnCPIt-1
− 0.270***
− 0.435
− 1.022*
− 0.408
0.001
− 0.304*
0.805*
2.022*
TROPt-1
0.054
0.116
0.131
− 1.493*
− 0.094
− 0.033***
0.120
0.021
lnE-Elt-1
0.466*
− 0.205
0.190
0.158
− 0.496**
0.321*
0.120
− 1.032*
lnE-NElt-1
− 0.553**
1.615**
0.321
− 2.991***
− 0.490
− 0.668*
0.054
1.488*
lnCt-1
1.056*
− 1.528
0.704
0.460
0.266
0.734*
0.281
− 3.346*
lnE-Impt-1
− 0.104
− 0.819*
0.161
0.212
0.248**
0.017
0.106
− 0.774*
Short-run Results
ΔlnGDPt-1
− 1.087*
− 0.761**
− 0.384
0.813
− 0.447*
− 0.497*
− 0.189
0.205
ΔlnKt-1
0.326*
0.146
0.895*
− 0.164
0.080
0.040
0.084
− 0.883*
ΔlnCPIt-1
1.163*
− 1.306**
1.563**
− 1.957***
0.012
0.135
− 0.174
− 1.110**
ΔTROPt-1
0.031
− 0.092
− 0.018
− 0.298**
− 0.010
0.002
− 0.005
0.201*
ΔlnE-Elt-1
0.296**
− 0.537***
0.079
− 0.933***
− 0.079
0.146**
0.035
− 0.391***
ΔlnE-NElt-1
0.571***
− 1.676***
1.630**
0.719**
1.400**
1.387*
0.670**
1.862*
ΔlnCt-1
− 0.518***
− 1.731***
− 0.505**
1.215
− 1.607**
− 0.591*
− 0.042
1.566**
ΔlnE-Impt-1
0.237*
− 0.315**
0.009
− 0.873*
0.256***
1.027**
0.143*
− 0.915*
Diagnostic Tests
LL
3051.1
       
AIC
− 5478.2
       
BIC
− 4691.4
       
χ2 Normal (JB)
2.776#
4.058#
0.671#
6.990**
1.604#
2.754#
0.060#
0.061#
χ2 Corr (LBQ)
27.98a, #
12.21a, #
46.17b, #
21.13a, #
18.68a, **
21.92a, #
48.41b, #
26.41a, #
χ2 ARCH
3.846#
1.337#
1.720#
0.259#
5.120#
0.113#
3.203#
1.098#
*Significant at the 1% level
**Significant at the 5% level
***Significant at the 10% level
#Significant above the 10% level
a20 lags involved in the Monte-Carlo Auto-correlation test
b45 lags involved in the Monte-Carlo Auto-correlation test
In the long-run, a 1% increase in GDP increases capital by 1.78%, but increases inflation (CPI) by 0.57%, whereas capital accumulation decreases inflation by 0.9% for every 1% rise in K. This effect is propagated to emissions as well, as K enables decoupling (0.7% decreased C), while inflation inhibits decoupling (0.8% increased C). CPI increase by 1% increases energy imports by 2% and decreases GDP by 0.27%. Industrial development and inventories (K) lead to inflation reduction, while fuel imports reduce K (− 0.82% for 1% increase in E-Imp). In past studies it was unclear as to how exactly capital and TROP affect macro-emissions in developing economies (Mohamed et al. 2022; Nasreen and Anwar 2014; Shahbaz and Feridun 2012). In light of resiliency determination for 3E systems, it can be inferred that capital and E-Imp are in a negative feedback loop, which ultimately affects emissions. The assumption of hypothesis III being proven, opens a new dimension in economic policies of decoupling for high-inflation economies like India, in that, decoupling has to be ensured against capital growth and E-Imp instead of GDP and TROP, respectively.
Following the findings of (Holland 1998), this propagation can be thought of as two characteristic phenomena in the Indian 3E nexus, which is broken down from a more complex feedback, involving the same indicator- Capital. Knowing these individual interactions, we can manage to reveal the exact state of decoupling and its evolution. Thus, decoupling is an emergent process of the 3E system and not absolute. Conclusively, the long-run feedback that is responsible for the resilience of model 6 predicting the rebound of emissions after the exogenous shock and, ultimately, predicting the state of decoupling through business cycles can be attributed to the following: K to CPI to E-Imp to K forms a feedback loop, herein termed inventory-price-energy security (IPES) linkage loop, with GDP and E-NEl being inputs to the loop (Fig. 10). The interactions of this newly discovered feedback affect emissions, when considering a higher-order behavioral system. This also proves hypothesis III of this study, linked to EKC exploration in developing economy contexts.
Additionally, the cause of the resilient model 6 can further be attributed to the differential effects of stochastic variable TROP on E-NEl and E-El. In the short-run (Table 12), 1% increase of E-Imp reduces TROP by 0.87%. However, increasing E-NEl increases TROP in the short-run, but decreases in the long-run. E-El growth reduces the short-run TROP. Extending the IPES linkage with the control variables of E-NEl and E-El, another feedback loop of E-NEl to E-Imp to TROP to E-NEl is observed, herein termed as ‘fossil imports degrowth effect’. Degrowth because fossil fuel in industries induces short-run export spikes, but long-run energy security reduction (Fig. 11). With this feedback loop we can ascertain that the decoupling causality with TROP in previous literature on developing economies were incomplete analyses (Nepal et al. 2021; Rafindadi 2016; Tiwari et al. 2013; Zameer et al. 2020). This is perhaps the most significant finding in this analysis, specifically because it sheds light on the structural setup of electricity and non-electricity sectors. While (Can and Korkmaz 2019) attempted a similar approach for RE only, the normalizing effect of E-Imp was not considered. As the result, the structural dynamics of the two energy sectors were not revealed for Bulgaria in their study. This effect proves aforementioned hypothesis I, extending the understanding of EKC. In fact, the structural causality may be quite different for other high-inflation economies, which begs the question of future investigations into the macroeconomic 3E structure.
Finally, a third feedback loop involves CPI, K, C, E-NEl and E-Imp. From Table 12, a 1% increase in E-NEl increases CPI by 1.63%, C by 0.67% and E-Imp by 1.86% in the short-run. On the contrary, a 1% increase in E-NEl reduces K by 1.68% and increases CPI by 1.56% in the short-run, followed by the impact of 1% increased C reducing K by 1.73% in the short-run. Thus, inflation promotes excess FF-use, which is supplied by FF imports. This drastically increases short-run emissions, which decreases energy inventories (capital), subsequently driving inflation further. This is termed as the ‘inflation-fossil imports whiplash’ effect (Fig. 12), which is extended from IPES feedback. Past studies have not examined the short-run decoupling causalities of capital and inflation in the same system (Basu et al. 2024; Ho and Siu 2007; Nepal et al. 2021; Tiwari et al. 2013), which have prevented visualization of the complex network that increases emissions non-linearly (Fig. 12). The existence of such dynamics shows how high-inflation countries sacrifice energy security for GDP growth, opening up deliberations for controlling the domestic energy inventory and propagating RE in the short-run, in addition to having long-term targets (Basu et al. 2024; Bhambu 2015).
From the resilience perspective, E-NEl rebounds early (early-adjustment (Hollnagel and Woods 2005)) due to a positive feedback with inflation and fueled by FF imports. E-Imp is proven to be critical to the modelling of the 3E nexus, as emissions cause E-Imp to increase, which is in turn increased by the ‘whiplash’ effect. Not only is hypothesis III reconfirmed, but also Fig. 9’s rebound speed of 3 quarters for GDP, C, energy and E-Imp is explainable by this phenomenon. However, the bigger question that this whiplash effect poses is that does a developing economy satisfy its growth targets in the aftermath of a crisis through capital reduction and inflation, or does decarbonization policies take center-stage, with capital building enabling decoupling? For ensuring sustained post-crisis decoupling, specifically after COVID-19, breaking of the inflation-FF whiplash and the IPES cycle are critical, else emissions will not only rebound, but grow further due to the business cycle being reset after a shock.

6 Conclusion and policy implications

Decoupling is a dynamic and adaptive macroeconomic process, the causes of which are explored in this study in the context of the fast-growing and high-inflation Indian economy. By tying together Zivot-Andrews test, adaptive-VECM and approximate entropy, the economic stress on decarbonization progress in light of business cycle movements and economic shocks is analyzed from the period 1996 to 2020, with a quarterly time-interval. Through an analysis of six models from different macroeconomic perspectives, it was found that a stochastic model better approximated macroeconomic higher-order movements and rebound from economic shocks over linear growth, Cobb–Douglas production, trade and finance models by internalizing the differential effects of electricity and non-electricity-use and the control effect of FF imports on TROP. The key findings are as follows:
1.
A stochastic control system internalizes the inherent randomness in economic perspectives of decoupling, resulting in more information content (ApEn value of 0.43, significantly higher than other modelled control systems).
 
2.
Stochasticity is an important determinant of decoupling, specifically during recession phases. Decarbonization policies based on traditional economic perspectives would fail to adjust to the economic stress of recession, prioritizing inflation-based growth over decoupling initiatives.
 
3.
EKC hypothesis interpretation is extended in this research, as decoupling is revealed to be an emergence of a 3E system and not an absolute characteristic. Decoupling from inflation should be prioritized in lieu of economic growth decoupling for a high-inflation economy like India.
 
4.
3E nexuses are stochastically resilient, and economic shocks are not an indicator of success of decarbonization. Emissions will always rebound, until policy interventions are carried out in the long-run.
 
5.
FF imports are causal effects of GDP and energy-use which directly affect capital and inflation. It is this interaction that ultimately causes the rebound of emissions in post-crisis periods.
 
The key discretized macroeconomic net-zero policy directions post-COVID-19 for India are as follows:
a.
Electricity and non-electricity are stochastically dynamic and coupled to TROP. RE in the Indian macroeconomy is limited to electricity-use, and there should be an active effort electrify primary sector. In growth phases of business cycles, FF import-injected inflationary growth should be disincentivized, which will break the IPES and inflation-FF whiplash feedbacks.
 
b.
When interest rates rise, FF imports should build capital of energy transition technologies. This will accelerate capital-based decoupling in recession phases, and limit inflation-based coupling in growth phases. Capital building can be in the form of domestic boost of RE technologies like giga-solar plants, electric vehicles in public transportation, smart cities, etc.
 
c.
From markets perspective, growth phases should accompany risk hedges, which can be incentivized in the form of green bonds to investors, which can limit inflation-emissions coupling.
 
From empirical evidences to practice, several future research directions need to be explored. For example, within existing policy mechanisms, power purchase agreements for RE and other clean energy (even modified FF sources like ultra-supercritical coal) can be made with business cycles in mind, such that inflation-decoupling can be macroeconomically engineered. Supply chain optimization studies and synergy-trade-off analysis for such discretized policy is of utmost importance. This also has the potential to not only reach the 175 GW RE target,1 but also build capital for energy transition enabling overall decarbonization of the energy sector. In a way, capital growth-oriented decoupling is the most major finding of this study in high-inflation developing economies. India has been considering a form of carbon taxation, wherein our findings show that the macroeconomic 3E dynamics should be in the form of carbon credits. This is because credits can be converted to assets, which taxes cannot be. Further research is required into the financial dynamics of a carbon credit system, and how decoupling is enabled with the 3E indices.
One limitation of discretized view of decoupling is that business cycle lengths are still not exactly identifiable, making policy introduction times a big question for political scientists in future works. Specifically, the authenticity of data, free of bias, is needed to be ensured from a sociopolitical aspect. While the macroeconomic perspective of a single country is shown here, individual sectors can have different behavior, and countries with dissimilar economic structure can also have varied feedbacks. Immediate future studies should focus on the impulse response determinations of other high-inflation economies to extract common discretized decoupling pathways for growth and inflation phases. In fact, future analyses can analyze the synchronization of the impulses of countries sharing FF trade agreements, such that net-zero interventions can not only be at a national-level, but be global. Secondly, while this study treats the financial crisis and COVID-19 from a similar macro-lens, individual crises solutions can lead to a better understanding of how decoupling and EKC behaves during different shocks. This way, the resiliency of net-zero policies can be proactive, rather than reactive.
Another line of research that can be further conducted in high-inflation developing economies, is how the decoupling pathways can be integrated with the human capital of the five-capitals (5C) concept. While this study focuses on the financial, manufactured, natural and social (socioeconomic) capitals, sociological research and the response of communities (human capital) is needed to be internalized for post-crisis decoupling pathways to be fully realized. This can include how each feedback pathways of the 3E system adapt and change as per the affluence and societies of the respective sectoral stakeholders. Moreover, high-inflation economies are ridden with poverty, which is where future studies can elucidate whether the “IPES loop” and “inflation-fossil imports whiplash” mitigation can lead to socioeconomic development and poverty alleviation.
Inflation-led growth is an easy economic tool for fostering a statistically powerful economy but ultimately will come at the expense of the climate. It is an uneconomic growth situation, and high-inflation countries like India should invest in long-term discretized strategies that can foresee a resilient net-zero progress, despite economic crises and recessions.

Acknowledgements

The authors are highly indebted to Kavin Paul, Khadija Usher, Hideyuki Okumura and Takaya Ogawa who had insightful comments on the research and greatly helped to improve the analysis. The authors are also grateful to Japan Science and Technology Agency for support and funding to Soumya Basu.

Declarations

Conflict of interest

The authors declare no conflict of interest.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://​creativecommons.​org/​licenses/​by/​4.​0/​.

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Anhänge

Appendix A: Model 1

See Tables 13, 14, 15 and Figs. 13 and 14.
Table 13
Lag length selection for Model 1 UVAR estimation
Lags
Log likelihood
AIC
BIC
0
418.83
− 831.65
− 825.86
1
639.03
− 1254.1
− 1231.1
2
666.77*
− 1291.5*
− 1251.5*
3
665.90
− 1271.8
− 1215.7
4
657.42
− 1236.9
− 1164.7
5
659.80
− 1223.6
− 1135.8
*Denotes selection of the lag order
Table 14
Johansen Cointegration test results for Model 1 (using H1 model)
Rank
Trace statistic
Maximum Eigen stat
Eigen value
R = 0
60.09*
37.37*
0.534
R ≤ 1
22.72*
17.37**
0.299
R ≤ 2
5.345**
5.345**
0.103
*,**Denotes significance at 1% and 5% levels, respectively
Table 15
Results of the VECM long- and short-run estimations of Model 1
Independent variable
Dependent variable
ΔLGDP
ΔLENE
ΔLEMS
Constant
− 0.186**
0.260*
0.151
LGDP (− 1)
− 0.067
0.092*
0.047
LENE (− 1)
− 0.036
− 0.289*
0.409**
LEMS (− 1)
0.205
0.068
− 0.538*
ΔLGDP (− 1)
0.149
− 0.081
0.117
ΔLENE (− 1)
0.194
0.913*
0.679**
ΔLEMS (− 1)
− 0.198***
− 0.020
0.210
Log-Likelihood
664.01
AIC
− 1280.2
BIC
− 1234.8
Diagnostic tests
JB
1.957#
1.012#
48.97*
Q (LBQ)
58.35a,#
48.32a,#
28.97b,#
ARCH
0.106#
0.497#
0.159#
*Significant at the 1% level
**Significant at the 5% level
***Significant at the 10% level
#Significant above the 10% level
a20 lags involved in the Monte-Carlo Auto-correlation test
b45 lags involved in the Monte-Carlo Auto-correlation test

Appendix B: Model 2

See Tables 16, 17, 18 and Figs. 15, 16.
Table 16
Lag length selection for Model 2 UVAR estimation
Lags
Log Likelihood
AIC
BIC
0
543.18
− 1078.4
− 1070.6
1
820.13
− 1600.3
− 1562.0
2
848.10
− 1594.2
− 1556.1
3
849.01*
− 1624.0*
− 1596.7*
4
836.98
− 1538.0
− 1412.1
5
850.35
− 1532.7
− 1379.1
*Denotes selection of the lag order
Table 17
Johansen Cointegration test results for Model 2 (using H1 model)
Rank
Trace statistic
Maximum Eigen stat
Eigen value
R = 0
64.40*
37.45*
0.534
R ≤ 1
26.97***
16.73
0.289
R ≤ 2
10.23
9.943
0.184
R ≤ 3
0.287
0.287
0.006
*, **,***: Denotes significance at 1%, 5% and 10% levels, respectively
Table 18
Results of the VECM long- and short-run estimations of Model 2
Independent variable
Dependent variable
ΔLGDP
ΔLCAP
ΔLENE
ΔLEMS
Constant
− 0.599**
1.775*
0.044
− 0.282
LGDP (− 1)
− 0.199*
0.581**
0.014
− 0.093
LCAP (− 1)
− 0.021*
0.062**
0.001
− 0.010
LENE (− 1)
0.436*
− 1.275**
− 0.031
0.205
LEMS (− 1)
0.091*
− 0.266**
− 0.006
0.043
ΔLGDP (− 1)
− 0.093
0.873**
− 0.226*
− 0.268
ΔLCAP (− 1)
0.178**
− 0.201
0.068**
0.147***
ΔLENE (− 1)
0.349
− 1.828***
1.157*
1.638*
ΔLEMS (− 1)
− 0.201***
− 0.105
0.009
− 0.143
ΔLGDP (− 2)
0.356**
− 0.081
0.238*
0.030
ΔLCAP (− 2)
0.139***
− 0.020
0.008
0.061
ΔLENE (− 2)
− 0.480
2.769**
− 0.498**
− 0.507
ΔLEMS (− 2)
− 0.103
0.134
− 0.048
− 0.536*
Log-Likelihood
835.95
AIC
− 1583.9
BIC
− 1501.6
Diagnostic tests
JB
0.405#
0.507#
0.719#
10.96**
Q (LBQ)
22.28a,#
18.96a,#
24.06a,#
14.14a,#
ARCH
0.474#
1.103#
2.330#
1.319#
*Significant at the 1% level
**Significant at the 5% level
***Significant at the 10% level
#Significant above the 10% level
a20 lags involved in the Monte-Carlo Auto-correlation test

Appendix C: Model 3

Tables 19, 20, 21 and Figs. 17, 18.
Table 19
Lag length selection for Model 3 UVAR estimation
Lags
Log likelihood
AIC
BIC
0
533.36
− 1058.7
− 1051.0
1
774.38
− 1508.8
1470.5
2
803.25
− 1534.5
− 1466.4
3
803.96
− 1503.9
− 1406.6
4
794.32
− 1452.6
1326.8
5
803.49
− 1439.0
− 1285.4
6
875.49*
− 1539.0*
− 1412.0*
*Denotes selection of the lag order
Table 20
Johansen Cointegration test results for model 3 (using H1 model)
Rank
Trace statistic
Maximum Eigen stat
Eigen value
R = 0
87.68*
45.53*
0.636
R ≤ 1
42.15*
26.61*
0.446
R ≤ 2
15.54**
11.63***
0.228
R ≤ 3
3.914**
3.913**
0.083
*, **, ***Denotes significance at 1%, 5% and 10% levels, respectively
Table 21
Results of the VECM long- and short-run estimations of Model 3
Independent variable
Dependent variable
ΔLGDP
ΔTROP
ΔLENE
ΔLEMS
Constant
0.645*
0.055
0.408*
0.819*
LGDP (− 1)
0.194*
0.325
0.131*
0.227*
TROP (− 1)
0.069*
− 0.517*
0.030*
0.110*
LENE (− 1)
− 1.037*
2.328***
− 0.544*
0.009
LEMS (− 1)
0.509*
− 2.561**
0.203*
− 0.684*
ΔLGDP (− 1)
− 0.406**
1.676
− 0.408*
− 0.818*
ΔTROP (− 1)
− 0.009
0.237
− 0.002
− 0.023
ΔLENE (− 1)
1.422*
− 0.293
1.596*
2.143*
ΔLEMS (− 1)
− 0.388*
1.427***
− 0.146*
0.283***
ΔLGDP (− 2)
0.251***
0.476
0.005
− 0.315***
ΔTROP (− 2)
− 0.112*
0.076
− 0.038*
− 0.084**
ΔLENE (− 2)
− 0.065
0.027
− 0.002
0.524
ΔLEMS (− 2)
− 0.665*
1.381
− 0.309*
− 0.199
ΔLGDP (-3)
0.045
− 0.591
− 0.049
0.213
ΔTROP (-3)
− 0.025
0.252
− 0.002
− 0.088**
ΔLENE (-3)
0.916**
0.058
0.451*
− 0.705
ΔLEMS (-3)
− 0.083
3.390*
− 0.090
− 0.084
ΔLGDP (-4)
− 0.609*
− 0.109
0.032
− 0.278***
ΔTROP (-4)
− 0.070**
− 0.449**
− 0.044*
− 0.009
ΔLENE (-4)
0.999**
− 5.108***
− 0.402*
0.430
ΔLEMS (-4)
− 0.422*
1.133***
− 0.221*
0.268**
ΔLGDP (-5)
0.133
0.624
− 0.137*
− 0.672*
ΔTROP (-5)
0.036
0.042
0.01
− 0.066
ΔLENE (-5)
0.430
1.814
0.981*
1.615*
ΔLEMS (-5)
− 0.029
2.264*
− 0.068**
− 0.129
Log-Likelihood
833.67
AIC
− 1451.4
BIC
− 1256.2
Diagnostic tests
JB
1.058#
0.478#
1.065#
2.027#
Q (LBQ)
26.31a,#
16.23a.#
24.47a,#
25.62a,#
ARCH
0.793#
17.61*
2.741#
2.161#
*Significant at the 1% level
**Significant at the 5% level
***Significant at the 10% level
#Significant above the 10% level
a20 lags involved in the Monte-Carlo Auto-correlation test

Appendix D: Model 4

Tables 22, 23, 24 and Figs. 19, 20.
Table 22
Lag length selection for Model 4 UVAR estimation
Lags
Log likelihood
AIC
BIC
0
696.22
− 1382.4
− 1372.8
1
1006.2
− 1952.4
− 1895.0
2
1071.6
− 2033.2
− 1929.1
3
1123.6*
− 2047.2*
− 1957.6*
4
1103.1
− 1996.1
− 1801.8
*Denotes selection of the lag order
Table 23
Johansen Cointegration test results for Model 4 (using H1 model)
Rank
Trace statistic
Maximum Eigen stat
Eigen value
R = 0
87.15*
31.22***
0.478
R ≤ 1
55.93*
25.31***
0.410
R ≤ 2
30.62**
14.91
0.267
R ≤ 3
15.71**
10.95
0.204
R ≤ 4
4.753**
4.753**
0.094
*, **, ***Denotes significance at 1%, 5% and 10% levels, respectively
Table 24
Results of the VECM long- and short-run estimations of Model 4
Independent Variable
Dependent variable
ΔLGDP
ΔLCPI
ΔTROP
ΔLENE
ΔLEMS
Constant
0.036
− 0.338
1.505
0.326*
0.152
LGDP (− 1)
− 0.013
− 0.116
1.083*
0.112*
0.045
LCPI (− 1)
− 0.005
− 0.160
− 1.178*
− 0.043
− 0.114
TROP (− 1)
0.041
0.011
− 0.777*
0.012
0.030
LENE (− 1)
0.064
0.711**
0.512
− 0.204**
0.374***
LEMS (− 1)
− 0.075
− 0.274
− 0.983
− 0.034
− 0.397**
ΔLGDP (− 1)
− 0.023
− 0.223
0.843
− 0.209*
− 0.094
ΔLCPI (− 1)
0.561***
0.838**
2.266**
0.186***
− 0.224
ΔTROP (− 1)
− 0.014
0.067
0.379**
0.007
0.063***
ΔLENE (− 1)
0.444
1.423*
− 2.495
1.07*
0.845**
ΔLEMS (− 1)
− 0.782**
− 0.982**
− 2.152
− 0.16
0.485
ΔLGDP (− 2)
0.460**
0.018
1.054
0.207*
− 0.055
ΔLCPI (− 2)
− 0.578***
− 0.385
− 2.391**
− 0.150
0.100
ΔTROP (− 2)
− 0.055
− 0.051
0.379**
− 0.024
− 0.056
ΔLENE (− 2)
− 0.337
− 1.005
1.641
− 0.341***
− 0.414
ΔLEMS (− 2)
0.665
− 0.055
3.852**
0.16
− 0.462
Log-likelihood
1081.2
AIC
− 1972.5
BIC
− 1794.7
Diagnostic tests
JB
0.422#
0.019#
0.293#
2.116#
0.041#
Q (LBQ)
62.81b, #
10.40a,#
12.68a,#
49.22a,*
13.27a,#
ARCH
3.225#
6.407**
4.939***
0.906#
6.546**
*Significant at the 1% level
**Significant at the 5% level
***Significant at the 10% level
# Significant above the 10% level
a20 lags involved in the Monte-Carlo Auto-correlation test
b45 lags involved in the Monte-Carlo Auto-correlation test

Appendix E: Model 5

Tables 25, 26, 27 and Figs. 21, 22.
Table 25
Lag length selection for Model 5 UVAR estimation
Lags
Log likelihood
AIC
BIC
0
665.41
− 1320.8
− 1311.2
1
961.20
1862.4
− 1805.1
2
1010.4*
− 1910.8*
− 1806.8*
3
1013.0
− 1866.0
− 1716.3
4
1022.4
− 1834.8
− 1640.5
*Denotes selection of the lag order
Table 26
Johansen Cointegration test results for Model 5 (using H1 model)
Rank
Trace statistic
Maximum Eigen Stat
Eigen value
R = 0
118.1*
51.17*
0.648
R ≤ 1
66.93*
32.73*
0.487
R ≤ 2
34.20**
24.32**
0.391
R ≤ 3
9.880
7.338***
0.139
R ≤ 4
2.547
2.547
0.051
*, **, ***Denotes significance at 1%, 5% and 10% levels, respectively
Table 27
Results of the VECM long- and short-run estimations of model 5
Independent variable
Dependent variable
ΔLCAP
ΔLCPI
ΔTROP
ΔLENE
ΔLEMS
Constant
0.153
− 0.182
− 0.333
− 0.131*
0.098
LCAP (− 1)
0.087
− 0.044
0.535*
0.073*
0.036
LCPI (− 1)
0.063
− 0.126
− 0.637*
0.061**
0.059
TROP (− 1)
− 0.029
− 0.034
− 0.721*
− 0.021
0.005
LENE (− 1)
− 0.123
0.165
0.369
− 0.112*
− 0.087
LEMS (− 1)
− 0.093
0.108
0.088
− 0.084*
− 0.060
ΔLCAP (− 1)
0.029
0.087
− 0.304
− 0.010
0.072
ΔLCPI (− 1)
− 0.135
0.622*
0.438
0.054
− 0.130
ΔTROP (− 1)
− 0.088
0.126**
0.404*
0.030**
0.096**
ΔLENE (− 1)
0.168
0.653***
− 1.280
0.638*
0.654**
ΔLEMS (− 1)
− 0.065
− 0.858*
− 0.478
− 0.016
0.122
Log-likelihood
993.32
AIC
− 1886.6
BIC
− 1792.0
Diagnostic tests
JB
0.073#
23.15*
1.133#
0.414
22.18*
Q (LBQ)
47.89b,#
119.9b,*
15.30a,#
19.58a,#
71.62a,*
ARCH
0.119#
1.143#
15.95*
0.404#
0.995#
*Significant at the 1% level
**Significant at the 5% level
***Significant at the 10% level
#Significant above the 10% level
a20 lags involved in the Monte-Carlo auto-correlation test
b35 lags involved in the Monte-Carlo auto-correlation test

Appendix F: Model 6

See Tables 28, 29, 30 and Figs. 23, 24.
Table 28
Lag length selection for Model 6 UVAR estimation
Lags
Log likelihood
AIC
BIC
0
1192.5
− 2368.9
− 2353.5
1
1596.4
− 3048.9
− 2911.2
2
1708.1
− 3144.2
− 2886.9
3
1783.7
− 3167.4
− 2793.1
4
1922.6*
− 3317.1*
− 2943.7*
*Denotes selection of the lag order
Table 29
Johansen Cointegration test results for Model 6 (using H1 model)
Rank
Trace statistic
Maximum Eigen stat
Eigen value
R = 0
474.6*
145.0*
0.954
R ≤ 1
329.7*
112.6*
0.909
R ≤ 2
217.0*
67.18*
0.761
R ≤ 3
149.9*
56.22*
0.698
R ≤ 4
93.64*
41.84*
0.590
R ≤ 5
51.79*
25.93*
0.424
R ≤ 6
25.86*
16.53**
0.296
R ≤ 7
9.335*
9.335*
0.180
*,**Denotes significance at 1% and 5% levels, respectively
Table 30
Results of the VECM long- and short-run estimations of model 6
Independent variable
Dependent variables
ΔLGDP
ΔLCAP
ΔLCPI
ΔTROP
ΔLELEC
ΔLENE
ΔLEMS
ΔLENIMP
Constant
− 0.319
1.130
− 0.020
2.462***
0.463
0.142
0.595
0.515
LGDP (− 1)
− 0.001
1.789*
0.570***
0.108
0.260
− 0.009
0.663**
− 0.137
LCAP (− 1)
− 0.241**
− 1.137*
− 0.894*
1.860*
− 0.081
− 0.004
− 0.703*
1.071*
LCPI (− 1)
− 0.270***
− 0.435
− 1.022*
− 0.408
0.001
− 0.304*
0.805*
2.022*
TROP (− 1)
0.054
0.116
0.131
− 1.493*
− 0.094
− 0.033***
0.120
0.021
LELEC (− 1)
0.466*
− 0.205
0.190
0.158
− 0.496**
0.321*
0.120
− 1.032*
LENE (− 1)
− 0.553**
1.615**
0.321
− 2.991***
− 0.490
− 0.668*
0.054
1.488*
LEMS (− 1)
1.056*
− 1.528
0.704
0.460
0.266
0.734*
0.281
− 3.346*
LENIMP (− 1)
− 0.104
− 0.819*
0.161
0.212
0.248**
0.017
0.706*
− 0.774*
ΔLGDP (− 1)
− 1.087*
− 0.761**
− 0.384
1.129
− 0.690*
− 0.420*
− 0.330**
0.336
ΔLCAP (− 1)
0.326*
0.146
0.895*
− 1.420*
0.362**
0.069***
− 0.684*
− 0.883*
ΔLCPI (− 1)
1.163*
− 1.219
1.563**
2.057
0.648
0.392*
0.643**
− 1.110**
ΔTROP (− 1)
− 0.130*
− 0.573*
0.028
1.217*
− 0.062
0.067*
0.057
0.201*
ΔLELEC (− 1)
− 0.258***
− 0.057
− 0.336
− 2.304*
− 0.259
− 0.002
− 0.151**
− 0.391***
ΔLENE (− 1)
1.818*
− 1.676***
1.630**
− 2.943
1.400**
1.387*
1.253**
1.862*
ΔLEMS (− 1)
− 1.926*
2.270***
− 2.111
− 3.835
− 1.607**
− 0.591*
− 0.592
1.566**
ΔLENIMP (− 1)
0.426*
0.895*
0.216
− 1.746*
0.256***
1.027**
0.156
− 0.915*
ΔLGDP (− 2)
− 0.118
− 0.269
− 0.103
− 1.730***
− 0.192
− 0.038
0.018
− 0.575**
ΔLCAP (− 2)
0.102
− 0.099
0.561*
0.311
0.350**
− 0.003
0.402*
− 0.259**
ΔLCPI (− 2)
0.758***
3.550*
− 0.563
0.344
0.596
0.174
− 0.561
− 0.373
ΔTROP (− 2)
− 0.274*
− 0.477*
− 0.191**
0.880*
0.061
− 0.066*
− 0.173**
0.099
ΔLELEC (− 2)
− 0.186
0.539
− 0.830*
− 1.245
− 0.131
− 0.257*
− 0.139
0.040
ΔLENE (− 2)
0.008
1.897
0.811
7.582*
1.236
− 0.102
0.267
0.241
ΔLEMS (− 2)
− 1.526**
− 4.33**
0.021
− 1.277
− 1.161
− 0.436
0.360
0.453
ΔLENIMP (− 2)
0.539*
− 1.493*
0.601*
− 0.045
0.125
0.126*
0.466*
− 0.226
ΔLGDP (-3)
0.292***
1.591*
0.380
− 1.632
0.215
− 0.178**
0.192
− 0.758*
ΔLCAP (-3)
− 0.028
0.312***
0.069
0.305
0.286*
− 0.076*
0.004
− 0.028
ΔLCPI (-3)
− 0.629
− 4.542*
0.472
2.752
− 0.661
0.605*
0.724
− 1.543**
ΔTROP (-3)
− 0.161*
0.043
− 0.251*
0.095
0.050
− 0.088*
− 0.191**
0.025
ΔLELEC (-3)
0.226**
− 0.358
− 0.114
− 0.460
− 0.007
0.089**
0.032
− 0.303**
ΔLENE (-3)
− 0.119
− 2.810**
− 0.415
3.527
0.419
0.192
0.032
0.214
ΔLEMS (-3)
0.766
5.687
− 0.822
− 4.418
0.429
− 0.795*
− 0.941
1.774**
ΔLENIMP (-3)
0.398*
0.431
0.480**
− 1.083**
− 0.220
0.304*
0.426**
0.293
Log-Likelihood
1917.9
AIC
− 3211.8
BIC
− 2634.5
Diagnostic Tests
JB
1.027#
1.494#
1.211#
1.339#
0.547#
0.080#
1.629#
2.237#
Q (LBQ)
17.59a,#
11.08a,#
7.943a,#
15.14a,#
11.34a,#
11.43a,#
9.864a,#
18.29a,***
ARCH
0.977#
0.700#
12.05a,#
2.999#
3.894#
3.676#
3.442#
2.553#
*Significant at the 1% level
**Significant at the 5% level
***Significant at the 10% level
#Significant above the 10% level
a10 lags involved in the Monte-Carlo auto-correlation test
Literatur
Zurück zum Zitat Bunnag, T.: Analyzing short-run and long-run causality relationship among CO2 emission, energy consumption, GDP, square of GDP, and foreign direct investment in environmental Kuznets curve for Thailand. Int. J. Energy Econ. Policy 13(2), 341–348 (2023). https://doi.org/10.32479/ijeep.14088CrossRef Bunnag, T.: Analyzing short-run and long-run causality relationship among CO2 emission, energy consumption, GDP, square of GDP, and foreign direct investment in environmental Kuznets curve for Thailand. Int. J. Energy Econ. Policy 13(2), 341–348 (2023). https://​doi.​org/​10.​32479/​ijeep.​14088CrossRef
Zurück zum Zitat Cheng, B.S.: Causality between energy consumption and economic growth in India: an application of cointegration and error-correction modeling. Indian Econ. Rev. 34(1), 39–49 (1999) Cheng, B.S.: Causality between energy consumption and economic growth in India: an application of cointegration and error-correction modeling. Indian Econ. Rev. 34(1), 39–49 (1999)
Zurück zum Zitat Cobb, C.W., Douglas, P.H.: A theory of production. Am. Econ. Rev. 18(1), 139–165 (1928) Cobb, C.W., Douglas, P.H.: A theory of production. Am. Econ. Rev. 18(1), 139–165 (1928)
Zurück zum Zitat Erkan, C., Mucuk, M., Uysal, D.: The impact of energy consumption on exports: The Turkish case. Asian J. Bus. Manag. 2(1), 17–23 (2010) Erkan, C., Mucuk, M., Uysal, D.: The impact of energy consumption on exports: The Turkish case. Asian J. Bus. Manag. 2(1), 17–23 (2010)
Zurück zum Zitat IEA: Global energy demand to plunge this year as a result of the biggest shock since the Second World War (2020a). IEA: Global energy demand to plunge this year as a result of the biggest shock since the Second World War (2020a).
Zurück zum Zitat Kraft, J., Kraft, A.: On the relationship between energy and GNP. The J. Energy Dev. 3(2), 401–403 (1978) Kraft, J., Kraft, A.: On the relationship between energy and GNP. The J. Energy Dev. 3(2), 401–403 (1978)
Zurück zum Zitat Raza Abbasi, K., Hussain, K., Abbas, J., Fatai Adedoyin, F., Ahmed Shaikh, P., Yousaf, H., Muhammad, F.: Analyzing the role of industrial sector’s electricity consumption, prices, and GDP: A modified empirical evidence from Pakistan. AIMS Energy 9(1), 29–49 (2021). https://doi.org/10.3934/energy.2021003CrossRef Raza Abbasi, K., Hussain, K., Abbas, J., Fatai Adedoyin, F., Ahmed Shaikh, P., Yousaf, H., Muhammad, F.: Analyzing the role of industrial sector’s electricity consumption, prices, and GDP: A modified empirical evidence from Pakistan. AIMS Energy 9(1), 29–49 (2021). https://​doi.​org/​10.​3934/​energy.​2021003CrossRef
Metadaten
Titel
On the resiliency of post-crisis decoupling in higher-order economy-energy-environment nexus in high-inflation developing economies
verfasst von
Soumya Basu
Keiichi Ishihara
Publikationsdatum
08.01.2025
Verlag
Springer Netherlands
Erschienen in
Quality & Quantity
Print ISSN: 0033-5177
Elektronische ISSN: 1573-7845
DOI
https://doi.org/10.1007/s11135-024-01999-3

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