A Cross-Sectoral Investigation of the Energy–Environment–Economy Causal Nexus in Pakistan: Policy Suggestions for Improved Energy Management

Abstract

This paper explored the energy–environment–economy (EEE) causal nexus of Pakistan, thereby reporting the causal determinants of the EEE nexus by employing the newly developed modified Peter and Clark (PC) algorithm. The modified PC algorithm was employed to investigate the causal ordering of energy consumption, CO₂ emissions and economic growth across Pakistan’s domestic, industrial, transportation and agricultural sectors. An empirical comparison, i.e., following Monte Carlo simulation experiments demonstrates that the proposed modified PC algorithm is superior to the original PC proposition and can differentiate between true and spurious nexus causalities. Our results show that significant causality is running from energy consumption in industrial and agricultural sectors towards economic growth. There is no causal association between energy consumption and economic growth in the domestic and transportation sectors. On the other hand, causality runs from energy consumption in the transportation, domestic and industrial sectors towards CO₂ emissions. It is concluded that energy consumption in industrial and agricultural sectors leads to economic growth alongside the associated CO₂ emissions. On the other hand, the contribution of domestic and transportation sectors in economic growth is trivial with significant CO₂ emissions. This paper provides novel empirical evidence of impacts of energy mismanagement at sectoral levels, economic output and environmental consequences; alongside policy recommendations for sustainable energy-based development on the national scale.

1. Introduction

Following the energy crisis of the 1970s, the focus of energy planning and management shifted to availability, abundance and diversification of energy resources. Soon it was realized that cost-effective and long-lasting alternative resources were required and had to be economically reasonable [1]. In the modern day, energy intake has emerged as an important variable for judging the quality of life and well-being globally [2]. Nevertheless, energy use in many contexts is having serious and damaging effects on the environment in the form of emissions, primarily greenhouse gases, otherwise known as GHGs [3]. To cater for the ever-rising demand for energy driven by the world’s increasingly unsustainable population growth, fossil fuel consumption is growing daily and especially in the developing countries [4]. Energy planning must now consider the environmental goals and appreciate economic growth has to be sustainable or carried out in a different way. Governments and policymakers must achieve energy sustainability, economic growth and environmental protection; they must adapt systems thinking and comprehend the nexus between energy, environment and economy (EEE).

Pakistan has observed a significant increase in energy demand over the past couple of decades due to its rising population, massive urbanization, industrial development and modernization. This has resulted into increased atmospheric pollution and especially the many types of pollutants [5,6,7]. Some of the leading factors responsible for bad air quality are: inefficient energy systems and subsystems across various sectors of the economy, ill-planned industrial development, adherence to obsolete vehicles, non-observance of environmental quality standards, and poor atmospheric quality data [7,8,9,10]. Similarly, the realities of urbanization, industrial activities, and construction have not only contaminated urban air quality but also made rural conditions worse [11]. Air quality of various Pakistani cities has been thoroughly investigated and Lahore is now the country’s most polluted city [12]. Respiratory diseases lined to air pollution is causing 1250 deaths in the city every year [12,13].

This paper is the first of its kind whereby a sectoral level understanding of the EEE nexus has been achieved by exampling Pakistan. The innovation in this work further lies in both case study (i.e., Pakistan) and choice of methods followed. It is because, Pakistan provides a unique example of an economy where energy consumption does not contribute towards economic growth on a national scale. However, as we reported in this paper; the situation at sectoral level is different. Hence, the results of this study provide a unique opportunity for policy and decision makers to revise energy planning and policies by targeting the key economic sector in the manner desired. Keeping in view the importance of key factors behind the EEE nexus in Pakistan, this paper explores the determinants of the EEE causal nexus at sectoral level. We believe that a sector-wise investigation of the EEE nexus will produce key insights such as national-scale policy and decision-making regarding decarbonization, changing energy sources and proper resource allocation to name a few. As reported recently by Fazal et al. [14], unidirectional causality runs from economic growth to CO₂ emissions in Pakistan. Based on their results, no causality is running from energy consumption to economic growth and vice-versa. It is crucial to break down the EEE nexus in Pakistan, i.e., to evaluate it across major sectors of the economy and understand what is driving it and people’s actions and behaviors.

The methodological framework adapted here is based on Graph Theoretic Approach (GTA), which lead to the development of modified Peter and Clark (PC) algorithm; a technique newly developed in this study. It is an econometrically flawless approach and the results obtained are easily interpretable. The theoretical basis of GTA is rich and been refined over time, i.e., following the Granger [15] test, it helped to determine the true causal relationship. It was later discovered that the Granger test is based on temporal ordering, i.e., it determines predictability only [16,17]. Furthermore, the Granger test does not consider structural ordering [18,19]. Recently, econometricians and social scientists discovered the PC algorithm of GTA—an approach based on structural equations to determine causal ordering. PC algorithms were initially considered unsuitable for applications to time-series data [20] because they were intended to decide the causal ordering of cross-sectional data.

In order to make the PC algorithm applicable for time series data, Swanson and Granger [21] used vector autoregressive (VAR) residuals in the PC algorithms by treating them as original variables to address the non-stationarity issue (and see Selva and Kevin [22], Kevin [23] and Hoover [24]). However, VAR model residuals carry only contemporaneous information about the cross-variable-effect, i.e., purging older information and causality results that cannot be relied on.

Consequently, this paper has developed modified PC algorithms by replacing VAR residuals with Malik [25] test using modified R recursive residuals. Doing so will determine the correct causal ordering and estimate and prove the superiority of modified PC algorithms. Monte Carlo simulation experiments are conducted to demonstrate the power of modified PC algorithms. This strategy is employed to explore the determinants of the EEE causal nexus in Pakistan. The following sections deal with, in order: energy-driven air pollution in Pakistan (Section 1.1); cross-sectoral energy consumption in Pakistan (Section 1.2); energy, environment and economic growth correlation in Pakistan (Section 1.3); theoretical and methodological framework (Section 2); results and discussion (Section 3); and conclusions and policy recommendations (Section 4).

1.1. Energy-Driven Air Pollution in Pakistan

Atmospheric pollutants co-exist as a gaseous form such as CO_x, NO_x, SO_x, ozone, etc., and in a solid state such as particulate matter (PM). Pollutants in the solid form require special attention due because they basically endanger people’s respiratory systems. Smaller-sized particulates having diameters of 2.5–10 µm are considered dangerous [26,27]. Particulate matter pollutants provide a surface area for the deposition of heavy metals and chemical reactions [13,28]. Aerosols such as black carbon (BC), organic carbon (OC), nitrate (NO³⁻), ammonium (NH₄⁺) and sulfate (SO₄²⁻) are the major types of aerosols in the atmosphere [29,30]. The concentrations of major air pollutants such as Pb, NO₂, CO, SO₂ and PM except ozone in Pakistan’s cities have now exceeded the WHO permissible limits [5]. One reason for poor air quality in Pakistan is the lack of testing and reporting stations [31,32].

Numerous anthropogenic activities lead to emissions of aerosols involving energy production and consumption created in various industries using older technologies. These activities include but are not limited to energy and power production, petroleum refineries, transport (vehicular emissions), industrial processes (building and infrastructure, manufacturing of cement and ceramics, mining, brick kilns and smelting, etc.), burning of crop residues mentioning just a few [33,34]. The activities stated here are ongoing in Pakistan with electricity production (thermal power plants) being a major process responsible for the emission of pollutants such as GHGs, NO_X, SO_X, etc. Thermal power plants run by fossil fuels, i.e., oil, gas and coal emit pollutants during their lifetime depending on the input fuel, production capacity, age, total technical life, and other technological details of power plants. Thermal power plans installed in Pakistan are called independent power plants (IPPs), and most located in the province of Punjab, Muzaffargarh and a few in Lahore near Raiwand [35].

Out of the total GHGs emissions on a global scale, only 0.8% can be attributed to Pakistan [36]. Rehman et al. [37] estimated GHGs emissions and major air pollutants under five different scenarios. Coal-based electricity generation technologies are still the norm for generating power, but they create both direct (primary particulates) and indirect (secondary particulates) particulate matter emissions. The nature and fate of these pollutants depend on the type of coal and technology being employed and other ambient factors, for instance, weather and climate [38,39].

Yet despite these problems the Pakistani government is still developing a strategy for increasing more and more coal-based power generation [40]. The government has planned to add 36 more units based on coal for electricity generation employing local coal resources (Thar coal). So, by 2040, up to 23,760 MW of power capacity will be added to the system based on coal-fired power plants [41]. One reason for this decision is to address the prevailing energy crisis in the country and to reduce dependence on imported fossil fuels [42]. However, as discussed above, thermal power generation schemes based on oil, gas and coal are simply damaging the environment despite fulfilling energy demand and economic growth. Flaws in energy structure of Pakistan i.e., energy inefficiency characterized by Malmquist indexes (e.g., total factor productivity change (TFPCH)) has also been pointed out in some recent studies comparing various countries [43]. To maintain the balance between energy, environment, and economy it is crucial for the government to target and prioritize less polluting and less energy efficient systems of energy production, transportation in industry and elsewhere. Energy-driven air pollution can be avoided by introducing policies such as decarbonization, emphasis on renewables, energy efficiency programs and stopping old and outdated equipment, etc., to name a few.

1.2. Cross-Sectoral Energy Consumption in Pakistan

The population of Pakistan is growing at a rate of about 2.4% every year, with energy requirements being mainly fulfilled from fossil fuels which constitute more than 54% of the energy fuel mix [44,45,46,47]. The domestic sector relies mainly on fuelwood that accounts for 53% followed by biomass energy, i.e., 47% in 70% of the country’s rural areas. Moreover, about 20% of people’s incomes in rural communities is used to acquire fuel wood for cooking and other purposes. Based on UN estimates, 29.2 million m³ of fuel wood was consumed in 2010 [44,48]. It is noteworthy that biomass-based energy such as burning of agricultural residues is a source of air pollution in Pakistan’s countryside [49,50].

Energy consumption throughout Pakistan varies (Figure 1) due to the nature of activities and demand for various fuels. Historically speaking, energy consumption has always been high in industry followed by transport and the domestic sector. However, energy consumption is not the same thing as energy demand. This is because all sectors are experiencing energy shortages, i.e., their actual energy demand is higher than their final energy consumption. Therefore, due to limited energy supply, activities across all these sectors have been undermined in various ways. Since most of the pollution and damage to the environment is the result of the quantity and quality of energy, it is crucial to assess energy consumption, economic output, and the emissions of air pollutants from these sectors according to the EEE causal nexus.

Different sources of air pollutants in these sectors can be classified as point and/or non-point sources comprising electricity production, manufacturing, incineration, domestic heating, cooking, and vehicular emissions. From the chemistry perspective, atmospheric contaminants are of two types, organic and inorganic. Inorganic contaminants are carcinogenic and are the most highly studied group comprising particulates containing trace elements like As, Cd, Cr, and Pb [42]. In contrast, organic pollutants generally contain pro-oxidant properties, mostly originating from vehicular exhausts and include VOCs (Volatile Organic Compounds), PAHs (Polycyclic Aromatic Hydrocarbons), and heavy metal complexes [51].

Similarly, fuel quality, which refers to the fuel type, is another factor that determines the extent of environmental damage. Here, policies such as changes in energy fuel mix, decarbonization strategies, fuel switching and substitution, and adoption of renewables can improve the air quality. Furthermore, resource optimization and energy efficiency strategies shall be adapted to minimize the environmental impacts of economic growth especially across industrial sector by following studies such as Han et al. [52] and Han et al. [53]. Unfortunately, in the case of Pakistan, energy fuel mix has always been highly skewed towards non-renewables, i.e., predominantly fossil fuels like oil, gas, and coal (Figure 2).

The diverse chemistry and properties of aerosols come from both natural and/or manmade sources. Aerosols and their precursors are emitted from a variety of processes, e.g., volcanic eruptions, forest fires, biogenic emissions, sea spray, windblown dust, crop-residue and biomass burning, industrial emissions, emissions from power plants and vehicular exhausts [54,55]. Similarly, the quantity of contaminants together with ambient environmental conditions determines the formation of complex aerosols [56]. Aerosols such as BC (black carbon) is a component of PM_2.5, which plays a role in perturbation of local meteorological conditions. BC-aerosols are radiative in nature, which means they can absorb infrared and visible light and hence, are climatologically important. BC are released during biomass burning and in various other process that involve incomplete combustion [57,58].

Some of Pakistan’s cities, especially Karachi and Lahore have been thoroughly investigated for their air quality situation. Both are climatologically different, yet they are equally polluted and notorious worldwide for their bad air quality having exceedingly large quantities of total suspended particulates [59,60]. However, more often, the concentration of PM_2.5 in Lahore is reported higher than the average concentration PM_2.5 in Karachi, i.e., 118 ± 79 mg/m³ versus 84 ± 21 mg/m³, respectively [61]. Similarly, of the two cities, many studies focusing on air pollution were done in Lahore [62]. In recent years, due to increased air pollution, the contribution of transboundary air pollution cannot be ruled out, for instance the movement of PM_2.5 from India (west), Afghanistan (east) and Iran (south-east) further aggravate atmospheric pollution [61]. Sector-wise emissions of aerosols consisting of SO₄, NO₃, NH₄, OC and BC from industrial, residential, transport and energy sectors were investigated by Shahid et al. [63]. Emissions of SO_X, NO_X and PM2.5 from the energy sector in particular were estimated by Mir et al. [64] using the GAINS (Greenhouse gas and Air pollution INteractions and Synergies) model combined with Pak-IEM. Lin and Ahmad [65] projected CO₂ emissions from the energy sector using Log Mean Divisia Index (LMDI) to explain the relationship of energy intensity, GDP and carbon intensity. However, emissions of air pollutants from electricity generation were investigated in-depth by Rehman et al. [37]. They estimated emissions of about 13 air pollutants under five electricity generation scenarios.

1.3. Energy, Environment and Economic Growth Correlation in Pakistan

Energy is a driving force for economic growth worldwide. Together with labor and capital, energy constitutes an important component of production and industry. The energy–economic growth correlation, i.e., the underlying behavior of the two variables is generally investigated under four distinct hypotheses by energy economists, i.e., growth, conservation, feedback and neutrality hypothesis [66]. In today’s world, energy demand is connected to a range of factors, such as lifestyle, incomes, consumerism, technological advances, goods and services, etc. [67]. Hence, an overall significant correlation exists between energy demand and economic growth, in that energy consumption is directly proportional to economic growth in most cases [68]. However, the environmental impacts and consequences attributed to energy consumption and/or economic growth require attention. Together with the energy-economic nexus the addition of environment gives rise to what is known as the energy–environment–economy nexus.

Being a developing country, the energy requirements in Pakistan are constantly increasing. Hence, energy use per capital, which is also called energy intensity is exponentially rising. This has caused much more reliance on imported oil and petroleum-based products. Since Pakistan has only limited reserves of oil and other fossil fuels, fulfilling local energy demand is a big challenge [69]. From 2001–2007, constant growth in GDP of about 5.4% was observed in Pakistan with 8.9% being achieved in 2005. The relationship between energy consumption and GDP growth is evident from the reduction in energy consumption (39.4 MTOE in 2008 compared to 37.3 MTOE in 2009) because of GDP decline of 0.36% in 2009. It is safe to assume that energy consumption and Pakistan’s economic growth (Figure 3) are two closely correlated variables [70]. It has been estimated that to achieve economic growth of 6.5% every year, about 198 MTOE of energy supply is required to fulfill growing energy demand until 2025 [71].

The underlying correlation between energy, environment and economy is one where the EEE nexus interweaves its three elements. Each node is represented by components/factors, e.g., energy use from electricity, gas, oil, coal consumption and others, economic growth from GDP growth, and environmental wellbeing from GHGs emissions. The energy, environment and economic growth correlation has been explored individually at various levels in Pakistan.

Impacts of energy consumption on economic growth and the environment (the latter through GHGs emissions) have been reported by Alam et al. [68], Ali and Abbas [72] and Nasir and Ur Rehman [73]. For instance, Mirza and Kanwal [74] explored the long-term relationship between energy consumption, CO₂ emissions and economic growth in Pakistan using Johansen–Julius co-integration tests. They confirmed that energy consumption and CO₂ emissions greatly effect economic growth in the long run. Abbasi et al. [75] investigated the asymmetric impacts of renewable and non-renewable energy resources on Pakistan’s economy from 1970 to 2018. They applied the Nonlinear Autoregressive Lag Distributed Model (NARDL) and their results agreed with those of Rehman et al. [76]. In effect, NREs have higher environmental costs. Similarly, Khan et al. [77], while determining the nexus among GHGs emissions and renewable energy resources (RERs) in Pakistan, found unidirectional causality from RERs to GHGs emissions. Their findings agreed with Rehman et al. [76]; GHGs emissions could be reduced by utilizing RERs.

Baloch et al. [78] empirically confirmed that growth and income inequality led to higher CO₂ emissions and environmental degradation. Shah et al. [79] discovered that economic growth simply increased CO₂ emissions. Their study highlighted the existence of an inverted U-shaped curve relationship between urbanization and CO₂ emissions. Zaidi et al. [80] reported that natural gas and coal consumption increase CO₂ emissions and pollution generally. Similarly, Danish et al. [81] proved that CO₂ emissions rise with increased energy consumption in the transport sector. Malik et al. [82] forecast CO₂ emissions and reported that increased dependence on NREs until 2030 will elevate CO₂ emissions. Usman et al. [83] compared nuclear energy with combustible renewable and waste energy options. Both Mahmood et al. [84] and Usman et al. [83] concluded that nuclear energy is a threat to the environment especially when accidents occur, whereas renewable energy is the best option. Danish et al. [81] explored the role of energy production in Pakistan’s economy. Ali et al. [85] took into account the influence of fossil fuel consumption on CO₂ emissions and confirmed that the latter simply increase [86].

The resultant relationship and behavior reported in the scientific literature pertaining to energy, environment and economic growth variables lacks consensus and especially what is causing the situation. These differences are because of varied underlying assumptions and methodologies. The techniques employed in all cases have their own limitations and emphases. On the other hand, the methodology adapted in this study, i.e., GTA based on modified PC algorithms, overcomes these limitations to successfully explore the determinants of the EEE causal nexus. Moreover, the capability of GTA-based protocols has been evaluated and examined using Monte Carlo simulations.

2. Theoretical and Methodological Framework

The modified PC algorithm provides an effective statistical and mathematical tool for finding causality among and between the variables of interest. The algorithm involves five steps for detecting this causality. In the first three steps, it learns from the data information and helps generate a skeleton graph, while in the last two steps, it constructs the final causal graph.

2.1. Development of GTA Based on Modified PC Algorithm

Various stages in the development of GTA based on modified PC algorithm are reported here:

• The algorithm initially constructs an undirected graph G, which is said to be a directed acyclic graph (DAG) if it contains only directed edges and has no directed cycles. Graph G is constructed according to graph theory containing V variables/nodes and E edges representing an association between a pair of variables. The links between the pair of variables without arrowheads are called undirected edges (A→B), while the link between two variables through a straight-line having an arrowhead is called a directed edge (A→B), which gives us the direction of causality. A graph showing only the nodes and strips away all arrowheads from the edges is called the skeleton. Furthermore, if node A is linked to node B by an arrow originating from A to B, i.e., (A→B) then node A is the parent of node B, and B is the child of A. It is shown in Figure 4 that $Y$ has two parents $Z$ and $X$, three ancestors ($X,Z,W$) and no children. Finally, the direction of causality between pairs of variables depends on the unshielded collider and screen-off.
• The following assumptions are set when applying the modified PC causality algorithm:
  • Causal Markov Condition: Let G be a causal graph relating a set of variables V with a probability distribution P. Let W be a subset of V. G and P satisfy the causal Markov condition if, and only if, for every W in V, W is independent of every set of variables that does not contain its descendants, conditional on its parents [87].
  • Faithfulness Condition: A graph G and probability distribution P is said to be faithful if and only if there is a one-to-one correspondence between the conditional independence relationship implied by causal Markov condition and the probability distribution [87].
    • Developing the modified PC algorithm involves five steps for detecting causality. The first three steps relate to the construction of a skeleton graph (undirected graph), while in the last two steps arrows heads are oriented to construct the final causal graph, otherwise known as the directed graph. These steps are described below:
    • Initially, the algorithm develops the skeleton graph in which all variables are connected through undirected links.
    • The algorithm then starts testing the unconditional correlation and removes the insignificant links between any two variables.
    • In the third step, the algorithm tests correlations between every two variables conditional on a third variable and deletes the insignificant links between the pairs of variables.
    • In step four, if two variables are correlated conditional on the third variable, arrows from the two variables are oriented to the third variable and is said to be an unshielded collider.
    • In the final step, arrows are oriented based on the screening relationship. If two nodes $A$ and $B$ are not directly connected but are connected through a third node $C$ i.e., $A$→$C$→$B$,this shows that the link from $A$ to $C$ (third node) is directed while the link between nodes $C$ and $B$ is undirected. Therefore, the resulting graph will orient the second link as $A$→$C$→$B$, because orienting the arrowhead toward $C$ indicates the unshielded collider which is already revealed in step 4. Thus, the intervening node or variable is a screen and not an unshielded collider, so the arrow cannot point toward node $C$.

During application, Fisher’s z-statistics serve to test whether the conditional correlations are significantly different from zero.

2.2. Monte Carlo Simulation Experiment: Testing the Performance of PC and Modified PC Algorithm

In order to evaluate the performance of both PC and modified PC causality algorithm we conducted a Monte Carlo Simulation experiment by using data series with embedded causality and vice versa to establish the power and size properties of these causality detecting algorithms. Selection of data generating process (DGP) for Monte Carlo simulation study is very important for comparative analysis. These causality algorithms can be compared in the same framework to recommend the superiority of one test over another. The data for testing properties of causality tests can be generated from a unified framework, which is given as below:

$$\left[\begin{array}{c}{x}_t\\ y_t\\ z_t\end{array}\right]=\left[\begin{array}{ccc}{\theta }_1& {\theta }_{12}& {\theta }_{13}\\ {\theta }_{21}& {\theta }_2& {\theta }_{23}\\ {\theta }_{31}& {\theta }_{32}& {\theta }_3\end{array}\right]\left[\begin{array}{c}{x}_{t-1}\\ y_{t-1}\\ z_{t-1}\end{array}\right]+\left[\begin{array}{cc}{a}_1& a_2\\ b_1& b_2\\ c_1& c_2\end{array}\right]\left[\begin{array}{c}1\\ t\end{array}\right]+\left[\begin{array}{c}{\epsilon }_{xt}\\ {\epsilon }_{yt}\\ {\epsilon }_{zt}\end{array}\right]$$

(1)

The above matrix form equation can be written in the following form:

$$X_t=A{X}_{t-1}+BDt+{\epsilon }_t\dots \hspace{1em}{\epsilon }_t~N\left(0,\Omega \right)$$

(2)

where $A=\left[\begin{array}{ccc}{\theta }_1& {\theta }_{12}& {\theta }_{13}\\ {\theta }_{21}& {\theta }_2& {\theta }_{23}\\ {\theta }_{31}& {\theta }_{32}& {\theta }_3\end{array}\right]$,$B=\left[\begin{array}{cc}{a}_1& a_2\\ b_1& b_2\\ c_1& c_2\end{array}\right], Dt=\left[\begin{array}{c}1\\ t\end{array}\right], {\epsilon }_t=\left[\begin{array}{c}{\epsilon }_{xt}\\ {\epsilon }_{yt}\\ {\epsilon }_{zt}\end{array}\right]$, $\Omega =\left[\begin{array}{ccc}1& \rho 1& \rho 2\\ \rho 1& 1& \rho \\ \rho 2& \rho & 1\end{array}\right]$.

The data generating process (DGP)given in Equations (1) and (2) generates data in different ways by imposing varied restrictions on matrix A and B. Matrix A can be used to specify conventional Granger type causality. As per definition of Granger causality, $y$ is caused by $x$ if lag value of $x$ can be used for predicting y. In DGP (1) suppose $A_{1i}=\left(\alpha ,0,0\right)$ and α € (0, 1) then $y_{t-1 }$ and $z_{t-1}$ does not appear in the equation of $x_t$_. Therefore $y_t$ and $z_t$ does not Granger cause $x_t$. On the other hand, if the second and third columns of the first row are non-zero ${\theta }_{12}\ne 0 and/or {\theta }_{13}\ne 0$, this means that $y_t$ and $z_t$ Granger cause $x_t$. Similarly If $A_{2i}=\left(0,\alpha ,0\right)$ then $x_{t-1 }$ and $z_{t-1}$ does not appear in the equation of $y_t$. Therefore $x_t$ and $z_t$ does not Granger cause $y_t$.

On the other hand, if the second and third columns of the second row are non-zero ${\theta }_{21}={\theta }_{23}\ne 0$, this means that x and z Granger cause y. The same causal direction can be examined if we have a case that $A_{1i}=\left(0,0,\alpha \right)$. In addition, if A is null matrix, the three series will be white noise with no autocorrelation. The coefficients ${\theta }_1{\theta }_2$ and ${\theta }_3$ show the autoregressive coefficients of the first, second and third series, respectively. If ${\theta }_1$= 0, it means that the first series generated is white noise. If $0<{\theta }_1<1$ then the series generated is stationary and auto-correlated, while if ${\theta }_1\ge 1$ then the generated series will become non-stationary.The series with drift and a trend can be generated by taking B ≠ 0.

The parameter B is known as the “nuisance”. Causality does not depend on the matrix of parameter B, but the test statistics for coefficient present in “A” which determines causality is heavily dependent on B and incorrect specification of B may create bias. So, to avoid any biases, we have to include this nuisance term.

3. Results and Discussion

3.1. Energy–Environment–Economy Causal Nexus According to Sector

The discovery of a sectoral level energy–environment–economy causal nexus is a major outcome of this study. It was revealed by Fazal et al. [14] that unidirectional causality runs from economic growth to CO₂ emissions in Pakistan; no causality is running from energy consumption to economic growth and vice-versa. These results appear quiet odd for a typical economy contradict the results of other studies based on various energy economic variables. For instance Aqeel and Butt [69], Nasir and Ur Rehman [73], Hye and Riaz [88], Raza et al. [89], Komal and Abbas [90] and Baz et al. [91] reported that unidirectional causality runs from economic growth to energy consumption in Pakistan.

A unidirectional causality in the opposite direction, i.e., from energy consumption to economic growth was revealed by Siddiqui [92], Shahbaz et al. [66], Shahbaz et al. [93], Khan et al. [94] and Rehman et al. [95]. Similarly, unidirectional causality between electricity consumption and economic growth was discovered by Aqeel and Butt [69], Shahbaz and Lean [33] and Balcilar et al. [96]. Ahmed et al. [97] revealed a direct relationship between income and energy consumption, followed by Khan and Ahmad [67] who reported that both electricity and natural gas consumption increase with income. According to Zaman et al. [98] a unidirectional causality is running from income, FDI and population growth to electricity consumption. An indirect relationship between energy prices and real interest rate, investment and stock prices was noted by Arshad et al. [99]. Unidirectional causal relationship between energy consumption and CO₂ emissions was reported by Khan et al. [94], Lahiani [100] and Zhang et al. [101]. Recent studies by Malik et al. [82] and Chandio et al. [102] directly linked energy consumption with CO₂ emissions and environmental deterioration throughout Pakistan.

With these findings in mind, it is crucial to investigate and confirm the results of Fazal et al. [14] by determining the factors responsible for the overall behavior of EEE causal nexus. Our results show that significant causality runs from energy consumption in industrial and agricultural sectors to economic growth. There is no causal association between energy consumption and economic growth in the domestic and transportation sectors. On the other hand, causality runs from energy consumption in transportation, domestic and industrial sectors to CO₂ emissions (Figure 5). This strongly suggests that energy consumption in the domestic and transportation sectors does not contribute to economic growth. Yet, energy consumption in agriculture and industry does promote economic growth and prosperity. This is evident from the data of the three variables used to indicates each node of EEE nexus across these sectors, i.e., energy consumption, CO₂ emissions and GDP share (Figure 6).

It is important to note that being an agriculture-based economy, the sectors contributing significantly to economic growth in Pakistan are shown in Figure 6. Due to the nature of its activities, the industrial sector leads both economic growth and CO₂ emissions at the same time. In the domestic and transportation sectors a significant proportion of total energy consumption is taking place. Nevertheless, the contribution of these sectors to economic growth is insignificant as evident from the data (Figure 6) and results of this study. To understand the underlying causes behind this outcome, we need to look into energy efficiency, i.e., energy flow and management across in detail. It is because the EEE nexus is driven by energy, which in turn drives the economy and shapes the EEE nexus in all its possible forms.

For instance, energy fuel mix of the transportation sector reveals that oil is the dominant fuel used (Figure 2) and it is imported from other countries. Being one of the most highly privatized sectors in the country, the revenue generated from transport mostly end up generating individuals’ wealth instead of contributing to national accounts. Currently, most of the energy consumption takes place in road-based and especially privately owned transport (Figure 7). Consequently, being the sixth-most populous country in the world, the energy footprint created by the transportation sector is huge alongside significant CO₂ emissions. This calls for fundamental reforms being made to the transportation sector, i.e., increasing rail-based transportation together with mass transit systems owned by government agencies.

Second to industrial and transportation is the domestic sector where energy consumption is higher compared to agriculture. Yet, according to the results of this study, the role of the domestic sector in economic growth is less significant. This is because energy consumption in the domestic sector is to satisfy residential activities that are essentially life-supporting tasks such as cooking, heating, and cooling, etc. (Figure 8). Nevertheless, opportunities for energy sustainability exist here in the form of energy conservation and using it more efficiently. Energy is provided at subsidized costs to the residential sector where most devices are old or outdated, using up precious energy resources especially in cooking and water heating.

On the other hand, energy efficiency in agriculture is encouraging based on the economic output and less energy consumption compared to other sectors. Based on our findings, a strong causality runs from agriculture’s energy consumption to economic growth. It is worth noting that Pakistan still has very traditional and conventional agricultural practices, because farming does not have access to modern limited technologies (Figure 9). Modernization and mechanization in the agriculture sector are yet to be taken up, and doing so can further lead to improved yields and economic output in Pakistan.

3.2. Performance Evaluation of PC and Modified PC Algorithms

As discussed earlier, the main objective of our simulation experiment is to find the size and power properties of methodologies to test causality. Size of a test imply the probability of false rejecting the true null hypothesis. Suppose the null hypothesis is that energy consumption causes CO₂ emissions which is true in the case of Pakistan and the methodology we have applied suggests that energy consumption does not cause CO₂ emissions. This mean that we have rejected the true null hypothesis, which is called size or type I error (Equation (3)).

$$Size=Probability\left(Reject\frac{H_0}{H_0}is True\right)$$

(3)

To calculate size, the data should be generated under the null hypothesis $\left(H_0\right)$ which is true, i.e., there is no causality between $x$ and $y$; while alternative hypothesis $\left(H_1\right)$ i.e., there is causality between $x$ and $y$. This means that both series $x$ and $y$ are independent of each other or there is no correlation, and if the results are significant it will indicate spurious causality. Similarly, for the calculation of power, we have generated a causal correlation $x_t$,$y_t$, and $z_t$ series, so when matrix A in Equation (2) is a non-diagonal, then A = $\left[\begin{array}{ccc}{\theta }_{11}& 0& 0\\ {\theta }_{21}& {\theta }_{22}& 0\\ {\theta }_{31}& {\theta }_{32}& {\theta }_{33}\end{array}\right]$ ≠ 0. The power properties of both algorithms are calculated by finding the probability of each of the two mentioned scenarios, in other words: Correct (link is present both in DGP and final results of PC algorithm); and Omitted (link is present in DGP but absent in PC algorithm results). The best performance is considered the procedure having the least size distortion and the highest power.

3.2.1. Size Analysis

Non-Stationary Series

From the DGP three independent non-stationary series are generated with different specifications. The generated series $x_t$, $y_t$, and $z_t$ are then referred to different testing procedures i.e., applying VAR model and modified R test developed by Malik [25] and residuals series are extracted. These residuals series are then treated as original variables in the PC and modified PC algorithms, respectively. The simulated results obtained from the PC algorithm using VAR residuals indicate about 7% on average significant results against 5% nominal size in all three different specifications. This implies there is on average 2% size distortion, which can be regarded as spurious causality. The results of the modified PC algorithm, treating modified R recursive residuals showing on average 46% significant result for all three different specifications, meaning on average there is a size distortion of about 41%. It means that in modified PC algorithms, the probability of incorrect decisions for all possible directions $x\to y, y\to z$, and $x\to z$ is much greater than the probability of incorrect causality obtained from the PC algorithm using VAR residuals series.

Stationary Series

In the case of the stationary series, we choose ${\theta }_{ij}=\{\begin{array}{cc}\rho & i=j\\ 0& otherwise\end{array} where \rho <1$, and impose various restrictions on matrix B, which means stationary series with different specifications are generated. The results suggest the probability of rejecting the null hypothesis of no causality (Table S2). Table S2 indicates the simulated results of PC and modified PC algorithms of $x$ causing $y$($x\to y$), $y$ causing $z$($y\to z$) and $x$ causing $z$($x\to z$) at autoregressive coefficients $({\theta }_{11},={\theta }_{22}={\theta }_{33}$) values −0.8, 0.6, 0.4, and 0.2. Results of the PC algorithm show that the probability of significant results fluctuates around 7% on average for three possible causal directions at nominal size of 5% for all three specifications. It means there is on average 2% probability of spurious causality in the three possible directions. The results of modified PC algorithms indicate that with stationary series with root close to unity, the probability of significant results remains high, which is about on average 27%. However, when the autoregressive coefficient value gets close to zero (0.2), the probability of significant results drops to 7% on average for all three possible directions. This shows the average 2% probability of spurious regression. It is concluded from the simulation results that when the series is highly stationary (low memory), the modified PC algorithm performs the same as the original PC algorithm in size distortion problem.

3.2.2. Power Comparison

Non-Stationary Series

For the calculation of power, we have imputed double cross-terms ${\theta }_{21}$ and ${\theta }_{32}$ in matrix A, and calculated the power of both algorithms. The cross-terms ${\theta }_{21}$ and ${\theta }_{32}$ establish a correlation between $x_t$ and $y_t$, and $y_t$ and $z_t$ in matrix A, which shows that $x\to y$ and $y\to z$, respectively. i.e., matrix A = $\left[\begin{array}{ccc}{\theta }_{11}& 0& 0\\ {\theta }_{21}& {\theta }_{22}& 0\\ 0& {\theta }_{32}& {\theta }_{33}\end{array}\right]$≠ 0. The performance of both algorithms in terms of power is displayed in Table S3. Tables S3–S5 depict the simulated results of PC and modified PC algorithms and each outcome is expressed as a proportion of the number of times it might have occurred. To explain Table S3, the results of the PC algorithm indicate that the probability of rejection of the null hypothesis of no causality (which can be regarded as power, since in DGP null is not true) is about on average 7%. Similarly, the probability of rejection of null of no causality is on average about 60% for both ${\theta }_{21}$($x\to y$) and ${\theta }_{32}$($y\to z$). The simulated results displayed in Table S4 reveal that on average 7% of correct causal direction has been identified by the PC algorithm, and this does not change significantly when crossing terms ${\theta }_{21}$ and ${\theta }_{32}$ changes from 0.9 to 0.2. Meanwhile, on average 75% correct causality is identified by the modified PC algorithm. The same results are found in Table S5. It is clear from the above-simulated results that the PC algorithm performs very badly in power properties when the generated series are nonstationary. However, the modified PC algorithm is performing better in all cases with fewer omissions.

Stationary Series

The performance of the PC and modified PC algorithms are evaluated when the underlying series are stationary. To generate stationary series, we put the diagonal entries ${\theta }_{11}$,${\theta }_{22}$, ${\theta }_{33}$ in DGP (1) to be less than unity. To create cross-dependencies, we choose some of the non-diagonal entries to be non-zero. We choose ${\theta }_{21}$> 0, ${\theta }_{32}$> 0, and ${\theta }_{31}$> 0 which make $x$ depend on $y$, $y$ depend on $z$ and $x$ depend on $z$, respectively. We have imputed causality between ($x$,$y$) and ($y$,$z$) and simulated results are displayed in Tables S6–S8.

The off-diagonal entries ${\theta }_{21, } {\theta }_{32}$ change from 0.9, 0.8, 0.4, and 0.2 in matrix A which implies that $x$ is causing $y$ and $y$ is causing $z$. The findings suggest that in Table S6 at ${\theta }_{21 }and {\theta }_{32}$= 0.9 at autoregressive coefficient (i.e., 0.8), the probability of rejection of null of no causality is about 6% and 45%, detected by the PC algorithm and modified PC algorithm, respectively. The value does not change significantly when off-diagonal entries (${\theta }_{21 }and {\theta }_{32}$) changes from 0.9 to 0.2. Table S6 reveals that the modified PC algorithm performs best while the original PC algorithm performs badly in case of power. However, when the autoregressive coefficient value is (0.2), the power of the modified PC algorithm wanes, as evident from Table S6. Similarly, Tables S7 and S8 display the same results as discussed in Table S6. It is concluded from the above discussions that the modified PC algorithm using modified R residuals does well with minimum power loss, both in nonstationary and stationary time series. In the meantime, the PC algorithm using VAR residuals performs very poorly in the power analysis.

It is summarized from the Monte Carlo simulation experiment that; the modified PC algorithm performs well in finding the true causal structure irrespective of the underlying data series i.e., whether stationary or nonstationary. This is because the modified PC algorithm is based on modified R residuals which contain both current and past information. On the other hand, the original PC algorithm uses VAR residuals containing contemporaneous information only and purge out the past information from the data series. Hence, it is concluded that the newly developed modified PC algorithm is more appropriate causal algorithm for finding the true causal paths.

4. Concluding Remarks and Policy Recommendations

This study set out to reveal the determinants of the energy–environment–economy (EEE) causal nexus in Pakistan that was reported by Fazal et al. [14]. Based on their results, no significant causality runs from energy consumption to economic growth and vice versa. However, causality has been reported to exist between CO₂ emissions and energy consumption. Therefore, the current research investigated the sector-wise components, i.e., determinants of EEE causal nexus. In doing so, explored here were the causal connections within each sector shaping the EEE nexus nationwide. Moreover, the Monte Carlo simulation experiment helped evaluate the performance of the original PC algorithm based on vector autoregressive model residuals and the newly developed modified PC algorithm based on modified R residuals.

In our Monte Carlo simulation, we had found the modified PC algorithm was successful in identifying the correct causal structures compared to the original PC algorithm. The latter did very poorly in finding the correct causal structure. Our results show that significant causality runs from energy consumption in the industrial and agricultural sectors to economic growth. However, no causal association exists between energy consumption and economic growth in the domestic and transportation sectors. Similarly, causality is running from energy consumption to CO₂ emissions in the domestic, transportation and industrial sectors. This implies that energy consumption in transportation and residential sectors causes CO₂ emissions but not necessarily economic growth. However, energy consumption in the two sectors combined is almost half of the country’s overall energy demand. For this reason, the national-scale EEE causal nexus has been shaped such that energy consumption is not causing economic growth. Similarly, energy efficiency in the agriculture sector is promising despite a smaller energy footprint and higher economic outputs.

Hence, it is concluded that irrespective of the scale of the EEE nexus, energy policy and management decisions guide its trajectory. For instance, the choice of energy devices in domestic and transportation sectors is very poor in Pakistan as evident from increased energy consumption with trivial economic improvements. This can be avoided by following policies such as renewable energy technologies, more energy efficient devices, increased share of mass-transit system, increased dependence on rail-based transportation, and removing non-renewables from the domestic sector. The task of energy transition, decarbonization and energy efficiency improvement is comparatively easy in the domestic and the transportation sectors.

However, in the industrial and commercial sectors, energy management options such as fuel substitutions, fuel switching, process optimization etc., are hard to achieve due to financial and technological constraints. Nevertheless, significant improvements in energy management and policies are required in all sectors of the economy to save the environment and avoid climate change. Moreover, the newly developed causality algorithm is equally important and applicable in global context in a similar way elsewhere and one can investigate the correct causal linkages among policy variables. The modified PC algorithm of GTA is a superior approach for finding causality compare to the already established methods due to numerous reasons. The key advantages of modified PC algorithm are that; it does not rely only on the temporal ordering but its roots lies in the structural relationship for determination of the causality. Asghar and Rahat [103] argue that causality tests (mainly based on Granger causality) constitute statistical tests for temporal ordering and do not allow for analyzing the causal relationship between contemporaneous variables while the causality algorithm of GTA can be used to contemporaneous variables in a straightforward manner.

The following policy recommendations are suggested for a sustainable and optimized EEE nexus at both national and sectoral levels:

• Significant changes are required in the energy fuel mix by including more and more RERs across all the sectors.
• Energy efficiency programs initiated throughout the building sector following the installation of solar power panels, improved designs, and adoption of energy-smart measures.
• Large-scale utilization of indigenous coal resources to be guided by state-of-the-art coal-energy conversion technologies, i.e., making it the safest and cleanest input fuel in the future.
• Carbon capture and storage technologies coupled with the upcoming coal-based energy projects to reduce the emissions produced.
• GHGs emissions reduction following carbon taxation and other policy-run regimes implemented especially targeting the industrial and transportation sectors.
• In order to enable sustainable energy transition nationally, the country’s nuclear industry should be updated to include the highest safety protocols.
• Decarbonization policies, for instance fuel substitution in electricity generation sector, using cleaner fuels, waste-to-energy conversion, solarization of industries, etc.

Therefore, to sum it up, new energy policy and planning processes must be backed up by research conducted in Pakistan by its scientific community. Moreover, efforts must be made to enhance the ability of local scientists and engineers to work with industry so that the abovementioned recommended policies can develop the economy, save the environment, and improve people’s living standards.