Repercussions of Pakistan's renewable and non-renewable energies to the environmental footprint: Applying the non-linear ARDL estimation

Abstract

The energy consumption in Pakistan, both renewable and nonrenewable, is examined herein as an important factor in carbon emissions. Employing a nonlinear ARDL (auto-regressive distributed lag), the research examines data from 1980 to 2021. The results show that the use of renewable energy has a negligible effect when it comes to the nation's overall carbon emissions. This is mainly because the key pollutants in Pakistan's energy sector come from nonrenewable sources, such as coal and natural gas. However, the report observes that the carbon emissions within the nonrenewable energy sector are directly related to economic growth. A further theorem of the nonlinear analysis has brought the limited role of renewable energy in resolving environmental problems into sharper focus, perhaps due to its lower proportion of Pakistan's total energy mix. According to the study, improving the proportion of renewable energy is the only way to combat environmental problems.

1. Introduction

The expanding global ecological footprint is unsettling, with humanity consuming resources equivalent to 1.7 of the earth [1]. It overshoots carbon, results in the loss of biodiversity, leads to massive soil erosion and puts unprecedented stress on ecology. As indicated by the [2], the extraction and processing of these materials account for 53 % of global carbon emissions. At the same time [3], point out that since 1970, the average reduction among wildlife populations has been 68 %, mostly due to habitat loss resulting from overexploitation. With such mind-boggling figures, the need to re-assess global consumption and seek sustainable alternatives becomes very clear. These problems also underline countries 'concentration in carrying out the climate actions called for by the Conference of Parties (COP) [4]. Energy consumption is rising around the world, and so are emissions of carbon. This is extremely damaging to the environment. According to Ref. [5] seventy-five per cent of global greenhouse gas emigrations occur in the energy sector. One of the main causes of global climate change is emigration. They pose severe trouble to global security. The United Nations Framework Convention on Climate Change (UNFCCC) and its Conference of Parties (COP26) seek to relieve these worries by circumscribing the rise in global temperatures at 2 °C. According to Ref. [6] the forthcoming COP26 represents a significant turning point in the trouble to stop the disastrous goods of global warming. The pattern of energy usage prevented this goal from being reached. As a result, the global agenda for managing energy production and consumption now includes addressing climate change through sustainable development. An economy can progress toward sustainability if it combines nonrenewable and renewable energy sources [7,8]. Therefore, how different forms of energy (renewable and nonrenewable) affect profitable growth and carbon discharges should worry policymakers.

Natural processes such as humidity and evaporation greatly influence the climate system's basic elements or forces acting on its surface, so pollution emissions of greenhouse gases like carbon are considered a major contributor [9]. That is no longer true today, at least so far as social consequences are concerned. This lesson was perhaps bound to be learned [[10], [11], [12]]. Among the major calamities which may be seen to result from environmental degradation are the recent fires in Russia and floods that hit Australia and Pakistan [13].

Pakistan has grappled with energy security and environmental sustainability challenges in recent years. The country's energy mix comprises both renewable and nonrenewable sources, with the latter, primarily fossil fuels, still dominating the energy landscape. According to Ref. [14], fossil fuels account for over 61 % of the country's total energy consumption. This heavy reliance on nonrenewable energy has led to substantial carbon emissions. Pakistan's total CO2 emissions reached 229 million tons in 2021, a significant increase from previous years [15]. On the brighter side, there has been a gradual uptick in renewable energy to gain traction.

It is never desirable to progress economically at the expense of the environment. In recent years, emerging economies have steadily increased energy consumption to raise living standards and advance their economies [16]. Meanwhile, the benefits of renewable energy to the environment and the economy have been widely acknowledged [17].After the turn of the century, opportunity arose from global warming and environmental damage caused by ceaseless economic activity. The use of renewable energy has seen huge increases worldwide [18]. As a result, hydroelectric facilities' energy consumption is substantially growing. Past studies demonstrate that using renewable energy tends to slow environmental deterioration [[19], [20], [21]]. In the case of Pakistan, our study looks for further proof of significant associations among renewable energy, environmental degradation, and economic growth.

The profound consequences of nonrenewable energies on the environmental footprint have been scrutinized in recent research. In China [22], deduced that coal dependence was the primary driver of its escalating carbon footprint, urging a swift transition to cleaner energy sources. Likewise, a study by Ref. [23] revealed India's soaring temperature projections due to persistent coal reliance. Both studies recommended enhanced investments in solar and wind energy. Having witnessed these global trends, European nations have spearheaded the renewable revolution. Also [24], commended the nation's blend of wind and solar power, attributing it to a palpable reduction in greenhouse gases. Their work emphasized replicating such models in similar climatic regions. Amidst the global push for renewables, challenges persist. Despite abundant sunlight, African nations grapple with solar technology adaptation, as noted [25]. They proposed harnessing regional collaborations to drive solar investments.

In Pakistan, with its complex "renewable and nonrenewable energy" sources and their attendant environmental footprints (especially measured in terms of carbon emissions), the interplay has been underexplored. It is noted that most studies have conventionally utilized linear models, which might not capture the potential non-linearities inherent in such relationships. However, this study seeks to explore both short-term dynamics and long-term equilibriums between energy types as well as carbon emissions by using the nonlinear ARDL estimation in a way that introduces an element of novelty. It is a fact that Pakistan, grappling with the juxtaposition of energy demands and environmental exigencies, provides a compelling backdrop for this investigation. In this regard, the nation's unique energy mix and susceptibility to climate change necessitate a deeper understanding of these interactions. This study, therefore, stands poised to bridge an existing knowledge gap. Hence, uncovering the nuanced associations through nonlinear estimations offers policymakers an enriched perspective, aligning energy strategies with environmental prudence in Pakistan's distinct socio-economic landscape.

Pakistan is a perfect case model for this scholarly investigation because of its rising share of emissions caused by energy. For a long, Pakistan has undergone some of the worst climate-related effects [26]. Pakistan has seen extremely high levels of climate change damage compared to its low per capita greenhouse gas emissions [27]. Additionally, Pakistan has experienced severe power outages since 2007 that have harmed its economic growth [28]. To overcome the energy problems, Pakistan has to switch towards renewable energy, which helps control the environmental consequences [29]. Even though the country has established many objectives and plans to promote renewable resources, the energy mix constitutes a higher proportion of nonrenewable energy, and a relatively small portion of consumption is generated from renewable sources [30]. Despite the start of Pakistan's renewable energy program in 2006 and the vital capacity for renewable energy generation, no timeline for achieving sustainable energy progress is currently available [31].

Pakistan is a prime candidate for empirical research that looks at the sustainability and growth consequences of any potential fuel substitutes soon because of its large population and status as one of the emerging countries with significant environmental issues [32]. In this study, we attempt to perform a corresponding dissected analysis to ascertain whether there are long- and short-term links between different energy consumption sources, carbon emissions, economic growth and the scale effect intended [9]. Looking at renewable and nonrenewable energy consumption, nationwide or broken down by industry type, makes the relationships between energy expenditures and the environment easier to see. Furthermore, disaggregated research is necessary to examine the challenges associated with switching from traditional energy sources to green ones, as followed by Ref. [33].

The analytical perspective is the key area where our research differs from the current literature. Firstly, previous research mainly employs simple time series analysis like FMOLS (Fully Modified Ordinary Least Square), DOLS (Dynamic Ordinary Least Square) and ARDL (Autoregressive Distributed Lag). However, we try to apply the nonlinear ARDL, which exhibits in detail how independent variables affect carbon emissions. Therefore, the nonlinear ARDL model splits a single independent variable into positive and negative shocks so as to identify an asymmetric impact of a change in one unit (on carbon emissions).

Secondly, we have extended the study of [34], which has taken the disaggregated energy components. On the contrary, we have augmented the models by including trade openness. With disaggregated-level analysis, the environmental impact of renewable and nonrenewable energy use can be viewed one by one. However, the importance of trade must be explored because it makes technology transfer easier. Technological transfer also helps change the energy system from nonrenewable to renewables [35]. A transformation of this sort in the energy system can slow down environmental degradation. However, the current study seeks to bridge this gap by including trade in our models. Our contributions also compare the usage of renewable and nonrenewable resources in an all-encompassing way to provide a holistic regulatory regime for reducing carbon emissions and the effectiveness of scale effects. Policymakers can significantly benefit from the analysis to construct the perfect combination of renewable and nonrenewable sources to satisfy the country's demand. The objectives of this study are as follows.

• 1.To fully consider the effects of energy variables on carbon emissions through a non-linear ARDL model, which can surpass previous methods such as FMOLS, DOLS, and simple ARDL.
• 2.To analyze the effects of different energy sources individually to explore what role renewable and nonrenewable forms play in environmental emissions.
• 3.To provide an optimal energy portfolio that allows Pakistan to balance its economy and environmental sustainability, which can also serve as the basis for policy-making.

The remaining sections of the article are divided as follows: The literature review portion reviews relevant literature. The methodology and data section presents how the study goes about collecting data and what econometric strategy it adopts. The section called empirical analysis and discussion of results contains both the results and discussion, while conclusions are conclusions.

1.1. Literature review

Recently, empirical studies have analyzed this complex relationship between foreign direct investment (FDI) and renewable energy, including how FDI affects innovation both within and outside of the country, what role opening up markets plays in all that, as well environmental sustainability's effect on foreign direct investors. On this matter, foreign direct investment (FDI), in particular, has had an especially important role to play as a promoter of technological innovations within the BRICS economies. The BRICS countries, in part defined by their status as emerging economies, are experiencing an era of technological upgrading with the influx of FDI. It is clear that the role of such nations in technological advancement cannot be overlooked [36]. In conclusion, the development of renewable energy in the BRICS contributes significantly to the reduction of CO2 emigration. One of the most pivotal aspects of the fight against climate change is the creation of renewable energy use; indeed, environmental invention and request regulation also play a significant part. Likewise, there is a clear confluence between advancements in renewable energy, applicable request programs, and creative results created in the environmental field [37]. Trade openness, for its part, has become an increasingly significant variable when talking about "renewable energy investment and governance," particularly in Belt and Road countries. This can be considered perfect proof that trade openness and renewable energy investing are factored in together and that the relationship between open markets and expanding consumption makes sustainable energy methods safer options [38]. [39,40] discuss the time-varying thermal performance of a commercial building. Both include a numerical model for analysis. In addition, the latter includes a set of experimental data for further comparison. Their studies indicate that under a clear sky, their results not only reveal daylight factors, thermal comfort, and energy performance on a daily and hourly basis but also shed light on future developments of sustainable building.

The relationship between energy consumption, both renewable and non-renewable, and profitable growth, as well as how it affects environmental performance, has drawn review from a number of empirical studies. For illustration, an exploration of the impact of renewable and non-renewable energy use on profitable growth in eighteen countries was carried out by Refs. [[41], [42], [43]]. Their results showed that in the countries they studied, the consumption of renewable energy was more important than the consumption of non-renewable electricity, indicating that investment in renewable energy systems is necessary to support profitable growth. To negotiate these objects, it is also essential to use less non-renewable electricity, fight global warming, and boost energy effectiveness [44] also studied the relationship between environmental quality, available renewable and non-renewable energy sources, per capita affair, and population in the South Asian region. The results of this study showed that there was Co-integration among the variables.

Moreover, a paper by Ref. [45] also looked at the same environmental problem. They used panel data from BRICS countries, random effects, and GMM methods. According to their research, using" non-renewable energy" raises carbon emissions, whereas using renewable energy improves environmental quality. Therefore, the report advised reducing dependence on non-renewable energy and swapping to renewable energy sources to create a sustainable environment for sustainable economic growth. For the G20 economies that are large producers of pollution, neither non-renewable energy nor renewable energy can be ignored [46]. studied the link amid energy use and pollution, accounting for other things like openness to trade, foreign direct investment, and total energy consumption. Cross-sectional dependence and country diversity were also taken into consideration, and the pooled mean group estimator was employed in the study. The findings demonstrated a negative short- and long-term impact of renewable energy on carbon emissions, as well as a positive and significant correlation between pollution and non-renewable energy. Therefore, in order to lower pollution within the G20, the study recommended that policymakers increase the chance of investment in renewable energy compared to non-renewable energy.

So, regarding South Asia, the relationship between environmental quality and green innovation also provides fertile ground for exploration. In other words, the green innovations that have become central pillars of sustainable economic growth work to improve environmental quality. The area this paper describes, with its complex integration of numerous and challenging economies, is a case in point [47]. More than that, the ASEAN bloc, which has been going through a series of fast economic transformations, also features a land of economic openings and new developments. Indeed, there is a strong sense of a symbiotic relationship between these economies' openness and their automated strides. For instance, their goods on various environmental aspects are fairly evident, indicating that a sensible compromise between profitable growth and environmental sustainability will be necessary [48].

Moving into the advanced world, information and communication technology (ICT) and globalization play a vital part. Looking at statistics in lesser detail, statistics from several countries in the Organization for Economics-operation and Development (OECD) show that in order to attain environmental sustainability, indeed though this is a veritably important and introductory factor, it is still important and more integrated than ever. In recent years, technological advancements and the growing globalization of the economy have, in many ways, reshaped the discourse on environmental sustainability. In conclusion, the promotion of cleaner energy mechanisms is inseparable from eco-innovations. Innovations of these two kinds Over factors such as energy pricing and human capital, these two kinds of innovations play important roles. With the global thrust coming from cleaner energy options, if we want to see breakthroughs in eco-innovation, human capital will be paramount, and the role of energy pricing will even be more central in shaping it all [49].

As [50] illustrates, there is a relationship between profitable growth and the terrain from the environmental sustainability perspective. Study results show a link between income and environmental pressure, with middle-income countries having the worst effect. Environmentalists assert that pollution in the terrain is a result of the world frugality's rapid-fire growth [51]. The “Environmental Kuznets Curve (EKC)” model was used to analyze the relationship between economic growth and environmental quality, paying particular attention to carbon emissions by Ref. [52]. The exploration supported the notion of a reversed U connection amongst profitable growth and carbon emigration. In a paper by Ref. [53], the authors use robust arbitrary influence and Housman- Taylor retrogression styles to examine whether profitable growth and energy coffers affect hothouse gas emigrations. The results showed a positive connection between profitable growth and non-renewable energy consumption, but increased renewable energy use contributed to reducing carbon emigration. The study indicates that programs for renewable energy structure stimulate frugality and reduce hot house gas emissions [54] studied the effect of profitable growth and fiscal development on renewable energy consumption in India. According to the DOLS estimation, outgrowth, profitable expansion, and fiscal development significantly impacted renewable energy consumption. Besides, the causality test showed a two-way mutual influence between economic growth and renewable energy consumption.

[55], in particular, examined the effect of "trade openness on the environment". The first is the scale effect, the second is the fashion effect, and the third is composition. These are the three ways that trade openness may impact the terrain, according to the authors. The study shows a significant negative correlation between environmental quality and the" technology effect". Environmental detriment was nonetheless also brought about by the goods of scale and composition. In their analysis of the three goods of trade openness [56]. came to the conclusion that technology had the topmost influence. It is further pointed out in another study by Ref. [57] states that improved trade openness policies on the exchange of natural resources can promote a green environment, for using these materials affects levels of international opening-up [58]. applied the STIRPAT model to examine the nexus among renewable energy, trade openness, industrialization, and technology on the one hand and economic development as well as ecological footprint on the other. They concluded that renewable energy could help cut pollution. Furthermore, trade-related activities also had higher resource consumption and caused an overall negative ecological effect.

In Pakistan, exploration has been conducted to investigate the impact of renewable and non-renewable energy consumption on economic growth and carbon dioxide emissions. These studies have used a number of econometric methods to study this relationship. However, existing research has been mostly limited to total energy consumption. For instance, in a recent study by Ref. [59], the nonlinear autoregressive distributed lag modelling approach was used to explore this relationship between overall and renewable energy use. The results of this study suggest that encouraging the use of renewable energy would boost economic expansion and reduce carbon discharges. For example, using non-renewable energy and renewable consumption in aggregate [30] also find a feedback effect between them. Since Pakistan depends on a mixed system of renewable and non-renewable sources, to understand how each source affects the environment, we must examine them piece by piece. This work closes that gap by examining each energy source separately. Furthermore, this paper also examines the impact of trade openness. Many developing countries, such as Pakistan, rely on free trade or heavily polluting industries to promote economic growth [55].

Given the above literature, it is vital to note that previous researchers have used multiple econometric models by using different variables and model formation. Few of them have used simple linear estimations, such as [[52], [53], [54]], whereas some of the used data is from Pakistan [30,59,60]. As per model formation, there is a study with a similar model [34]. However, the study needs to include one of the important variables, trade openness, which has been argued to be one of the key factors in technology transfer. Such technological transfer is useful for adopting non-renewable energy and energy-efficient mechanisms, leading to minimizing environmental degradation. However, there needs to be more model formation by adding trade openness with renewable and non-renewable energy sources through nonlinear estimations, as in the case of Pakistan. In contrast to earlier exploration, this study aims to close the current gap, which could have useful policy implications.

2. Data and methodology

This research explains how factors such as renewable energy and non-renewable energy consumption, economic development measures, and trade openness affect carbon emissions. It goes into the specific impact on aspects such as economic growth, trade value, energy consumption, and carbon emissions. This study examines the relationships among carbon emissions, renewable and non-renewable energy consumption, gross domestic product (GDP) and trade openness, applying the traditional linear-logarithmic model. Specific models are used to analyze the effects on carbon emissions of each individual. Eq-1 and Eq-2 represent the economic model of the study.

$${CO}_{2t}=f\left(GDP,Open,Hydro,Nuclear\right)$$ 1

$${CO}_{2t}=f\left(GDP,Open,Oil,Coal,Gas\right)$$ 2

${CO}_2$ stands for carbon emissions, $GDP$ stands for gross domestic product, $andopen$ ness refers to trade openness. $Hydro$ stands for hydroelectricity; $Nuclear$ stands for nuclear energy, representing renewable energy. $Oil$, $Coal$ and $Gas$ represent the oil, coal and gas use, respectively; ${\epsilon }_t$ is the error term. $\mathit{ln}$ is the natural logarithm. To measure the various contributions of “renewable and non-renewable energy consumption” to carbon emission, we split the preceding model into two different models, as presented inEq-3 and Eq-4.

Model 1

Renewable energy consumption.

$${CO}_{2t}={\alpha }_0+{\beta }_1{lnGDP}_t+{\beta }_2{lnOpen}_t+{\beta }_3{lnHydro}_t+{\beta }_4{lnNuclear}_t+{\epsilon }_t$$ 3

Model 2

non-renewable energy consumption.

$${CO}_{2t}={\alpha }_0+{\beta }_1{lnGDP}_t+{\beta }_2{lnOpen}_t+{\beta }_5{lnOil}_t+{\beta }_6{lnCoal}_t+{\beta }_7{lnGas}_t+{\epsilon }_t$$ 4

Model 1 in this study shows the correlation of hydroelectricity and nuclear power consumption to GDP and trade openness with carbon emissions. On the other hand, Model 2 examines the effect of consuming non-renewable energy sources (oil, coal, and natural gas) in terms of GDP, trade openness, and carbon emissions. For this analysis, the research utilized time series data from 1980 to 2021, obtained from two primary sources: BP Statistics [61] and the World Development Indicators [62]. Statistics covered carbon emissions and oil, coal, natural gas, hydroelectric, and nuclear energy consumption taken from BP Statistics. Furthermore, GDP per capita and trade openness data were taken from the World Development Indicators.

2.1. Estimation technique

This study employs the ARDL (Auto-Regressive Distributed Lag) bounds testing approach to detect both short-term and long-term trends at a granular level. To test for co-integration among different variables [63], developed the ARDL method in 2001. This method has several advantages and can be used regardless of whether the variables are integrated at level I (0) or the first difference I (1). It provides reliable results regardless of the sample size because the model's lag structure can be adjusted, and long-term estimates are precise with valid t-statistics [64,65]. The ARDL method uses a simple linear transformation to build a flexible, unrestrained error-correction model using long-term data while accounting for short-term variations in the long-term equilibrium. This model is especially well-suited to time series data with serial correlation and endogeneity.

For the purposes of this research, the ARDL model was applied to two distinct models. The first (Model 1) looks at renewable energy consumption, GDP, trade openness, and carbon emissions. The second (Model 2) examines consumption of non-renewable energy, GDP, trade openness, and carbon emissions. These models are as follows:

ARDL Model 1: Renewable energy consumption, GDP, trade openness and carbon emission is reported in Eq-5.

$$\Delta {CO}_{2t}=c_0+\sum _{i=1}^p{\beta }_1{\Delta CO}_{2,t-r}+\sum _{i=0}^p{\beta }_{2i}{\Delta lnGDP}_{t-r}+\sum _{i=0}^p{\beta }_{3i}{\Delta lnOpen}_{t-r}+\sum _{i=0}^p{\beta }_{4i}{\Delta lnHydro}_{t-r}+\sum _{i=0}^p{\beta }_{5i}{\Delta lnNuclear}_{t-r}+{⋋}_1{lnCO}_{2,t-1}+{⋋}_2{lnGDP}_{t-1}+{⋋}_3{lnOpen}_{t-1}+{⋋}_4{lnHydro}_{t-1}+{⋋}_5{lnNuclear}_{t-1}+{\epsilon }_t$$ 5

Where $\Delta$ is the first difference operator and $\rho$ denotes the lag length. We derived two hypotheses from Eq. (4) for the long relationships. The first is the null hypothesis of no co-integration $\left(H_O:{⋋}_1={⋋}_2={⋋}_3={⋋}_4={⋋}_5=0\right)$, which tested against the second one, i.e., the alternative hypothesis $\left(H_1:{⋋}_1\ne {⋋}_2\ne {⋋}_3\ne {⋋}_4\ne {⋋}_5\ne 0\right)$.

ARDL Model 2: Non-renewable energy consumption, trade openness and carbon emission is presented in Eq-6.

$$\Delta {CO}_{2t}=c_0+\sum _{i=1}^q{\beta }_1{\Delta CO}_{2,t-r}+\sum _{i=0}^q{\beta }_{2i}{\Delta lnGDP}_{t-r}+\sum _{i=0}^q{\beta }_{3i}{\Delta lnOpen}_{t-r}+\sum _{i=0}^q{\beta }_{4i}{\Delta lnOil}_{t-r}+\sum _{i=0}^q{\beta }_{5i}{\Delta lnCoal}_{t-r}+\sum _{i=0}^q{\beta }_{6i}{\Delta lnGas}_{t-r}+{\gamma }_1{lnCO}_{2,t-1}+{\gamma }_2{lnGDP}_{t-1}+{\gamma }_3{lnOpen}_{t-1}+{\gamma }_4{lnOil}_{t-1}+{\gamma }_5{lnCoal}_{t-1}+{\gamma }_6{lnGas}_{t-1}+{\epsilon }_t$$ 6

Where $\Delta$ is the first difference operator, and $q$ denotes the lag length. The null hypothesis of no co-integration $\left(H_O:{\gamma }_1={\gamma }_2={\gamma }_3={\gamma }_4={\gamma }_5={\gamma }_6=0\right)$, which tested against the second one, i.e., the alternative hypothesis $\left(H_1:{\gamma }_1\ne {\gamma }_2\ne {\gamma }_3\ne {\gamma }_4\ne {\gamma }_5\ne {\gamma }_6\ne 0\right)$.

3. Preliminary analysis

3.1. Descriptive

Initially, we apply the descriptive test to inspect the descriptive nature of the studied variables and the presence of potential outliers in the studied series. We have distributed the variables in four sections; the dependent variables, carbon emissions, GDP, and trade openness, are control variables. The renewable energy section consists of hydro and nuclear energy consumption. Nonrenewable energy sources include “oil, coal, and gas”. According to the mean, standard deviation, minimum, and maximum values, there is no evidence of an outlier in the studied series, as reported in Table 1. However, we can use the variables for econometric analysis.

Table 1.

Descriptive analysis.

Variable	Mean	Std. Dev.	Min	Max
Dependent variable
lnCO2	15.3011	1.2757	13.0924	15.6707
Control variable
lnGDP	23.3242	0.9686	22.5249	23.9937
lnOpen	3.1619	1.5505	1.0483	4.7713
Renewable energy variables
lnHydro	28.0922	0.9071	27.2646	28.6166
lnNuclear	25.6930	1.7135	22.4395	27.4301
Nonrenewable energy variables
lnOil	3.2456	0.7487	2.8553	3.5445
lnCoal	28.4782	0.9593	27.4788	29.1544
lnGas	5.0145	0.7289	4.7873	5.1778

Notes: ln represents the natural logarithm. CO₂ is the dependent variable, which represents the carbon emission. GDP and openness are the control variables that represent economic growth and trade openness. Renewable energy variables are lnHydro and lnNuclear, which mention hydro and nuclear energy consumption. Oil, coal, and gas reflect the nonrenewable energy consumption given by oil, coal, and gas consumption.

3.2. Multicollinearity

We further investigate the multicollinearity of the variables reported in Table 2. For this purpose, we have used the variance inflation factor test (VIF). The values of the variables are less than 10, indicating no evidence of multicollinearity. LnNuclear has the highest value of VIF (9.06), whereas lnHydro has the lowest value of VIF (4.04).

Table 2.

Multicollinearity.

Variables	VIF
lnCO2	7.93
lnGDP	8.01
lnOpen	6.75
lnHydro	4.04
lnNuclear	9.06
lnOil	7.72
lnCoal	5.88
lnGas	4.76
Mean VIF	6.77

3.3. Structural break test

However, as we use macroeconomic variables for the estimations, it is important to examine the “structural breaks” in the data series. For this purpose, we used the Quandt-Andrews structural break test, as in Table 3. The findings confirm that there are no structural breaks in the studied period. As a result, we have to apply the simple unit root tests to investigate the stationarity of the data series instead of the structural break unit root test.

Table 3.

Structural break test.

Quandt-Andrews structural break test	Maximum LR	Expected LR	Average LR
F-Statistics	128.15	121.42	106.39

Note: The null hypothesis for the Quandt-Andrews test is "no breakpoint." The results of maximum LR, expected LR and average LR are insignificant, but the null hypothesis is accepted.

3.4. Unit root test

The Augmented Dickey-Fuller (ADF) and the Phillips-Perron (PP) tests are crucial first steps in this study to evaluate whether or not any of the data series contains a unit root. The results of these unit root tests are shown in Table 4. As one can see, all the variables are non-stationary in their initial forms, the only exception being coal consumption. Statistically, such variables reach stationarity at the 1 percent level or lower. In other words, the null hypothesis is rejected. Moreover, this study includes the KSS unit root test of [66], which is generally considered the state of the art of its kind. Taking this test as a criterion, hydrogen and coal consumption are constant at their original levels, and other variables are integral. When the first difference is taken, the sets of variables under study all achieve stationarity. These results show a variable degree of stationarity among the factors studied. However, under such conditions, the ARDL method is the most suitable to consider for econometric analysis in this regard.

Table 4.

Unit root test.

Variable	Augmented Dicky Fuller test		Phillips Pearson test		KSS
	Level	Difference	Level	Difference	Level	Difference
lnCO2	0.943	0.001***	0.892	0.001***	0.518	0.000***
lnGDP	0.951	0.002***	0.973	0.001***	0.483	0.000***
lnOpen	0.378	0.000***	0.614	0.000***	0.934	0.000***
lnHydro	0.256	0.000***	0.273	0.000***	0.068*	0.000***
lnNuclear	0.785	0.001***	0.873	0.002***	0.967	0.000***
lnOil	0.534	0.000***	0.519	0.000***	0.787	0.000***
lnCoal	0.013**	0.000***	0.012***	0.000***	0.000***	0.000***
lnGas	0.572	0.000***	0.372	0.000***	0.365	0.000***

Notes: ***, **, * indicate the level of significance at 1 %, 5 % and 10 %.

3.5. Cointegration

Once the unit root verifies, we go on to ARDL-bound testing to see whether the variables are cointegrated. The integration findings for models 1 and 2 are reported in Table 5. The findings demonstrate a long-term relationship between all of the variables. The estimated F-statistics exceed the necessary upper-bound critical values. That rules out the null hypothesis that there is cointegration. The Breusch-Godfrey test and the ARCH test, two diagnostic procedures for serial correlation and heteroscedasticity, provide conclusive evidence that the error term is white noise. Additionally, the Ramsey RESET test confirms the adequacy of the model. Table 6 provides a robust cointegration analysis, confirming a long-run relationship between the studied models.

Table 5.

Bouncointegrationon test.

Estimated model	Bound testing approach			Diagnostic tests
	F-statistics	Lag selection	Decision	LM-test		χ2 Arch		χ2 Ramsey
Model 1: lnCO2=f(lnGDP, lnOpen, lnHydro, lnNuclear)
	5.312**	(1, 0, 2, 0, 2)	Yes	0.218	0.646	2.043	0.133	0.059	0.843
Model 2: lnCO2=f(lnGDP, lnOpen, lnOil, lnCoal, lnGas)
	6.009***	(4, 4, 5, 4, 3, 1)	Yes	1.102	0.289	0.001	0.927	2.072	0.159
Pesaran et al. (2001)	1 % significance level			5 % significance level				10 % significance level
	Lower bound	Upper bound		Lower bound	Upper bound			Lower bound	Upper bound
Critical values	4.28	5.61		3.20	4.41			2.65	3.85

Notes: ***, ** represent the significance level at 1 % and 5 %, respectively.

Table 6.

Johansen cointegration.

Model 1: Renewable Energy Consumption
Hypothesized	Trace statistic	Prob.b	Trace statistic	Prob. a	Cointegration
No. of CE(s)
None a	54.80543	0.00870	30.40645	0.03450
At most 1	24.39985	0.16590	16.99890	0.18960
At most 2	7.01783	0.65890	7.67320	0.46720
At most 3	7.40677	0.54510	7.35878	0.44130
At most 4	0.04823	0.83390	0.04828	0.84500

Model 2: Non-Renewable Energy Consumption
Hypothesized	Max-Eigen statistic	Prob. b	Max-Eigen statistic	Prob. b	Co-integration
No. of CE(s)
None a	89.0454	0.0009	42.1876	0.0044	Yes
At most 1	46.8514	0.0713	23.1678	0.1670	No
At most 2	24.6781	0.1601	13.1519	0.1040	No
At most 3	23.6981	0.2237	12.9789	0.4675	No
At most 4	10.7341	0.2335	7.5724	0.4378	No
At most 5	3.1398	0.0987	3.1451	0.0981	No

The trace test and the maximum eigenstatistic reveal one integrating equation at the 5 % significance level.

^arefers to rejecting the hypothesis at the 5 % significance level.

^bp-values from MacKinnon-Haug-Michelis (1999).

4. Results and discussion of findings

4.1. ARDL estimation

We investigate the long- and short-term dynamics of models 1 and 2 after the bound integration approach has established the actuality of cointegration. The results for both models are shown in Table 7. Advanced profitable growth is one of the main causes of environmental decline in Pakistan, according to the long-run estimation in Model 1, which is verified by the GDP and also shows a significant and positive measure. This conclusion is similar to those of the following studies [30,60,67,68] and Nepal, independently. This connection suggests that rising economic growth increases energy demand in the industrial sector, transport sector, etc., which raises carbon emissions [69,70]. The findings show that the population of Pakistan is growing, its cities are becoming more developed, and its industry is expanding, so energy consumption has increased. Since fossil energies are responsible for most of Pakistan's energy consumption, renewable options only comprise a small portion of the total energy mix. Thus, like in the example of Brazil and Algeria [71,72], a rise in energy consumption boosts the GDP concurrently with increased carbon emissions. According to some researchers, renewable energy reduces carbon emissions as GDP rises, just like [18,73] discovered for developed countries. However, this statement does not apply to Pakistan due to the fundamental difference between economies. According to Refs. [56,74], Pakistan's carbon emissions are anticipated to increase until it reaches a certain level of economic activity because it is now functioning below that level. When energy consumption falls below the optimal threshold, the scale and composition of goods become more prominent, and the technological impact is negligible. In the short run, GDP is insignificant, indicating no relationship between GDP and carbon emissions.

Table 7.

ARDL estimation.

Variable	Long-run estimates		Variable	Short-run estimates
	Coefficient	Prob.		Coefficient	Prob
Model 1: Renewable energy sources
lnGDP	1.646**	0.019	D(lnGDP)	−0.084	0.593
lnOpen	0.155	0.790	D(lnOpen)	−0.050	0.531
lnHydro	0.124	0.741	D(lnHydro)	0.043	0.526
lnNuclear	0.021	0.496	D(lnNuclear)	0.002	0.523
C	−4.846***	0.000	Count Eq (-1)	−0.145**	0.031
Model 2: non-renewable energy sources
lnGDP	−0.945	0.122	D(lnGDP)	−0.203	0.424
lnOpen	−0.331***	0.007	D(lnOpen)	−0.258***	0.000
lnOil	0.215	0.121	D(lnOil)	0.327***	0.000
lnCoal	0.340***	0.008	D(lnCoal)	0.277***	0.000
lnGas	0.524***	0.000	D(lnGas)	0.209***	0.000
C	−3.923***	0.000	Count Eq (-1)	−0.070*	0.098
Diagnostic test
${\mathrm{R}}^2$	0.994	0.993
Adjusted ${\mathrm{R}}^2$	0.994	0.992
F-statistics	1400.972	1377.436
Prob. F-statistics	0.000	0.000
Durbin-Watson stat	1.289	1.045
χ2 Arch	0.278 [0.600]	0.238 [0.628]
χ2 LM	1.658 [0.131]	1.255 [0.295]
χ2 RESET	9.176 [0.004]	0.093 [0.761]

Notes: ***, ***,* mention the significance level at 1 %, 5 %, and 10 %, respectively.

In model 1, the portions of trade openness are insignificant in long-run and short-run estimations, indicating that trade openness has no relationship with the environmental decline process in the case of Pakistan. The reason for this insignificance is the lower volume of trade in Pakistan [75]. Renewable, hydrogen, and nuclear energy consumption have reported an insignificant impact on carbon emissions. The findings are analogous to Ref. [60], reporting that renewable energy requirements need to be more mature to fight the environmental decline process in Pakistan.

When considering the relationship between non-renewable energy consumption, GDP, trade openness, and carbon emissions, it's evident — despite the emphasis on Model 2 — that there's a negligible short- and long-term correlation between GDP and carbon emissions. However, this is different from the scenario. For instance Refs. [76,77], claimed that the decline in carbon emissions brought on by income levels only lasts up to a specific point before carbon emissions start to rise with further increases in income. The study suggests that when income grows, carbon emissions will rise as well [78,79], showing a positive relationship between them for Pakistan. Non-renewable energy consumption acts as a bridge in this equation. In Pakistan, the usage of fossil fuels leads to increased carbon emissions, which lower the country's economic energy efficiency and damage the environment [80].

Moreover, the financial benefits of utilizing non-renewable resources are now outweighed by their costs because of the long-term detrimental effects of carbon emissions [81,82]. To avoid a decline in GDP due to the inappropriate and extensive utilization of non-renewable energy sources, Pakistan must implement sensible regulations regarding the consumption of fossil fuels [[83], [84], [85], [86]]. The trade intensity results in Model 2 show a negative and substantial correlation with both short- and long-term carbon emissions. Results show that during the estimation period, trade growth lowers carbon emissions. Our results are similar to the findings of [87,88].

The short- and long-term connections between coal consumption and carbon emissions are positive and significant. According to exploration by Refs. [[89], [90], [91]]for China [92], for India, and [93,94] for Pakistan, coal consumption may increase profitable growth, but it has a significant negative impact on the environment. In their disquisition of the divided relationship between coal consumption and carbon emissions in China and India [[95], [96], [97]] found that China's coal consumption has a major long-term influence on carbon emissions and economic growth. China has implemented various strategies to reduce its coal consumption, but doing so has come at the expense of profitable growth. Pakistan is in an analogous situation. Carbon emissions from burning coal can still have an impact on the terrain, but technology can lessen it. Policymakers believe that Pakistan should lower its proportion of coal consumption in its overall energy mix [98]. Both in the short and long terms, there is a positive and statistically significant correlation between natural gas consumption and carbon emissions. Pakistan's entire energy mix is dominated by natural gas [99,100].

Our findings indicate that natural gas is not sustainable in Pakistan because it emits carbon dioxide. The results of this study indicate that natural gas is more environmentally friendly than other energy sources in the case of Saudi Arabia; still, the findings of [101,102] contradict these estimates. The difference may be due to the profitable circumstances in the two nations as well as the extent of reliance on natural gas as energy. The sustainability of original coffers could be bettered, in line with [56], where natural gas dominates the entire energy blend. According to projections made by Pakistan's Planning Commission in 2017, the country's natural gas reserves will run out seventeen times if consumption continues at the current rate. Therefore, Pakistan must switch its natural gas consumption to coal or other renewable energy sources.

Although crude oil is the alternate-largest source of energy consumption in the nation, there is no perceptible long-term correlation between its emissions and carbon emissions. A rising energy crisis and a significant drop in natural gas supplies have increased Pakistan's reliance on crude oil. However, the uncertainty has also surged in addition to the availability of oil [103,104]. It is necessary to look into environmentally friendly ways to generate energy in Pakistan. More specifically, all non-renewable energy sources away from oil consumption have a considerable long-term impact on carbon emissions. The cumulative sum (CUSUM) and cumulative sum of squared recursive residual (CUSUMSQ) plots are used to test the stability of the long- and short-term liaison. Fig. 1, Fig. 2 present the parameter stability, as substantiated by the CUSUM and CUSUMSQ values, the figures in the (a) are for CUSUM. The panel (b) in Fig. 1, Fig. 2 show the CUSUM of square (CUSUMSQ). The findings confirm that the lines are within the upper and lower critical bounds, which confirm the model stability.

Fig. 1.

Cusum and CUSUMSQ for Model 1 (a) CUSUM for Model 1 (b) CUSUMSQ for Model 1.

Fig. 2.

Cusum and CUSUMSQ for Model 2 (a) CUSUM for Model 2 (b) CUSUMSQ for Model 2.

4.2. Nonlinear ARDL estimation

In order to verify the asymmetry in the study variables, we used nonlinear ARDL estimation after ARDL, as shown in Table 8 and the diagnostics in Table 9. The application of nonlinear ARDL is helpful in providing estimates for positive and negative shocks in comparison to linear estimations like ARDL, dynamic ordinary least squares (DOLS), and fully modified ordinary least squares (FMOLS). However, the applicability of nonlinear ARDL is superior to simple linear estimations.

Table 8.

Nonlinear ARDL estimation.

Long-run	Model-1	Model-2
lnCO2 t-1	1.905**	1.638***
lnGDP + t-1	0.713**	0.251**
lnGDP- t-1	0.323*	0.169*
lnOpen + t-1	1.546	1.080
lnOpen- t-1	0.360	0.547
lnHydro + t-1	−0.149
lnHydro- t-1	0.025
lnNuclear + t-1	0.007
lnNuclear- t-1	0.036
lnOil + t-1		1.372**
lnOil- t-1		0.891**
lnCoal + t-1		0.745**
lnCoal- t-1		−1.466
lnGas + t-1		0.183**
lnGas- t-1		0.017
Short-run
ΔCO2 t-1	0.428**	0.190***
ΔGDP + t-1	0.676*	0.342**
ΔGDP- t-1	0.381	1.107
ΔOpen + t-1	0.019	0.268
ΔOpen- t-1	0.120	−0.074
ΔHydro + t-1	−0.328
ΔHydro- t-1	0.747
ΔNuclear + t-1	0.382
ΔNuclear- t-1	−0.019
ΔOil + t-1		0.051**
ΔOil- t-1		0.132
ΔCoal + t-1		0.667*
ΔCoal- t-1		0.140*
ΔGas + t-1		0.195*
ΔGas- t-1		−0.943
Constant	11.478***	23.086***

Notes: CO2 stands for carbon emission, GDP represents economic growth, and trade represents trade openness. Hydro and nuclear energy present hydro and nuclear energy, highlighting renewable energy. Oil, coal, and gas consumption shows oil, coal, and gas consumption. (+) and (−) indicates the positive and negative shocks in the respective variables.

***. ** And * represents the level of significance at 1 %, 5 % and 10 % respectively.

Table 9.

Asymmetric and model diagnostics.

	Long run (+)	Long run (−)	Long run asymmetry (p-value)	Short run asymmetric (p-value)
CO2 = f (lnGDP, lnOpen, lnHydro, lnNuclear)
lnGDP	3.153***	0.029*	0.012	0.628
lnOpen	1.128	−1.003	0.907	0.859
lnHydro	1.467	0.619	0.170	0.213
lnNuclear	0.290	2.492	1.531	1.354
Cointegration				−2.174
Portmanteau test				0310
Heteroskedasticity				0.566
Ramsey test				0.849
J-B test				0.253
CO2 = f (lnGDP, lnOpen, lnOil, lnCoal, lnGas)
lnGD	0.137	−0.162***	0.015**	0.003***
lnOpen	0.384	−0.281	0.710	0.383
lnOil	0.132**	0.473	0.001***	0.041**
lnCoal	0.095*	0.104	0.061*	0.891
lnGas	0.108*	0.429	0.045**	0.206
Cointegration				−6.821
Portmanteau tes				0.374
Heteroskedasticity				0.190
Ramsey test				0.225
J-B test				0.103

Notes: CO2 is carbon emission, GDP, and Open represents economic growth and trade openness. Hydro and nuclear energy present hydro and nuclear energy, highlighting renewable energy. Oil, Coal and Gas shows the oil, coal, and gas consumption. (+) and (−) indicates the positive and negative shocks in the respective variables.

***. ** And * represents the level of significance at 1 %, 5 % and 10 % respectively.

Sifting through Model 1's complex dynamics, the long-run portions tell a fascinating story about how trade openness, profitable growth, and different energy consumptions and carbon emissions are related. In an environment of profitable growth, increases in CO2 emissions are linked to both positive and negative shocks to GDP, albeit to differing degrees of significance and magnitude. Previous exploration has also shown an asymmetric relationship between GDP and emissions. For illustration [105], set up that profitable growth has a positive long-term correlation with environmental decline, especially in rising economies.

The disparity in the coefficients' magnitudes might hint towards the nonlinear and complex relationship between economic activities and emissions, where positive economic shocks amplify industrial activities and emissions more than negative shocks dampen them.

In contrast to findings from Ref. [106], who linked a nuanced relationship between trade and the environment, contingent on the country's development stage and regulatory frame, positive and negative shocks in trade openness do not exhibit a statistically significant relationship with carbon emissions over the long run. The non-significant coefficients in this model suggest that other macroeconomic factors or policies could offset trade's impact on emissions, warranting a deeper exploration into the underlying mechanisms.

Turning attention towards renewable energy consumption variables, positive and negative shocks in hydro energy showcase a rather intriguing dynamic. The negative coefficient of positive shocks (−0.149), albeit non-significant, subtly hints towards the potential of positive shocks in hydroelectric energy consumption to mitigate CO2 emissions, aligning with findings from Ref. [107], who affirmed the emission-reducing capabilities of renewable energy consumption. Still, the positive measure of negative shocks (0.025), despite being significant as well, may suggest that decreases in hydro energy consumption do not always affect a corresponding rise in emissions. This could be because of the effect of energy negotiations with alternative sources. Over an extended period, there is no perceptible correlation between the use of nuclear energy and carbon emissions. This could be explained by the fact that nuclear energy has a comparatively lower carbon footprint than fossil energy, as supported by Ref. [108].

In the short-run dynamics, the significant coefficient of previous carbon emissions at the 5 % level indicates that past emissions continue to influence current levels, potentially due to the inertia in the system and the delayed impact of mitigation strategies. The portions of positive and negative shocks to GDP indicate that, although to differing degrees, profitable oscillations continue to impact emissions in the near term. This emphasizes the need to break down profitable conditioning in order to comprehend their immediate goods on the terrain.

Model 2 unfolds a rich narrative, intertwining mon-renewable energy consumption, profitable growth, and trade openness with carbon emissions, crafting a multifaceted disquisition into the environmental counteraccusations of various profitable and energy dynamics. In the long-run frame, the measure of carbon emission at 1.638, significant at one position, underscores a robust linkage between history and present carbon emissions, suggesting a lingering impact of literal emissions patterns on the present scenario. This persistent nature of emissions might be attributed to the cumulative and, perhaps, irreversible impact of past industrial activities and policy paradigms on the environment. The portions for positive and negative shocks in GDP, both positive, signify that economic growth, whether through positive or negative shocks, is associated with an increase in CO2 emissions. However, the asymmetry in the impact is subtle yet noteworthy, with positive shocks having a slightly more pronounced impact on emissions.

Regarding the positive and negative trade openness shocks, there is no statistically significant correlation between them and carbon emissions. This is somewhat consistent with research conducted by Ref. [109], who discovered that the correlation between trade openness and CO2 emissions depends on the income level and industrial structure of the nation. Further investigation into the underlying mechanisms is required, as the non-significant coefficients in this model indicate that other macroeconomic factors or regulatory frameworks are potentially offsetting the impact of trade on emissions. When we move into non-renewable energy consumption, we find that the portions for both positive and negative shocks in crude oil consumption are positive and significant. This means that shocks in crude oil consumption, whether they are increases or diminishments, are linked to a shift in CO2 emissions. This is in line with the results of [110], who verified that, when considering MENA countries, crude oil consumption greatly increases CO2 emissions, pressing the environmental cost of counting on fossil energies.

The coefficient of carbon emissions in the short-run dynamics is significant at the 1 % level, suggesting that historical emissions are still influencing current levels, possibly as a result of system inertia and the delayed effects of mitigation efforts. The coefficients of positive and negative shocks to GDP indicate that, although to differing degrees, economic fluctuations continue to impact emissions in the near term. This emphasizes the need to break down economic activities in order to comprehend their immediate effects on the environment.

It is clear from Table 9's results that there are asymmetric long- and short-term relationships between carbon emissions and different energy and economic variables. A significant positive long-run impact of GDP on CO2 emissions is rejected in the first model; the p-value of 0.012 indicates a statistically significant asymmetry. This means positive and negative shocks in GDP do not symmetrically impact CO2 emissions, a finding that resonates with the nonlinear economic-environmental relationships documented in prior research [111].

Regarding the second model that includes non-renewable energy variables, there is a remarkably significant asymmetry in the long-term relationship between GDP and CO2 emissions (p-value = 0.015) and an even more pronounced asymmetry in the short-term (p-value = 0.003). This underscores the criticality of dissecting the nature and direction of economic fluctuations when exploring their environmental implications. Furthermore, the long-term significant positive and negative coefficients for coal and oil consumption, respectively, highlight the intricate relationship between energy and the environment and are consistent with the findings of [112]which emphasized the complex effects of different energy sources on environmental quality.

It can be noted that the model diagnostics, such as the cointegration test, portmanteau test, and heteroscedasticity, among others, further validate the robustness and reliability of the models, ensuring the findings are grounded in statistical rigour and are not marred by common econometric issues, such as autocorrelation or misspecification, thereby providing a solid foundation for policy inference and future research endeavors.

4.3. VECM estimation

The long-term relationships between variables are shown by the integration results. We employ the VECM to determine the directions of causal relations. According to Ref. [113], if a long-term link is present, the direction of causality can be ascertained using an error correction model. An error correction model allows us to differentiate between Granger's reason with long-term and short-term time frames. The Wald statistic calculates the difference and lag difference coefficients in VECM Granger causality for all independent variables. Table 10 shows the causality findings for models 1 and 2.

Table 10.

VECM Granger causality.

Model 1	Δ lnCO2	Δ lnGDP	Δ lnOpen	Δ lnHydro	Δ lnNuclear		ECTt−1
Δ lnCO2		4.2441 (0.0487)**	4.1144 (0.0441)**	0.1335 (0.7458)	0.0020 (0.9926)		−0.1562 (0.0687)*
Δ lnGDP	0.6453 (0.4425)		0.7881 (0.3567)	0.7534 (0.3339)	0.2886 (0.6146)		−0.1567 (0.1307)
Δ lnOpen	0.4244 (0.4201)	0.1367 (0.3339)		0.1288 (0.7349)	1.2457 (0.6058)		−0.1903 (0.1707)
Δ lnHydro	0.3607 (0.5724)	0.0329 (0.8936)	0.0198 (0.8336)		1.6984 (0.1876)		−0.4345 (0.0003)***
Δ lnNuclear	4.9354 (0.0211)**	3.6856 (0.0568)**	3.2856 (0.0458)**	3.6768 (0.0398)*			−0.3295 (0.0172)**
Model 2	Δ lnCO2	Δ lnGDP	Δ lnOpen	Δ lnCoal	Δ lnOil	Δ lnGas	ECTt−1
Δ lnCO2		1.4978 (0.2289)	1.2983 (0.2013)	0.0137 (0.8932)	2.0175 (0.1611)	2.1156 (0.1509)	−0.0556 (0.5098)
Δ lnGDP	7.6928 (0.0046)***		1.6051 (0.2134)	1.6198 (0.2145)	7.7298 (0.0156)***	0.9441 (0.3531)	−0.4445 (0.0029)***
Δ lnOpen	7.7829 (0.0049)***	1.6220 (0.2167)		1.6345 (0.2275)	7.7109 (0.0059)***	0.9045 (0.3154)	−0.4031 (0.0021)***
Δ lnCoal	6.1399 (0.0154)*	0.0456 (0.8223)	0.0309 (0.8089)		0.2567 (0.6233)	7.0012 (0.0069)*	−0.2489 (0.0045)***
Δ lnOil	3.5652 (0.993)	1.7873 (0.1987)	1.6872 (0.1801)	0.7402 (0.3987)		0.9405 (0.3398)	−0.1825 (0.0020)***
Δ lnGas	0.0836 (0.7556)	0.2125 (0.6097)	0.1970 (0.5324)	0.8234 (0.3789)	0.9226 (0.3347)		0.0065 (0.0638)

Notes: ***,**,* indicates the level of significance at 1 %, 5 %, and 10 % respectively.

The F-statistic derived from the Wald test evaluates short-term causality, whereas the error correction term determines long-term causality (ECT). Long-term causation is indicated by an ${ECT}_{t-1}$ that is statistically important and has a negative coefficient [80]. Following are the econometric equations for models 1 and 2:

$$\text{Model}1:\left[\begin{array}{c}{\Delta \text{LCO}}_{2it}\\ {\Delta LGDP}_{it}\\ {\Delta LOpen}_{it}\\ {\Delta LHydro}_{it}\\ {\Delta LNuclear}_{it}\end{array}\right]=\left[\begin{array}{c}{\delta }_1\\ {\delta }_2\\ {\delta }_3\\ {\delta }_4\\ {\delta }_5\end{array}\right]+\sum _{p-1}^q\left[\begin{array}{c}{\theta }_{11p}{\theta }_{12p}{\theta }_{13p}{\theta }_{14p}{\theta }_{15p}\\ {\theta }_{21p}{\theta }_{22p}{\theta }_{23p}{\theta }_{24p}{\theta }_{25p}\\ {\theta }_{31p}{\theta }_{32p}{\theta }_{33p}{\theta }_{34p}{\theta }_{35p}\\ {\theta }_{41p}{\theta }_{42p}{\theta }_{43p}{\theta }_{44p}{\theta }_{45p}\\ {\theta }_{51p}{\theta }_{52p}{\theta }_{53p}{\theta }_{54p}{\theta }_{55p}\end{array}\right]\times \left[\begin{array}{c}{\Delta \text{LCO}}_{2it-1}\\ {\Delta LGDP}_{it-1}\\ {\Delta LOpen}_{it-1}\\ {\Delta LHydro}_{it-1}\\ {\Delta LNuclear}_{it-1}\end{array}\right]+\left[\begin{array}{c}{\alpha }_1\\ {\alpha }_2\\ {\alpha }_3\\ {\alpha }_4\\ {\alpha }_5\end{array}\right]{ECT}_{it-1}+\left[\begin{array}{c}{\mu }_1\\ {\mu }_2\\ {\mu }_3\\ {\mu }_4\\ {\mu }_5\end{array}\right]$$

$$\text{Model}2:\left[\begin{array}{c}{\Delta LCO}_{2it}\\ {\Delta LGDP}_{it}\\ {\Delta LOpen}_{it}\\ {\Delta LOill}_{it}\\ {\Delta LCoal}_{it}\\ {\Delta LGas}_{it}\end{array}\right]=\left[\begin{array}{c}{\delta }_1\\ {\delta }_2\\ {\delta }_3\\ {\delta }_4\\ {\delta }_5\\ {\delta }_6\end{array}\right]+\sum _{p-1}^q\left[\begin{array}{c}{\theta }_{11p}{\theta }_{12p}{\theta }_{13p}{\theta }_{14p}{\theta }_{15p}{\theta }_{16p}\\ {\theta }_{21p}{\theta }_{22p}{\theta }_{23p}{\theta }_{24p}{\theta }_{25p}{\theta }_{26p}\\ {\theta }_{31p}{\theta }_{32p}{\theta }_{33p}{\theta }_{34p}{\theta }_{35p}{\theta }_{36p}\\ {\theta }_{41p}{\theta }_{42p}{\theta }_{43p}{\theta }_{44p}{\theta }_{45p}{\theta }_{46p}\\ {\theta }_{51p}{\theta }_{52p}{\theta }_{53p}{\theta }_{54p}{\theta }_{55p}{\theta }_{56p}\\ {\theta }_{51p}{\theta }_{52p}{\theta }_{53p}{\theta }_{54p}{\theta }_{55p}{\theta }_{66p}\end{array}\right]\times \left[\begin{array}{c}{\Delta \text{LCO}}_{2it-1}\\ {\Delta LGDP}_{it-1}\\ {\Delta LOpen}_{it-1}\\ {\Delta LOil}_{it-1}\\ {\Delta LCoal}_{it-1}\\ {\Delta LGas}_{it-1}\end{array}\right]+\left[\begin{array}{c}{\alpha }_1\\ {\alpha }_2\\ {\alpha }_3\\ {\alpha }_4\\ {\alpha }_5\\ {\alpha }_6\end{array}\right]{ECT}_{it-1}+\left[\begin{array}{c}{\mu }_1\\ {\mu }_2\\ {\mu }_3\\ {\mu }_4\\ {\mu }_5\\ {\mu }_6\end{array}\right]$$

The results corroborate the long-term unproductive relationship between trade openness, GDP, nuclear power, hydroelectricity, and carbon emissions. 〖 ECT 〗, (t- 1) has important long-term goods on carbon emissions, trade openness, and hydroelectricity using nuclear power. Our findings show that there is a bidirectional relationship between carbon and nuclear emissions, meaning that changes in one of these sources would have an impact on the other and vice versa. Also, we observe a one-way unproductive relationship between GDP and trade openness, GDP and nuclear power, GDP and hydroelectricity, and GDP and carbon emissions. The short-term results of Model 1 also demonstrate the unidirectional, unproductive relationship between GDP and trade openness, as well as the relationship between hydroelectricity and nuclear and carbon emissions. Short-term trade openness, GDP, nuclear power, and carbon emissions have no unproductive relationship with hydroelectricity. Multitudinous experimenters [53,81,[114], [115], [116]] have verified the correlations between the consumption of renewable energy, profitable growth, trade openness, and carbon emissions. As opposed to short-term values, which are represented by p-values and the chi-square measure, long-term values are shown using t-statistics.

Long-term results for Model 2 indicate a complementary relationship between GDP and crude oil and coal. This finding is harmonious with the findings of [[117], [118], [119], [120]]. The conclusion drawn by Refs. [121,122] that GDP growth is possible indeed in the absence of rising carbon emissions establishes the unproductive relationship between GDP and carbon emissions. The findings show a unidirectional, unproductive relationship between carbon emissions and coal use, meaning that rising carbon emissions beget rising coal consumption. Our exploration establishes that compared to other non-renewable energy sources, natural gas emits more carbon. We agree with [34,123] that Pakistan can maintain its GDP rate if its government looks into alternative energy sources to meet its energy needs.

5. Discussion

There is little questioning that economic development and environmental pollution are directly correlated, given the large, positive GDP coefficient. We should also note that the large positive coefficient between GDP and environmental deterioration in Pakistan reflects the "Environmental Kuznets Curve Hypothesis" (Smith et al., 2017). It may be a result of the stage of industrialization in Pakistan, where economic maximization often comes at the expense of sustainability. Alongside that, urbanization and the growth of the middle class would encourage people to buy more products, thus exerting a greater impact on the environment. However, many developing nations have seen similar patterns, as there have always been environmental consequences to rapid economic development. It is noteworthy that there is very little correlation, either in the short or long term, between trade openness and environmental degradation. This contradicts existing literature that postulates that increased trade could lead to the "race to the bottom" phenomenon, where countries might have lesser environmental standards to gain competitive advantages. In Pakistan's context, its trade portfolio or the nature of goods it imports and exports do not significantly contribute to environmental degradation.

The blend of energy consumption in Pakistan yields inconsistent issues. The country's main energy sources, coal and natural gas, greatly increase carbon emissions, but the relationship between crude oil and emissions is intriguing and needs further explanation. The long-term impact on carbon emissions is declining despite crude oil being Pakistan's alternate-largest energy source. This could indicate that crude oil is a substantial energy source, but its use could be more effectively controlled for emissions than coal or natural gas. It is also important to note how little the use of nuclear and hydrogen energy affects carbon emissions. While global trends often highlight the potential of these sources for curbing carbon footprints, their role in Pakistan seems peripheral. The existing infrastructure or policies still need to support the wide-scale integration of these sources. Contrasting with prior studies, it is evident that Pakistan's unique socio-economic and policy landscape shapes its environmental trajectory. Many countries have observed coal as a major polluter, which is consistent with our study, yet the inconsequential role of trade and specific energy sources deviates from conventional wisdom. This emphasizes the importance of contextual nuances in shaping environmental discourse. For Pakistan, future policy interventions must address the growing strain GDP growth exerts on the environment while reconsidering energy policies that heavily lean on coal and natural gas.

6. Conclusion

An essential comparison between Pakistan's non-renewable and renewable energy sources and their corresponding carbon emissions has provided insightful data. This question and its ferocity are firmly rooted in Pakistan's rapidly increasing environmental concerns coupled with an energy path characterized by a lack of hope. It is an academic activity and a reply to the country's socio-economic and environmental issues. Empirical estimations shed light on a critical dichotomy: the untapped potential of renewables versus the environmental cost of non-renewables. Renewables have become the only viable solution, which is cleaner and offers lesser emissions. However, while the move is economically justifiable in the short run, the country is extremely dependent on non-renewables and must implement quick and effective mitigation policies.

Policy implications

From a policy point of view, these results constitute a clarion call for change. However, policymakers should focus on a paradigm shift toward renewables in a phased manner to discontinue non-renewable reliance. This aligns with global sustainability and may result in economic gains such as green job creation and technology-driven innovations. However, the study has limitations. Despite providing detailed information, some findings may not be universally applicable due to their geographical specificity to Pakistan. In addition, the data's temporal scope also imposes limitations and may not capture long-term trends or sudden shifts. Future research avenues are vast. Such cross-country comparisons provide useful insights into how economies with diverse energy-environment matrices respond.

Lastly, new renewable energy technologies are emerging. Their integration and feasibility need deeper investigations. Essentially, this study deciphers the intricacies associated with the energy quagmire in Pakistan and prescribes a strategy for promoting economic growth while maintaining environmental health. Such a balance is not only desirable but compulsory to have for a sustainable future.

Funding

This work has no funding.

Availability of data and materials

The data will be provided on the reasonable demand. Consent to participate: Not applicable.

Consent to publish

Not applicable.

CRediT authorship contribution statement

Ghazala Aziz: Writing – original draft, Formal analysis, Conceptualization. Hussam Buzaid M. Bakoben: Writing – review & editing. Suleman Sarwar: Writing – review & editing, Supervision, Software, Resources, Methodology, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.