Do Environmental Tax and Energy Matter for Environmental Degradation in the UK? Evidence from Novel Fourier-Based Estimators

Abstract

Currently, the UK has ambitious plans to reach net zero by 2050, despite other countries such as Russia and India targeting 2060 and 2070, respectively. Assuming that the UK emissions unceasingly decline at a given rate annually towards achieving net zero by 2050, its economy would need to ensure a reduction of 105 MtCO2 per year of its emissions from the current 2021 levels. Given that global greenhouse gas emissions have not peaked and continue to rise, the UK seeks to implement costly and aggressive emission reduction policies towards fulfilling commitments under the 2021 Glasgow Climate Pact. This paper investigates the effect of environmental taxes on environmental degradation in the UK between 2000Q1 and 2019Q4 using novel Fourier approaches. Using the novel Fourier ARDL estimator, the long-run equilibrium estimates indicate that gross domestic product and environmental tax cause a fall in carbon emissions. However, in trade and primary energy use, a unit change caused rising carbon emissions in the UK. Especially, the results indicate that environmental taxes have a negative effect on environmental degradation in the UK, and ecological tax policy could be considered as an effective channel to attain environmental sustainability. The outcome provides the following policy insights: (i) The government of the UK should support international environmental tax coordination mechanisms, especially on carbon pricing, to avoid relocation of carbon-intensive investments. (ii) The UK government must note that imposing more taxes to encourage emissions reductions could bring complexity to the tax system and unnecessarily bring costly ways to deal with climate change. Higher domestic electricity prices could disproportionately hit low-income households and create distributional cost concerns, which require benefit payouts or compensation schemes. (iii) Switching to electric vehicles simultaneously requires investments in charging infrastructure and battery technologies. To avoid this chicken-and-egg problem, the government of the UK could play a coordinating role, including deploying targeted subsidies, regulations, direct government involvement, or setting higher carbon prices in special cases.

1. Introduction

Historically, the relationship between the growing economic activity of nations and environmental degradation has been an undisputed fact relative to production structure [1]. Theoretically, this relationship is rooted in the environmental Kuznets curve, particularly when linked to fossil fuel use [2,3]. Ecological degradation is generally explained to refer to damage to the quality and quantity of naturally endowed resources to humanity, such as air, forest, water, and land. Economists (under the Pigouvian Framework, [4]) claim this environmental damage arises once the marginal social cost of consuming environmental resources surpasses the marginal social benefits [5]. In recent times, environmental economists have recognized that environmental damage relates directly to rising global warming, a critical existential global crisis largely found to be caused by energy-related greenhouse gas (GHG) emissions [6,7]. These greenhouse gas (GHG) emissions are observed through vehicles and factories’ emissions of poisonous gasses into the air, waste generation, deforestation for agriculture, and chemical use for fishing. The consequential effects include global warming and climate change, poor agricultural output, various weather conditions, flooding, and poor human health [7].

Globally, the United Nations has, in contemporary decades, led the campaign for the reduction in carbon emissions that cause global warming. To achieve this goal, the United Nations urges the global economy to urgently take policy actions that promote low-carbon economies. Although existing global environmental initiatives, such as the Kyoto Protocol, the Paris Agreement, and the United Nations Framework Convention on Climate Change, have made significant gains, some environmentalists and scientists have observed that global initiatives cannot sufficiently deliver global climate change mitigation and emissions reduction goals due to disagreements on important policy issues. Accordingly, the United Nations urges economies to implement sustainable policy actions through administrative orders, economic incentives, and environmental taxes. While several experts claim that administrative orders and environmental regulations tend to be rigid and ineffective, economic incentive policies are relatively useful only in some economic cycles [8].

Recently, several scholarly studies have cited and proposed environmental taxes as having the best potential to reduce environmental degradation and mitigate the effects of global warming, notwithstanding the role of renewables and financial innovation [9,10,11,12]. Theoretically, environmental pollution occurs due to corporations’ or individuals’ failure to account for environmental harm created by others through their decision making [4]. Environmental taxes are generally hinged on principles of precaution, polluters pay, risk prevention, public participation, and integration of decision making. Experts claim environmental tax gains are needed for revenue-recycling benefits and energy gains [9,10]. Figure 1 is an illustration of Pigourian environmental theory and social effects [4]. If emissions tax revenues are not used to increase economic efficiency through cutting distortionary taxes (or through funding socially desirable spending), the net benefits from emissions taxes are greatly reduced (e.g., [9,13,14]). The case for using environmental taxes on cost-effectiveness grounded on regulatory approaches (e.g., emissions standards) can be substantially undermined (e.g., [14]). Environmental taxes tend to have a bigger impact on energy prices than regulatory policies (because the former involves the pass-through of tax revenue into prices), and the revenue-recycling benefit is needed to offset the effect of these greater energy price increases on exacerbating factor tax distortions. Although several economists traditionally argue that environmental regulations increase corporate costs and affect the competitiveness of the local industry if policy variations exist across countries [9,14], however, many others claim that environmental regulations could foster innovations in environmental technologies and leadership towards increased economic growth [4,13].

The question that continues rumbling in the ears of environmental economists is whether environmental taxes can truly reduce environmental degradation. To answer this continuously echoing academic question on the role of an environmental tax on carbon emissions, the economy of the United Kingdom of Great Britain (UK) presents an inspiring case for investigation. After leaving the EU, the UK passed the Environment Act in 2021 to empower the government with powers to establish new environmentally friendly binding targets on air quality, water, biodiversity, and waste reduction. The new Environment Act also established the Office for Environmental Protection (OEP), replacing existing EU environmental oversight functions and other regulations that were expiring at the end of 2023. Additionally, the country has an ambitious climate policy of net zero by 2050. Historically, the UK’s attempt to develop environmental policies has conflicted with competing interests and perspectives of different groups in society, especially industry and local communities. Throughout history, the UK has been a signatory of several global agreements on the environment, e.g., the Convention for the Preservation and Protection of Fur Seals with the United States, Japan, and Russia (1911); the Convention for the Protection of Migratory Birds (1916) with the United States which was later extended to Mexico; and Convention on Preservation of Fauna and Flora (also referred to as London Convention of 1933).

According to [15], public advocacy on environmental taxation in the UK originated from the Minority Report of the Royal Commission on Environmental Pollution in 1972. This report set the British political and environmental agenda in 1989 when environmental taxes were presented through a meeting for a revenue-neutral carbon regulatory action. Environmental taxation in the UK was eventually influenced by the introduction of carbon taxes in Nordic countries during the 1990s but received a blow with the introduction of VAT on domestic energy in 1993. In 2001, the UK implemented the Climate Change Levy—a downstream tax on corporate energy use to promote energy efficiency and renewable energy development. In general, the UK’s environmental taxes have covered energy, transport, pollution, and commercial exploitation of natural resources. Available data from the UK’s Office of National Statistics (May 2023) indicate that, by using the internationally agreed framework, the UK’s environmental tax revenue increased by 6.9% from GBP 44.3 billion in 2021 to GBP 47.4 billion in 2022 for energy (74.7%), transport (22.3%), and pollution and resource use (3.0%). This represented 1.9% of gross domestic product (GDP) in 2022, the lowest record since 1997. To disincentivize emissions from waste disposal, the UK government imposed landfill taxes, with consistent rate increases since its introduction. Between 2004 and 2021, the landfill taxes increased from GBP 15 to GBP 96.70 per ton. Figure 2 presents the tax types in the UK.

These notwithstanding, the UK has been urged by experts to do more to reduce carbon emissions as it lags behind several European economies [17]. Given that very limited studies have been conducted on environmental taxes on carbon emissions, this paper fills the gap and brings clarity to relevant arguments on environmental taxes using novel Fourier autoregressive distributive lag econometric approaches. The study is motivated by the Pigourian tax [4] and the cap-and-trade theoretical system of environmental tax by [18].

The paper progresses as follows: The next section reviews the relevant literature for conceptual frames and to construct the assumptions for the empirical study. This is followed by separate sections for methodology and empirical outcomes. The last section deals with conclusions and policy recommendations.

2. Brief Literature Review: The Environmental Tax–CO₂ Emissions Nexus

Several studies have explored the determinants of CO₂. For example, [19] uncovered that economic growth intensified CO₂ emissions, though green energy, remittances, and globalization decreased CO₂ emissions. [20] revealed that gross domestic product (GDP), urbanization, and globalization increased CO₂ emissions in China, while hydroelectricity consumption lessened CO₂ emissions. Recently, some studies have also discussed environmental sustainability by probing the determinants of renewable energy (e.g., [21,22,23]) and exploring the importance of firm and sovereign environmental, social, and governance sustainability activities [24,25].

Particularly, the relationship between environmental taxation and environmental degradation has been a matter of intense debate among researchers, policymakers, and economists over the past decades. This section systematically reviews relevant studies for insights into crafting a conceptual framework and positioning the study for empirical analysis.

Environmental taxes are an efficient policy instrument to decrease carbon emissions. [26] found that environmental taxes generally seek to decrease carbon emissions by influencing a fall in fossil fuel demand. They are ultimately implemented to achieve global environmental delivery targets of the Kyoto Protocol and the Paris Climate Agreement. Historically, environmental taxes (e.g., carbon taxes) have been implemented by several economies and sub-national governments. Globally, two waves of enactments of environmental taxes have occurred, beginning from the early 1990s (Denmark, Finland, Norway, and Sweden), and in the 2000s, countries such as Switzerland, Iceland, Ireland, Japan, Mexico, and Portugal enacted such laws.

Theoretically, the basis of environmental taxes is severely documented as improving social welfare if the consumption or production of particular goods results in a negative externality [12,27]. Environmental degradation has been generally classified as problematic due to the failure of corporations or individuals to damage control in their decision making to fully price resources for production or consumption. Given the divergence between private and social costs of pollution, [4] claimed that taxing pollution equates to social marginal damage and private costs while ensuring efficient market outcomes. Critics, however, argue that no consensus globally exists on the optimal effectiveness of energy and carbon taxes, subsidies, and transfers. They claim that environmental taxes may tend to be regressive against poorer households that could be compelled to purchase cheaper and less energy-efficient appliances [28].

Similarly, environmental taxes are distortionary, given the narrow tax base, and create double taxation on both intermediate input and final output [29,30]. As an alternate theory, others have recommended a cap-and-trade system, given that the carbon tax places costs on CO₂ pollution and permits markets to determine pollution. A cap-and-trade system rather caps pollution, allowing markets to have the right to pollute. In this case, politicians do not directly set prices [18]. However, [18] argues about three factors favoring carbon taxes over cap-and-trade systems. First, he argues that a cap-and-trade system allows price variations with changing market conditions, leading to price volatility and uncertainty, since corporations cannot plan for long-lived, capital-intensive projects. Second, the cap-and-trade system is administratively complex, requiring new administrative structures for tracking, holding auctions, and developing rules to avoid fraud and abuse. Finally, the cap-and-trade system has the potential for adverse policy interactions, which could be counterproductive [31].

Empirically, several studies investigating the effect of environmental taxes on pollution control have found it to be positive [32,33,34]. Ref. [35] found that environmental taxes significantly reduce carbon emissions. Furthermore, the outcomes of the investigation indicated that environmental taxes are instrumental in facilitating the development of renewable energy technologies and could help reduce energy demands. [36] investigated EU policies on carbon emissions mitigation and found environmental taxes to be a very effective approach to carbon emission reduction across member economies. A similar investigation by [37] on the effects of international competitiveness of environmental taxes in European countries indicated that environmental taxes are very effective in promoting the welfare of economies and market competitiveness. Another study by [38] examined the effects of carbon taxes on economic growth and energy intensity in China. The results indicated increases in carbon tax have negative effects on energy intensity and carbon emissions. However, some experts in their investigations found environmental taxes to have very little effect on reducing carbon emissions [39,40]. For example, [41] claimed environmental taxes could only protect environmental quality if investments in energy and environmental technologies could be prioritized. Using data from 1995 to 2005 on 25 European economies, [42] investigated the long-run effects of environmental taxes on energy use. The outcomes indicated that environmental taxes have little effect on energy consumption in the studied countries.

Based on the above review, the effects of environmental taxes on pollution vary, and the findings are inconclusive. Accordingly, the study seeks to bring clarity to the arguments on the effects of an environmental tax on pollution using the UK as a case study. To achieve the stated objectives, the paper gives the following hypothesis:

Hypothesis 1 (H1). 

Environmental taxes have negative effects on environmental degradation in the UK.

3. Methodology

3.1. Data

This paper aims to capture the effect of an environmental tax on environmental degradation in the UK between 2000Q1 and 2019Q4. To achieve the established objectives of the paper, economic growth, primary energy consumption, and trade in the UK are controlled. All variables are in the log form to avoid scaling [43]. Data were sourced on (i) carbon dioxide emissions (as a proxy variable for environmental degradation) from UNFCC. Carbon dioxide emissions are determined in kt (kiloton). Carbon dioxide (CO2) is a gas produced from the burning of carbon and the respiration of living organisms and is measured in parts-per-million (ppm) [44]. (ii) Data on environmental tax were sourced from OECD. (iii) Data were sourced from gross domestic product (GDP) as a proxy variable for economic growth. (iv) Data were sourced on primary energy consumption from OECD. Primary energy measures a country’s total energy demand. (v) Data on trade were sourced from the IMF. Trade involves voluntary exchanges of goods or services between economic actors. Trade is measured by the difference between a country’s exports and imports of goods. Figure 3 presents the analysis flowchart.

3.2. Control Variables

Towards achieving the objectives of the study, economic growth, trade, and primary energy consumption are controlled to assess the pollution effect of environmental tax in the case of the UK. First, for several decades, the UK’s energy market has been largely driven by coal, fossil energy, nuclear, and renewables. With increasing renewable use, fossil energy has halved, while coal generation in the UK is expected to be phased out by 2024. Gas supply has largely been supplied locally (54% in 2022), while the remaining was imported from Norway, Netherlands, Qatar, Algeria, Belgium, and, to some extent, Russia before the ban in 2023 due to the Ukraine invasion [45]. Electricity generation from nuclear sources stood at 15% in 2022. In general, according to ESO’s analysis, the energy mix for the UK from 2022 is made up of gas—38.5%; wind—26.8%; nuclear—15.5%; biomass—5.2%; coal—1.5%; solar—4.4%; imports—5.5%; hydro—1.8%; and energy storage—0.9%.

Hypothesis 2 (H2). 

Based on these, an assumption is made for this paper that primary energy use in the UK positively moderates CO₂ emissions (H2), i.e.,ϑ₂ = ${\displaystyle \frac{\mathit{\vartheta }\mathit{L}{\mathit{C}\mathit{O}}_2\mathit{E}}{\partial \mathit{L}\mathit{P}\mathit{E}\mathit{C}\mathit{i}\mathit{t}}}$ ˃ 0; where ϑ represents the interest parameter; LPEC signifies the natural log of primary energy use; LCO₂E is the natural log of CO₂ emissions (as a proxy for environmental degradation).

For economic growth, the UK has, for several years, committed to the cause of climate change with several policies. After the 2008 climate action, which helped the economy sustain reductions in GHG emissions, the UK 2019 enacted an ambitious new law to further commit itself to reaching net zero greenhouse gas emissions by 2050. Accordingly, in 2021, the UK government adopted the sixth carbon budget to drastically cut emissions by 78% by the close of 2035. Being the pioneer of the Climate Act, the economy’s climate actions have set the pace and as a model for climate legislation in several countries, including Denmark, France, Germany, Ireland, Mexico, New Zealand, and Sweden. Notwithstanding the 2007 peaking of emissions in the UK, due to a combination of environmental policies and a transition to less carbon-intensive service-based industries, the UK has witnessed imported emissions mainly from China and the neighboring EU countries. Critics have argued that the increasing proportion of the UK’s economy to the higher-value services sector raises emissions through international trade flows and exaggerates apparent declining records in territory-based emissions. According to this view, there is the need for rethinking the EKC theory [46] on growth and carbon emissions.

Hypothesis 3 (H3). 

Based on these, this study hypothesizes that rising economic growth in the UK significantly causes CO₂ emissions to be reduced, i.e., (H3) =ϑ₃= ${\displaystyle \frac{\mathit{\vartheta }\mathit{L}{\mathit{C}\mathit{O}}_2\mathit{E}}{\mathit{\vartheta }\mathit{L}\mathit{G}\mathit{D}\mathit{P}\mathit{i}\mathit{t}}}$$<$ 0; where ϑ is linked to the interest parameter; LGDP is the natural log of gross domestic product (GDP) (a proxy variable for the UK’s economic growth); LCO₂E is the natural log of the UK’s carbon dioxide emissions.

Another factor considered as a determinant of carbon emissions in the UK is trade. In 2020, carbon dioxide emissions represented approximately 79% of the UK’s total GHG emissions. However, records from the [47] indicate that the United Kingdom witnessed rising consumption-based emissions, suggesting that historically falling rates in total emissions were offset by rising consumption-based emissions. UK’s exports of goods and services in 2022 amounted to GBP 834 billion. The country also imported a total of GBP 902 billion in goods and services, with the EU alone accounting for 47% of the total in 2022. Theoretically, the environmental effects of output in trade lends are explained by the pollution haven hypothesis—a framework that claims to reallocate dirty industries by corporations to economies with less strict environmental regulations [47]. Despite the negative effects of trade, several scholars argue that trade could provide knowledge and technology transfer, which helps to eventually improve environmental performance [48,49].

Hypothesis 4 (H4). 

Based on the arguments, the authors of this paper hypothesize that the trade increases environmental degradation in the UK, i.e., (H4) =ϑ₄= ${\displaystyle \frac{\mathit{\vartheta }\mathit{L}{\mathit{C}\mathit{O}}_2\mathit{E}}{\mathit{\vartheta }\mathit{L}\mathit{T}\mathit{R}\mathit{A}\mathit{i}\mathit{t}}}$$>$ 0; where ϑ is the interest parameter; LTRA is a log of trade; and LCO₂E is a log of carbon dioxide emissions in the UK.

3.3. Model

Theoretically, productive and efficient energy use can promote environmental quality [50]. With growing global concerns about energy use for growth, environmental degradation, and global warming, new policy pathways are required for successful energy transformation. One major policy pathway for dealing with increasing environmental degradation is environmental tax [11]. Despite major critiques, [4] claimed that, with the divergence between private and social costs of pollution, taxing pollution equates social marginal damage and private costs, while ensuring efficient market outcomes. To estimate the nexus between environmental degradation, environmental tax, economic growth, trade, and primary energy consumption, the study employs the Stokey framework, which can establish how environmental pollution and abatement affect the regulation [51]. Similarly, the study is motivated by a balanced growth model, the role of abatement and technological progress towards improving growth and environmental quality over time, although the growth rate of output could equally be lowered, given the strength of scale, composition, and technique effects as espoused by the EKC hypothesis [52]. The Stokey framework highlights how rapidly increasing population and economic growth could eliminate any possibility of sustainable growth. It also highlights how convergence is demonstrated across countries involved in trade and pollution abatement, justifying how environmental taxes can level variations across countries and facilitate induced innovation in energy use, growth, pollution abatement, and general technological progress. Accordingly, the empirical model for this study is as follows:

$${\mathit{CO}}_2\mathbf{E}=f(GDP,PEC,TRA,ETAX)$$

(1)

where CO₂E is carbon dioxide emissions (as a proxy for environmental degradation in the UK); GDP is gross domestic product (as a proxy for economic output); PEC is primary energy use; TRA is trade; and ETAX is environmental tax.

Next, by logging variables, the model is specified as follows:

$${\mathit{LCO}}_2\mathbf{E}=f(LGDP+LPE+LTRA+LETAX+e_t)$$

(2)

where LCO₂E is a log of carbon dioxide emissions (as a proxy for environmental degradation in the UK); GDP is GDP output; and LPEC is primary energy use; LTRA is a log of trade; LETAX is a log of environmental tax; and e_t is the error term.

3.4. ADF Unit Root Test with Breakpoint

Next, after descriptive statistical assessments, the paper checks the integration order of variables using Augmented Dickey–Fuller (ADF) unit root tests with breakpoints. In the field of econometrics, when variables are integrated to varying degrees, it makes models not testable for cointegration using the conventional cointegration methods. This paper adopts the novel ADF unit root tests with breakpoints, which provide better and more reliable information for cointegration assessment despite integration order. To estimate the unit roots for ADF with breaks, the model used is as follows:

$$x_t=\mu +\rho x_{t-1}+e_t$$

(3)

here x_t refers to variables of interest; μ is the constant term; and e_t is the error term. By unit differencing, the model becomes Δx_{t =} μ + e_t; where Δ = (1 − B); ρ refers to parameter slopes for lagged variables and becomes 1 whenever there occurs a unit root. The study illustrates the alternative unit root for ADF with breaks in Equations (4) as follows:

$$x_t=\mu +{\beta }_t\delta D{U}_t+\theta D\left(T_B\right)+e_t$$

(4)

The re-specifications of error correction form; and after applying the augmentation factor, ADF with breaks equation is estimated as follows:

$$\mathsf{\Delta }{x}_t=\mu +{\beta }_t+{\gamma }_1\sin \left({\displaystyle \frac{2\pi k_t}{N}}\right)+{\gamma }_2\cos \left({\displaystyle \frac{2\pi k_t}{N}}\right)+(\rho -1)x_{1-1}+{\displaystyle {\displaystyle {\sum }_{i-1}^p{C}_i\Delta x_{i-1}+\epsilon }}$$

(5)

here c refers to the slope parameter of the augmented parts; p is the lag length with minimum information criteria values in the augmentation process; k is Fourier regularity; structural break date is T_B; and break fraction refers to λ.

3.5. Fourier ARDL Cointegration Analysis

The traditional ARDL cointegration approach has historically been employed extensively by researchers for decades [53]. The limitation of this estimator is that it is unable to detect hidden long-term nonlinear relationships among variables. Accordingly, in this paper, the Fourier ARDL estimator is employed to estimate long-run equilibrium relations among interest variables. The estimators can detect the existence of unknown structural breaks, time, and structures related to the variables. In essence, the Fourier-based ARDL long-run estimator can provide more robust outcomes than the traditional ARDL approach [54,55]. The Fourier function is modeled in Equation (6).

$$\mathit{d}\left(\mathit{t}\right)=\sum _{\mathit{k}=1}^{\mathit{n}}{\mathit{a}}_{\mathrm{k}}\mathbf{sin}\left({\displaystyle \frac{2\mathit{\pi }\mathit{k}\mathit{t}}{\mathit{T}}}\right)+\sum _{\mathit{k}=1}^{\mathit{n}}{\mathit{b}}_{\mathrm{k}}\mathbf{cos}\left({\displaystyle \frac{2\mathit{\pi }\mathit{k}\mathit{t}}{\mathit{T}}}\right)$$

(6)

where n indicates the number of frequencies, π = 3.14, k is the number of special frequencies selected, t is the trend, and T is the sample size. A single frequency value is suggested [56,57] as in Equation (7).

$$\mathit{d}\left(\mathit{t}\right)={\mathit{\gamma }}_1\mathit{s}\mathit{i}\mathit{n}\left({\displaystyle \frac{2\mathit{\pi }\mathit{k}\mathit{t}}{\mathit{T}}}\right)+{\mathit{\gamma }}_2\mathit{c}\mathit{o}\mathit{s}\left({\displaystyle \frac{2\mathit{\pi }\mathit{k}\mathit{t}}{\mathit{T}}}\right)$$

(7)

The FARDL model for this study is shown in Equation (8).

$$\begin{array}{l}∆\mathit{L}\mathit{C}\mathit{O}2{\mathit{E}}_{\mathrm{t}}={\mathit{\beta }}_0+{\mathit{\gamma }}_1\mathit{s}\mathit{i}\mathit{n}\left({\displaystyle \frac{2\mathit{\pi }\mathit{k}\mathit{t}}{\mathit{T}}}\right)+{\mathit{\gamma }}_2\mathit{c}\mathit{o}\mathit{s}\left({\displaystyle \frac{2\mathit{\pi }\mathit{k}\mathit{t}}{\mathit{T}}}\right)+{\mathit{\beta }}_1{\mathit{L}\mathit{T}\mathit{R}\mathit{A}}_{\mathrm{t}-1}+{\mathit{\beta }}_2{\mathit{L}\mathit{G}\mathit{D}\mathit{P}}_{t-1}\\ +{\mathit{\beta }}_3{\mathit{L}\mathit{P}\mathit{E}\mathit{C}}_{t-1}+{\mathit{\beta }}_4{\mathit{L}\mathit{E}\mathit{T}\mathit{A}\mathit{X}}_{t-1}+{\displaystyle \sum _{\mathit{i}-1}^{\mathit{\rho }-1}}{\mathit{\phi }}_i\mathit{\prime }{∆\mathit{L}\mathit{C}\mathit{O}2\mathit{E}}_{t-i}\\ +{\displaystyle \sum _{\mathit{i}-1}^{\mathit{\rho }-1}}{\mathit{\delta }}_i\mathit{\prime }{∆\mathit{L}\mathit{T}\mathit{R}\mathit{A}}_{t-i}+{\displaystyle \sum _{\mathit{i}-1}^{\mathit{\rho }-1}}{\mathit{\varnothing }}_i\mathit{\prime }{∆\mathit{L}\mathit{G}\mathit{D}\mathit{P}}_{t-i}+{\displaystyle \sum _{\mathit{i}-1}^{\mathit{\rho }-1}}{\mathit{\vartheta }}_i\mathit{\prime }{∆\mathit{L}\mathit{P}\mathit{E}\mathit{C}}_{t-i}\\ +{\displaystyle \sum _{\mathit{i}=1}^{\mathit{\rho }-1}}{\mathit{\vartheta }}_i\mathit{\prime }{∆\mathit{L}\mathit{E}\mathit{T}\mathit{A}\mathit{X}}_{t-i}\\ +{\mathit{e}}_t\end{array}$$

(8)

Several experts apply the frequency value to the minimum sum of squared residuals [55,58,59]. In addition, the study employs the Fourier TY Causality Test to support the outcomes of the Fourier ARDL test.

4. Empirical Outcomes

In this paper, the effect of an environmental tax on environmental degradation in the case of the UK is investigated using data from 2000Q1 to 2019Q4. To achieve this objective, economic progress, trade, and primary energy consumption are controlled positions.

Table 1. Descriptive statistics.

	LCO2E	LGDP	LETAX	LPEC	LTRA
	Production-Based CO2 Emissions	GDP (Constant 2015 USD)	Environmental Taxes	Primary Energy Consumption	Trade
Mean	5.680814	12.40656	0.883805	3.394797	12.10137
Median	5.718796	12.42153	0.883395	3.407255	12.14079
Maximum	5.737927	12.50671	0.941662	3.432993	12.28227
Minimum	5.535779	12.27547	0.821466	3.324600	11.81647
Std. Dev.	0.063209	0.063380	0.032983	0.033321	0.125218
Skewness	−0.971417	−0.440579	0.118102	−0.557668	−0.648029
Kurtosis	2.508673	2.263405	2.149941	1.785334	2.420849
Jarque–Bera	17.40268	5.715721	3.373034	11.78403	8.732460
Probability	0.000166	0.057391	0.185163	0.002761	0.012699
Observation	80	80	80	80	80

is a statistical description of the variables examined.

Based on the outcomes of the descriptive analysis (Table 1), it is apparent that there are no outliers in the dataset. Similarly, the results suggest all variables are distributed normally. This suggests that further estimation action could proceed.

It is noteworthy to highlight that, historically, structural breaks have been overlooked in econometric studies, causing biases in unit root estimates. Before carrying out estimations to observe the integration order of interest variables, the paper conducted the Broock, Dechert, and Scheinkman (BDS) test [60] for any existence of stochastic hidden and nonlinear patterns (i.e., dependence or independence). The BDS test can also guide against any model misspecification and judgmental errors. The model for this econometric application is as follows (9):

$${\mathit{BDS}}_{\mathit{mT}}(\varepsilon )={\mathit{T}}^{\mathbf{1}/\mathbf{2}}[{\mathit{C}}_{\mathit{m},\mathit{T}}(\varepsilon )-{\mathit{C}}_{1,\mathit{T}}{(\varepsilon )}^{\mathrm{m}}]/{\mathit{\delta }}_{\mathit{mT}}(\varepsilon )$$

(9)

where T is the sample size, ɛ is the randomly adopted proximity parameter, and δ_mT^ (ɛ) is the standard deviation of the numerator which varies with dimension “m” [61].

Based on the BDS estimates (

Table 2. BDS test.

LCO2E
Dimension	BDS Statistic	Std. Error	Z-Statistic	Prob.
2	0.189814	0.008048	23.58658	0.0000
3	0.315299	0.012877	24.48520	0.0000
4	0.398736	0.015439	25.82620	0.0000
5	0.455943	0.016203	28.14013	0.0000
6	0.496496	0.015733	31.55727	0.0000
LETAX
Dimension	BDS Statistic	Std. Error	Z-Statistic	Prob.
2	0.180957	0.005157	35.09075	0.0000
3	0.301061	0.008204	36.69570	0.0000
4	0.377348	0.009776	38.60040	0.0000
5	0.422836	0.010194	41.48058	0.0000
6	0.447332	0.009834	45.48929	0.0000
LPEC
Dimension	BDS Statistic	Std. Error	Z-Statistic	Prob.
2	0.184377	0.005693	32.38848	0.0000
3	0.305464	0.009069	33.68316	0.0000
4	0.385017	0.010821	35.58063	0.0000
5	0.437600	0.011300	38.72657	0.0000
6	0.473069	0.010917	43.33401	0.0000
LGDP
Dimension	BDS Statistic	Std. Error	Z-Statistic	Prob.
2	0.207899	0.005438	38.23326	0.0000
3	0.352709	0.008651	40.76968	0.0000
4	0.454483	0.010309	44.08579	0.0000
5	0.526880	0.010751	49.00911	0.0000
6	0.578796	0.010372	55.80252	0.0000
LTRA
Dimension	BDS Statistic	Std. Error	Z-Statistic	Prob.
2	0.205597	0.006003	34.25065	0.0000
3	0.349311	0.009585	36.44176	0.0000
4	0.450381	0.011465	39.28194	0.0000
5	0.521916	0.012002	43.48589	0.0000
6	0.573000	0.011624	49.29533	0.0000

), hidden nonlinear patterns exist in the time series data since variables have significant dimensional critical values higher than their respective BDS estimates. These outcomes imply nonlinear correlations between the interest variables.

The outcomes of the ADF unit root test with breakpoint (

Table 3. ADF unit root test with breakpoint.

Variables	ADF with Breakpoint
LCO2E	−2.276 (2013Q1)
LETAX	−3.510 (2002Q1)
LGDP	−5.062 *** (2009Q1)
LPEC	−2.145 (2006Q4)
LTRA	−3.881 (1994Q4)
DLCO2E	−6.406 (1996Q1) **
DLETAX	−6.011 (2009Q1) **
DLGDP	NA
DLPEC	−6.790 (1996Q1) **
DLTRA	−5.391 (1997Q1) **

Note: ** and *** denote 5% and 1% significance levels, respectively.

) indicate the interest variables. LGDP is integrated at level (i.e., I(0) with a breakpoint at 2009Q1 at a 10% significance level). However, while LCO₂E, LPEC, LTRA, and LRTAX are integrated at order ONE (i.e., I(1) with several breakpoints in 1996Q1, 2009Q1, 1996Q1, and 1997Q1, respectively, at a 5% significance level). The outcomes of the unit root analysis demonstrate that the time series variables integrate in a mixed order.

The next step involves investigating cointegration properties among the interest variables using the Fourier ARDL Cointegration estimator. This helps to ascertain how LETAX, LGDP, LPEC, and TRAL individually and collectively impact LCO₂E in the case of the UK.

Table 4. Fourier ARDL Cointegration Analysis.

Model		Frequency	Min AIC
LCO2E = f(LETAX, LGDP, LTRA, LPEC)	−7.853977	0.6	−3.572768

shows the Fourier ARDL cointegration analysis.

The Fourier ARDL Cointegration estimates (ARDL Bounds test) indicate the F-stats are significantly higher in value than the target critical values. This outcome suggests that both the dependent and independent variables possess long-term equilibrium relationships. This means the Fourier ARDL long-run cointegration test (

Table 5. Fourier ARDL long-run form.

Variables	Coefficient	Std. Error	t-Statistic	Prob.
LGDP	−2.198802	0.521931	−4.212819	0.0001
LTRA	0.737557	0.303497	2.430194	0.0183
LETAX	−0.395106	0.153661	−2.571279	0.0128
LPEC	1.645885	0.429862	3.828864	0.0003
C	1.757406	0.279609	6.285216	0.0000
@TREND	8.31 × 10−5	1.49 × 10−5	5.561438	0.0000
SIN	0.000710	0.000249	2.849281	0.0061
COS	0.000104	0.000270	0.383857	0.7025
CointEq(-1) ***	−0.093755	0.014914	−6.286291	0.0000

Note: *** denote statistical significance at the 1% level.

) could be used since the estimator could detect any hidden information.

Based on the long-run Fourier ARDL estimates, LGDP has negative coefficients with a significant statistical value. The LGDP has a coefficient of −2.198802, signifying that unit change in LGDP causes a fall in LCO₂E by −2.198802% in the UK. This outcome validates hypothesis 3 (H3) established for the study and supports [62]. Theoretically, increasing economic growth creates environmental degradation as a direct result of more demand for energy and material resources for production. According to the EKC framework, the initial phase of economic growth culminates in environmental destruction until a time when environmental regulatory and technological effects set in to correct the anomaly. This outcome suggests that the UK’s economy is currently beyond the EKC threshold, where rising GDP generates falling carbon due to increased technology application. This growth and environmental theory have been extensively validated by other growth frameworks such as the Source-and-Sink framework [63], Solow model [64], and Smulders and Stokey’s AK theoretical model [51].

Similarly, LETAX has a negative coefficient with a significant statistical value. From the estimates (Table 5), the coefficient of −0.395106 signifies that a unit change in LETAX causes a fall in LCO₂E by −0.395106% in the UK. This estimate validates hypothesis 1 (H1) established in the paper. The result also confirms similar outcomes of the study by [65] for the case of Sweden. For policy insight, the UK government needs to use regulatory measures such as environmental tax to facilitate the delivery of globally agreed-upon nationally determined contributions. According to [66], while the government of the UK could continue imposing environmental taxes, such action must be coherent and fittingly adjusted within the tax system.

Further, the long-run Fourier ARDL estimates (Table 5) indicate that both LTRA have positive coefficients with a significant statistical value. The LTRA has a coefficient of 0.737557, signifying that unit change in LTRA causes a rise in LCO₂E by 0.737557% in the UK. It must be noted that the result validates hypothesis 4 (H4) established for the study and aligns with [67]. It is instructive to note that, in 2020, carbon dioxide emissions amounted to an estimated 79% of the UK’s total GHG emissions. According to investigations by [68], the United Kingdom has witnessed increasing demand-based carbon emissions in recent years, suggesting that rising consumption-based emissions actually offset the historically falling rates in UK’s total emissions. Available data show, in 2022, that the UK’s exports of goods and services amounted to GBP 834 billion. While its imports totaled GBP 902 billion in goods and services. In theory, the environmental impact of trade lends support to the pollution haven hypothesis.

Furthermore, the coefficient of LPEC is positive and significant (Table 5). Based on Table 5, LPEC has a coefficient of 1.645885, signifying that unit change in LPEC causes an increase in LCO₂E by 1.645885% in the UK. This finding validates hypothesis 2 (H2) established in the paper. The estimate suggests that Russia’s invasion of Ukraine, together with subsequent sanctions leading to rising energy costs, have led to the increasing use of coal in electricity production in the UK. Although the UK is committed to increasing the consumption of renewable energy, total primary energy consumption in 2019 was 141,951 ktoe (1651 TWh), largely from fossil fuels: petroleum products (44%) and natural gas (31%) (BEIS, 2020). It is not surprising that a unit change in primary energy use causes a whopping 1.645885% upward adjustment relative to carbon emissions in the UK for the period under study. It must, however, be noted that 2019 was equally a milestone when the UK heralded sourcing more energy from non-carbon resources than fossil fuels. It is no wonder why the economy has committed immensely to a net-zero emissions target by 2050. Between 1990 and 2019, the UK drastically reduced carbon emissions by 40%, making it the country with the largest carbon reductions among the OECD and G20 member countries.

Model Diagnostic Tests

Historically, scientists have considered model stability and residual diagnostic tests very essential in empirical research. Towards reducing LCO₂E in the UK, the coefficient values in the error-correction model must be stable to enable policy decisions on them to be reliable relative to the behavior of economic output, primary energy use, trade, and environmental taxes. Accordingly, the paper captures model stability using the cumulative stability test (CUSUM and CUSUM of squares estimators) of [69]; the estimates of both CUSUM and CUSUM of squares indicate the statistical figures are within acceptable limits. Figure 4 shows the CUSUM and CUSUM of squares estimators.

Similarly, the paper checks if the model is free from heteroskedasticity and serial correlation issues using both the Breusch–Godfrey serial correlation LM test and residual diagnostic test, respectively. The results (

Table 6. Heteroskedasticity test and serial correlation LM tests.

Breusch–Pagan–Godfrey
F-statistic	0.790948	Prob. F(39,57)	0.7790
Breusch–Godfrey Test
F-statistic	0.371832	Prob. F(6,51)	0.8935

) indicate the model is free from both heteroskedasticity and serial correlation. This means the outcomes of the Fourier ARDL long-run equilibrium model could be used to provide policy recommendations.

To further support the outcomes of the Fourier ARDL model, the Fourier Toda Yamamoto Causality Test was carried out. The estimates indicate that LGDP, LTRA, LETAX, and LPEC individually and unidirectionally cause LCO₂E in the UK.

Table 7. Fourier TY Causality Test.

		T-Stat	p-Value
Ho1	LGDP does not cause LCO2E	16.88529 **	0.031326
Ho2	LTRA does not cause LCO2E	25.33331 ***	0.000662
Ho3	LETAX does not cause LCO2E	16.94006 **	0.017787
Ho4	LPEC does not cause LCO2E	10.85399 *	0.07612

Note: *, **, and *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

shows the Fourier TY Causality Test results. Overall, Figure 5 shows the Summary of empirical findings with methods.

5. Conclusions

In response to the Paris Agreement, the United Kingdom is a part of developed economies committed to reducing domestic greenhouse gas emissions. They have historically achieved broad political consensus on policy initiatives on energy transition towards reaching net-zero emissions by 2050. The government seeks policy pathways toward achieving stated emissions targets. In this paper, the authors investigated the effect of an environmental tax on environmental degradation in the UK between 2000Q1 and 2019Q4. To achieve this objective, economic progress, trade, and primary energy consumption are controlled positions. Using the novel Fourier ARDL estimator, the long-run equilibrium estimates indicate that both LGDP and LETAX cause a fall in carbon emissions. However, in the case of both LTRA and LPEC, a unit change caused rising carbon emissions in the UK.

5.1. Policy Recommendations

These outcomes have profound environmental policy insight as follows: First, in periods requiring policy response to environmental degradation, the UK economy could safely deploy environmental tax to discourage pollution-intensive activities. It is conceivable to equally deploy environmental taxes on corporate managers to spur growth in green innovation, increase output, and assure environmental quality. Corporations that invest hugely in green production could derive environmental tax advantages over other pollution-intensive enterprises in terms of cost savings and subsequent competitive edge on product pricing.

Second, the UK government must simplify the environmental tax system while ensuring an equitable incentive system to bring relief to vulnerable households. This study has noted that the current UK environmental policy landscape has many overlapping and complex policy cases, especially in the energy sector, where incentives to abate vary across sectors, fuel types, and consumers. This inconsistency within environmental taxes eventually increases the costs of transitioning to net zero. Policy simplification could entail ensuring uniform, effective environmental tax rates and regulatory guidelines. Additionally, the UK government should continue seeking broad-based policy consensus to assure policy stability, as this helps corporations and households to plan. Third, for purposes of the emissions effect of trade, the government of the UK should support international environmental tax coordination efforts, such as those on carbon pricing towards avoiding relocation of carbon-intensive investments. For local coordination, the government of the UK could play a coordinating role, including deploying targeted subsidies and regulations, direct government involvement, or setting higher carbon prices in specific sectors. It is noteworthy that switching to electric vehicles simultaneously requires investments in charging infrastructure and battery technologies to avoid chicken-and-egg situations. Fourth, contrary to some other G7 economies, the United Kingdom does not track support measures with potential environmental impacts. This makes it difficult to accurately quantify the extent of support and failure in the delivery of policy objectives. Moreover, ring-fencing corporate income tax to exclude them from environmental tax is not entirely helpful since, generally, corporations fully deduct decommissioning expenses from profits.

Fifth, the UK government could offer improved private incentives for researching, developing, and deploying new green technologies. The government could recycle environmental tax revenue to support developing clean technologies and infrastructure. This will increase popular support for environmental policies and direct carbon pricing instruments. Essentially, this will require allocating portions of carbon pricing revenue to public and private investments in green infrastructure, research, development, and deployment of green technologies, including carbon capture and storage.

5.2. Limitations and Future Research

Currently, data on environmental subsidies are not fully captured within the environmental tax systems in the UK, and this affects the quality of the research outcomes. Essentially, the broad measure of environmental revenues fails to capture the effect of subsidies and compensation payments. Future studies could consider using data that capture the complete picture of the UK’s environmental tax revenues and subsidies to accurately determine their impact on environmental degradation.

Additionally, the study focuses only on the UK economy. However, due to contextual and policy differences across economies, it would be better to conduct such a study across several economies to be able to accurately capture the true effect of environmental taxes on environmental degradation. It is instructive to note that environmental policy objectives for developing economies will be quite different from developed nations. With such variations, environmental tax development and implementation may quite likely differ in their effects on pollution and environmental quality. Future scholars should take a cue from this limitation.