The asymmetric and long-run effect of environmental innovation and CO₂ intensity of GDP on consumption-based CO₂ emissions in Denmark

Abstract

The study explores the relationship between globalization, GDP, the carbon intensity of GDP, patents, and its effect on consumption-based carbon emissions (CCO₂E). For analysis, novel econometric approaches include nonlinear ARDL and Fourier ARDL, and for robustness, dynamic OLS applied. The results from cointegration tests reveal that there exists a significant long-run relationship between CCO₂E, globalization, economic growth, patents, and the carbon intensity of GDP. Additionally, the empirical results indicate that only positive shock in patents on environmental innovations have a negative and significant impact on CCO₂E, while positive and negative shocks in GDP and carbon intensity of GDP significantly increase CCO₂E. However, only a negative shock in globalization demonstrates the increase in CCO₂E. Also, dynamic OLS findings confirmed the robustness. Given the outcome, it is recommended that the Danish government be cautious when approving policies intended to increase economic growth, as this could negatively affect environmental sustainability. More so, research and development must contribute to technological advancement in the Danish manufacturing sector. Despite this, it is important to prioritize patent promotion. Patent protection can enable Denmark to develop eco-friendly technologies that can reduce carbon emissions, thus enabling life to be more sustainable by utilizing fewer resources and energy. Denmark can reduce CO₂E and foster economic development through a strong patent system on environmental technologies.

Introduction

In environmental debates, energy plays a crucial role as an input to the economy. It is true that energy is a vital component of a growing economy; however, it also hinders achieving sustainable environmental goals and reducing CO₂. Worryingly, according to the World Meteorological Organization, on December 14, 2021, a new-record high temperature for the Arctic reached 38 degree Celsius, alerting humanity to limit its emissions and adopt an environmentally friendly lifestyle that will gradually assist Mother Nature in restoring itself and replenishing resources in a sustainable manner for our future generations (Hall et al. 2021). The Earth’s system has always been susceptible to disasters linked to climate and weather extremes. Global warming, however, is increasing their frequency and intensity. The last four years were the hottest on record. The World Meteorological Organization (WMO) reported in September 2019 that no continent is safe from heatwaves, droughts, typhoons, and hurricanes. Temperatures around the world are becoming more extreme as a result of climate change. Globally, extreme temperatures have gripped countries. In the UK, for example, in 2022, temperatures have not topped 40 degree Celsius like they did during the July heatwave, and extreme heat has lasted longer. Moreover, temperatures reached as high as 38 °C (100 °F) in France and Spain (Pisa et al. 2022). High temperatures have caused deaths in eastern China. In Europe, a scorching heatwave has sparked wildfires (Xu and You 2022). The question still remains, what are the responses to the twenty-first century global climate change and are they adequate? Furthermore, industrialization led to the rapid expansion of the world economy as well as the release of greenhouse gasses, which contributed to global warming. Despite the unprecedented growth of economies, particularly developing countries, as a result of international trade, climate change has been caused at the same time by an increase in carbon dioxide emissions. The rapid expansion of world trade after World War II has led to the economic growth of various countries, but on the other hand, it has also contributed to the pollution of the atmosphere. Specifically, Denmark, a top exporter in the EU and the rest of the world, is only taken into account when considering the top-exporting economies, which might increase territory-based CO₂ emissions, as they expand their capacity to import more goods.

Due to recent climate change, severe weather events pose a growing threat to society and ecosystems. There are both human factors, such as the growing population and infrastructure, which impact the number of extreme events that causes loss each year. Natural variability of the climate also affects the number of extreme events that causes loss in any given year. A number of extremes have changed in frequency, especially warm temperature extremes and heavy rainfall events. In recent times, innovation, patents, and renewable energy have become important contributors to reducing carbon emissions. Green innovation, also known as environmental-related technologies (ERT), is an important component of the reduction of CO₂ strategies to reduce CO₂E as well as CCO₂E (Xin et al. 2021). Whether it is global climate change or regional pollution, collaboration on technology development is critical. In addition, patenting environmental innovations and providing them with patent protection can provide local businesses with a variety of benefits. It is intuitive because government collaboration (patent right) in both ecological innovation and research and development can improve market entry and make existing technologies more available to local/small businesses. Since global warming variability is one of the greatest threats to the future of our planet, any new, innovative technology option must be protected by intellectual property rights. Patents can be a useful tool for accelerating climate change solutions as well as facilitating ideas’ exchange. Although, there has been an increase in patents relating to low-carbon technologies worldwide over the past few decades, there is a risk of the world at large copying, misappropriating, or using this new discovery unlawfully in a technology-driven world. Consequently, it is necessary to trademark carbon capture technologies in order to maximize their value. Patents are crucial in protecting and minimizing competitive advantage in a market becoming ever more competitive and busy as we transition toward a truly green economy (Berger et al. 2012).

The carbon neutrality target can be achieved in many ways in emerging and developing economies. According to World Bank statistics, the contribution of international trade has grown from 27.3% in 1970 to 60.3% in 2019 (World Bank 2019). Trade fell sharply in 2020 but rebounded in 2021. Global trade reached historic highs in May and June of 2021 regarding volume and year-on-year growth rates. The reason for the decline is partly a result of the disrupted trade in the first half of 2020 (causing a low base), combined with the effect of releasing pent-up demand from 2020, as well as a shift in demand from services to goods, and unwinding of supply chain backlogs (Arriola et al. 2020). Moreover, trade activity increased even faster over the last year. In international trade, one of the most important reasons is the comparative advantage that some countries possess over others regarding their productive capabilities. Trade is expanding primarily due to the comparative advantage of some countries over others in terms of their productivity. Frequent expansions often result in ecological degradation, which is why international trade plays an increasingly important role in global warming and environmental pollution (Hasanov et al. (2018); Heil and Selden (2001)). Economists suggest that international trade practices determine an efficient economic system since they balance market failures, enhance globalization potential, and boost foreign exchange reserves. At the same time, income and productivity from globalization will increase, and pollution will decline because of the technique and scale effects (Cole and Elliott 2003). As part of a discussion on environmental research and innovation, this article explores how environmental innovations contribute to the mitigation, stabilization, and reversal of global warming and the effects of environmental innovation on consumption-based carbon emissions. Two research questions are being addressed. Firstly, how does the number of patents increase environmental breakthroughs? Second, we also ask, Also, given Denmark’s uniquely oriented economy, is there any evidence in this analysis that supports the pollution haven hypothesis? Many studies have examined the effects of production or territory-based carbon emissions while ignoring the multinational production process. Carbon emissions based on consumption were ignored since they are adjusted for international trade (imports and exports) (Ali and Kirikkaleli 2022; Kartal et al. 2022; He et al. 2021). Consumption-based and production-based CO₂E are the two methods by which carbon emissions are measured. Conventionally, carbon emissions are measured based on production, not including imports and exports. In order to develop this carbon emission database, a production-based carbon emission database with imports and exports has been created (Peters et al. 2011). As a result of these two carbon emission approaches (Liddle 2018); Khan et al. (2020a, b)), different findings have been identified for developed and developing countries (Liddle (2018)). There have been concerns raised about the possibility that developed countries can reduce carbon emissions by transferring emissions to developing countries that produce these products as a result of international trade. Dogan and Aslan (2017) stated that greenhouse gasses are gathered in nations due to air pollution produced by the use of fossil fuels and motorized vehicles, while Dogan et al. (2020) mentioned energy intensity and energy structure are major environmental variables. According to Dogan and Seker (2016a, b), one feasible way to reduce emissions is to boost the share of renewable resources and energy in the energy mix.

There is still tremendous concern about climate change in the international community. Numerous studies on climate change risks revealed consequences, including extreme weather events threatening humans and ecosystems (Hale and Long 2020; He et al. 2021). Due to recent climate change, severe weather events pose a growing threat to society and ecosystems. There are both human factors, such as the growing population and infrastructure, which impact the number of extreme events that causes losses each year. Natural variability of the climate also affects the number of extreme events that causes a loss in any given year. Several extremes have changed in frequency, especially warm temperature extremes and heavy rainfall events. Global warming can be linked to economic activity through the emission of greenhouse gasses during the production of goods and the export of them to other parts of the world. One of the drivers of environmental pollution discussed in the literature is globalization since it increases levels of production and consumption and aids in the diffusion of environmental technologies. Globalization increases the number of production and consumption activities (Acheampong et al. 2021). The process of globalization will deteriorate the environment if production methods remain unchanged. However, if adopting eco-friendly technologies accompanies globalization, environmental standards will improve with increased trade volumes and foreign direct investment (Leah et al. 2021). According to pro-globalists, globalization positively affects environmental standards, while anti-globalists argue otherwise.

Furthermore, taking the perspective that globalization has negative consequences on the environment across the world, it might be argued that globalization may harm the environment in Denmark, based on the premise that over time, economic development and prosperity are impacted by globalization, as well as the environment and culture. The economic price of goods could be reduced by outsourcing production to, for example, the UK or Denmark. In addition, the countries to which Danish or UK production is outsourced are experiencing rising incomes and living standards. Innovation plays a key role in tackling climate change, as stated in the Paris Agreement on Climate Change (Article 10), which states: “To provide an effective and long-term global response to climate change and to promote economic growth and sustainable development is essential to enable, encourage and accelerate innovation.” Technological development and innovation are important drivers of economic growth and productivity. The dimension of technological development is observed in the evolution of patent application filings in the field of climate change. Environmental innovation and patent protection on environmental innovations are essential to addressing climate change and other environmental challenges. Patents are essential in today’s increasingly competitive and crowded market for protecting and maintaining competitive advantage. Also, collaboration, such as cooperation, tends to result in the creation of more intellectual property. Nevertheless, it is unclear which is most important for scaling up: green technology development or patents for environmental advancement. In order for the future of our planet to remain viable, we must protect our intellectual property when developing any new, innovative technology. It is especially important to promote cooperation on technology development when fighting global climate change or tackling regional pollution.

Additionally, international collaboration in research and development can assist local businesses in leveraging existing technology (i.e., helps build absorption capacity in the local market). As a result, cleaner technology is adopted more widely across the globe. In order to protect their inventions, inventors seek protection in countries where they plan to invest, export, or market their products. Often, they do so in multiple jurisdictions (geographic markets). Economic-environmental conflict can be managed through green technology innovation. A growing number of patents are also being filed for low-carbon technology. This innovation is at risk of being copied, misappropriated, or illegally used. Markets are expected to become more competitive and may be copied or misappropriated. In order to maximize the value of carbon capture technologies, patenting them is necessary.

With a population of 5.8 million, a GDP of $61,063 (a figure that doubled in 2004), and a per-capita income of $32,200, Denmark is among the richest nations in the world. The country has a high GDP per capita, low unemployment, large welfare entitlements, and high employment rates for men and women (World Bank 2019). Denmark’s international trade policy promotes free trade globally and ensures market openings with key trade partners. Denmark’s economy is considered one of the world’s small open economies that is highly dependent on the ability to freely trade goods, commodities, and services across borders. Danish economists believe an increase in international trade will benefit the global economy, including developing nations. Denmark and the other EU member states closely relate to their international trade policy. Furthermore, real GDP growth in Denmark averaged 1.8% per year over the decade preceding the COVID-19 pandemic, largely due to increases in labor productivity. Danish governments have prioritized policies that boost employment flexibility, market competition, the use of digital resources, and a business-friendly climate that boosts investment and productivity; Denmark’s recovery strategy focuses on reducing carbon emissions; furthermore, greenhouse gasses are generated mainly by livestock in agriculture, which is a major source. Agricultural emissions have barely decreased in recent years.

The Danish economy is also experiencing an uncertain and turbulent period, similar to many other countries. While the economic impact of the pandemic is not known with certainty, Statistics Denmark estimates a 2.7% contraction in real output between 2020 and 2025. Denmark has consistently enjoyed current account surpluses due to global trade in the last three decades. Denmark is a net exporter of food and energy, and its principal exports are machinery, instruments, and food products. Denmark’s trade volume is roughly 105% of its GDP. The current crisis has resulted in a decline of 8.5% in global trade (and 9.1% in advanced economies). This signaled serious challenges for the Danish economy. Overall, domestic and international economic shocks continue to impact Denmark’s economy. Danish trade liberalization and development facilitation rank the highest among the EU member states, and the Danish government promotes its position with other countries. Given the preceding discussion, it is vital to examine the link between globalization, GDP, the carbon intensity of GDP, and patents and its effect on consumption-based carbon emissions in Denmark by asking questions such as the following: Does importation deteriorates environmental quality in Denmark? Is exporting more environmentally friendly in the case of Denmark, given its net exportation of food and energy as well as its principal exports, machinery, instruments, and food products? Are export prices likely to fall due to the supply of energy-intensive products?

In order to provide an empirical explanation, the present research uses nonlinear ARDL, Fourier ARDL, and dynamic OLS techniques to analyze the asymmetric relationships between the variables of interest. Additionally, one of the world’s few studies on Denmark quantifies the asymmetry links among the examined indicators and provides new energy and environmental innovation paradigm. The study’s conclusions provide citizens, academic researchers, economists, and policymakers with a better understanding and critical information and evidence. This study has crucial implications for regulators, environmentalists, and government officials regarding environmental protection. Our study is beneficial to the environmental quality of the developing world, which is suffering environmental and energy issues due to a lack of infrastructural development.

Here is a summary of how the rest of the paper is structured. The remainder of the manuscript is organized as follows: the “Literature review” section provides an assessment of relevant studies. This section describes the empirical modeling, the data collection methods, and the estimation methods. Results and discussion are presented in the “Empirical results” section, and conclusions and policy implications summarize the article with a concluding note and relevant policy implications.

Literature review

Without a doubt, rising CO₂ emissions contribute significantly to climate change. According to Inglesi-Lotz and Dogan (2018), knowing the drivers of emissions is critical in order to develop suitable strategies. Several inconclusive studies have sought to explain the relationship between globalization, GDP, patents, and other factors with CO₂ emissions. For instance, Zafar et al. (2019) looked into this nexus for OECD countries, while Zheng et al. (2022) and Zhou and Wang (2022) looked into Pakistan, Deng et al. (2022) looked into 107 countries, Ahmed et al. (2021) looked into it for China, Arogundade et al. (2022) looked into it for 31 African nations, and Ndiaya et al. (2019) looked into it for Senegal. This section includes a comparative literature review to showcase researchers’ recent findings.

Globalization and environment

The globalization and industrialization of economies have resulted in higher carbon dioxide emissions resulting from the continuous increase in demand across borders made possible by global trade. Environmental economists are concerned about the downside of globalization and rapid economic development, where interconnected economies and higher living standards are achieved. As a result of the recent focus on climate change and environmental degradation, advanced economies have pledged to reduce their carbon emissions (territorial/production-based emissions) either through low-carbon emission activities or moving to greener production (renewable energy). The demand for carbon-intensive products in advanced economies results in reduced territorial emissions, but more consumption-based CO₂E as economies with relaxed environmental regulations (developing economies) feed those needs. A good deal of previous research has focused on highly exporting countries and resource-rich developing countries (see below), but our study examines Denmark, a single country with a robust economy, which has evolved into a modern, market economy with a highly advanced industrial sector as well as a high-tech agricultural sector. The Danish economy is highly developed, high-income, and highly connected. Futuristically, imports/exports are going to be on the rise, triggering environmental sustainability and a rise in carbon pollution. Our objective in this section is to gain a deeper insight into the interconnections between the above-cited variables, as shown below.

Economic development and environment

Recently, Kirikkaleli and Oyebanji (2022) used some robust econometric techniques and a data set from 1970 to 2019. The study’s empirical analysis investigated the effect of trade and economic expansion on CCO₂E. Results of the study indicate that exports and GDP have an adverse impact on CCO₂E, while imports and globalization have a favorable impact on CCO₂E, which is statistically significant. Furthermore, the study by Hassan et al. (2022) investigated the correlation between financial, economic, political, and composite risks and CCO₂E in selected RCEP economies from 1990 to 2020. The empirical test methods used are cross-sectional dependence, slope heterogeneity, cross-sectional–augmented panel unit root test, Westerlund cointegration, second-generation cross-section–augmented autoregressive-distributed lag model, and panel causality test. According to the empirical results, less political risk mitigates CCO₂E, while the lower financial, economic, and composite risks increase them in selected RCEP economies. Additionally, CCO₂E is reduced by exports and renewable energy, whereas imports lead to an increase. Adebayo et al. (2022) used second-generation panel cointegration techniques to investigate the impact of globalization and renewable energy usage on CCO₂E and the impact of nonrenewable energy use on economic growth in the MINT countries (Mexico, Indonesia, Nigeria, and Turkey) over the period 1990 to 2018. Testing for slope heterogeneity and cross-sectional units revealed cross-sectional dependence and heterogeneity between nations. In addition, the results of the cointegration test showed that CCO₂E is closely related to the regressors. Both the CCEMG and the AMG revealed that while economic growth contributes to the degradation of the environment, globalization and the use of renewable energy help to counteract this issue. According to Amin et al. (2022), energy productivity, eco-innovation, and international trade can contribute to filling the research gap on consumption-based CO₂E. This research provides updated data for the Next Eleven (N-11) economies to assess their trading-adjusted consumption-based CO₂E. Methodologically, this study utilized cross-sectional autoregressive-distributed lag models (CS-ARDLs), the Westerlund cointegration tests, and the AMG method. As a result of these methods, cross-section dependence and heterogeneity were addressed. Empirical findings of the study confirmed that CCO₂E has a long-term cointegration with exports, imports, gross domestic product, energy use, and green technology. A growing economy and increased imports are, however, leading to increased carbon emissions. Also, all policies targeted at ecological innovation, energy productivity, exports, imports, and economic expansion should be effective at achieving equilibrium within approximately 1 year of being implemented. Research evidence provided by Gyamfi (2022) indicates that interconnectedness and international trade significantly impact macroeconomic indicators and their environmental-friendly implications. Thus, this analysis investigates how oil-producing sub-Saharan Africa’s CCO₂E is associated with FDI, economic growth, natural resources, and urbanization from 1990 to 2018. The results of a balanced panel econometric analysis used to determine the strength of the correlation between the analysis of the variables was conducted in conjunction with the AMG, CCEMG, and Driscoll-Kraay (DK) OLS techniques, along with a robustness analysis that used system-GMM methods. It was found that CCO₂E related positively to all understudied variables in the oil-producing sub-Saharan African countries, thus supporting the pollution haven hypothesis on the premise that foreign direct investment adversely impacts receiving economies together with natural resource extraction. For a cleaner and friendlier environment, it is recommended that low-carbon strategies be implemented.

Carbon intensity, patents, and consumption-based CO₂E

Lately, Abbasi et al. (2022b) investigated how the carbon intensity of GDP affected environmental deterioration in Turkey from 1990 to 2018 while controlling for economic development, foreign direct investment, and renewable energy use. The Gregory and Hansen cointegration test, bounds test, nonlinear autoregressive-distributed lag (NARDL) model, fully modified ordinary least squares (FMOLS), dynamic ordinary least squares (DOLS), and canonical cointegrating regressions (CCR) were used to exemplify the potential effect of CO₂ intensity of GDP, economic growth, foreign direct investment, and renewable energy consumption on environmental pollution. According to the empirical findings, the CO₂ intensity of GDP is essential in determining Turkey’s environmental deterioration. Also, a literature review indicated a link between greenhouse gas emissions, patents on environmental breakthroughs, consumption-based CO₂E, and globalization’s influence on consumption-based CO₂E. Moreover, Abbasi et al. (2021b) investigated the influence of economic globalization, financial growth, energy usage, economic development, and technological innovation on consumption and territory-based CO₂E in Pakistan from 1990Q1 to 2019Q4. Dynamic autoregressive-distributed lag (ARDL) simulations and frequency domain causality (FDC) approaches were employed in the research. The empirical research demonstrated that financial and economic growth promotes both consumption and territory-based emissions in the short and long term. Furthermore, in the short term, economic globalization has a negative impact on consumption and territory-based emissions, whereas in the long run, only consumption-based emissions increase. However, technological advancements reduce these emissions significantly in the long run. Finally, FDC results supported the idea. Literature on the link between globalization and the environment has examined the impact of population growth on the environment reported mixed findings. Through global trade and FDI, globalization adds to the liberalization of the economy and financial development, economic activities, and energy consumption that adversely affect the environment (Saud et al. 2020). A plethora of studies has been formulated by businesses, organizations, and individuals on ways to mitigate pollution. With the method of moments quantile regression (MMQR) and the heterogeneous granger causality test, Arogundade et al. (2022) investigated the influence of diaspora money on the ecological footprint of 22 African nations. Their results demonstrated that diaspora wealth and financial growth negatively and statistically significantly influence the ecological footprint of more polluting African nations.

Furthermore, innovative ecological products are not only geared toward a greener environment but also contributed to its development. A brand’s innovation is measured primarily by product innovation (Gotsch and Hipp (2012)). Branding is a powerful tool when developing new technologies or products (Flikkema et al. 2019). Furthermore, the brand identifies specific products and services from their source and distinguishes them from others in the same field (Castaldi and Dosso 2018). Beginner brands are often advantaged by trademarks that provide protection and add value to their products (Mendonça et al. 2014). Innovation in the market can set a company apart from its competitors, contributing to its success and protecting the environment. Albino et al. (2014) suggest patenting new technologies for pollution reduction. In addition to patents, innovations relating to climate change are determined by CO₂E within country emissions and other greenhouse gasses. Climate change-related technologies are invented and patented based on a country’s level of greenhouse gas emissions. The most effective way to develop innovative products or technologies is by using brands as a tool (branding is the best strategy for developing technologies and products (Su and Moaniba 2017). Interestingly, only a few studies have examined the role of patents on environmental technologies in the determinants of CO₂E, as innovation and technological advancement play a crucial role in reducing emissions.

Researchers have found mixed findings examining whether globalization increases CO₂E or decreases them. In fact, supplementary variables, periods, and sample sizes could all contribute to contradicting results (Dogan and Seker (2016a). The majority of panel data studies fail to account for cross-sectional dependence. Moreover, most studies only consider aggregate emissions of CO₂E, which may limit the scope of policy insights at the sectoral level. Therefore, we have taken CO₂E from coal, oil, and gas sources to provide better policy insight to reduce emissions. Existing studies offer no clear conclusions regarding the impact of globalization on environmental performance or consumption-based CO₂E, which point to the need for further investigation in a more coherent way. Kirikkaleli and Oyebanji (2022) used quarterly data from 1990 to 2015 to assess the interconnectivity of CCO₂E-GDP-REN in India. The authors discovered that the interaction between CCO₂E and GDP is positive but insignificant, whereas the DOLS and FMOLS techniques revealed a negative relationship between REN and CCO₂E. In contrast, using the dual adjustment approach, He et al. (2021) discovered positive and strong connectivity between CO₂E and GDP in Mexico from 1990 to 2018. Adebayo and Rjoub (2021) employed AMG and CS-ARDL to evaluate a dataset from 1990 to 2000 for MINT economics. Based on the nonlinear ARDL results, patents on environmental technologies enhance environmental sustainability in Spain (Oyebanji et al. 2022).

Methods and materials

Data sources

This paper intends to capture the impact of environmental innovation and CO₂E intensity of GDP on CCO₂E in Denmark while controlling economic growth and globalization. Economic growth is measured as real GDP per capita; globalization is the trade globalization index, and we obtained its data from the KOF Swiss Economic Institute’s online page. It is measured by an aggregate index that takes into account the three major dimensions of globalization: economic, political, and social globalization; CO₂E intensity of GDP is measured as carbon dioxide emissions per unit of GDP; and environmental innovation is calculated as a resident and non-resident patent applications. Data for the parameters are collected using the OECD database. Figure 1 reveals the pictorial view of data and method, while the data trend is presented in Fig. 2 in the Appendix.

Fig. 1.

Analysis flowchart

Variable specifications

This section describes how several independent variables influence CO₂E. Expanding cross-border trading and investment encourages industrial activities that need the use of electricity and energy, resulting in increased emissions. According to Dogan 2015 and Abbasi et al. (2021a), GDP is the main factor of elevated CO₂E since economic growth is built on intense energy usage, which ultimately undermines environmental practices. However, one of the major causes of globalization is that it introduces businesses to new regions where they might sell their goods and acquire labor, unprocessed materials, and materials. Due to these facts, finished goods go further than ever before across the globe. Traditionally, things were more probably to be mass-produced, traded, and expended regionally (Adebayo and Kirikkaleli 2021). This enhanced transportation of merchandise may have several environmental magnitudes, such as higher emissions: as merchandise travels lengthier, additional fuel is used and spare greenhouse gas emissions are created. Habitat obliteration: transportation, predominantly when land is constructed, and essential groundwork such as roads and bridges. The construction of such infrastructure may result in difficulties such as habitat damage and pollution. Introduced species: Each freight container and pitcher delivers a casual for a live thing, such as a shrub, animal, or toadstool, to snag an excursion to a new place where it may develop offensive and progress without the checks and balances that occur in its standard ecosystem. Despite sustained emission rise, the power industry has undergone tremendous restructuring recently. The mean carbon intensity of energy produced now is 475 g CO₂/kWh, a 10% reduction over 2010. Without it, world CO₂ emissions would have been 1.5 Gt greater, accounting for 11% of current energy sector emissions (EIA (2019). Carbon dioxide emissions are directly and indirectly affected by technological advancement. The direct impact of environmental technology innovation on carbon emissions is that it may effectively cut carbon emissions by enhancing energy consumption efficiency Abbasi et al. (2021b).

Given the importance of tackling climate change, the changing paths of economies will be greatly hampered by a lack of carbon emissions. In this situation, Denmark must strengthen its prospective energy infrastructure to facilitate a low-carbon transition while still making economic and social growth. Consequently, the essential method for meeting the twin goals of economic growth and CO₂E mitigation is to continuously lower the CO₂E intensity of GDP (He et al. (2019). Therefore, the study employs dependent variable consumption-based CO₂ emissions (CCO₂E), whereas the independent variables are economic growth, globalization, CO₂E intensity of GDP, and environmental innovation. The following model was utilized in this research:

$${{\mathrm{LCCO}}_2\mathrm{E}}_{\mathrm{t}}=\mathrm{f}\left({\mathrm{LGDP}}_t,,,{\mathrm{LGLO}}_t,,,{\mathrm{LCINT},\mathrm{LPATENTS}}_t\right)$$ 1

where LCCO₂E, LGDP, LGLO, LCINT, and LPATENTS in Eq. 1 signify consumption-based CO₂ emissions, economic growth, globalization, CO₂E intensity, and environmental innovation.

Econometric model (NARDL approach)

The NARDL model is utilized in this research to investigate the variables’ long- and short-term dynamics. The linear autoregressive-distributed lag (ARDL) model has been asymmetrically extended (Pesaran et al. 2001). Because the NARDL model combines cointegration and asymmetric nonlinearity into a single equation, it is more suited for small-sample numbers than other approaches. This approach works with integration orders of 1(0), 1(1), or a combination of the two (Abbasi et al. 2021a, b, c, d, e). The NARDL blends short-run and long-run symmetry, considering the long-run data provided by the distinctive traits (Shin et al. 2014). Furthermore, traditional techniques such as the vector error correction model (VECM) or the smooth-transition model (STM) are ineffectual in addressing the divergence issue in the face of a proliferation of estimates. This method is ideal for tackling this problem. Similarly, this technique works at any order of integration, emphasizing the NARDL’s superiority over other approaches (Abbasi et al. 2022a, b). Similarly, this technique overcomes the multicollinearity problem by adopting efficient automatic lag selection and selecting the optimal model (Abbasi et al. (2022a, b). Furthermore, by accounting for both positive and negative shocks, the NARDL allows for more in-depth knowledge of LGDP, LGLO, LCINT, and LPATENTS, as well as their relationships to LCCO₂E emissions, making it a preferable option to previous standard approaches. Because the NARDL is a more advanced variation of the ARDL, the simplified version is specified as follows:

$${\mathrm{\Delta }Y}_t=\mu +{\rho Y}_{t-1}+\stackrel{\prime }{\theta }{\dot{x}}_{t-1}+\sum _{j=1}^{p-1}{\alpha }_j{\mathrm{\Delta }Y}_{t-1}+\sum _{j=0}^{q-1}{\pi }_j{\mathrm{\Delta }x}_{t-1}+{\epsilon }_t$$ 2

where $\mathrm{\Delta }$ represents the first difference operator, $Y_t$ represents the outcome variable,$\mu$ represents the intercept, ${\stackrel{{}^{\prime }}{\theta }x}_{t-1}$ represents the regressor vector, and $\rho$ and $\theta$ indicate the long-run coefficients. While ${\alpha }_j$ and ${\pi }_j$ represents short-run coefficients, p and q represent the lag order of chosen variables and ${\epsilon }_t$ is a white noise error component. The H0 affirms that the variables are irrelevant, although the H1 avers are linked through time. The inferential rule is evaluated based on predicted F-stats values to critical values calculated from the data (Pesaran et al. 2001). If the predicted F-stats values are greater than the upper limit values, I(1), the long-term association between factors is true. If on the other side, the predicted F-stats values are smaller than the lower threshold values, I(0), this indicates that the variables included in the simulations have no long-term rapport. Lastly, if the projected F-stats values are amid the upper and lower boundaries, determining whether or not there is a long-run relationship is inconceivable. However, the ARDL method’s underlying principle is that independent variables have a symmetric impact on the dependent variable, which may be misleading. Shin et al. (2014) introduced the NARDL model, which could be built utilizing the underlying asymmetric long-run equilibrium associations.

$$Y_t={\beta }^{+}{X}_t^{+}+{\beta }^{-}{X}_t^{-}+{\mu }_t$$ 3

where ${\mu }_t$ denotes deviation from long term symmetry and ${\beta }^{+}$ and ${\beta }^{-}$ denote associations of uneven long-term restrictions. While $X_t^{+}$ and $X_t^{-}$ are partial sums of positive and negative fluctuations, the vector can be deconstructed as specified

$$X_t^{+}=\sum _{j=1}^t{\mathrm{\Delta }X}_j^{+}=\sum _{j=1}^t\max \left({\mathrm{\Delta }X}_j,,,0\right)$$ 4

$$X_t^{-}=\sum _{j=1}^t{\mathrm{\Delta }X}_j^{-}=\sum _{j=1}^t\min \left({\mathrm{\Delta }X}_j,,,0\right)$$ 5

where j and ${\mathrm{\Delta }X}_j$ denote the asymmetric distributed and asymmetric distributive lags of X. Combining Eqs. (2) and (3) yields the massive error correction model. The following is the definition of the integrated approach:

$${\mathrm{\Delta }Y}_t=\mu +{\rho Y}_{t-1}+{\theta }^{+}{X}_{t-1}^{+}+{\theta }^{-}{X}_{t-1}^{-}+\sum _{j=0}^q\left({\pi }_j^{+},{\mathrm{\Delta }X}_{t-j}^{+},+,{\pi }_j^{-},{\mathrm{\Delta }X}_{t-j}^{-}\right)+{\epsilon }_t$$ 6

The NARDL and ARDL use a comparable strategy to get an error correction model from an equation expending the standardized ordinary least squares (OLS) technique (8). The bound test is then used to detect the existence of an unbalanced long-term connection. Since the direction of parameter integration affects F-statistics, the functionality bound test technique suggested by (Pesaran et al. 2001) is also applied in the NARDL framework. On the other hand, the Wald test is intended to measure both long- and short-term asymmetries. Consequently, the asymmetric dynamic multiplier may be characterized as follows, which encompasses all present and prior impacts of positive and negative variation in the explanatory variables on predictor variables:

$$m_h^{+}=\sum _{j=0}^h\frac{{\partial y}_{t+j}}{{\partial x}_t^{+}},m_h^{-}=\sum _{j=0}^h\frac{{\partial y}_{t+j}}{{\partial x}_t^{-}},h=1,,,,,n$$ 7

The present study employs the NARDL cointegration approach after establishing the unit root and order of integration. The general version of this method, using the main variables in p and q forms, is as follows:

$$\begin{array}{c}{\mathrm{\Delta }{\mathrm{LCCO}}_2\mathrm{E}}_t={\alpha }_0+{\mathrm{\Delta }{\mathrm{LCCO}}_2\mathrm{E}}_{t-1}+{\theta }_1^{+}{\mathrm{LGDP}}_t^{+}+{\theta }_1^{-}{\mathrm{LGDP}}_{t-1}^{-}\hfill \\ +{\theta }_2^{+}\sum _{j=1}^2{\beta }_j{\mathrm{LGLO}}_{t-1}^{+}+{\theta }_2^{-}\sum _{j=1}^2{\beta }_j{\mathrm{LGLO}}_{t-1}^{-}\hfill \\ \begin{array}{c}+{\theta }_3^{+}\sum _{j=1}^2{\beta }_j{\mathrm{LCINT}}_{t-1}^{+}+{\theta }_3^{-}\sum _{j=1}^2{\beta }_j{\mathrm{LCINT}}_{t-1}^{-}\hfill \\ +{\theta }_4^{+}\sum _{j=1}^2{\beta }_j{\mathrm{LPATENTS}}_{t-1}^{+}+{\theta }_4^{-}\sum _{j=1}^2{\beta }_j{\mathrm{LPATENTS}}_{t-1}^{-}+{\epsilon }_t\hfill \end{array}\hfill \end{array}$$ 8

where t denotes time and ${\alpha }_0$ denotes the variable to be assessed. LCCO₂E, LGDP, LGLO, LCINT, and LPATENTS denote consumption-based CO₂E, economic growth, globalization, CO₂E intensity of GDP, and environmental innovation, respectively, denote the controlled and control factors. Moreover, this research uses a novel autoregressive-distributed lag (ADL) cointegration test in the context of nonlinear breaks represented by a Fourier function. If there is a break or a structural change, this test performs far better than the conventional ARDL bounds test. The examination provides a straightforward method for identifying gradual structural shifts in time series data. There is no need for exact break dates, and the technique that has been offered can accept an unknown quantity and shape of progressive structural change.

Empirical results and discussion

The descriptive statistic shown in Table 1 is used to investigate the characteristics of the variables. It summarizes the variables’ mean, maximum, minimum, and standard deviations. It describes the summary statistics, shows the peak using Kurtosis, and confirms the nonlinear distribution pattern employing Jarque–Bera test stats.

Table 1.

Descriptive statistics

	LCCO2E	LCINT	LGDP	LGLO	LPATENTS
Variable	Per capita consumption-based CO2 emissions	CO2 intensity of GDP, CO2 emissions per unit of GDP	GDP (constant 2015 US $)	Globalization index	Patents on environment technologies
Source	Our World in Data	World Bank	World Bank	KOF	OECD
Unit	Metric tons per capita	CO2 emissions per unit of GDP	Real per capita GDP in 2015 US $	Index	Number
Mean	0.968740	− 0.711993	11.42527	1.931114	1.089255
Median	1.004335	− 0.682729	11.44292	1.938908	1.026059
Max	1.159512	− 0.471842	11.52810	1.948117	1.418335
Min	0.698493	− 1.069128	11.30365	1.882435	0.793459
SD	0.113603	0.157361	0.061925	0.015663	0.223044
Skewness	− 0.581191	− 0.389689	− 0.499378	− 1.110804	0.183465
Kurtosis	2.197835	2.147446	2.247028	3.268035	1.280681
Jarque–Bera	9.972992	6.671395	7.822411	25.03695	15.45348
Probability	0.006830	0.035590	0.020016	0.000004	0.000441

The unit root tests are utilized as the initial phase in the study to ensure that all components are stationary. The augmented Dickey-Fuller (ADF) unit root test is employed to establish stationarity. However, according to ADF statistics, LCCO₂ and LGDP are non-stationary at I(0), but LCCO₂, LPATENTS, LGLO, LGDP, and LCINT turn stationary at the first difference I(1) in Table 2.

Table 2.

Unit root tests

		LCCO2	LPATENTS	LGLO	LGDP	LCINT
At level
ADF	Test stat.	− 0.667	− 4.523**	− 4.271*	− 3.104	− 0.817***
	Break point	2008Q1	2004Q1	1990Q4	1993Q2	2010Q2
At first difference
ADF	Test stat.	− 6.553***		− 6.073***	− 5.457***	− 6.606***
	Break point	1991Q1		1991Q4	1993Q1	1992Q1

*, **, and *** signify significant at the 10%, 5%, and 1% levels, respectively

As a reliability coefficient, we used the well-known BDS independence test established by Broock et al. (1996) to assess nonlinearity in the data set. Table 3 shows that the computed variables are not distributed uniformly and independently. It demonstrates that nonlinearity exists in the observed values. In this scenario, the NARDL model is required for this research to explain the relationship between the variables. To analyze the nonlinear ARDL model, we must segregate our explanatory variables, LPATENTS, LGLO, LGDP, and LCINT, into positive and negative integers.

Table 3.

BDS test

Dimension	BDS statistic	SD	z-stats	Prob
LCCO2E
2	0.185564	0.005369	34.56351	0.0000
3	0.309821	0.008546	36.25383	0.0000
4	0.393825	0.010189	38.65224	0.0000
5	0.451720	0.010631	42.49047	0.0000
6	0.492074	0.010262	47.94909	0.0000
LGLO
2	0.203229	0.007087	28.67593	0.0000
3	0.344786	0.011306	30.49464	0.0000
4	0.443608	0.013515	32.82449	0.0000
5	0.511868	0.014139	36.20309	0.0000
6	0.559319	0.013686	40.86760	0.0000
LGDP
2	0.203783	0.005595	36.42236	0.0000
3	0.345509	0.008929	38.69537	0.0000
4	0.444634	0.010673	41.65783	0.0000
5	0.515738	0.011166	46.18833	0.0000
6	0.567178	0.010807	52.48142	0.0000
LPATENTS
2	0.180495	0.004117	43.84435	0.0000
3	0.299504	0.006564	45.62533	0.0000
4	0.375884	0.007839	47.95291	0.0000
5	0.424029	0.008191	51.76950	0.0000
6	0.457160	0.007918	57.73867	0.0000
LCINT
2	0.187452	0.004870	38.48982	0.0000
3	0.312374	0.007742	40.34816	0.0000
4	0.395894	0.009217	42.95028	0.0000
5	0.452086	0.009604	47.07425	0.0000
6	0.491568	0.009257	53.10178	0.0000

The cointegration method is also used in the research to establish the existence of a long-term link amid the model’s variables. Different cointegration models exist in this context. To discover the symmetric long-run connection, this research utilizes the Fourier autoregressive-distributed lag (FARDL) model, which was newly established by Banerjee et al. (2017), to the variables. Table 4 displays the findings of the symmetric long-run connection between the variables. The $F_{\mathit{ADL}}\left(K^{\wedge }\right)$ value is − 6.646, according to the data in Table 4. This means that the null hypothesis of no cointegration among the study’s variables could be rejected. To reject the null hypothesis, k denotes the frequency with the shortest AIC lag.

Table 4.

Nonlinear and Fourier-based cointegration tests

Model	Test statistics	Frequency (k)	Min AIC
Fourier ARDL cointegration analysis
LCCO2E = f (LPATENTS LGLO, LGDP, LCINT)	− 6.646492***	1	− 6.063885
Nonlinear ARDL bounds test
F-bounds test	Value	Signif.	I(0)	I(1)
F-statistic	3.931674**	10%	1.85	2.85
k	8	5%	2.11	3.15
		2.5%	2.33	3.42
		1%	2.62	3.77

*, **, and *** symbolize significant at the 10%, 5%, and 1% levels, respectively. The verdicts are taken established on the critical values of Banerjee et al. (2017)

Table 4 also shows the cointegration at a significance level of 5%. The nonlinear ARDL upper and lower limit maximum values are 2.62 and 3.77, respectively. The estimated F-statistics value, however, is 3.93, which is more than the upper limit value, indicating that the H0 is rejected at a level of 5%, implying that cointegration exists among the variables anticipated. We can − .

The empirical outcome of the long-term asymmetric connection is shown in Table 5. The findings revealed a positive and negative coefficient in the long-term connection between LPATENTS, LGDP, LCINT, LGLO, and LCCO₂E. The LPATENTS_POS coefficient is significant at 5% level, implying that 1% positive shock in environmental technology reduces consumption-based CO₂E by 0.05%. In contrast, negative shock in LPATENTS_NEG has an insignificant impact on LCCO₂E. Hence, it is inferred that a rise in patents on environmental technologies helps diminish CO₂E in Denmark. For instance, green technology innovation directly and significantly impacts carbon dioxide emissions. One is the impact of green technology innovation on carbon emissions, which is that it may effectively cut emissions by increasing energy consumption efficiency. The outcomes align with Mensah et al. (2018); Khan et al. (2020a, b) stated that eco-innovation helps to propagate environmental sustainability.

Table 5.

Nonlinear ARDL long-run form

Variable	Coefficient	Std. error	t-statistic	Prob
LPATENTS_POS	− 0.052382	0.020898	− 2.506541	0.0143
LPATENTS_NEG	0.126392	0.084296	1.499380	0.1379
LGDP_POS	0.654948	0.173540	3.774054	0.0003
LGDP_NEG	0.957602	0.234191	4.088976	0.0001
LCINT_POS	1.199224	0.139828	8.576432	0.0000
LCINT_NEG	0.757730	0.108244	7.000185	0.0000
LGLO_POS	− 0.503991	0.307478	− 1.639115	0.1053
LGLO_NEG	1.182977	0.656347	1.802366	0.0754
C	0.972711	0.009039	107.6151	0.0000
CointEq(− 1)*	− 0.091891	0.013867	− 6.626628	0.0000

*, **, and *** mean significant at the 10%, 5%, and 1% levels

Furthermore, LGDP coefficients are positive and statistically significant in the face of a positive and negative shocks. It demonstrates that a 1% positive shock in LGDP_POS increases LCCO₂E by 0.655%, but a 1% negative shock in GDP_NEG raises LCCO₂E by 0.958%, having a greater effect than a 1% positive shock in GDP_POS. According to the findings, increased economic activity in Denmark increases carbon emissions, but decreased economic activity is more detrimental to the country’s long-term environmental sustainability. The relationship is positive, meaning that growing GDP results in increased carbon dioxide emissions. Higher levels of economic activity are often associated with increased energy use and natural resource demand. For example, our socioeconomic systems demand resources and energy on a constant basis for human activity, agriculture, livestock, and manufactured commodities, all of which result in emissions of greenhouse gasses (GHGs), air and water pollution, and trash. Given the findings, the research proposes “decoupling,” which refers to de-linking our resource-hungry economic activity from environmental challenges. This may be accomplished in two ways: first, decoupling GDP growth from the resources it needs, which include energy and material usage. Second, decoupling GDP development from its downstream consequences, such as GHG emissions, air pollutants, and waste, all directly affect human well-being. The results are consistent with Kalmaz and Kirikkaleli (2019), Chen et al. (2019), and Abbasi and Adedoyin (2021) which revealed that economic growth caused the emissions.

Also, LCINT shows a positive relationship with LCCO₂E at a 1% level. It indicates that a 1% positive change in LCINT_POS rises LCCO₂E by 1.199%, whereas the negative change in LCINT_NEG rises 0.758% LCCO₂E. It is inferred that the growing CO₂E intensity of GDP is not a good indication of attaining a sustainable environment objectively, and Danish policymakers must lower the CO₂E intensity of GDP to accomplish the sustainable environment goal. The outcomes are consistent with Zhang et al. (2019) while inconsistent with He et al. (2018a, b). Finally, the globalization coefficient of negative shock found a significant impact on LCCO₂E while insignificant in response to positive shock. Globalization may help Denmark to expand the positive effects of environmentally sustainable technologies and practices. This might assist the country to reduce pollution by importing greener technology or enacting stricter environmental rules and standards. The result reveals that 1% negative change in globalization rises LCCO₂E emissions by 1.183%. The outcomes are corroborating with Kalaycı and Hayaloğlu (2019); Ahmed and Le (2021) and Sun and Higham (2021).

The robustness of the nonlinear ARDL estimator’s long-run coefficients was tested using an alternate single equation model, including the DOLS technique. The DOLS technique has the primary advantage of considering the existence of a diversified order of integration of the various parameters in the cointegrated foundation. DOLS was estimated by regressing one of the I(1) variables against other parameters, several of which are I(1) variables with leads $\left(\rho \right)$ and lags $\left(-,\rho \right)$ of the first difference, others are I(0) variables with a constant term (Alcántara and Padilla 2009). As a result, our estimate addressed two significant limitations: potential endogeneity and tiny-sample prejudice. Furthermore, the cointegrating vectors produced by DOLS estimation methods were asymptotically effective. As per the magnitude of the coefficient, the DOLS finding is compatible with the nonlinear ARDL, as shown in Table 5. The outcome indicates that a 1% rise in LGDP and LCINT rises LCCO₂E while a 1% rise in LGLO and LPATENTS declines LCCO₂E, which is statistically significant (Table 6).

Table 6.

Robust tests

DOLS
Variable	Coefficient	SD	t-stats	Prob
LGDP	0.962387	0.045881	20.97548	0.0000
LGLO	− 0.402656	0.128738	− 3.127725	0.0025
LCINT	0.969840	0.010233	94.77311	0.0000
LPATENTS	− 0.040143	0.003144	− 12.77006	0.0000
C	− 8.513482	0.316056	− 26.93659	0.0000
R2	0.999785	Mean-dependent var		0.976358
Adjusted R2	0.999699	S.D.-dependent var		0.107341
S.E. of regression	0.001863	Sum-squared resid		0.000278
Long-run variance	9.00E-06

*, **, and *** indicate significant at the 10%, 5%, and 1% levels

Conclusion and policy recommendations

To the best of our knowledge, the environmental innovation and CO₂E intensity of GDP on consumption-based CO₂E in Denmark has not been explored in detail using recently developed empirical approaches. The present study uses Fourier ADL cointegration and nonlinear ARDL approaches to capture the long-run and asymmetric effect of globalization, economic growth, patents on environmental technologies, and the CO₂E intensity of GDP on CCO₂E. The findings of our study suggest that patents on environmental innovations reduce consumption-based CO₂E in Denmark. Since Denmark has a high digitalization rate and a large and steady demand for software and IT products, intellectual property can serve as an incentive for the development of climate change technologies. Furthermore, patents on environmental technologies constitute an important economic mechanism incentivizing the development of technologies. Thus, Denmark should enhance the role of patents in the general discussion of climate change mitigation, given the urgent need for global access to effective emission-cutting technologies. Similarly, the empirical findings suggest to promote the development of environmental innovation in order to reduce consumption-based carbon emissions, besides levying a fee on imported items high in emissions and using the proceeds to tighten environmental rules and limit imported emissions.

Denmark’s GDP positively affects consumption-based CO₂E. According to the findings, increased economic activity in Denmark increases carbon emissions, but decreased economic activity is more harmful to the country’s long-term environmental sustainability. This study recommends that the Danish economy target domestic consumption levels reduce economic growth’s impact on consumption-based CO₂E, especially in more energy-intensive sectors that contribute to carbon emissions.

Furthermore, globalization is found to significantly impact consumption-based CO₂E in the Danish economy. Accelerating the pace of globalization might alleviate the environmental consequences of exhaustible energy and economic development through technological advancements associated with the globalization process. Consequently, we recommend that carbon taxes be encouraged, energy-intensive enterprises are carefully overseen, and environmental regulations are rigorously implemented to minimize the detrimental impact of globalization on the environment due to the predicted faster increase in energy use. Economic growth and energy consumption are boosted by globalization, leading to increased carbon emissions. Therefore, we suggest a consumption charge on carbon-intensive materials of CO₂E; this would incentivize resource efficiency and substitution of such materials, resulting in a reduction in Denmark’s carbon footprint. A broad range of mitigation strategies, such as sustainable procurement, infrastructure improvement, embodied carbon standards, and trade agreements promoting products with lower embodied carbon, are also options to explore.

Lastly, our study found that the rising CO₂E intensity of GDP shows a positive relationship with consumption-based CO₂E; to achieve a sustainable environment goal, Denmark must constantly decrease the carbon intensity of GDP. A shift away from fossil fuels to non-fossil fuels, energy efficiency measures, new and improved technologies, increased productivity, and shifting production from sectors that consume much energy (like manufacturing or mineral processing) to others that do not (like services) can reduce the energy intensity of the economy. We recommend that Denmark’s policymakers need to decline the CO₂E intensity of GDP to achieve a sustainable environment goal.

We expect our study to inspire further studies on developing countries’ links between international trade and consumption-based CO₂ emissions. There is a significant vacuum in this research field, and we feel our research will help fill it.

Appendix

Fig. 2.

Trend of data

Author contribution

Dervis Kirikkaleli and Modupe Oluyemisi Oyebanji conducted the investigation and gathered the data. Dervis Kirikkaleli wrote the introduction and the literature review, while Modupe Oluyemisi Oyebanji prepared the methodology and the empirical findings as indicated in this paper. In addition, Kashif Raza Abbasi assisted in the explanation of the results. Finally, as the corresponding author, I confirm that the final version of this paper was reviewed and endorsed by all authors.

Data availability

The data supporting this research’s results are accessible from the World Bank and OECD.

Declarations

Ethics approval

We declare that this paper is original, has not been published before, and is not currently being considered for publication by another journal. Therefore, this research does not require ethical authorization or informed consent.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.