Introduction

CO2 emissions are a major component of greenhouse gases (GHGs) around the globe, which has enhanced global warming (Lacis et al. 2010). The faster-growing technologies and a desire for higher economic development are putting further fuel on this fire. For instance, innovations and technological progress may lead to higher energy demand and pollution emissions (Saidi and Ben Mbarek 2016; Uddin et al. 2023), which may be termed a scale effect of innovations. In this regard, the United Nations (UN) has declared the Sustainable Development Goals (SDGs). Western European countries are striving to achieve the agenda of SDGs of the UN by reducing the CO2 emissions per capita between 0.5% and 1.5% per year. But still, the performance of the entire region is not satisfactory to achieve the SDGs by the year 2030 (Barrera-Santana et al. 2021). To reduce GHGs emissions, Western European countries are trying to shift toward clean sources of energy. However, this adoption is slow and heterogeneous among the nations (Inglesi-Lotz 2016). Innovation should target technological progress in favor of a sustainable environment. Western Europe should focus on the technological progress to reduce energy intensity in the production process to achieve the SDGs in the whole region as this region is interlinked due to their trading and environmental agreements.

Western European countries have performed well in innovations in the recent years. As per most patents in force in the year 2020, 12 Western European economies are among the top 20 economies in the Globe (Statista 2021). In the year 2020, Germany stands at first position in Western Europe by filing 62,105 patent applications. Onwards, the UK, France, Italy, and Poland carry the next positions by filing 20,649, 14,313, 11,008, and 4098 patent applications, respectively (World Bank 2023). Moreover, the performance of Western Europe is pretty impressive in using Renewable Energy Consumption (REC) in 2021. Iceland holds the first position in Europe as 87% of Total Primary Energy Consumption (TPEC) is sourced from renewable sources. The major sources of REC are geothermal, hydropower, and wind power energy. Moreover, Iceland produces 99% of its electricity from renewable sources. Out of which, about 70% of electricity is produced from hydroelectric power. Fossil fuels are just used in the transportation sector in Iceland. Norway, Sweden, and Denmark hold the next positions in using REC about 72%, 51%, and 41% of TPEC, respectively. Moreover, Austria, Switzerland, Finland, and Portugal are using REC for more than 30% and Latvia, Spain, Slovenia, and Greece are using REC for more than 20% of TPEC. On average, the whole of Western Europe is using REC about 21% of TPEC (BP 2023). Hence, the REC carries a significant proportion of total primary energy consumption and can help in combating pollution in Western Europe.

Innovation and renewable energy transition (RET) would help achieve environmental sustainability in Western Europe. Some Western European economies have shown remarkable progress in RET while others have low levels of RET. Thus, there is a pressing need to investigate the environmental effect of RET in the whole of Western Europe as the whole region shares the same landscape. Moreover, the most of economies in this region are well-connected due to trading and environmental agreements. Therefore, we aim to analyze the roles of RET and innovation in fostering environmental sustainability within the Western European context. Particularly, the innovations would reduce energy intensity and pollution emissions in an economy and Western European literature has investigated this issue using a limited sample of countries (Apergis et al. 2013; Shahbaz et al. 2020). However, comprehensive research to gauge the environmental effect of patents in a maximum sample of Western Union countries is missing in the European literature. Moreover, the European literature has investigated the effects of REC on pollution (Pham et al. 2020; Jonek-Kowalska 2022; Altıntaş and Kassouri 2020; Bekun et al. 2019; Sulaiman et al. 2020; Dogan and Seker 2016; Neves et al. 2020; Barrera-Santana et al. 2021). However, the investigation of the effect of RET on emissions is missing in Western European literature. Therefore, the present study contributes to the Western European literature by developing the RET variable by using a ratio of REC to the sum of non-REC from oil, gas, and coal and by testing the effect of RET on CO2 emissions. Thus, the objective of this research is to find the effects of patents, RET, and income growth on CO2 emissions in 25 Western European countries from 1995–2020. Western European countries are members of the European Union and active partners in many environmental treaties to achieve some environmental goals. Because of trading and environmental agreements, Cross-sectional Dependence (CD) is expected in the model (Eberhardt 2012). Thus, the present research has applied CD techniques to care for the CD issue in the Western European panel.

Literature review

On the positive environmental side of technological progress, technological innovation may enhance energy efficiency and renewable energy (Zhou et al. 2010; Saqib et al. 2023), which would change the overall energy mix of the economy. Further, technological progress would decrease fossil energy share in an economy (Tang and Tan 2013). In addition, innovation may accelerate the productivity of inputs, and an economy may have a greater amount of output using a lesser amount of energy (Mensah et al. 2018). Thus, innovation may help in supporting the climate by using less energy. Moreover, technical innovation would generate effective technologies (Maranville 1992; Sharif et al. 2022) and would shift the economy toward less-polluted industries. Thus, innovation would help to achieve the technique and composition effects. Consequently, technological progress can help in promoting the environmental profile of the economies.

Literature has been conducted to explore the environmental effects of innovation variables and REC. For instance, Uche (2022) investigated 21 top remittance economies from 1990–2019 by using dynamic estimation techniques. The results exposed that REC and human capital helped in raising environmental quality. However, urbanization and structural transition reduced environmental quality. Obiakor and Uche (2022) examined African and Latin American economies from 1990–2018 and found that clean energy helped to enhance environmental quality. Moreover, the economic transition could support these economies’ environment in the short run. Comparatively, the agricultural transition had better environmental effects than the manufacturing and mining sectors. Onuoha et al. (2023) investigated 29 Sub-Saharan African economies and found that FMD, CO2 emissions, public debt, and economic growth reduced REC. However, urbanization enhanced REC. In a similar sample, Okere et al. (2023) originated that public debt raised many indicators of energy poverty. Uche et al. (2023a) analyzed BRICS economies and found that FDI’s interaction with environmental innovation helped to mitigate pollution. Moreover, REC and human capital also reduced pollution. Uche et al. (2023b) explored G10 from 1985–2021 and substantiated that public R&D on green technology and REC helped to achieve environmental sustainability by reducing energy-induced emissions and temperature. Moreover, energy tax reduced emissions, and fossil fuels enhanced emissions. Uche et al. (2023d) analyzed India from 1980–2018 by using multiple threshold nonlinear Autoregressive Distributive Lag (ARDL) technique and substantiated the EKC. However, environmental-control technologies and trade openness could not support a clean environment, and energy consumption and urbanization enhanced pollution. Uche et al. (2023c) investigated India from 1997Q1–2021Q4 and found that carbon intensity and green technologies reduced emissions in the long run. Moreover, the EKC was validated. Muoneke et al. (2022) examined the Philippines and substantiated the EKC. However, agricultural development was lower than the threshold level. Moreover, de jure financial and trade globalization aggravated and reduced ecological footprint, respectively. Moreover, urbanization, economic growth, and fossil fuels enhanced the ecological footprint.

Considering the positive role of innovation in the environment, European literature has investigated this issue using a proxy of R&D. For example, Škrinjarić (2020) compared the sustainable development of European economies and found that countries with higher R&D, Gross Domestic Product (GDP) per capita, and education had better performance in sustainable development. Literature has also focused on particular Western European countries. Apergis et al. (2013) explored Germany, France, and the UK from 1998–2011 and found that R&D after following international financial standards encouraged innovations and reduced CO2 emissions. Later on, literature realized the role of R&D in shaping the Environmental Kuznets Curve (EKC) hypothesis in European countries. For example, Lapinskienė et al. (2015) examined 20 European Union (EU) economies from 1995–2011 and validated that R&D, nuclear energy, and energy taxes reduced GHGs emissions. The EKC was also corroborated. However, agriculture, industry, and construction sectors and solid fuels had positive effects on GHGs emissions. The same findings were shared by Lapinskienė et al. (2017) using a sample of 22 EU economies from 1995–2014.

Auci and Trovato (2018) investigated and verified the EKC in 25 EU economies from 1997–2005. The results of the composition effect showed that CO2 emissions from dirty industries decreased with increasing economic growth. Moreover, the technique effect was corroborated by a reduction in emissions with increasing private R&D activities. However, public R&D increased emissions. By increasing the sample size of the EU, Nepal et al. (2021) investigated 28 EU countries from 1980–2018 and validated that energy efficiency and R&D reduced environmental degradation. Moreover, the EKC was also validated. Particularly, they claimed that energy efficiency would reduce petroleum consumption, which could reduce energy imports. Shahbaz et al. (2020) examined the UK from 1870–2017 and found that R&D reduced CO2 emissions. Moreover, the EKC was also substantiated. However, energy consumption increased CO2 emissions.

Another strand of literature utilized a proxy of patents for innovation in ecological studies of Europe. For instance, Khurshid et al. (2023) investigated 15 European economies and found that green innovations and ecological policies reduced emissions. de Araújo et al. (2020) investigated EU economies and found that technological advancement reduced CO2 emissions. However, exports increased emissions and outweighed the pleasant role of technological advancement. Mongo et al. (2021) explored 15 EU countries and found that environmental innovations decreased CO2 emissions.

Ignoring innovation in analyses, European literature has also examined the REC and emissions nexus. For instance, Pham et al. (2020) probed 28 EU economies from 1990 to 2014 and found that REC reduced CO2 emissions. Moreover, the EKC hypothesis was also corroborated. However, FDI, income, urbanization, population, and trade had positive effects on emissions. Moutinho et al. (2015) claimed that CO2 emissions in different European regions significantly declined due to switching to cleaner energy and reducing dependency on fossil fuels in end-user energy production. In the same way, Jonek-Kowalska (2022) found that replacing coal with REC and nuclear energy reduced CO2 emissions in Europe. Salahodjaev et al. (2022) investigated Europe and Central Asia from 1990–2015 and substantiated the EKC. Further, REC mitigated emissions, and tourism increased CO2 emissions. Altıntaş and Kassouri (2020) investigated 14 European economies from 1990–2014 and REC improved the environment. The EKC was also found in the ecological footprint model but not in the CO2 emissions model. Moreover, fossil fuels damage the environment.

Sulaiman et al. (2020) investigated 27 EU countries from 1990–2017 and realized that wood biomass energy usage reduced emissions. However, fossil fuels, income growth, and trade openness increased CO2 emissions. Dogan and Seker (2016) investigated 15 EU economies from 1980–2012 and corroborated the EKC. REC and trade openness reduced CO2 emissions and non-REC increased emissions. Neves et al. (2020) examined 17 EU countries and environmental laws regarding REC and FDI decreased CO2 emissions. Thus, the European Union economies had attracted innovative investment. Rodrigues et al. (2020) examined 28 EU economies from 2000–2015 and found that REC and efficiency gains reduced emissions from electricity production.

Bekun et al. (2019) investigated 16 EU economies and found that non-REC increased carbon emission flaring and REC decreased CO2 emissions. Lee (2019) investigated EU economies from 1961–2012. The author found that exports and REC had negative effects, and economic growth and industrialization had positive effects on CO2 emissions. Acaroğlu and Güllü (2022) investigated Turkey from 1980–2019. REC reduced temperature and non-REC increased precipitation. Marques et al. (2011) probed the drivers of RET in the EU and found that industrial lobbying was a hurdle in the way of the RET. Particularly, this lobbying effect was more prominent at the earlier stage of this transition. Apostu et al. (2022) examined and compared forty-two EU and non-EU countries from 1990–2018 and concluded that RET with allocated funds for transition was more in the EU compared to non-EU countries. In the particular case of Western Europe, Barrera-Santana et al. (2021) investigated 16 Western European countries from 1980–2019 and found that the countries’ growth depending on energy-intensive sectors had adverse environmental consequences. However, REC decreased emissions by reducing energy intensity. Nwani et al. (2023) examined 20 European economies from 1995–2019 and found that REC helped to reduce consumption-based energy and carbon intensities. Moreover, the EKC was also validated in both environmental proxies. Alola et al. (2023) examined France, Germany, Italy, and Spain from 1995–2020 and found that REC helped to achieve carbon-neutrality targets. Moreover, the EKC was also substantiated.

Some studies applied spatial econometrics in the relationship between pollution emissions and REC in Europe. For instance, Wang et al. (2022) investigated 36 European economies from 2000–2018 using spatial econometrics and substantiated the EKC. Geothermal energy, hydropower, and FDI reduced local emissions. Nevertheless, solar, wind, and bioenergy had positive or insignificant effects on local CO2 emissions and energy intensity increased local and neighboring economies’ CO2 emissions. Furthermore, solar and bioenergy generation in neighboring economies increased domestic pollution. Shahnazi and Shabani (2021) examined Europe from 2000–2017 and exposed the negative effect of REC on CO2 emissions. Moreover, the EKC was substantiated and the spillovers of CO2 emissions in neighboring economies were found statistically significant.

Ignoring REC and innovation variables, some European literature has investigated pollution emissions models. For instance, Mohsin et al. (2022) investigated European and Central Asian economies and found the causality from FDI and income level to CO2 emissions. Xu et al. (2022) examined 34 European countries from 2000–2020 and found that lending rates decreased and domestic credit increased emissions from the transport industry. Clora and Yu (2022) investigated 31 European economies and found that decarbonization ambitions reduced GHGs emissions. However, it reduced competitiveness by damaging the trade balance in the supply-side mitigation measures. However, the demand-side mitigation measures improved both the trade balance and the environment. Akdag and Yildirim (2020) investigated 29 European economies from 1995–2016 and concluded that energy efficiency reduced GHGs emissions.

Li et al. (2016) explored 18 European economies and found that decreasing energy intensity reduced CO2 emissions. Moreover, 7 Western European countries showed the highest potential to reduce emissions. Zhang et al. (2021) did efficiency analyses in Central and Western European economies to compare energy and environmental efficiencies. The authors found the UK and Ireland in first and second position in getting sustainable development. Wu et al. (2022) examined European economies and corroborated that energy prices reduced domestic and neighboring emissions. Christoforidis, Katrakilidis (2021) investigated Central and Eastern Europe from 1995–2014 and found that energy usage increased CO2 emissions.

Mulatu et al. (2010) investigated manufacturing firms in 16 European economies and found that environmental regulations shifted the dirty industry to lower-regulated countries. Jamel and Maktouf (2017) investigated forty European countries from 1985–2014 and found bidirectional causality between income and pollution. Koengkan and Fuinhas (2021) investigated 14 EU economies and found that the gender gap increased emissions. However, income, globalization, and urbanization did not affect CO2 emissions. Alonso et al. (2014) investigated and mentioned that two-thirds of EU flights landed in the UK, Spain, France, Italy, and Germany, which increased CO2 emissions. Frodyma et al. (2022) investigated the EU from 1970–2017 and the EKC was validated in panel models of production and consumption-based emissions. However, the EKC could not be validated in country-specific analyses of most analyzed economies.

Munir (2023) investigated 21 EU countries from 1990–2018 in nonlinear settings. The author found that increasing and decreasing coal, electricity, and oil consumption increased and decreased CO2 emissions, respectively. Acaravci and Ozturk (2010) investigated European economies and found that energy usage increased emissions in some Western European economies. Moreover, the EKC was substantiated. Kauppi and Tomppo (1993) investigated Western Europe and found that forests helped to reduce carbon in the atmosphere. Ali et al. (2018) investigated some Western European countries and found that the transport sector contributed to CO2 emissions in France, Italy, Germany, and the UK. Németh-Durkó (2021) examined Hungary from 1974–2014 and found that electricity consumption and urbanization increased carbon emissions.

Muoneke et al. (2023a) investigated Med-9 economies from Europe and found that government effectiveness helped to raise the pleasant effects of public debt, migration, and unemployment on environmental sustainability. However, urbanization’s interaction with government effectiveness harmed environmental sustainability. Okolo et al. (2023) investigated EU27 economies from 2006–2019 and found that credit from private and government sectors to small and medium enterprises improves environmental sustainability. Muoneke et al. (2023b) examined and found that coal consumption had a dampening effect on CO2 emissions. Moreover, bureaucracy amplified this effect and socioeconomic factors mitigated it.

The reviewed literature sheds light on the role of innovation in combating pollution emissions. The patents are the direct source of innovations and are not tested on CO2 emissions in a particular case of Western Europe. Moreover, the effect of RET is tested on CO2 emissions. Thus, this present study is motivated to fill this literature gap by investigating the impact of patents, RET, and economic growth on CO2 emissions in 25 Western European countries.

Methods

While testing the growth and emissions nexus, we cannot ignore the EKC hypothesis. Economic growth could have different environmental effects at different stages of growth. For instance, the environment may be sacrificed in achieving initial growth and it may be protected at a later stage. Thus, Grossman and Krueger (1991) advocated testing a nonlinear impact of economic growth on emissions. Therefore, we hypothesize the quadratic effect of economic growth on CO2 emissions. Innovation would play an effective role in reducing pollution. For instance, innovation could develop environmentally friendly technologies to mitigate pollution and achieve a sustainable environment. Albino et al. (2014) suggested a proxy of patents for innovation to develop low-carbon technology. Similarly, Raiser et al. (2017) also suggested that patents would mitigate climate change. Patents would help an economy to transform from fossil fuels to clean technologies and/or cleaner sources of energy. Thus, we hypothesize a negative effect of patents on CO2 emissions. Moreover, literature suggested that REC would mitigate pollution in an economy (Gessinger 1997; Khan et al. 2020). In addition, Chiu and Chang (2009) claimed that a high percentage of REC in the energy mix is required to combat pollution. Hence, an economy should reduce non-REC and enhance the REC in the energy mix to combat pollution. Moreover, a balance between REC and non-REC is required to meet the environmental challenges. Therefore, we use the renewable energy transition (RET) variable, which is captured through a ratio of REC to non-REC. Thus, RET may reduce pollution and we hypothesize a negative effect of RET on CO2 emissions. RET and patents are included in the model of the EKC in Western Europe in the following way:

$${{{\mathrm{CO2}}}}_{{{{{it}}}}} = {{{{f}}}}\left( {{{{{Y}}}}_{{{{{it}}}}},{{{{Y}}}}_{{{{{it}}}}}^2,{{{\mathrm{RET}}}}_{{{{{it}}}}},{{{\mathrm{PAT}}}}_{{{{{it}}}}}} \right)$$
(1)

Yit is the natural logarithm of GDP per capita in constant US dollars and Yit2 is the square of Yit. PATit reflects the thousands of filed patent applications. GDP data and patents are obtained from the World Bank (2023). RETit is a ratio of REC in exajoule to the sum of energy consumption from oil, gas, and coal in exajoule. These variables are sourced from BP (2023). RETit and PATit are not taken in the natural logarithm because of the presence of zero values in some sample years. CO2it is per capita tCO2 in the natural logarithm form and sourced from the Global Carbon Atlas (2023). All series are taken for the period 1995–2020 and from 25 Western European countries, i.e., Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Luxembourg, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland, and the UK. Some small economies in Western Europe are ignored in the analysis due to data unavailability.

Most Western Europe countries are members of the EU. Due to trading and environmental agreements, we may expect the CD in the model, and CD should be considered in the estimations to have unbiased results (Eberhardt 2012). Breusch and Pagan (1980) suggested LM statistic to test the CD in each individual variable of the model and the residual. Moreover, Pesaran et al. (2008) and Pesaran (2021) provided unbiased versions of LM tests, which are utilized to verify the presence of CD in each individual variable and the residual of a model. If the CD is validated, then the CD unit root tests of Pesaran (2007) will be applied to check the unit root problem in the panel series. The Cross-sectional Augmented-Dickey-Fuller (CADF) test equation is as follows:

$$\Delta y_{it} = \mu _0 + \mu _{1i}y_{it - 1} + \mu _{2i}\overline {y_{t - 1}} + \mu _{3i}\overline {\Delta Y_t} + \pi _{it}$$
(2)

\(\overline {y_{t - 1}}\) and \(\overline {\Delta Y_t}\) are the cross-sections’ average. The unit root may be tested with a null hypothesis of μ1i = 0. Moreover, Cross-sectional Im-Pesaran-Shin (CIPS) statistics may be calculated with estimated CADF statistics in the following way:

$${\rm{CIPS}} = N^{ - 1}\mathop {\sum }\limits_{i = 1}^N {\rm{CADF}}_i$$
(3)

After inquiring about the unit root in series, Westerlund’s (2007) CD procedure is used to verify a cointegration in the hypothesized relationships in Eq. (1) with the following test statistics:

$$G_t = N^{ - 1}\mathop {\sum}\limits_{i = 1}^N {\frac{{\mathop {\Omega }\nolimits_i }}{{{\rm{SE}}\widehat{{\left( {\mathop {\Omega }\nolimits_i } \right)}}}}}$$
(4)
$$G_a = N^{ - 1}\mathop {\sum }\limits_{i = 1}^N \frac{{T\Omega _i}}{{\mathop {\Omega }\limits^\prime \left( 1 \right)}}$$
(5)
$$P_t = \frac{{\widehat{{\mathop {\Omega }\nolimits_i }}}}{{{\rm{SE}}\widehat{{\left( {\mathop {\Omega }\nolimits_i } \right)}}}}$$
(6)
$$P_a = T\hat{\Omega }$$
(7)

\(\hat{\Omega }\) is a parameter, which is calculated from the error correction model. Afterward, we apply the procedure of Pesaran and Yamagata (2008). This procedure helps us to verify the possibility of slope-heterogeneity in the model using Δ-statistic and Δadj-statistic. The presence of slope-heterogeneity would lead us toward the methodology of Pesaran and Smith (1995), which does not care about the issue of CD in estimations (Eberhardt 2012). Caring the CD in analysis, Chudik et al. (2017) suggested efficient estimators in the following way:

$$\begin{array}{l}{\rm{CO2}}_{it} = a_i + \mathop {\sum }\limits_{j = 1}^k g_{ij}{\rm{CO2}}_{it - j} + \mathop {\sum }\limits_{j = 0}^k b_{1ij}Y_{it - j} + \mathop {\sum }\limits_{j = 0}^k b_{2ij}Y_{it - j}^2 \\\qquad\quad\;\; + \mathop {\sum }\limits_{j = j}^k b_{3ij}{\rm{RET}}_{it - j} + \mathop {\sum }\limits_{j = 1}^k b_{4ij}{\rm{PAT}}_{it - j} + \mathop {\sum }\limits_{j = 0}^k c_{1j}\overline {{\rm{CO2}}_{it}}\\\qquad\quad\;\; + \mathop {\sum }\limits_{j = 0}^k c_{2j}\overline {Y_{it}} + \mathop {\sum }\limits_{j = 0}^k c_{3j}\overline {Y_{it}^2} + \mathop {\sum }\limits_{j = 0}^k c_{4j}\overline {{\rm{RET}}_{it}} + \mathop {\sum }\limits_{j = 0}^k c_{5j}\overline {{\rm{PAT}}_{it}} + e_{it}\end{array}$$
(8)

Equation 8 represents the CD-ARDL model. The estimates can be obtained by normalizing the coefficients after averaging the variables, \(\hat{\beta } = \mathop {\sum }\nolimits_{j = 0}^k \hat{b}_{ij}/1 - \mathop {\sum }\nolimits_{j = 0}^k \hat{g}_{ij}\). Moreover, short-run effects can be estimated by cij after incorporating the error correction term (ECTt−1) in Eq. (8).

Data analyses

Table 1 displays descriptive statistics and the mean values of all series are more than the standard deviation (SD) except PATit. Thus, all variables are under-diverse except PATit. The PATit is over-diverse, which explains that all Western European countries show a diverse performance in terms of patents. Moreover, the minimum values of PATit and RETit are zero, which explains that some countries have zero performance in terms of RET and patents in some years.

Table 1 Descriptive statistics.
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CD tests are applied for individual variables and the residual of regression in Table 2. All the CD tests show the existence of CD in all the tested series and the residual of regression. Thus, all tests suggest incorporating CD in further econometric analyses. Moreover, the slope heterogeneity is also corroborated by statistically significant Δ and Δadj statistics.

Table 2 CD and slope heterogeneity tests.
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Table 3 displays the results of CADF and CIPS tests to confirm stationarity. All series at the level are non-stationary. Further, all series at first difference are stationary. Thus, the order of integration is one.

Table 3 Panel unit root analyses.
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In Table 4, we apply the Westerlund cointegration technique, which verifies a cointegration in the model with significant Gt and Pa statistics at 10% level of significance. Thus, the hypothesized model is suitable for further long and short run analyses.

Table 4 Westerlund cointegration test.
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The long run results in Table 5 show the positive parameter of Yit and the negative parameter of Yit2, which corroborated the EKC hypothesis in the panel of Western Europe. Thus, the hypothesis of an inverted U-shaped (quadratic) association between GDP per capita and CO2 emissions is substantiated. The estimated turning point is found at GDP per capita of 50,287 US dollars [exponent of −(11.2477)/2(−0.5195)]. As per the last sample year 2020, Denmark, Iceland, Sweden, Ireland, Norway, Luxembourg, and Switzerland are found in the 2nd phase of the EKC with a GDP per capita of more than 50,287 US dollars. Thus, the economic growth of these countries is reducing CO2 emissions. The rest analyzed Western European economies are in the first phase in the long run and have ecological consequences of growth. In the European EKC literature, some studies verified the existence of the EKC in 25 EU countries (Auci and Trovato 2018), in 20 EU economies (Lapinskienė et al. 2015), in 22 EU countries (Lapinskienė et al. 2017), in 28 EU countries (Pham et al. 2020), in 14 European economies (Altıntaş and Kassouri 2020), in 17 EU countries (Neves et al. 2020), and in all EU economies (Frodyma et al. 2022). However, the mentioned studies could not verify the EKC in the particular Western European region. Thus, the present study exploits this opportunity to validate the EKC in 25 Western European countries.

Table 5 Regression analyses.
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RETit has a negative parameter and the hypothesis of a negative relationship between RET and CO2 emissions is substantiated. Thus, the renewable energy transition from non-REC to REC helps to lower emissions in Western Europe. The results substantiate that the renewable energy transition has helped Western European economies to reduce the environmental effects of energy consumption. This result is natural as a whole Western Europe has transited more than 20% of total energy need from REC (BP 2023), and this transition helped this region to reduce CO2 emissions. The transition from non-renewable to REC reduces the dependence on fossil fuels and CO2 emissions are reduced consequently. Using renewable energy consumption variable, Barrera-Santana et al. (2021) corroborated the negative impact of REC on CO2 emissions in 16 Western European countries. Moreover, some other studies reported the negative effect of REC on pollution emissions in 28 EU countries (Pham et al. 2020; Rodrigues et al. 2020), in aggregated data of all EU countries (Lee 2019), and in 36 European countries (Wang et al. 2022). However, the mentioned studies worked on the REC variable. The result of RET in this present study suggests that RET can help in reducing CO2 emissions, which might be achieved by reducing non-REC and/or increasing REC. Thus, both movements of energy usage can help in reducing CO2 emissions.

The coefficient of PATit is negative and the hypothesis of a negative association between patents and emissions is proven. Thus, the increasing number of patents in Western Europe is helping to reduce CO2 emissions. It shows that increasing patents are attached to the development of clean technologies in Western Europe and are thus helping in environmental sustainability. This finding is matched by the fact that 12 Western European economies are among the top 20 economies in producing patents (Statista 2021). Thus, patents are developing new clean technologies and reducing CO2 emissions in the region. Using different proxies of innovation, the literature has substantiated the negative impact of innovation on pollution emissions. For instance, some studies revealed a negative effect of R&D on pollution in some Western European economies (Apergis et al. 2013), in the UK (Shahbaz et al. 2020), and in some EU economies (Nepal et al. 2021; Lapinskienė et al. 2017; Auci and Trovato 2018). Moreover, Khurshid et al. (2023) corroborated the negative effect of green innovation on pollution in 15 European countries, de Araújo et al. (2020) validated the negative impact of technological advancement on emissions in the EU, and Mongo et al. (2021) substantiated the negative effect of environmental innovations on pollution in 15 EU economies.

In the short run results, the parameter of ECTt−1 is negative, which shows the convergence of short run disequilibrium to long run equilibrium. Moreover, the EKC is also validated in the short run with a turning point at GDP per capita of 57,320 US dollars [exponent of –(19.5835)/2(−0.8937)], and Denmark, Iceland, Ireland, Norway, Luxembourg, and Switzerland are at 2nd stage of the EKC as per their GDP per capita in the last sample year 2020. Further, RET also helps to reduce emissions. However, patents have a negative but insignificant coefficient. Thus, patents do not affect CO2 emissions in the short run. Patents need time to be generalized and come in the form of workable technologies, which could help in reducing pollution emissions. So, the short-run results could not validate the positive environmental impact of patents. However, Mongo et al. (2021) corroborated the short-run positive impact of ecological innovations on CO2 emissions in 15 EU economies.

Conclusions

This research examines the effects of the RET, the number of patents, and economic growth on CO2 emissions in 25 Western European countries from 1995–2020. The study utilizes CD techniques to investigate long and short run relationships. The results disclose the validity of the EKC in the long run with a turning point at GDP per capita of 50,287 dollars and Denmark, Iceland, Sweden, Ireland, Norway, Luxembourg, and Switzerland are at the 2nd stage of the EKC. Thus, these economies are enjoying the pleasant environmental effects of economic growth. However, the remaining Western European economies are found at an early phase of the EKC, and their economic growth has ecological concerns. Therefore, it is recommended to rest Western European countries to take immediate action to control pollution by devising environmentally friendly policies. Further, the EKC is corroborated in the short run with a turning point at GDP per capita of 57,320 dollars, and Norway, Luxembourg, and Switzerland are at 2nd stage of the EKC. RET reduces CO2 emissions in the long and short run. Thus, RET helps mitigate the environmental degradation. Patents have negative effects on emissions in the long run but patents do not affect emissions in the short run. This result explains that patents need a long time to be generalized and to have pleasant effects on the environment.

The results suggest that RET helped reduce CO2 emissions. Thus, switching to renewable in the transition of energy would reduce ecological problems. So, we strongly suggest Western European economies for a fast transition from non-REC to REC to attain a sustainable environment in the countries. This transition may be achieved by setting a target of a low proportion of non-REC in the energy mix, which would help these economies to control ecological problems. For this purpose, Western Union countries should invest in developing the infrastructure to enhance the production capacity of renewable energy. On the consumption side, the government should give subsidies to promote the REC and should tax the energy consumption from fossil fuels. Moreover, renewable energy standards should be improved. Governments may provide tax incentives and credits for renewable energy investments. We also find that patents could reduce CO2 emissions in the long run. Thus, Western European economies should invest in R&D activities to generate further patents with environmentally friendly technologies to achieve a green environment. Moreover, governments should encourage collaboration between public and private research organizations for the development of clean technologies. Furthermore, governments should also spend on educational and training programs to develop manpower for high-level research and the application of such research in favor of a pleasant environment. In addition, Western European economies should foster research collaboration within the region to promote environmentally friendly technologies.

The present study could work on the RET from aggregated REC. However, future research may develop RET proxies from different sources of renewable energy to segregate the impact of each RET proxy on the environment. Moreover, the increasing sample of European countries could enhance the generalization power of the research for a wide region.