Because of its role as a global trade hub, Singapore is an ideal case study for exploring the trade environment. The given synopsis outlines the key conclusions of ten empirical studies, specifically focusing on the environmental implications of trade openness and their relevance to Singapore’s situation. Arif et al. (2022) demonstrated that trade openness positively influenced the economic growth of South Asian economies; however, they did not directly address the environmental impact. Sultana et al. (2023) found that trade openness significantly increases CO₂ emissions. Khan et al. (2022) measured 176 countries, including Singapore, and concluded that trade openness could reduce CO₂ emissions when institutional strength and innovation capabilities are robust. According to Sannassee and Seetanah (2016), trade openness contributes to the increase in CO₂ emissions in Mauritius due to manufacturing growth. Dou et al. (2021) studied the free trade agreement between China, Japan and South Korea from 1970 to 2019, finding that increased trade openness leads to higher emissions. Afridi et al. (2019) discovered an N-shaped curve in SAARC countries and found that trade openness led to CO₂ emissions. Akbar et al. (2020) compared countries in Southeast Asia, including Singapore, and proved that the level of trade openness indirectly increases CO₂ emissions due to increased energy consumption and, eventually, affects health spending. Usman et al. (2023) found that trade openness and non-renewable energy use increased CO₂ emissions in Pakistan between 1990 and 2017, while renewable energy improved environmental quality.

Nica et al. (2023) examined the effects of trade liberalization on female employment in SAARC countries between 1991 and 2021, observing an increase in workforce participation in the manufacturing and services industries. Although the findings are not directly environmental, they shed light on the socio-economic impacts of trade in Singapore and how these might affect environmental policy-making processes. The U-shaped ecological footprint trajectory observed by Destek and Sinha (2020) in OECD countries and Singapore is consistent with the broader trend of environmental degradation associated with increased trade openness between 1980 and 2014. Due to the mitigating effect of renewable energy, Singapore looks to sustainable energy policies to address its energy issues. Overall, the empirical data invariably suggests that trade openness enhances CO₂ emissions and environmental destruction.

Studying gross domestic product (GDP), foreign direct investment (FDI) and environmental sustainability in Singapore would reveal the multifaceted effects of carbon dioxide (CO₂) emissions and eco-footprints. According to Raihan et al. (2022), although economic growth helps reduce CO₂ emissions in the long term, tourism and energy consumption contribute to their increase. This is why renewable energy sources and strict regulatory measures, including carbon taxes, should be used. Mehmood (2021) shows that the negative impact of globalization on the economy and society is a reduction in emissions. However, the positive effect of political globalization is an increase in emissions of 2.06% for every 1% increase in political integration (Ngoc & Awan, 2022). Ngoc and Awan also note that economic growth increases ecological footprints, but this increase is mitigated by improvements in human capital. Ozturk et al. (2023) identify economic and population growth as key contributors to emissions, stating that reducing carbon intensity can enable sustainability. Luo et al. (2022) argue that foreign direct investment (FDI) can stimulate economic growth, but it increases emissions when coupled with a dependence on non-renewable energy. Conversely, implementing renewable energy can mitigate this impact. Meirun et al. (2021) conclude that green technology innovation significantly decreases emissions while leading to growth. Islam (2021) examines the South Asian setting involving Singapore and finds that economic growth, energy use and urbanization contribute to increased emissions, but industrial value added has no impact. According to Raihan et al. (2023), agricultural value added can also lower emissions in China. This implies that climate-smart agriculture could be relevant in Singapore too. As Awan and Azam (2022) point out, emissions in G20 economies, including Singapore, can be reduced by advancing technology and improving financial conditions. Overall, these studies emphasize the importance of adopting renewable energy, technological advancement and robust policy frameworks to minimize the environmental impact of economic development and foreign direct investment (FDI), while also identifying gaps in research related to urbanization and trade openness.

This section reviews some of the key studies indicating their applicability to Singapore within the broader context of South and East Asia. Lao and Luo (2024) compared the environmental effects of industrial development and agricultural value addition in South and East Asian economies, revealing that CO₂ emissions increased by 0.563 and 0.758 percent respectively when agricultural value addition and industrial development increased by 1 percent. The article by Abbasi et al. (2022) examines the relationship between energy consumption, agricultural value added and CO₂ emissions in 22 forested states, including Singapore, and reveals that positive shocks to agricultural value added cause environmental degradation to decline, whereas negative shocks cause emissions to rise. Adedoyin et al. (2021) discuss empirical research on agricultural development, energy consumption and economic growth in E7 countries, revealing that the agricultural sector and economic growth contribute to CO₂ emissions, while renewable energy helps reduce them. Adegbeye et al. (2020) inform emerging countries about sustainable agricultural practices based on the concepts of localized technology and sustainable intensification. These practices could help to reduce greenhouse gas emissions by 30%. Some of the methods include precision farming, nutrient recycling and integrated systems. Yurtkuran (2021) examines agriculture, agricultural renewable energy and globalization in Turkey, concluding that agriculture and the globalized economy contribute to CO₂ emissions. Xi and Zhai (2023) study the time-varying characteristics of economic growth and industrial structure upgrading in China between 2000 and 2019. They confirm an inverted U-shaped EKC and the negative moderating role of industrial upgrading on environmental pollution. Alam (2015) analyzed South Asian countries and found that the agricultural, industrial and service sectors minimize CO₂ emissions. Sharma and Das (2024) emphasize the environmental footprint of value-added agriculture and globalization in South Asia, calling for the adoption of solar energy and sustainable agricultural practices such as precision agriculture. Chandio et al. (2025) discuss the nexus between energy, climate and agriculture in Asian economies, including Singapore. They found that renewable energy boosts agricultural production, while climate change has an adverse effect on it. Ehigiamusoe et al. (2024) examined sectoral growth in Malaysia and revealed that the agriculture and services sectors increase CO₂ emissions, whereas renewable energy reduces them. Singapore’s service industry can use the same approach to renewable energy to minimize its environmental impact.

Although the relationship between trade and the environment has been extensively researched, there are gaps in the literature on foreign direct investment (FDI) and the effects of both sectors on CO₂ emissions. The narrowness of discussion of the indirect impacts of urbanization in Singapore’s high-density setting, as identified by Islam (2021), should be investigated. The particular structure of trade that accounts for the influence of differential emission effects, as suggested by Dou et al. (2021), also needs to be thoroughly studied. Additionally, the nonlinear dynamics of GDP and agriculture, as indicated by Afridi et al. (2019), should be confirmed by longitudinal studies. The lack of integration of real-time data on green technology adoption and global trade transitions indicates a need for research to improve policy relevance.

The present study is anchored in a synthesis of established theoretical perspectives that illuminate the intricate relationships among trade openness, foreign direct investment, economic growth, sectoral contributions, renewable energy consumption and environmental degradation in a highly open economy such as Singapore. Central to this framework is the Environmental Kuznets Curve (EKC) hypothesis, which posits an inverted U-shaped relationship between economic growth and environmental pollution. As income rises, environmental degradation initially intensifies due to scale effects associated with expanded production and consumption, but beyond a certain income threshold, technique and composition effects driven by technological progress, stricter regulations and shifts toward less polluting activities lead to improvements in environmental quality.

In the context of Singapore’s trade-driven economy, this hypothesis suggests that while rapid GDP growth and trade expansion may lead to increased CO₂ emissions in earlier stages, the country’s advanced institutional quality, innovation capacity and increasing reliance on renewable energy could facilitate passage through the EKC turning point. The model is typically expressed in quadratic form as

CO2_t = α₀ + α₁GDP_t + α₂GDP_t² + α₃Z_t + ε_t

where CO2_t denotes carbon dioxide emissions, GDP_t represents economic growth (or its logarithm in per capita terms), Z_t is a vector of additional controls (including trade, FDI, and sectoral shares), and ε_t is the stochastic error term. A positive α₁ and negative α₂ would confirm the inverted U-shape.

Complementing the EKC is the pollution haven hypothesis, which argues that trade openness and FDI inflows may relocate pollution-intensive industries to jurisdictions with relatively lax environmental standards, thereby increasing emissions in the host economy. In Singapore’s case, this dynamic is particularly relevant given its strategic position as a trade and financial hub, where total trade (exports plus imports) as a share of GDP has averaged around 349% over the study period. The hypothesis implies that without sufficient countervailing forces, such as strong institutions and renewable energy penetration, trade liberalization and capital inflows could exacerbate environmental pressures through scale and composition effects.

The trade–environment nexus further elaborates these mechanisms by decomposing the overall impact of trade into scale, technique and composition effects. Trade openness may amplify emissions via the scale effect (higher economic activity), yet it can mitigate them through the technique effect (import of cleaner technologies) and composition effect (reallocation toward less emission-intensive sectors). In the case of Singapore, distinguishing between merchandise trade (MRCHNDS) and total trade (TRADE) is crucial because the former can facilitate the import of technology that reduces emissions, while the latter captures a broader range of activities that could increase emissions. This distinction can be formalized in an extended model:

C O 2 t = β 0 + β 1 T R A D E t + β 2 M R C H N D S t + β 3 F D I t + β 4 R E t + + ∑ s γ s S E C T O R s , t + δ P O P t + ϵ t

where TRADE_t and MRCHNDS_t capture trade dimensions, FDI_t represents foreign direct investment inflows, RE_t denotes renewable energy consumption share, SECTOR_s,t includes value-added shares of agriculture (AGRI), industry (INDS) and services (SRVS), and POP_t accounts for population growth.

This framework explicitly addresses sectoral dynamics. Industrial activities typically have a stronger positive impact on emissions due to energy intensity. In contrast, services that dominate Singapore’s economy tend to have a smaller environmental footprint. The adoption of sustainable practices in agriculture can have mixed effects. In particular, the services sector is theorized to moderate emissions thanks to its lower direct energy requirements and potential for green innovation:

ΔCO2_t = ϕ₁ΔINDS_t + ϕ₂ΔSRVS_t + ...

with the expectation that |ϕ₂| < ϕ₁ in absolute terms when services displace or complement industrial activity.

To accommodate potential asymmetries in responses to economic shocks such as those arising from trade liberalization episodes or fluctuations in renewable energy adoption the framework incorporates insights from nonlinear dynamics. Positive and negative shocks in explanatory variables may produce differential impacts on CO₂ emissions, reflecting rigidities in capital stock, policy responses or technological adjustment costs. This motivates the Nonlinear Autoregressive Distributed Lag (NARDL) specification, where each variable X_t (e.g., TRADE, FDI, GDP) is decomposed into positive and negative partial sums:

X t + = ∑ j = 1 t max ( Δ X j , 0 ) , X t − = ∑ j = 1 t min ( Δ X j , 0 )

The NARDL model then takes the form:

Δ C O 2 t = α + ρ C O 2 t − 1 + θ + X t − 1 + + θ − X t − 1 − + ∑ i = 1 p − 1 γ i Δ C O 2 t − i + + ∑ i = 0 q − 1 ( π i + Δ X t − i + + π i − Δ X t − i − ) + ∫ t

where θ⁺ and θ^– capture long-run asymmetric effects, and short-run dynamics are reflected in the differenced terms. Rejection of the null hypothesis θ⁺ = θ^– indicates the presence of asymmetries relevant to Singapore’s exposure to external shocks.

Consistent with theoretical arguments that shifts toward cleaner energy sources decouple economic activity from emissions, renewable energy consumption enters as a key mitigating factor. Including this factor reflects the technical effects within the EKC and the potential to offset pollution havens associated with foreign direct investment (FDI) and trade.

Together, the theoretical strands of the environmental Kuznets curve (EKC), pollution havens, trade-environment mechanisms, sectoral differentiation and asymmetric adjustment provide a coherent foundation for the empirical analysis. These perspectives justify the multi-model approach (FMOLS, CCR, ARDL, and NARDL) used to examine linear long-run equilibria and nonlinear short-run dynamics from 1991 to 2024. Integrating these perspectives allows the framework to contextualize Singapore’s unique position as a high-trade, service-oriented economy and generate testable hypotheses about the conditions under which economic openness can be reconciled with environmental sustainability. The subsequent empirical sections will evaluate how well Singapore’s institutional strengths and renewable energy trajectory enable it to navigate theoretical tensions toward greener growth.

The paper employed a large amount of data to analyze the relationship between trade openness, foreign direct investment (FDI), economic growth, and sectoral contributions (agriculture, industry and services), as well as environmental sustainability in Singapore, focusing on CO2 emissions as a measure of environmental degradation.

The time series dates back to 1991-2024 with 34 observations per year, thus accommodating a strong econometric analysis of long- and short-run dynamics. The choice of variables and operationalization are informed by previous research examining the nexus of trade, the environment, economic growth and sectoral impacts on environmental outcomes in Singapore and other similar economies (Khan et al., 2022; Raihan et al., 2022; Lao & Luo, 2024). The data was obtained from trusted World Bank databases, making it reliable and consistent.

In order to explore the connections between trade openness, foreign direct investment [FDI], economic growth, sectoral contribution (agriculture, industry, and services), population growth, renewable energy consumption and environmental degradation (represented by CO 2 emission) in Singapore, this study adopts a set of econometric models that can take into consideration both the linear and nonlinear relationships. The theoretical frameworks underlying the model specifications include the Environmental Kuznets Curve (EKC), which Afridi et al. (2019) discuss; the pollution haven hypothesis, as expressed by Sultana et al. (2023); and the trade-environment nexus, as analyzed by Khan et al. (2022).

These models were developed to address the issues of stationarity, long-run and short-run relationships, and potential asymmetries in the impact of explanatory variables on CO₂ emissions. They use a combination of linear regression models, including Ordinary Least Squares (OLS) and cointegration-based models such as Fully Modified Ordinary Least Squares (FMOLS), Canonical Cointegrating Regression (CCR), Autoregressive Distributed Lag (ARDL), and Nonlinear ARDL (NARD).

The baseline model is specified as a linear regression to estimate the relationship between CO₂ emissions and the explanatory variables. The functional form is given by

CO₂ = β₀ + β₁MRCHNDS_t + β₂TRADE_t + β₃RE_t + β₄GDP_t + β₅AGRI_t + + β₆INDS_t + β₇SRVS_t + β₈POP_t + β₉FDI_t + ε_t

The dependent variable, CO2t, is the level of carbon dioxide emissions in megatons of CO2 equivalent (Mt CO2e) at time t.

The intercept, b0, is the coefficient of the constant term.

The coefficients of the other explanatory variables are b1 through bn. The stochastic disturbance is represented by ε₀. The explanatory variables include merchandise trade (MRCHNDS), total trade (TRADE), renewable energy consumption (RE), gross domestic product growth (GDP), agricultural value added (AGRI), industrial value added (INDS), service value added (SRVS), population growth (POP) and foreign direct investment (FDI). Ordinary least squares and ridge regression are used to estimate the model, which reduces the harmful impact of multicollinearity between the trade-related variables (MRCHNDS and TRADE).

The variables are non-stationary at the level, as the ADF-Fisher unit-root test shows. As a result, cointegration-based methods are used to test long-run relationships. Cointegration does exist, as the F-bounds test supports. These findings justify the use of fully modified ordinary least squares (FMOLS), canonical cointegrating regression (CCR) and autoregressive distributed lag (ARDL) estimators. The long-run specification is given below:

CO₂ = α₀ + α₁MRCHNDS_t + α₂TRADE_t + α₃RE_t + α₄GDP_t + α₅AGRI_t + + α₆INDS_t + α₇SRVS_t + α₈POP_t + α₉FDI_t + μ_t

where α₀ is the intercept, α₁ to α₉ are the long-run coefficients, and μ_t is the error term. The FMOLS and CCR models correct for endogeneity and serial correlation in the cointegrating relationship, ensuring robust estimates (Phillips & Hansen, 1990; Park, 1992). The ARDL model, based on Pesaran et al. (2001), is specified to capture both long- and short-run dynamics:

Δ C O 2 t = γ 0 + ∑ i = 1 P γ 1 i Δ C O 2 t − 1 + ∑ i = 0 q γ 2 i Δ M R C H N D s t − 1 + + ∑ i = 0 q γ 3 i Δ T R A D E t − 1 + ∑ i = 0 q γ 4 i Δ R E t − 1 … v t

Here, ∆ denotes the first difference, γ_1i to γ_10i capture short-run dynamics, λ₁ to λ₁₀ represent long-run coefficients and ν_t is the error term. The lag lengths p and q are determined using information criteria [AIC, BIC] to ensure model parsimony.

To account for potential asymmetries in the relationships, particularly in response to positive and negative shocks in the explanatory variables, the NARDL model is employed (Shin et al., 2014). The NARDL model decomposes each explanatory variable into positive [X⁺_t ] and negative [X⁻_t ] partial sums, defined as

X t + = ∑ j = 1 t max [ Δ X j , 0 ] , X t − = ∑ j = 1 t min [ Δ X j , 0 ]

where X_t represents each explanatory variable (MRCHNDS, TRADE, RE, GDP, AGRI, INDS, SRVS, POP, FDI). The NARDL model is specified as

Δ C O 2 t = δ 0 + ∑ i = 1 P δ 1 i Δ C O 2 t − 1 + ∑ i = 0 q δ 2 i Δ M R C H N D s t − 1 + + ∑ i = 0 q δ 3 i Δ T R A D E t − 1 + ∑ i = 0 q δ 4 i Δ R E t − 1 + … v t

This specification permits asymmetric responses to positive and negative changes in explanatory variables. This is particularly relevant for Singapore’s trade-driven economy, where environmental impacts of shocks, such as trade liberalization and renewable energy adoption, may differ (Lao & Luo, 2024).

The study uses advanced econometric models to examine the relationships between trade openness, FDI, economic growth, sectoral contributions (agriculture, industry, services), population growth, renewable energy and CO2 emissions in Singapore, addressing stationarity, multi collinearity and asymmetries (Phillips & Hansen, 1990; Park, 1992). FMOLS, CCR and ARDL models, supported by an F-bounds test, analyze long- and short-run dynamics, while NARDL captures asymmetric shock responses in Singapore’s trade-driven economy (Pesaran et al., 2001; Shin et al., 2014). Diagnostic tests confirm model reliability, with no heteroskedasticity, managed serial correlation or normal residuals, aligning with the Environmental Kuznets Curve and pollution haven hypothesis (Afridi et al., 2019; Sultana et al., 2023). This theoretical framework uses economic theories to study the relationship between Singapore’s trade and environment. H1: Trade openness increases CO2 emissions via scale effects, mitigated by cleaner technologies (Dou et al., 2021). H2: FDI boosts growth but raises emissions unless green-focused (Luo et al., 2022). H3: Renewable energy reduces emissions, supporting sustainable growth (Meirun et al., 2021). H4: Services sector has lower environmental impact than industry (Xi & Zhai, 2023). H5: Population growth increases emissions via consumption and urbanization (Ozturk et al., 2023). H6: Agricultural value-added may reduce emissions with sustainable practices (Chandio et al., 2025).

The correlation table relating to Singapore’s economic indicators shows a strong positive correlation between the trade variables MRCHNDS and TRADE, and CO₂ emissions. This proves that trade intensity is a major contributor to emissions.

The sectoral variables Services (SRVS) and Industry (INDS) have moderate positive correlations with CO₂ emissions, which are recorded as 0.879 and 0.909, respectively. Hence, they have a significant influence on the environment. Conversely, Renewable Energy (RE) has a poor negative correlation with CO₂, with a coefficient of -0.755, meaning it has very little ability to control emissions. GDP growth has a weak positive correlation with CO₂ of 0.392, while population and foreign direct investment have marginal correlations of 0.315 and 0.454, respectively. The agriculture sector is reported to have a poor negative correlation of -0.254, indicating its comparatively small role in emissions. Overall, the correlation matrix highlights trade and sectoral activities as key CO₂ level factors, and renewable energy has a moderate compensating effect.

According to the ADF-Fisher unit root tests, the null hypothesis of a unit root at the level specification is rejected for most of the series [CO2, INDS, MRCHNDS, RE, SRVS, and TRADE], with p-values greater than the traditional 0.05 value [CO2: 0.5144; INDS: 0.8884]. However, they are stationary when first differenced, with p-values less than 0.05. Conversely, both FDI and POP are stationary. GDP is at a stable level, and the p-value of 0.0002 indicates its significance. The similarity of stationarity following differentiation (p = 0.0000 in all series) justifies the use of cointegrated analysis in the long run. Thus, the issue of nonstationarity in the data is overcome.

The F-Bounds test indicates that there was a long-run co-integration relationship between the variables at the time period under study, with a resulting F-statistic of 4.800151 and eight explanatory variables (k = 8). The calculated F-statistic is greater than the upper critical value at the 1% significance level (4.35), and the sample size of 33 observations supports this finding. Therefore, although one can calculate nonstationarity in the level series, as evidenced by the ADF-Fisher test, the following variables co-move in the long-run equilibrium with CO2 emissions: trade openness, renewable energy, GDP growth, sectoral contribution, population and FDI. The appropriateness of using the F-bounds test is based on its ability to incorporate mixed integration orders (I[0] and I[1]), making it suitable for the dataset. Furthermore, the results justify using cointegration estimators, including FMOLS, CCR, and ARDL, in the subsequent empirical analysis.

Coefficient {Std. Error} [t-Statistic] [Prob.].

The FMOLS, CCR and ARDL results prove that there are strong long-term relationships between economic variables and CO₂ emissions. These results provide a comprehensive view of the relationship between trade and the environment. Foreign direct investment (FDI) positively impacts CO₂ emissions, and the ARDL specification of this impact is the most significant. This observation suggests that increased outflows of foreign capital are a major driver of emissions. Conversely, the impact of the FMOLS outcome and the CCR result are less well-defined and only marginally significant. This means that the effect of changes in foreign direct investment (FDI) depends on the model specification. The growth of gross domestic product (GDP) is always positive and insignificant in all specifications. Economic growth has a low direct effect on emissions, which may be due to elimination mechanisms, including efficiency gains. In the models, industrial activity positively influences CO₂ emissions, which serve as the environmental cost of industrial output. The ARDL specification shows a weaker positive trend, indicating that there may have been a structural change or control measures over the years. Merchandise trade consistently has a negative effect on CO₂ emissions across the models, which can probably be explained by imports of cleaner technologies. However, total trade has a positive effect. The impact of population growth on CO₂ emissions is highly negative, probably due to policy-based population management or urban efficiency. Consumption of renewable energy significantly decreases CO2 emissions, and the ARDL estimate shows the most significant impact. The coefficients are marginal, which supports the importance of green energy in mitigation. The services sector also reduces CO2 emissions significantly in all models, which is consistent with Singapore’s service-oriented economy and focus on sustainability. The constant value [C] is statistically significant, though its statistical importance is weakened in the ARDL specification, which reflects the emission level at the base. The R-squared and adjusted R-squared values indicate that the models fit well. The range of the standard errors testifies to the accuracy of the estimations. Additionally, the ARDL specification is optimal, as evidenced by the F-statistic and Durbin-Watson statistic, which prove the absence of autocorrelation and the presence of significant long-run relationships.

When the approximation is done using ordinary least squares, the NARDL model shows asymmetrical effects on carbon dioxide emissions. The model has a strong coefficient of determination (R² = 0.977) and an adjusted R² = 0.944, suggesting an excellent fit. The overall significance of the regression is proven by the significant F-statistic of 51,040 (p = 1.16⁻⁸). The intercept is also significant [0 = 0.0019, p = 0.0070], forming a level of emissions. Merchandise trade (MRCHNDS) has a negative overall impact (-0.1232, 0.0390). Decreases and increases in trade emissions are positively correlated with positive and negative shocks to trade, respectively. Total trade has a positive impact [TRADE = 0.2367, p = 0.0060]. Conversely, positive changes in total trade decrease emissions (-0.2454, p = 0.0060), while negative changes increase them (0.1316, p = 0.0420). The overall impact of renewable energy (RE) is not statistically significant (8 = -0.1699, p = 0.9620), and thus it has no significant asymmetric impact on emissions. Although there is a positive trend in economic growth in terms of GDP (= 0.0692, = 0.2290), positive GDP shocks have a significant positive impact on emissions (= 0.2345, =0.0000). Negative shocks also have a positive effect (= 0.1780, = 0.0000). The agriculture industry is one of the largest contributors to emissions, with a baseline coefficient of 109.3017 (p = 0.0330). Positive (217.9102, p = 0.0290) and negative (108.6090, p = 0.0550) shocks increase the level of emissions. The positive coefficient (= 1.0000, = 0.0040) of the industry (INDS) is non-significant without a substantial asymmetric effect. Services have a negative effect on emissions (0.0030), but negative shocks to the service sector result in the opposite effect. The population has a slightly positive change in the baseline (0.2005, p = 0.1310). The response to negative population shocks is related to a decrease in emissions (-0.5291, p = 0.0380). The coefficient of foreign direct investment (FDI) does not have any significant value at the baseline (0.0460, 0.1180) and does not show any scope of asymmetry. The lagged CO₂ value of 0.2605 and p-value of 0.0040 support the presence of short-run persistence in emissions. The log-likelihood value of -45.551, along with the diagnostic tests, proves the adequacy of the specification and emphasizes the significance of the specified asymmetric relations in policy development.

The LR (Likelihood Ratio) test summary compares the restricted and unrestricted models to evaluate their respective goodness of fit. The restricted model has a log-likelihood of -54.12815 and an unrestricted log-likelihood of -53.86855, indicating only a slight improvement in fit. However, the absence of formally reported test statistics and p-values precludes clear inference. Typically, the likelihood ratio (LR) statistic is compared to a chi-square test with a number of degrees of freedom equal to the number of constrained parameters. The LR statistic is calculated by taking the log likelihood difference and subtracting it from -2. In this case, the LR statistic is -0.5198. Since this statistic is insignificant (p > 0.05), it would be best to keep the constrained model, though a better description of degrees of freedom is needed to make an unambiguous statement.