This study relies on Indonesia's annual series spanning 1980 – 2022; therefore, the length of observation is 43 years. The number of observations is sufficient for econometrics methods such as ARDLBT and the GC test. To establish multivariate analysis, CO₂ serves as a response variable. The predictor variables under consideration include economic growth, private credit, per capita energy consumption, and renewable energy.

The response variable of CO₂ emissions is expressed in metric tons. Economic growth is proxied by per capita GDP (constant 2015 $US). In addition, per capita GDP squared (YPC²) is computed to establish a non-linear model. Private credit is measured by total credit to the private non-financial sector, adjusted for breaks (% of GDP). Per capita energy consumption is measured in terawatt-hours (TWh). Renewable energy is proxied by the percentage of primary energy consumption from renewables. The datasets are gathered from Federal Reserve Economic Data (FRED), Our World in Data (OWD), and the World Bank Database (World Development Indicators-WDI).

The baseline model for the ECK hypothesis can be defined as Eq. (1) [47].

wherein CO₂ signifies carbon dioxide emissions. YPC and YPC² depict per capita income and per capita income squared. The term Ln is the operator of the natural logarithm. μ shows the error term. The subscript t represents that the data relies on a time series. Following previous studies, Eq. (1) is modified by integrating the impact of private credit and energy consumption. Therefore, Eq. (2) shows the empirical model.

wherein CRD stands for private credit. REU signifies renewable energy consumption. ENC is energy consumption. CRD can have a positive or negative effect on CO₂. REU is supposed to have a negative sign; conversely, ENC is expected to have a positive sign. The EKC hypothesis will be verified only if α₁ > 0 while α₂ < 0. The monetary value of an Income Turning Point (ITP) can be estimated through Eq. (3) [27];

Integrating a stationary test is crucial in time-series modeling, including the application of ARDLBT. It should be noted that ARDLBT is not a proper regression method for second-order stationary variables, I(2). Hence, this study applies the augmented version of the Dickey-Fuller test (ADF) to assess whether the unit root is present in the series analyzed [48]. A model for the ADF test is specified as Eq. (4).

wherein ∆ stands for first-difference notation. e is assumed to be the white noise error term; y_t denotes the time series being tested; v is the constant term. m shows the maximum lag length. The subscript t signifies a time trend. As part of the robustness check, this study includes the Phillips-Perron (PP) unit root test to provide reliable and valid findings regarding the order of integration.

Following the stationary test, ARDLBT is preferred for analyzing the nexus between CO₂ and a set of independent variables (YPC, YPC², CRD, REU, and ENC) since it offers notable advantages for time series modeling. First, it can be applied to stationary or non-stationary (integrated of order one) variables. Second, it produces short- and long-run parameters of the nexus between variables, as well as a cointegration model [49]. Third, it is a proper method to unravel hidden cointegration in the case of a small sample size [50]. Last of all, it can handle series correlation and endogeneity issues by incorporating sufficient lags [23]. Following Eq. (2), the ARDLBT (k) model is specified in Eq. (5).

wherein k signifies the optimal lag length, determined by working with the Akaike Information Criterion (AIC) test. η₁….η₅ are short-run coefficients. α₁…α₆ are long-run coefficients. ∆ shows the first difference term.

The bounds test procedure is applied to assess whether a cointegration association among CO₂, YPC, YPC², REU, CRD, and ENC is evident. Therefore, the H₀ of no-level relationships (α₁=α₂=α₃=α₄=α₅=0), is evaluated in comparison with the H₁ (α₁≠α₂≠α₃≠α₄≠α₅≠0). The rule of thumb is that H₀ must be rejected only if the computed F-statistics exceed the upper bounds. Otherwise, there is no cointegration.

Within the framework of ARDLBT, an Error Correction Model (ECM) can be specified as Eq. (6).

where φ shows the speed of adjustment. There is a long-run equilibrium if φ varies between 0 and -1 and is statistically significant. To ensure reliable findings, the diagnostic and stability tests are included shortly after the application of ARDLBT.

To assess causal relations between the model variables, this study applies the GC test [51]. The GC test is employed within the framework of the Vector Autoregressive (VAR) system to ascertain the causal linkage. Since the GC test is sensitive to the lag included, AIC is considered for selecting the optimal lag length. By proxing the model variables using X and Y notations, models for the GC test can be written as Eqs. (7) and (8), respectively.

wherein v₁ and v₂ signify the constant term. ϵ₁ and ϵ₂ are the error terms. π, ω, υ, and ϖ are parameters to be estimated. n represents the optimal lag length. The null hypothesis, H₀: ω₁=ω₂…ω₃=0, is evaluated against the alternative hypothesis, H₁: ω₁≠ω₂…ω₃≠0. The GC test relies on the Wald statistics in examining the significance of lagged variables [51].

Testing the order of integration is a crucial step before the application of ARDLBT. Thus, two types of stationarity tests are considered, the ADF and PP approaches. The outcomes of the ADF approach denote that all the model variables, i.e., CO₂, YPC, CRD, REU, and ENC, fail to reject the null hypothesis at the level. They are non-stationary at their level. Nonetheless, CO₂, YPC, CRD, REU, and ENC are stationary after the first difference is computed. Similarly, the results of the PP test demonstrate that CO₂, YPC, CRD, ENC, and REU are first-order stationary, 1(1). Since none of the variables are second-order stationary, I(2), ARDLBT is a proper method for CO₂ emissions modeling. Table 2 reports the combined findings of unit root tests, obtained from ADF and PP approaches.

Having determined the order of integration of the model variables, the next step is to assess the presence of cointegration. However, an essential preliminary step before proceeding with cointegration analysis is the identification of the optimal lag length. For this purpose, this study works with the AIC test in the model specification. Table 3 suggests that lag order 2 represents the maximum lag length.

Using the selected lag length, the next analysis is to examine the presence of cointegration. The findings of the Bounds test are documented in Table 4. The H0 is observed to be rejected given that the estimated F-statistic (18.11) surpasses the upper bounds (4.15). Thus, it can be inferred that the cointegration relationship between CO₂, YPC, YPC², CRD, ENC, and REU is strongly confirmed.

The presence of cointegration reveals that potential spurious regression is not evident. Thus, the dynamic short- and long-run estimates are meaningful to be interpreted. Table 5 displays the results of long-run parameters. YPC is negatively associated with CO_2, whereas YPC² is positively linked to CO₂, denoting the absence of the EKC hypothesis. The inverse U-shaped linkage between per capita GDP and CO₂ emissions is not validated. Instead, there is a U-shaped (ball-shaped) association. Economic growth initially leads to CO₂ reduction, but after a certain point, it positively influences emissions. The estimated ITP is US$1,879 per capita. Although the findings contradict the EKC framework, the U-shaped relationship between income and CO₂ is similar to earlier studies [52], [53]. It should be highlighted that the lack of evidence for the EKC hypothesis indicates that economic development cannot be utilized as a sole instrument for CO₂ reduction.

Total credit to the private non-financial sector is found to have a positive and significant effect on CO₂ at a 1% critical value. The estimated parameter of CRD is 0.077. This implies that a 1% increase in total credit to the private non-financial sector results in a 0.077% rise in CO2, indicating an inelastic relationship. This finding suggests that credits accessed by non-financial firms contribute to environmental degradation by increasing emissions.

Credit can directly and indirectly impact emissions. A positive link between credit and CO₂ indicates that the vast majority of financial credits accessed by firms are used for unsustainable business. Credits mainly contribute to air pollution through fossil fuel financing and energy-intensive industries such as mining extraction, transportation, cement, chemicals, and steel. As an emerging economy, it is difficult for Indonesia to decouple emissions from businesses that drive economic growth [39]. Another channel is that private credits induce CO₂ by financing unsustainable agriculture practices, particularly those involving land use change.

Since the positive impact of credit on CO₂ is evident, enhancing green financing is crucial for Indonesia. Neglecting the detrimental impact of credit may impair the endeavor to satisfy the principle of sustainable development, including the CO₂ reduction target. Thus, financial products related to green credit should be promoted. Sustainable finance policies are verified to have the capacity to drive the green transformation of heavily polluting firms [54]. Green financial credit, combined with disruptive low-carbon innovation, is confirmed to significantly foster carbon reduction [55].

A further novel result is that the percentage of primary energy consumption from renewable sources is found to have a negative influence on CO₂ emissions, as expected. This empirical evidence corroborates findings reported in prior investigations in the case of G-20 countries [56] and OECD members [57]. The estimated parameter of REU is -0.10604. Thus, a 1% hike in primary energy consumption from renewable sources leads to a 0.11% decrease in CO₂, demonstrating an inelastic relationship.

The negative association between CO₂ and clean energy gives an insight into the pivotal role of the Renewable Energy Transition (RET). Higher clean energy consumption corresponds to lower emissions produced. The bright side is that Indonesia has a massive potential for clean energy development, including solar PV, geothermal, wind power, bioenergy, and hydropower [58]. As mentioned in the National Energy Policy (NEP) 2014, Indonesia intends to have 23% of its energy mix supplied by clean sources by 2025 [59].

Regarding control variables, per capita total energy consumption is positively associated with CO_2, while, surprisingly, trade openness is negatively linked to CO₂. The damaging impact of energy consumption on the environment is verified, consistent with several earlier studies [60], [61]. This evidence emphasizes that the vast majority of energy generators in Indonesia are derived from fossil fuel sources. Next, the negative connection between trade openness and emissions suggests that export and import activities have the ability to support environmental sustainability by lowering emissions. This finding is consistent with previous works reported in Europe [62] and Indonesia [63].

The results of the short-run and the ECT parameters are displayed in Table 6. The short-run estimates denote that the EKC hypothesis is validated. The linkage between per capita GDP and CO₂ reveals the inverse U-shaped pattern in the short run. Another novel finding is that private credit to non-financial sectors positively affects CO₂. Therefore, it can be inferred that increased access to borrowing contributes to environmental degradation by raising CO₂ levels. This evidence emphasizes the crucial need for green credit products.

Other short-run estimates demonstrate that renewable energy holds a pivotal position in promoting sustainable development since it is negatively associated with emissions, consistent with the long-run estimates. Conversely, per capita total energy consumption has a detrimental impact on the environment, given that it is positively linked with CO₂, as predicted. These results imply that clean energy can be applied as a key instrument for pollution reduction. Thus, it can be stated that promoting RET is a crucial scheme for reducing the level of emissions.

The ECT parameter is confirmed to be negative, consistent with theoretical expectations. It is statistically significant at a 1% level. The estimated parameter of ECT is -0.801. This result suggests that short-run shocks that cause deviations are adjusted by around 80% within a year toward the long-run equilibrium. This evidence corroborates the evidence of cointegration as reported by the Bounds test.

This study includes diagnostic tests to ensure reliable findings derived from the ARDLBT. Table 7 jointly displays the outcomes of the diagnostic tests. Following the Breusch-Godfrey and Breusch-Pagan analyses, issues regarding serial correlation and heteroskedasticity are not evident. Instead, error terms are not serially correlated and are homoscedastic. Furthermore, the Ramsey RESET test signifies no clear signs of model misspecification. The JB test signifies that error terms exhibit a normal distribution. Therefore, these diagnostic results provide strong statistical support that the estimated ARDLBT model is robust and reliable for inference.

In addition to diagnostic tests, this study includes the stability parameter test by employing the cumulative sum (CUSUM) test of recursive residuals. The null hypothesis of parameter consistency is proposed. As shown in Figure 3, the cumulative sums (red plots) fluctuate within the critical lines at a 95% level. Thus, it can be stated that the ARDLBT (1,0,0,0,0,0) model is stable during the period of analysis. In other words, a structural break is not evident.

Figure 3.

cumulative sum test results

To check the robustness of the estimated parameters obtained from ARDLBT, this study employs the Fully Modified OLS (FMOLS). The FMOLS estimator is chosen given that it has the power to tackle serial correlation and endogeneity [64]. Furthermore, it is more relaxed in terms of the order of integration and nonstationary series. Table 8 displays the results of the FMOLS estimation. The computed coefficients from FMOLS exhibit consistency with the long-run estimates obtained from the ARDLBT procedure. There is a U-shaped pattern for the linkage between income and emissions, suggesting the absence of the EKC hypothesis. Other findings denote a positive connection between private credit, per capita energy consumption, and CO₂, as well as an adverse association between clean energy and CO₂. Hence, it can be inferred that the empirical findings in this study are robust and reliable.

The ARDLBT analyses do not imply the causal direction between the variables. Therefore, with the lag order set to one, this study performs the GC test, and the corresponding results are collectively presented in Table 9. This study focuses on the causal relationships related to CO₂. There is a bidirectional causality between CO₂ and YPC. In practical terms, this implies that variations in per capita income significantly influence the level of CO₂, as higher income levels are often associated with increased fossil fuel consumption, industrial activities, and shifts in consumption patterns that lead to greater emissions.

Another novel finding denotes the presence of a bidirectional causal nexus between CO₂ and CRD, as expected. The feedback relationship between emissions and total private credit to nonfinancial firms demonstrates that the past value of emissions impacts the amount of loans accessed by firms. This evidence is relevant since pollutions are associated with transactional, physical, and reputational risks.

Furthermore, the results of the GC test signify a unidirectional causal linkage moving from per capita energy consumption toward CO₂. This finding emphasizes that energy consumption is a significant driver of environmental deterioration by increasing emissions, corroborating the evidence obtained from the ARDLBT model. Higher per capita energy usage corresponds to a greater release of CO₂.

Last of all, there is unidirectional causality moving from primary energy consumption from renewable resources toward CO₂. This evidence implies that clean energy exerts a measurable influence in facilitating CO₂ reduction, whereas changes in CO₂ levels do not have a reciprocal effect on the utilization of clean energy. In this regard, advancing green energy infrastructure, in conjunction with promoting energy efficiency and implementing low-carbon technologies, constitutes an essential prerequisite for facilitating Indonesia’s transition toward a sustainable development trajectory.