Aligning Energy and Macroeconomic Policies Toward Carbon Dioxide Emissions Reduction for Sustainable Development Planning: An Error Correction Model Approach

The imperative for climate change mitigation, as enshrined in the Sustainable Development Goal of Climate Action, has put carbon dioxide (CO₂) emissions at the forefront of the global policy agenda. Increasing greenhouse gas concentrations pose a significant threat to environmental sustainability and socio-economic stability, thus demanding a paradigm shift in development planning [1, 2]. As the country with the largest economy in Southeast Asia and significant natural capital, Indonesia occupies a central position in this global effort. Indonesia's commitment to achieve Net Zero Emissions by 2060, with a temporary emission reduction target of 29% (unconditional) to 41% (conditional) by 2030, requires a deep understanding of the complex interplay between energy policy, macroeconomic dynamics, and environmental impacts [3-5].

Academic discourse on the determinants of CO₂ emissions is extensive, with a focus largely centred on the Environmental Kuznets Curve (EKC) hypothesis, which posits an inverse U-shaped relationship between economic growth and environmental degradation [6]. A substantial body of literature has explored this relationship, examining the roles of energy consumption, trade, and investment. For example, various studies consistently confirm that the transition to renewable energy sources—such as solar, hydro, and geothermal—is fundamental to decoupling economic growth from emissions [5, 7]. At the same time, the impact of macroeconomic variables such as trade openness and Foreign Direct Investment (FDI) presents a more nuanced picture. While some experts argue that trade and FDI can facilitate cleaner technology transfer, "the halo effect", others warn that developing countries may become "pollution havens" by attracting carbon-intensive industries [1, 8, 9].

Although a considerable amount of research exists, critical gaps remain in the literature, particularly in the Indonesian context. Most previous studies have employed static methods, which often fail to capture the complex and time-sensitive dynamics inherent in macroeconomic systems. These studies tend to focus on long-term relationships without adequately distinguishing them from short-term adjustment pathways. As a result, a crucial question remains unanswered: When there are policy shocks—such as new investments in renewable energy or changes in trade policy—how do CO₂ emissions and related economic variables react in the short term, and how quickly do they reintegrate into their long-term equilibrium? This temporal dimension is critical for policymakers who must navigate urgent economic pressures while steering countries toward long-term sustainability goals. The absence of a model that simultaneously analyzes long-term equilibrium, short-term dynamics, and adjustment velocity is a significant gap that this study aims to fill.

This paper introduces a significant methodological novelty to address this gap by using a dynamic Error Correction Model (ECM). The ECM framework is uniquely suited for this analysis because it allows differentiation between short-term effects and long-term equilibrium relationships [10]. By integrating the term error correction, it not only estimates the impact of renewable energy consumption, economic growth, trade openness, and FDI on CO₂ emissions but, more importantly, measures the speed at which the system adjusts to correct short-term deviations and restore its long-term balance. This approach provides a more robust and policy-relevant understanding than conventional static models, while also offering insights into the resilience and responsiveness of economic, energy, and environmental relationships.

Therefore, the primary objective of this study is to analyse the short-term and long-term effects of renewable energy consumption, economic growth, trade openness, and FDI on CO₂ emissions in Indonesia for the period 2000-2023 using a dynamic ECM. Thus, this study aims to provide empirical evidence to inform the alignment of energy and macroeconomic policies, ensuring that these two policies reinforce each other in achieving sustainable development and the country's climate commitments. The findings of this study aim to provide policymakers with actionable insights for designing effective and sustainable interventions in both the short and long term.

The rest of this paper is arranged as follows. Section 2 presents a detailed review of the relevant literature. Section 3 outlines the data sources and specifications of the ECM. Section 4 presents and discusses empirical results, including diagnostic tests and robustness tests. Finally, Section 5 closes the paper with key policy implications and suggestions for future research.

To develop a dynamic model of CO₂ Emissions to achieve sustainable development, the ECM approach is used. The advantage of this ECM model is that it can analyze the dynamics of adjustments between variables that affect CO₂ emissions. The data used are annual statistics on the state of Indonesia for the period 2000-2023, which include CO₂ emissions, renewable energy consumption, economic growth, trade openness, and FDI, presented in detail in Table 1.

Table 1. Data and data sources

The dependent variables in this study are LCO₂ emissions, while the independent variables are renewable energy consumption, economic growth, trade openness, and LFDI.

a. Dynamic model approach

The dynamic model used in this study enables the interpretation of the long-term behaviour of economic variables, as economic theory generally explains the long-term relationships between economic variables [15, 16]. The results of the economic model estimation can be used as an analytical instrument for testing economic theory and estimating future values. In certain economies, reactions to specific actions often occur gradually over time [17].

The variation of dependent variables is determined not only by the variation of explanatory variables in the same period, but also by their variations in the past and in the future [15]. In this case, economic agents face an imbalance because the desired phenomenon is not necessarily the same as what happens and what is needed to adjust. Therefore, a model that is in tune with reality is dynamic. Since the reaction resulting from a rare action is instantaneous, the dynamic model then involves a lag variable in its analysis [10, 16].

b. ECM

The ECM model can encompass more variables in analysing both short-term and long-term economic phenomena, examine the consistency of empirical models with economic theory, and identify solutions to problems associated with nonstationary time series variables and spurious regressions in econometrics [18]. The ECM model is used to achieve equilibrium by minimising imbalance costs and adjustment costs [10, 15, 19].

c. ECM model specifications

$\mathrm{D Y}_t=\beta_0+\beta_1 \mathrm{D X}_t+\beta_2 \mathrm{B X}_t+\beta_3 \mathrm{B}\left(\mathrm{X}_t-\mathrm{Y}_t\right)+\varepsilon_t$    (1)

where, $\mathrm{DX}_t=\mathrm{X}_t-\mathrm{X}_{t-1}, \mathrm{BX}_t=\mathrm{X}_{t-1}$, t = time trend and $\mathrm{X}_t$ is the observed variable in period t, and B is the backward lag operator.

Based on the basic ECM equation (Eq. (1)), the equation of the CO₂ emission model can be written as follows:

$\begin{aligned} & \text { DLCO}_{2 t}={\beta_0}+\beta_1 \text { DLREN}_t+\beta_2 \text { DLGrowth}_t +\beta_3 \text { DLTrade}_t+\beta_4 \text { DLFDI}_t +\beta_5 \text { BLREN}_t+\beta_6 \text { BLGrowth}_t \\ & +\beta_7 \text { BLTrade}_t+\beta_8 \text { BLFDI}_t +\beta_9 B\left(\left(\text {LREN}_t+\text { LGrowth}_t\right.\right. \left.\left.\left.+ \text { LTrade}_t+\text { LFDI}_t\right)- \text { LCO}_{2 t}\right)\right) +\varepsilon_t\end{aligned}$    (2)

where,

$\beta_1 \ldots . \beta_9$ = Coefficient of the ECM equation,

LCO₂ = CO₂ emissions,

LREN = Renewable energy consumption,

LGrowth = Economic growth,

LTrade = Trading openness,

LFDI = Foreign Direct Investment.

From the above equation, it can be seen that economic actors made a marginal adjustment to the rate of LCO₂ emissions from BLCO₂ (LCO₂ in the t-1 period) in response to changes in independent variable components in the previous period. Coefficient $\beta_1 . . \beta_4$ can be used to see short-term effects, while other coefficients can describe long-term effects. Coefficient $\beta_9$ is $\mathrm{ECT}_{t-1}$ to see the speed of adjustment of economic agents to changes in economic policies. ECT is a lagged residual from the cointegrating relation. If the coefficient $\beta_9$ is statistically significant, sustainable development is achieved.

To obtain an equation that represents a long-term equilibrium relationship between variables, a cointegration approach is necessary, which involves a stationarity test consisting of a unit root test and a degree of integration [16, 20]. The cointegration approach can also be viewed as a test of economic theory and as a crucial component in the formulation and estimation of dynamic models [21].

The ECM can be derived directly from the form of Autoregressive Distributed Lag (ARDL) [2]. The form ARDL(p,q) in the level can be written as follows:

$\mathrm{Y}_t=\alpha_0+\sum_{i=1}^p \emptyset_i Y_{t-i}+\sum_{j=0}^q \beta_{j_i}^{\prime} X_{t-j}+\varepsilon_t$    (3)

By transforming to the first differential form and adding a long-term equilibrium component, the above model can be rewritten as a form of ECM:

$\begin{gathered}\Delta \mathrm{Y}_t=\gamma_0+\sum_{i=1}^{p-1} \gamma_i \Delta Y_{t-i}+\sum_{j=0}^{q-1} \delta_j^{\prime} \Delta X_{t-j}+\lambda \mathrm{ECT}_{t-1} +\mu_t\end{gathered}$    (4)

The error correction term (ECT) represents the deviation from the long-term equilibrium in the previous period, $\mathrm{ECT}_{t-1}$. The λ coefficient is expected to be negative and statistically significant, indicating the presence of an error correction mechanism that drives the system back to equilibrium. Thus, ECM allows for a clear separation between short-term influences and long-term relationships.

d. Unit root test

This test is considered a test of data stationarity. It is designed to determine whether a particular coefficient of an autoregressive model estimate has a value greater than one or not (in absolute terms). If the coefficient has a value of one or less, then the data is not stationary. The first step to be taken in this test is to assess the autoregressive model of each variable that will be used in the study as a test [15, 19]:

$\mathrm{DX}_t=a_0+a_1 \mathrm{BX}_t+\sum_{i=1}^k b_i \mathrm{~B}_i \mathrm{DX}_{\mathrm{t}}$    (5)

$\mathrm{DX}_t=c_0+c_1 T+c_2 \mathrm{BX}_t+\sum_{i=1}^k d_i \mathrm{~B}_i \mathrm{DX}_{\mathrm{t}}$    (6)

where, $\mathrm{DX}_t=\mathrm{X}_t-\mathrm{X}_{t-1}, \mathrm{BX}_t=\mathrm{X}_{t-1}, \mathrm{t}=$ time trend and $\mathrm{X}_t$ is the variable observed in period t, and B is a backward lag operator.

The second step is to calculate the statistical values of the Dickey-Fuller (DF) and Augmented Dickey-Fuller (ADF) tests. The values of DF and ADF are used to test the hypothesis that a1 = 0 and c2 = 0, indicated by the value of t in the coefficient $\mathrm{BX}_t$ from the equation above. The optimal lag is determined by the AIC/SBIC value in the STATA program [5].

e. Integration degree test

If the data observed in the unit root test is not stationary, the next step is to perform the integration degree test. This test is performed to determine the degree or order of differentiation at which the observed data will be stationary [10]. The definition of data integration means that X time series data is integrated to degree d. The data needs to be differentiated up to d times to become stationary data or I(0) [15, 16, 22].

The first step in the integration test level is to estimate the autoregressive model by Ordinary Least Squares (OLS):

$D^2 \mathrm{X}_t=e_0+e_1 \mathrm{BDX}_t+\sum_{i=1}^k f_i \mathrm{~B}_i D^2 \mathrm{X}_{\mathrm{t}}$    (7)

$D^2 \mathrm{X}_t=g_0+g_1 T+g_2 \mathrm{BDX}_t+\sum_{i=1}^k h_i \mathrm{~B}_i D^2 \mathrm{X}_t$    (8)

where, $\mathrm{D}^2 \mathrm{X}_{\mathrm{t}}=\mathrm{DX}_t-\mathrm{DX}_{t-1}, \mathrm{BDX}_t=\mathrm{DX}_{t-1}$.

The values of DF and ADF in this test can be determined by examining the statistical value t in the regression coefficient of the above equation. If e₁ and g₂ are equal to one, then variable X is stationary at the first differential or integrated by one degree. If e₁ and g₂ are not different from zero, it means that the variable is not stationary at the first differential. In this case, the integration test level needs to be continued until stationary conditions are obtained $\mathrm{BDX}_t$.

f. Cointegration test

The cointegration test is a continuation of the unit root and the degree of integration test. The method used is the Engle-Granger method. The cointegration test is designed to determine whether the residual regression is stationary [10, 15, 22]. To perform the cointegration test, it must be ensured that the observed variables have the same level of integration. If one or more variables have different degrees of integration, e.g., X = I(1) and Y = I(2), then they cannot be cointegrated.

g. Diagnostic tests

In addition to the above tests, diagnostic tests are also required to determine if the regression lines obtained can be effectively used to predict dependent variables. The tests carried out were normality tests, linearity tests, heteroscedasticity tests, and autocorrelation tests [10].

The results of the Jarque–Bera normality test indicate that the residual p-value is 0.173, so the null hypothesis that the residuals are normally distributed is not rejected. This indicates that the data support the assumption of residual normality. The results of the linearity tests, using the Ramsey RESET test, showed that the p-value was 0.332, indicating that the null hypothesis of adequate model specification was not rejected. In heteroscedasticity tests, we test whether the residual variance is constant using the Breusch–Pagan test. The test produced a p-value of 0.509, so the hypothesis of zero homoscedasticity was not rejected. This indicates that there is no significant heteroscedasticity in the final model. The results of the multicollinearity test using the Variance Inflation Factor (VIF) indicated a relatively low VIF value, well below the specified threshold, suggesting no multicollinearity.

This study aims to analyse the short-term and long-term dynamic relationships between renewable energy consumption, economic growth, trade openness, FDI, and CO₂ emissions in Indonesia from 2000 to 2023. Using the ECM, this study provides new empirical evidence regarding the dynamics and speed of adjustment in Indonesia's economic and environmental systems.

The results of the analysis indicate that, in the short term, renewable energy and trade openness have a mitigating effect on emissions. The positive impact of trade in the short term suggests that the benefits of faster technology transfer through imports are evident. In the long term, renewable energy consumption has proven to be the most significant factor in reducing CO₂ emissions. Conversely, economic growth has been shown to increase CO₂ emissions significantly. The variable of FDI can increase CO₂ emissions in the short and long term, which confirms that Indonesia is still in a carbon-intensive development phase and supports the pollution haven hypothesis.

The error correction mechanism is the most crucial finding of this study, namely, the existence of a high-speed and overshooting error correction mechanism. This indicates that the economic and environmental systems in Indonesia are very responsive to shocks.

The results of the study have important policy implications for the Indonesian government in designing an effective sustainable development strategy, namely, (1) prioritising the acceleration of renewable energy. Given its substantial impact in reducing emissions, the government must place the energy transition as a top priority. The necessary policies include simplifying regulations, offering attractive fiscal incentives for renewable energy investors, and developing network infrastructure to support the intermittent integration of renewable energy sources. (2) FDI is sought to go towards the green sector. The results show that FDI contributes to increased emissions, serving as a strong signal for governments to reform their investment policies. It is necessary to implement strict green investment criteria, where investment incentives should be associated with environmental performance. Governments can create green investments to attract FDI to sectors that support low-carbon economies, such as electric vehicle manufacturing, energy efficiency, and the recycling industry. (3) Encourage green economic growth. The positive relationship between economic growth and emissions highlights the need for a paradigm shift from conventional growth to sustainable or green growth. Policies should be geared towards promoting clean technology innovation, supporting the circular economy, and implementing policy instruments such as carbon taxes or cap-and-trade to internalize the environmental costs of economic activities. And (4) prudent policy calibration. The high speed of system adjustment implies that policies must be designed and implemented with great care. Drastic policy changes can trigger unwanted volatility. A more gradual approach, accompanied by a strong monitoring and evaluation mechanism, is more advisable to ensure stability while still moving towards long-term goals.