This study utilizes annual time-series data for Vietnam from 1990 to 2023, collected from the World Development Indicators (WDI) database of the World Bank. Specifically, per capita CO₂ emissions are taken from the data code EN.GHG.CO₂.PC.CE.AR5; GDP per capita from NY.GDP.PCAP.CD; energy consumption per capita from EG.USE.PCAP.KG.OE; and the share of hydropower in electricity production from EG.ELC.HYRO.ZS. These are reliable data sources widely used in empirical studies on environmental economics and energy. No missing values were found during the study period; no interpolation or missing data processing was required. Although emissions are reported as CO₂ equivalents according to the AR5 methodology, the study still uses the term “CO₂ emissions” to ensure consistency with most previous studies.

Based on theoretical foundations and recent studies, the model includes four main variables: per capita CO₂ emissions, per capita GDP, energy consumption, and the share of hydropower in electricity production. Including both the overall energy consumption variable and the hydropower share variable in the same model aims to differentiate between the scale impact of energy demand across the entire economy and the structural impact of renewable energy sources. Given Vietnam’s continued heavy reliance on fossil fuels, the energy consumption variable reflects the extent of energy demand expansion, while the hydropower variable reflects the degree of structural shift in electricity generation towards cleaner sources, consistent with recent studies emphasizing the importance of energy structure separation [7][9].

All variables were transformed to natural logarithms to reduce variance, limit heteroskedasticity, and allow for elastic interpretation of regression coefficients. For the hydropower weight variable, a logarithmic transformation was appropriate because all values were positive during the study period; it also stabilized the data series and improved the interpretability of the estimated coefficients. However, the coefficient of the hydropower variable should be understood as the marginal impact of changes in the electricity production structure, holding overall energy consumption constant. Table 1 provides a detailed description of the variables used in the study.

Table 1.Description of research variables.

Source: Author’s compilation.

The selection of variables in this study is based not only on theoretical foundations but also reflects the practical characteristics of the Vietnamese economy, where energy consumption remains significantly dependent on traditional sources. At the same time, hydropower plays a crucial role in the electricity production structure. This approach allows simultaneous assessment of the impacts of economic growth, energy demand, and the energy transition on CO₂ emissions in both the short- and long-term.

Based on the theoretical framework linking economic growth, energy consumption, and environmental emissions, a research model was developed to assess the impacts of GDP, energy consumption, and hydropower on CO₂ emissions in Vietnam. When the variables are transformed into natural logarithms, the long-term equation can be expressed as a log-linear equation as follows:

In this case, the coefficients β i reflect the long-term elasticity of CO₂ emissions with respect to the explanatory variables. However, since time series data are often non-stationary, directly estimating the above equation can lead to spurious regression. To overcome this problem and simultaneously analyze short-term and long-term dynamics, the study applies the ARDL model proposed by [11]. The optimal lag structure of the ARDL model was determined using the Akaike Information Criterion (AIC). Given the relatively small sample size, the maximum lag length was restricted to two to avoid overparameterization and preserve degrees of freedom. At the same time, this method is particularly suitable for small samples and is widely used in recent studies on energy and the environment [7]. The general form of the ARDL (p, q₁, q₂, q₃) model in the study can be rewritten as an unconstrained error correction model (UECM) as follows:

The coefficients of the first-differenced variables capture the short-run dynamics among the variables, while the lagged level variables are used to examine the existence of a long-run equilibrium relationship within the ARDL framework. However, the long-run effects are interpreted based on the normalized long-run coefficients derived from the estimated ARDL model rather than directly from the lagged level terms in the UECM specification [11]. The existence of cointegration among the variables is evaluated using the Bounds testing approach, which assumes no long-run relationship between the variables.

When a long-term relationship exists, the ARDL model can be converted to an Error Correction Model (ECM), allowing for the assessment of the system’s rate of adjustment to long-term equilibrium after short-term shocks. The general form of the ECM model is represented as follows:

E C T t − 1 is the correction error derived from the long-term equation, and the expected coefficient ϕ is negative and statistically significant, reflecting the rate of adjustment to equilibrium. A larger absolute value of this coefficient indicates a faster rate of adjustment, which is particularly important in assessing the long-term stability of the economic-environmental system [8].

Before estimating the ARDL model, the study conducted unit root tests to determine the degree of integration of the variables. Specifically, two common tests, the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP), were used to test for stationarity of the data series. Combining these two tests increases the reliability of the results, especially for time-series data that may be affected by autocorrelation and heteroskedasticity [12]. A necessary condition for applying the ARDL model is that the variables are only integrated at degree I(0) or I(1), and no variable is integrated at degree I (2) [11].

After determining the degree of integration, the Bounds test is performed to assess the presence of a cointegrating relationship between the variables. This test is based on the F-statistic and is compared with the critical values for the case where the variables are I(0) or I(1). If the F-statistic exceeds the upper threshold I(1), the hypothesis that there is no long-term relationship is rejected. Conversely, if the F-value is less than the lower threshold I(0), there is no evidence of cointegration; in the case between the two thresholds, the result is considered indeterminate [11]. This is one of the outstanding advantages of the ARDL method compared to traditional cointegration methods.

When confirming the existence of a long-term relationship, the Error Correction Model (ECM) is used to analyze short-term dynamics and the rate of adjustment to equilibrium. The coefficient of the correction error is expected to be negative and statistically significant, reflecting the system’s ability to return to equilibrium after short-term shocks [13].

To strengthen the reliability of the ARDL model estimates, this study uses two additional stability testing methods: Fully Modified Ordinary Least Squares (FMOLS) and Dynamic Ordinary Least Squares (DOLS). Combining these methods enables the assessment of the consistency of long-term cointegration among CO₂ emissions, energy consumption, economic growth, and hydropower. In time-series studies, especially with relatively small sample sizes, the use of supplementary estimation methods to confirm the stability of long-run coefficients is an important practice to minimize the risk that conclusions are influenced by the specific characteristics of each estimation technique [14][15].

The combination of FMOLS and DOLS in this study is particularly important. While ARDL provides a clear distinction between short- and long-term effects through error-correction mechanisms, FMOLS and DOLS validate the stability of long-term cointegration coefficients using different correction strategies. If the results show consistency in the sign and statistical trend of the effect across the three methods, it will strongly reinforce the reliability of the research conclusions. This approach has been widely applied in recent studies on the relationships among energy consumption, economic growth, and carbon emissions to strengthen the persuasiveness of empirical evidence.

To ensure the model’s fit, a series of diagnostic tests was performed. First, the Breusch-Godfrey test was used to detect autocorrelation in the residuals, and the Breusch-Pagan-Godfrey test was applied to test for heteroskedasticity. In addition, the Jarque-Bera test was used to assess the normality of the residuals, a crucial assumption in regression models. Furthermore, the Ramsey RESET test was performed to detect model misfits, thereby ensuring that the model was correctly specified [16].

The model’s stability is tested using the CUSUM and CUSUMSQ tests, which assess the stability of the estimated coefficients over time. If the test curves fall within the confidence interval, the model is considered stable. In addition, the Granger causality test is used to determine the direction of interaction among the model’s variables, thereby providing further evidence of the dynamic relationships among economic growth, energy consumption, hydropower, and CO₂ emissions [17].

Before proceeding with ARDL model estimation, the study performed unit root tests to determine the integration order of the variables. Two common tests, ADF and PP, were used to ensure the consistency of the results. Table 3 presents the results of the unit root tests for the model’s variables.

Table 3.Unit root test results (ADF and PP).

***: statistically significant at the 1% level; ^NS: non-statistically significant; Source: Author’s calculation results.

The unit root test results from both the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests indicate that all variables are non-stationary at their levels but become stationary after first differencing, implying that they are integrated of order one, I(1). Although the PP test provides weak evidence of stationarity for certain specifications of the GDP variable, the overall results across model specifications and testing approaches consistently support treating LNGDP as an I(1) variable. The use of both ADF and PP tests enhances the robustness of the stationarity assessment because the PP test is more flexible in correcting for serial correlation and heteroskedasticity in the error term [12]. Since none of the variables is integrated of order two, I(2), the ARDL bounds testing approach remains appropriate for the analysis, consistent with the framework proposed Pesaran [11]. One important advantage of the ARDL methodology is its ability to accommodate variables integrated of order I(0) and I(1) within the same empirical framework.

After confirming that none of the variables is integrated of order two, I(2), the study proceeded to examine the existence of a long-run relationship using the ARDL Bounds testing approach. The Bounds test results indicate that the calculated F-statistic (2.886) exceeds the lower critical bound but remains below the upper bound at the conventional significance levels. Therefore, the evidence of cointegration is not conclusive based solely on the Bounds test results. However, the error-correction term estimated in the ARDL-ECM framework is negative and statistically significant, suggesting a stable long-run adjustment mechanism among CO₂ emissions, energy consumption, economic growth, and hydropower generation in Vietnam. Accordingly, the long-run relationship identified in the model should be interpreted with caution, particularly given the relatively small sample size and the borderline nature of the Bounds test results (Table 4).

Table 4.Bounds test results.

Source: Author’s calculation results.

In addition, studies using the ARDL method in Vietnam also record the existence of a long-term relationship between CO₂ emissions and macroeconomic variables, thereby further strengthening the robustness of the results in this study. Given the statistically significant and negative error-correction term, the ECM results (Table 5) are interpreted as indicative of a stable adjustment mechanism, although the long-run relationship should be treated cautiously due to the inconclusive Bounds test.

Table 5. ECM model results.

Source: Author’s calculation results.

The coefficient on the error correction term, CointEq (−1), is negative and statistically significant at the 1% level, suggesting the presence of a stable, though gradual, adjustment process toward equilibrium following short-run disturbances. Specifically, the estimated coefficient of −0.083 implies that approximately 8.3% of short-run disequilibrium is corrected in each period, indicating a relatively slow adjustment toward long-run equilibrium. In the short run, energy consumption exerts a positive and statistically significant effect on CO₂ emissions, indicating that higher aggregate energy demand directly intensifies environmental pressure in Vietnam. By contrast, hydropower’s share in electricity generation does not exhibit a statistically significant short-run effect on CO₂ emissions, suggesting that its environmental contribution is not statistically robust within the estimated period. Economic growth displays a negative, statistically significant short-run coefficient, suggesting that short-term increases in GDP may be associated with temporary improvements in energy efficiency, technological progress, or structural adjustment. The results indicate that aggregate energy consumption remains the dominant short-run determinant of CO₂ emissions in Vietnam.

The study estimates the long-term coefficients from the ARDL model (Table 6).

Table 6.Conditional error correction regression results.

***: statistically significant at the 1% level; Source: Author’s calculation results.

Based on the AIC criterion (−3.7748), the ARDL(1, 1, 1, 1) specification was identified as the optimal model for the analysis. The estimation results indicate that the ARDL model provides a satisfactory fit to the data, with an R² of 0.7664 and an adjusted R² of 0.7331. This suggests that approximately 73% - 77% of the variation in CO₂ emissions is explained by the variables included in the model. In addition, the F-statistic is significant at the 1% level, confirming the model’s overall explanatory power. The Durbin-Watson statistic of 1.8867 further suggests the absence of serious autocorrelation problems, supporting the reliability of the estimated ARDL specification.

In the short run, this finding suggests that energy consumption has a positive, statistically significant impact on CO₂ emissions. Specifically, the coefficient for ΔLNENERGY is 0.6066 (p = 0.0006), indicating that a 1% increase in energy consumption is associated with an approximate 0.61% increase in CO₂ emissions. This finding confirms that energy consumption remains the primary driver of environmental degradation in Vietnam and reflects the economy’s continued dependence on aggregate energy consumption-intensive energy sources. The result is consistent with previous empirical studies. For example, Nathaniel et al. [18] found that energy consumption plays a dominant mediating role between economic growth and environmental degradation, while Dogan and Inglesi-Lotz [7] also reported that increasing energy demand significantly raises CO₂ emissions in emerging economies. Similarly, Ali et al. [19] emphasized that economies with carbon-intensive energy structures tend to experience stronger environmental pressures from rising energy use.

Hydropower generation does not exhibit a statistically significant short-run effect on CO₂ emissions. Although the coefficient for ΔLNHYDRO is positive, its insignificance suggests that hydropower’s contribution to emission mitigation remained limited during the study period. This finding may reflect the relatively modest share of hydropower within Vietnam’s overall energy structure or the continued dominance of fossil-fuel-based energy consumption. The result differs from studies such as Dong et al. [20] and Balsalobre-Lorente et al. [9], which found that renewable energy contributes significantly to emission reduction. However, the present findings suggest that the environmental benefits of renewable energy may depend not only on its existence but also on its scale and integration within the national energy mix.

Economic growth exhibits a negative and statistically significant short-run relationship with CO₂ emissions, with the coefficient on ΔLNGDP estimated at -0.1876 (p = 0.0025). This result suggests that short-term increases in GDP may be associated with temporary improvements in production efficiency, technological upgrading, and gradual structural adjustment toward less emission-intensive economic activities. However, based on the normalized long-run estimates, economic growth does not exert a statistically significant long-run effect on CO₂ emissions within the estimated ARDL framework. This finding implies that while short-run economic expansion may coincide with transitional efficiency gains, it does not appear to systematically determine Vietnam’s long-term emissions trajectory.

This result is consistent with previous empirical evidence emphasizing the context-dependent nature of the growth–environment nexus. For example, Acheampong [21] argued that the environmental consequences of economic growth depend heavily on national energy structures, technological capacity, and institutional quality. Similarly, Bekun et al. [22] highlighted that energy consumption often serves as the principal transmission channel through which economic growth affects environmental outcomes. Nathaniel et al. [18] also found that the relationship between economic growth and environmental degradation is frequently mediated by energy-use intensity and the composition of the energy mix.

The empirical findings suggest that aggregate energy consumption plays a more substantial role than economic growth or hydropower’s share in electricity generation in explaining CO₂ emissions in Vietnam. The results indicate that environmental pressure is driven more strongly by the structure and intensity of energy use than by economic expansion alone. Therefore, policies aimed at reducing carbon emissions should prioritize improvements in energy efficiency, accelerated diversification toward cleaner energy sources, and broader structural transformation of the national energy system.

Table 7 presents the long-run estimation results obtained from the ARDL, FMOLS, and DOLS approaches. The comparison across estimation techniques provides additional robustness for evaluating the long-term relationship between economic growth, energy consumption, hydropower generation, and CO₂ emissions in Vietnam.

Table 7. Long-run estimation results: ARDL, FMOLS, and DOLS.

Note: Values in parentheses are t-statistics (ARDL) and z-statistics (FMOLS/DOLS); Source: Author’s calculation results.

The results consistently indicate that energy consumption is the most important long-run determinant of CO₂ emissions. In the ARDL model, the coefficient on LNENERGY is positive and statistically significant at the 5% level, and the FMOLS and DOLS estimators also report positive, highly significant coefficients. Specifically, the FMOLS and DOLS estimates suggest that a 1% increase in energy consumption increases CO₂ emissions by approximately 1.54% and 1.52%, respectively. The close similarity between FMOLS and DOLS coefficients demonstrates the robustness and stability of the estimated long-run relationship. These findings confirm that Vietnam’s energy structure remains heavily dependent on fossil-fuel-intensive sources, making energy consumption the principal driver of environmental degradation. This result is consistent with previous studies emphasizing the dominant role of energy use in increasing carbon emissions in developing economies [7][18].

In contrast, the long-run effect of hydropower generation remains statistically insignificant across all estimation methods. Although the ARDL model reports a negative coefficient for LNHYDRO, it is not statistically significant, whereas both FMOLS and DOLS produce coefficients close to zero and are also statistically insignificant. This consistency across estimators suggests that hydropower generation has not yet produced a sufficiently strong or stable long-run effect on reducing CO₂ emissions in Vietnam. One possible explanation is that, despite its importance as a renewable energy source, hydropower still accounts for a relatively limited share of the overall energy mix compared with fossil fuels. In addition, the environmental benefits of hydropower may be constrained by seasonal dependence, production limitations, and increasing national energy demand. Therefore, the expansion of hydropower alone appears insufficient to offset the environmental pressure generated by rapid industrialization and growing energy consumption.

The results for economic growth reveal mixed evidence across estimation approaches. In the ARDL model, the coefficient on LNGDP is positive but statistically insignificant, suggesting that economic growth does not have a stable long-run effect on CO₂ emissions. However, both FMOLS and DOLS estimates yield negative, statistically significant coefficients for LNGDP. This finding suggests that, in the long-run equilibrium relationship, economic growth in Vietnam may gradually become less emission-intensive, possibly due to improvements in energy efficiency, technological progress, or structural transformation toward less carbon-intensive sectors. The divergence between ARDL and the two cointegration estimators may reflect ARDL’s greater sensitivity to dynamic adjustments and small-sample properties, whereas FMOLS and DOLS are designed to estimate the long-run equilibrium relationship more directly while correcting for endogeneity and serial correlation. Overall, the mixed evidence suggests that the relationship between economic growth and environmental quality in Vietnam remains conditional on structural and energy-related factors rather than economic expansion alone.

The robustness analysis using FMOLS and DOLS estimators further strengthens the reliability of the empirical findings. Although some coefficient magnitudes differ across estimation techniques, the overall conclusions remain broadly consistent, particularly regarding the dominant role of energy consumption in driving CO₂ emissions. The convergence of the FMOLS and DOLS estimates, especially for LNENERGY, provides strong evidence that the long-run relationship identified in the study is not merely model-specific but reflects a stable empirical pattern.

To verify the reliability and stability of the estimated ARDL model, several post-estimation diagnostic tests were conducted. The results indicate that the model satisfies the major assumptions of classical linear regression and is therefore suitable for interpretation and policy analysis.

The Breusch-Godfrey Serial Correlation LM test confirms the absence of serial correlation in the residuals. The probability values of both the F-statistic and Obs*R-squared statistic are substantially higher than conventional significance levels, indicating that the null hypothesis of no serial correlation cannot be rejected. This suggests that the dynamic specification of the ARDL(1, 1, 1, 1) model is appropriately defined and that the lag structure successfully captures the temporal dependence among variables (Table 8).

Table 8.Results of model diagnostic validation.

Source: Author’s calculation results.

The Breusch-Pagan-Godfrey heteroskedasticity test indicates that the residuals remain homoskedastic. Since the probability values exceed the 5% significance level, there is insufficient evidence to reject the null hypothesis of constant variance. This finding implies that the estimated coefficients are efficient and that the standard errors are reliable for statistical inference.

The Ramsey RESET test indicates that the model is not misspecified for functional form. The insignificant RESET statistics indicate that no major omitted nonlinear relationships exist in the estimated equation. Therefore, the selected ARDL specification appears to provide an adequate representation of the relationship among CO₂ emissions, economic growth, energy consumption, and hydropower generation in Vietnam.

The diagnostic test results indicate that the estimated ARDL model satisfies the major assumptions of classical linear regression. The Breusch-Godfrey LM test confirms the absence of serial correlation, while the Breusch-Pagan-Godfrey test suggests that the residuals are homoskedastic. In addition, the Jarque-Bera statistic indicates that the residuals are normally distributed. The Ramsey RESET test further confirms that the model is not subject to functional form misspecification. Overall, these results support the reliability and stability of the estimated ARDL model.

The CUSUM test results show that the standardized cumulative residual curve consistently remains within the 5% significance limit throughout the entire study period. This indicates that the ARDL model parameters are highly stable and do not exhibit significant structural breaks over time. Although the CUSUM curve fluctuated slightly in some periods, particularly around 2005-2010 and 2012-2015, it remained within the acceptable test range. This result confirms that the relationship between CO₂ emissions, energy consumption, economic growth, and hydropower is not affected by short-term fluctuations or economic shocks during the study period (see Figure 1).

Source: Author’s calculation results.

Figure 1. CUSUM and CUSUMSQUARE test result.

The stability of the estimated ARDL model was further examined using the CUSUM and CUSUMSQ tests. The results indicate that both the CUSUM and CUSUM of Squares statistics remain within the 5% critical bounds throughout the sample period. This confirms the structural stability of the estimated coefficients and suggests that the model does not suffer from significant parameter instability or structural breaks. Therefore, the estimated ARDL model can be considered stable and reliable for empirical interpretation (Table 9).

Table 9.Results of the granger causality test.

Source: Author’s calculation results.

These results imply that not only does economic growth affect the environment, but environmental factors can also have a reciprocal impact on growth. In particular, the two-way relationship between hydropower and CO₂ emissions is a significant finding, demonstrating the complex interaction between energy policy and environmental quality.

Empirical results show that energy consumption remains the primary factor driving increased CO₂ emissions, while hydropower plays a crucial role in reducing emissions, especially in the short term. These findings are not only consistent with environmental economics theory but also provide important empirical evidence for energy policy planning in Vietnam.