For data collection and classification, the WDI (World Development Indicators) database was employed in this study. However, due to objective factors, a significant number of countries had missing data for variables. Therefore, a thorough trade-off between the number of countries and the size of the dataset was made to guarantee a balanced panel data and a long enough research period. After the extended period of adjustments and attempts, the focus of the study was narrowed down to the G20 nations from 1995 to 2015, during which energy transformation, freight transport innovation, and decarbonized transportation underwent rapid development. The decision to select this time frame was based on careful consideration of the research objectives. The panel data set was chosen for analysis due to the advantages of time-series and cross-sectional data, which allow for the utilization of more information in examining the dynamic relationships of the research.

After conducting initial research, a pool of 17 indicators were identified as potential variables. However, due to incomplete sequences for some of the indicators, a further screening process was conducted to ensure the balance of the panel data.

The Panel Vector Autoregression (PVAR) model was first introduced by Holtz-Eakin et al. (1988). The model could be characterized by elaborate structure and capacity to capture diverse aspects of the data by modeling research variables as endogenous variables while treating each variable as a function of the lag value of all variables in the system. (Holtz-Eakin et al. 1988). Therefore, to examine the dynamic relationship from freight transport demand and supply factors to the context of decarbonized transportation, the PVAR model would be used to investigate and elucidate the research. Moreover, the PVAR presentation format provides the intuitive representation of the interactions between variables in the transport system.

From the theoretical perspective, the PVAR model utilized for the purpose of analysis could be characterized as follows: Y i t = C i + ∑ p = 1 m A p Y i , t − p + Ξ i t

As t represents the t th period ( t = 1 , 2 , . . . , T i ), i indicates the i th nation ( i = 1 , 2 , . . . , N ) and the lag length would be expressed by p = 1 , 2 , . . . , m . Y i t = Y 1 i t Y 2 i t ⋮ Y 6 i t , Y i , t − 1 = Y 1 i , t − 1 Y 2 i , t − 1 ⋮ Y 6 i , t − 1 , … , Y i , t − p = Y 1 i , t − p Y 2 i , t − p ⋮ Y 6 i , t − p Y i t would be represented by a column vector of dimensions 6 × 1 , incorporating six proxy variables: RailTrGood, AirTrFre, EleProRe, AltNuE, ReEneCon and CO2EmTra. The lag term of Y i t , denoted as Y i , t − p , reflects the value of variable which p time periods prior from the i th nation.

C i represents a column vector with dimensions of 6 × 1 , which contains the constants as intercept for the model: C i = C 1 i C 2 i ⋮ C 6 i A 1 = α 11 1 α 12 1 ⋯ α 16 1 α 21 1 α 22 1 ⋯ α 26 1 ⋮ ⋮ ⋱ ⋮ α 61 1 α 62 1 ⋯ α 66 1 , … , A p = α 11 p α 12 p ⋯ α 16 p α 21 p α 22 p ⋯ α 26 p ⋮ ⋮ ⋱ ⋮ α 61 p α 62 p ⋯ α 66 p A p refers to a matrix with dimensions of 6 × 6 , representing coefficients in the analysis for a lag length of p periods. Ξ i t = ε 1 i t ε 2 i t ⋮ ε 6 i t Ξ i t refers to a column vector with dimensions of 6 × 1 , representing the forecast disturbances and errors in the analysis. Each component of Ξ i t would be independent and serially uncorrelated.

Integrated with the framework of the analysis, the quantification of the freight transportation demand side, supply side, and decarbonized transportation components within the system in the scenario could be expressed as follows:

Demand side: R a i l T r G o o d i t = C i + ∑ p = 1 m A p R a i l T r G o o d i , t − p + Ξ i t A i r T r F r e i t = C i + ∑ p = 1 m A p A i r T r F r e i , t − p + Ξ i t

Supply side: E l e P r o R e i t = C i + ∑ p = 1 m A p E l e P r o R e i , t − p + Ξ i t A l t N u E i t = C i + ∑ p = 1 m A p A l t N u E i , t − p + Ξ i t

Decarbonized transportation:   R e E n e C o n i t = C i + ∑ p = 1 m A p R e E n e C o n i , t − p + Ξ i t   C O 2 E m T r a i t = C i + ∑ p = 1 m A p   C O 2 E m T r a i , t − p + Ξ i t

Ensuring the stationarity of variables could be crucial before beginning the analysis process. If non-stationarity would be present in the variable sequence, the estimation of the model would deviate from the principles of asymptotic theory, potentially leading to distorted subsequent analysis results. Moreover, non-stationary variables may result in spurious regression estimates. In order to guarantee the dependability of the analysis findings, a Fisher-type examination, predicated on the Augmented Dickey-Fuller test, would be utilized to scrutinize the presence of unit roots in the six variables extracted from the panel data. After undergoing unit-root testing, all the variables (RailTrGood, AirTrFre, EleProRe, AltNuE, ReEneCon, and CO2EmTra) chosen for incorporation into the PVAR model were found to have rejected the null hypothesis. (Please refer to the Supplementary Appendix for the test results due to space constraints).

The selection of lag order could be a critical step that impact the estimation outcomes of the model. To determine the reasonable lag order, relevant information criteria would be commonly employed. Based on the 1 to 4 lag values of the variables, the first to third order PVAR models were evaluated and considered as reasonable choices.

Based on the data presented in Table 1, the determination coefficients for each lag were comprehensively evaluated. In accordance with the selection criteria proposed by Andrews and Lu (2001), the first order PVAR model was deemed to be a relatively reasonable choice, given that it had the lowest MBIC, MAIC and MQIC among the criteria for 1 to 3 lags. Therefore, the subsequent analysis and estimation focused on the PVAR model with first order.

In order to estimate the models, the initial four lag periods were utilized as instruments. The outcomes presented in Table 2 suggest that the regression analysis indicates a notable level of significance for the variables examined. Specifically, the lag term of EleProRe and AltNuE exhibited a considerable level of significance at the 1% and 5% levels respectively. Moreover, the statistical significance of RailTrGood, AirTrFre, and ReEneCon was demonstrated at a 10% significance level.

The subsequent phase of the analysis involves addressing missing data and enhancing estimation accuracy through the implementation of the Generalized Method of Moments (GMM) instruments recommended by Holtz-Eakin et al. (1988). As noted by Hall (2004), the utilization of GMM facilitates the automatic exclusion of observations without valid instruments and the imputation of missing values. Consequently, the effective sample size could be expanded, thereby improving the estimation efficiency of the model.

Table 3 indicates that the variable parameters estimated through the use of GMM exert a relatively stronger influence compared to presented in Table 2. The lagged term of RailTrGood and AltNuE has the enhancement of 5% and 1% significance level for CO2 emissions from transport respectively.

Following the estimation of the aforementioned process, the investigation of the influence of past values of one variable on the identification and prediction of another variable could be performed through Granger causality analysis (Granger, 1969), thereby providing insight into the interdependence between the variables. The examination of the relationship between the variables could serve as a valuable quantitative foundation for the analysis of decarbonized transportation and related proxy variables.

Tables 4, 5 indicate the results that reveal the causal relationships among the variables in the model system.

From the perspective of Demand side: RailTrGood could Granger-cause the CO2EmTra at 5% significance level while CO2EmTra could not be observed Granger-cause the RailTrGood. Single direction causality could be existed from the goods transported by railway to CO2 emissions from transport. A two-sided causality could be indicated as AirTrFre could Granger-cause CO2EmTra at 10% significance level while CO2EmTra could be observed Granger-cause the RailTrGood at 1% level.

From the perspective of Supply side: A single way causality could be observed from electricity production from renewable sources to CO2 emissions from transport, which EleProRe could Granger-cause the CO2EmTra at 1% significance level. Similarly, AltNue could Granger-cause the CO2EmTra at 1% significance level while CO2EmTra could not be observed Granger-cause AltNue. Moreover, AltNue could Granger-cause the ReEneCon at 10% significance level while ReEneCon could relatively more significantly Granger-cause the AltNue at 1% level.

As noted by Abrigo and Love (2016), the causal effects that explain the relationship among PVAR variables could not be elucidated without identifying the constraints on the parameters. Consequently, it would be of considerable importance to assess the stationarity of the PVAR model prior to conducting procedures such as IRF and FEVD analysis. By satisfying the stationarity condition, it would become possible to derive meaningful interpretations for IRF and FEVD analysis in the following stage.

According to the findings presented in Table 5; Figure 1, it could be concluded that the PVAR model meets the criterion for stability. The result could be supported by the observation that all of the eigenvalues are situated within the interior of the unit circle, as well as the fact that the modulus of the companion matrix for the variables is less than 1.

The Impulse Response Function (IRF) plot depicts the response pattern and trajectory of the delayed impact of the target variable under the assumption of independent shocks with a standard deviation of one from other variables (Abrigo and Love, 2016). Thus, the analysis could reveal the influence and directionality of the effects from demand-side and supply-side interventions on the decarbonization of the transportation through the impact on proxy variables.

The FEVD technique could be used to determine how much each variable in the created scenario system contributes to the forecast for the target variable. As a result, the technique emphasises the matching levels of importance associated with each variable. The FEVD would concentrate on the implications from variables of demand and supply side interventions for decarbonizing transportation.

Based on the results shown in Figure 7, in terms of CO2EmTra, the largest contribution could be attributed to the supply-side technology AltNuE, accounting for approximately 31%. The contribution from EleProRe would be relatively lower, at approximately 3.8%. The demand-side technologies RailTrGood and AirTrFre have contributions of approximately 20% and 13%, respectively. As for ReEneCon, the largest contribution could be derived from the own lagged values, which remains at 74.08% from the first period to the tenth period, only slightly decreasing to 73.84%. The supply-side technology EleProRe has the highest contribution among the remaining variables, accounting for approximately 10%. The lowest contribution could be observed from AltNue, at around 2.2%. The demand-side variables RailTrGood and AirTrFre both have contributions of approximately 6.5%.