Forecasting province-level ${\text {CO}}_{2}$ emissions in China

Abstract

Due to criticisms of potential identification issues within spatial panel data models, this study contributes to the literature by comparing forecasts of province-level carbon dioxide emissions against empirical reality using dynamic, spatial panel data models with and without fixed effects. From a policy standpoint, understanding how to predict emissions is important for designing climate change mitigation policies. From a statistical standpoint, it is important to test spatial econometrics models to see if they are a valid strategy to describe the underlying data. We find that the best model is the spatio-temporal panel data model which controls for fixed effects. Our findings demonstrate the importance of considering not only spatial and temporal dependence but also the individual or heterogeneous characteristics within each province.

Appendices

Appendix A

1.1 A.1 Empirical results of dynamic pooled panel data model

The estimation results of the dynamic pooled panel data models of the within-sample (the first fifteen years) is presented in Table 2.

Table 2 Estimation results of the dynamic pooled panel data models

From the results, we found that the spatial autocorrelation parameter of $\rho$ in the SAR model is shown as statistically significant, but the spatial autocorrelation parameter of $\delta$ in the SEM model and the parameters of $\rho$ and $\lambda$ in the STPD model are shown as non-significant. The SAR model is suggested as a more appropriate specification than the non-spatial model as well as the other spatial models (SEM and STPD) for the within-sample pooled regression analysis. We also perform the Lagrange Multiple (LM) tests to test the hypotheses whether the SAR model and SEM is prefer than the non-spatial model. The LM test results show the SAR model is statistically significant, but the SEM model is not (the results can be provided as required).

A.2 Empirical results of dynamic fixed effect panel data model

The estimation results of the dynamic fixed effect panel data models of the within-sample (the first fifteen years) is presented in Table 3.

Table 3 Estimation results of the dynamic fixed effect panel data models

From the results, we found that the spatial autocorrelation parameter of $\rho$ in the SAR model, the parameter of $\delta$ in the SEM model, and the parameters of $\rho$ and $\lambda$ in the STPD model are shown as statistically significant, the spatial models are suggested as a more appropriate specification than the non-spatial models for the within-sample fixed effect regression analysis.

As an additional step, we perform Likelihood Ratio (LR) tests to test the hypotheses whether the STPD model can be simplified to the SAR or SEM model. According to the LR test result (7.221, 2 df, $p < 0.01$), the null hypothesis of the STPD model could be simplified to SAR model is rejected at a one percent significant level; the null hypothesis of the STPD model could be simplified to SEM model is also rejected at a one percent significant level based on the LR test result (48.985, 2 df, $p < 0.01$). These results imply that the SAR and SEM models are rejected in favor of STPD model.

A.3 Empirical results of dynamic random effect panel data model

The estimation results of the dynamic random effect panel data models of the within-sample (the first fifteen years) is presented in Table 4.

Table 4 Estimation results of the dynamic pooled panel data models

From the results, we found that the spatial autocorrelation parameter of $\rho$ in the SAR model, the parameter of $\delta$ in the SEM model, and the parameters of $\rho$ in the STPD model are shown as statistically significant, the spatial models are suggested as a more appropriate specification than the non-spatial models for the within-sample random effect regression analysis.

We also perform the Lagrange Multiple (LM) tests to test the hypotheses whether the SAR model and SEM is preferred over the non-spatial model. The LM test results show the SEM model is statistically significant, but the SAR model is not (the results can be provided as required).