## 4 Regression Variables, Data Sources, and Econometric Framework
We still could not predict whether \(\beta_{5}\) (the coefficient of MYS) is expected to be negative. For ecological consumption and income, there is a monotonically increasing linear relationship if \(\beta_{6}>0\) and \(\beta_{7}=0\), there is a monotonically decreasing linear relationship if \(\beta_{6}<0\) and \(\beta_{7}=0\), there is an inversed U-shaped relationship if \(\beta_{6}>0\) and \(\beta_{7}<0\), which validates the EKC hypothesis, and there is a U-shaped relationship if \(\beta_{6}<0\) and \(\beta_{7}>0\), which is contrary to the EKC hypothesis. For the inversed U-shaped or U-shaped relationship, it is easy to be calculated that the turning point values of income are exp (\(-\beta_{6}/2\beta_{7}\)) (the marginal impacts of \(\mathit{Ln}(\mathit{GNIPC})\) on \(EF\) are equal to \(\frac{\mathit{dEF}}{\mathit{dLn}(\mathit{GNIPC})}=\beta_{6}+2\beta_{7}\mathit{ Ln}(\mathit{GNIPC})\). At the turning points, the marginal impacts are zero, and the corresponding values of \(\mathit{Ln}(\mathit{GNIPC})\) are \(-\beta_{6}/2\beta_{7}\). Therefore, the corresponding values of \(\mathit{GNIPC}\) are exp (\(-\beta_{6}/2\beta_{7}\))). Because values of \(\mathit{Ln}(\mathit{GNIPC})\) are above zero, an inversed U-shaped or U-shaped relationship between ecological consumption and income cannot be validated if \(\beta_{6}=0\) and \(\beta_{7}\
eq 0\). Furthermore, it could not be concluded that income is not a significant influencing factor of ecological consumption if \(\beta_{6}=0\) and \(\beta_{7}=0\). Under the circumstances, a liner relationship rather than an inversed U-shaped or \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Obs** & **Mean** & **SD** & **Min** & **Max** \\ \hline EF & 830 & 5.27 & 1.73 & 1.09 & 10.48 \\ URB & 840 & 70.41 & 13.27 & 39.47 & 97.88 \\ REN & 840 & 15.79 & 12.95 & 0.61 & 60.19 \\ SER & 838 & 59.22 & 7.96 & 35.70 & 76.92 \\ INT & 826 & 45.83 & 29.29 & 0.00 & 96.81 \\ MYS & 832 & 10.93 & 1.49 & 6.50 & 14.10 \\ GNIPC & 835 & 24,869.68 & 13,180.40 & 2180.00 & 68,100.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical descriptions of the variables for the developed countries (1996–2015). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Obs** & **Mean** & **SD** & **Min** & **Max** \\ \hline EF & 960 & 1.78 & 0.99 & 0.50 & 6.83 \\ URB & 960 & 45.50 & 21.97 & 7.41 & 91.50 \\ REN & 956 & 49.57 & 30.17 & 1.15 & 98.09 \\ SER & 948 & 47.73 & 8.08 & 17.99 & 77.02 \\ INT & 952 & 11.41 & 16.10 & 0.00 & 76.63 \\ MYS & 941 & 5.63 & 2.58 & 0.90 & 11.70 \\ GNIPC & 959 & 5587.91 & 5123.61 & 450.00 & 26,360.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistical descriptions of the variables for the developing countries (1996–2015). U-shaped relationship between ecological consumption and income should be explored and estimated. Therefore, we needed to revise Equation (2) and another estimation equation was proposed. The new estimation equation is as follows:  
\[ \begin{array}{l}EF_{i,t}=\alpha+\beta_{1}URB_{i,t}+\beta_{2}REN_{i,t}+\beta_{3 }SER_{i,t}+\beta_{4}INT_{i,t}+\beta_{5}MYS_{i,t}\\ +\beta_{6}Ln(GNIPC)_{i,t}+\varepsilon_{i,t}\end{array}  \tag{3}\]  
In order to explore the lagged impacts of the independent variables on \(EF\) (lagged by one year), the following two equations were estimated:  
\[ \begin{array}{l}EF_{i,t}=\alpha+\beta_{1}URB_{i,t-1}+\beta_{2}REN_{i,t-1}+ \beta_{3}SER_{i,t-1}+\beta_{4}INT_{i,t-1}+\beta_{5}MYS_{i,t-1}\\ +\beta_{6}Ln(GNIPC)_{i,t-1}+\beta_{7}Ln(GNIPC)^{2}_{i,t-1}+\varepsilon_{i,t-1} \end{array}  \tag{4}\]  
\[ \begin{array}{l}EF_{i,t}=\alpha+\beta_{1}URB_{i,t-1}+\beta_{2}REN_{i,t-1}+ \beta_{3}SER_{i,t-1}+\beta_{4}INT_{i,t-1}+\beta_{5}MYS_{i,t-1}\\ +\beta_{6}Ln(GNIPC)_{i,t-1}+\varepsilon_{i,t-1}\end{array}  \tag{5}\]  
We could present the regression results by mainly estimating Equations (2) and (4). If an inversed U-shaped or U-shaped relationship between ecological consumption and income could not be validated, Equations (3) and (5) were estimated instead to explore the linear relationship.