## 3 Empirical Results and Analysis
### Robustness Test
#### 3.2.3 Replacing the Explained Variable Test and the PSM-DID Estimation  
In order to further verify the robustness of the conclusion, this paper analyzes whether the APCP Action Plan policy still has a promotional effect on \(GTFP1\) by replacing the explained variable \(GTFP\) with \(GTFP1\) calculated without carbon dioxide emissions by a regression analysis which is consistent with the benchmark Models (1) and (2). Furthermore, the DID method is prone to the problem of \"selection bias\". It is difficult to guarantee that the treatment group and the control group have the same individual characteristics before the implementation of the policy. The sample of this paper covers 30 provinces in the whole country, and there are great differences among the samples, such as in the aspects of territory, economic development, industrial structure and environmental situation, so there will be great individual differences in the sample data. To solve the possible problems of the DID estimation, this paper matches the cities of the treatment group with those of the control group by using the propensity score matching method to take the control variable as the sample point. The matched data are further used for the DID regression, namely, the PSM-DID estimation [27]. By means of the PSM-DID estimation method, this paper further verifies the promoting effect of the APCP Action Plan policy on \(GTFP\). The regression results of the above two methods are displayed in Table 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **OLS (1)** & **FE (2)** & **OLS (3)** & **PSM-DID (4)** & **FE (5)** \\ \hline  & _InGTFP1_ & _InGTFP1_ & _InGTFP1_ & _InGTFP_ & _InGTFP_ \\ \hline Policy2009 & & 0.0012 & & 0.0012 & 0.0027 & \\  & & (0.37) & & (0.35) & (0.54) & \\ Policy2010 & 0.0058 & & 0.0058 & & 0.0062 \\  & (1.64) & & (1.64) & & (1.11) \\ time & & & & & \(-0.0199\)\({}^{***}\) & \(-0.0178\)\({}^{***}\) \\  & & & & & (\(-8.67\)) & (\(-7.05\)) \\ treated & & & & & \(-0.0073\)\({}^{**}\) & \(-0.0072\)\({}^{**}\) \\  & & & & & (\(-2.16\)) & (\(-2.12\)) \\ Control variables & YES & YES & YES & YES & YES & YES \\ Individual effect & YES & YES & YES & YES & YES & YES \\ Time effect & YES & YES & YES & YES & YES & YES \\ \_cons & \(-0.0264\) & \(-0.0293\) & \(0.0338\) & \(0.0275\) & \(-0.0184\)\({}^{**}\) & \(-0.0223\)\({}^{***}\) \\  & & & & & (\(-1.01\)) & (\(-2.87\)) & (\(-3.98\)) & (\(0.12\)) \\ \hline N & 420 & 420 & 420 & 420 & 354 & 354 \\ \hline \hline \end{tabular} Note. \({}^{***}\) and \({}^{***}\) represent passing the significance test of \(10\%\),5\(\%\) and \(1\%\), respectively, the same below.  
\end{table} 
Table 5: Benchmark model parameter estimates of the counterfactual test. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **OLS (1)** & **FE (2)** & **OLS (3)** & **FE (4)** & **OLS (5)** & **OLS (6)** \\ \hline  & _InGTFP_ & _InGTFP_ & _InGTFP_ & _InGTFP_ & _InGTFP_ & _InGTFP_ \\ \hline Policy2009 & & 0.0012 & & 0.0012 & 0.0027 & \\  & & (0.37) & & (0.35) & (0.54) & \\ Policy2010 & 0.0058 & & 0.0058 & & & 0.0062 \\  & (1.64) & & (1.64) & & (1.11) \\ time & & & & & \(-0.0199\)\({}^{***}\) & \(-0.0178\)\({}^{***}\) \\  & & & & & (\(-8.67\)) & (\(-7.05\)) \\ treated & & & & & \(-0.0073\)\({}^{**}\) & \(-0.0072\)\({}^{**}\) \\  & & & & & (\(-2.16\)) & (\(-2.12\)) \\ Control variables & YES & YES & YES & YES & YES & YES \\ Individual effect & YES & YES & YES & YES & YES & YES \\ Time effect & YES & YES & YES & YES & YES & YES \\  & \(-0.0264\) & \(-0.0293\) & \(0.0338\) & \(0.0275\) & \(-0.0184\)\({}^{**}\) & \(-0.0223\)\({}^{***}\) \\  & & (\(-1.01\)) & (\(-1.14\)) & (0.87) & (0.71) & (\(-2.42\)) & (\(-2. The estimated regression coefficients of the Policy in Table 6 are significantly positive in Columns (1)-(5). Columns (4) and (5) display the regression results estimated by the PSM-DID. This suggests that APCP Action Plan still significantly improves the \(GTFP\). Thus, the conclusion of this paper is robust.