## 3 Results and Analysis
### Analysis of Model Results  
The study used Stata 16.1 measurement software to conduct the regression to investigate the efficiency of FMI in increasing carbon sinks in 40 key SOFRs in Heilongjiang Province. The specific results are shown in Table 4.  
Model (1) showed the regression result of the individual fixed-effects model, which verified the cost-effectiveness of increasing the carbon sink by FMI without considering the lagging impact of FMI on the carbon sink. Model (2) and Model (3) examined the efficiency of FMI in increasing the carbon sink when FMI lagged by one and two periods. Model (4) used the carbon sink as the threshold variable to examine the differences in the efficiency of FMI under different levels of the carbon sink. (1) Model (1) showed that the impact of FMI in SOFRs on the carbon sink did not pass the 10% significance test. However, from a theoretical point of view, FMI includes forest tending investment, forest management and protection investment, forestry fixed asset investment, afforestation and renewal investment, NFPP investment, forest quality improvement investment, and other aspects. These funds will increase the forest stock to varying degrees, thereby increasing the forest carbon sink, but the results of the model had no significant impact. The possible reasons are as follows. First, after the investment of forestry funds, the implementation of measures such as afforestation and forest tending take a certain amount of time. Second, some forest management and protection measures do not have an immediate positive impact on \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Threshold Type** & **F Value** & **\(p\) Value** & **BS Times** & **Threshold** & **Confidence Interval** \\ \hline Single threshold (pfgc1) & 78.20 *** & 0.0000 & 300 & 5,327,211.8707 & [5,289,995.8337, 5,341,231.7847] \\ Double threshold (pfgc1) & 90.44 *** & 0.0000 & 300 & 5,327,211.8707 & [5,289,995.8337, 5,341,231.7847] \\  (pfgc2) & & & & 2,494,641.9549 & [2,461,170.3222, 2,506,791.0606] \\ \hline  & & & & & \\ \end{tabular} Note: *** indicates significance at the levels of 1%; the \(p\) value and critical value are obtained by repeated sampling 300 times using the bootstrap method.  
\end{table} 
Table 3: Test results of threshold effect. forest carbon sinks. For example, thinning will cause a short-term decline in carbon storage. In addition, measures such as forest tending and artificial afforestation require a certain amount of time to affect the carbon sink, and they do not have an immediate impact on the carbon sink. Therefore, it takes a certain period from the investment to produce obvious effects--that is, the influence of the variable \(Innvest_{it}\) on \(Incarbonsink_{it}\) lags. 2. We determined the reasonable lag period for FMI in 40 key SOFRs and used this as a basis to analyze the efficiency of increasing the carbon sink, such as in Models (2) and (3). Since we took the logarithm of all variables, the coefficient in the result indicated the sensitivity of the carbon sink to changes in FMI. The results showed that the elasticity coefficients of FMI for the first and second periods of lag were 0.01419 and 0.00750, respectively. The elasticity coefficient (sensitivity) was the largest when the FMI lagged for a period, which was 0.01419. This result means that for every 1% increase in the amount of FMI, the carbon sink will increase by 0.0142%. Therefore, we chose one lagging period of FMI as a reasonable lag period. 3. The efficiency of FMI in forest regions with high carbon sinks was greater than that of regions with low carbon sinks, as shown in Model (4). At different carbon sink levels, FMI had a significant positive impact on the carbon sink (\(p<0.01\)), but there was strong heterogeneity. The carbon sink of each forest region can, to a large extent, represent the scale of the forest region and the endowment of forest resources. The areas with higher carbon sinks were mostly forest regions with large scales and better endowments of forest resources.