## 4 Discussion  
This paper used panel data from 40 SOFRs in Heilongjiang Province from 2001 to 2019 for 19 periods, selected the panel threshold model to divide the carbon sink threshold, and examined the efficiency and difference of FMI in increasing the carbon sink value under different carbon sink levels. The analysis of the results showed that the amount of carbon sink greatly affected the efficiency of FMI and verified the law of diminishing marginal returns of FMI. The main differences from previous studies are as follows: (1) We visualized the changes in the carbon sink and FMI in key SOFRs in Heilongjiang Province in time and space to facilitate dynamic analysis. (2) We excluded the sensitivity of FMI changes to carbon sinks on a large scale. (3) We used the panel threshold model to fully investigate the impact of the carbon sink in each forest region on investment efficiency, and then identified efficient FMI areas. (4) Partially linear functional-coefficient panel data models were used to verify that the FMI in the key SOFRs in Heilongjiang Province followed the law of diminishing marginal returns. The research significance of this article mainly lies in the following: carbon sinks were used to characterize the natural conditions, forest resources, and scale of each forest region, and natural factors were included in the system to measure the efficiency of FMI in increasing carbon sinks. According to the differences in FMI in different forest regions, the results provided a decision-making basis for SOFR management, capital allocation, and high-quality forest development, and promoted the realization of the \"dual carbon\" goal. During the study period, the overall carbon sink level of the key SOFRs in Heilongjiang Province fluctuated greatly. The possible reason is that the SOFRs, as one of the country's timber supply producing areas, have an annual timber output of up to 4 million cubic meters, and the objects of logging are mostly mature forests and overmature forests. The carbon storage in mature forests and overmature forests is higher than that in young, middle-aged, and near-mature forests, and logging will result in a short-term decline in carbon storage. Additionally, the annual net productivity of young forests and middle-aged forests will reach the highest value after a certain period of time and do not immediately contribute to the increase in carbon storage. In addition, measures such as forest tending and artificial afforestation require a certain amount of time to affect the carbon sink, so immediate results are not visible. In addition, forests are affected by multiple factors, such as pests, wind breaks, and drought. Especially in 2007 and 2011, the annual rainfall was  
Figure 8: Partially linear functional-coefficient panel data model estimation results. significantly lower than that in other years, which restricted the growth of trees and caused a short-term decline in the carbon sink. In addition, in 2015, the state issued a policy stating that logging was prohibited in all natural forests in northeast China [49; 50], and the carbon sinks of forest regions increased. Therefore, there were large fluctuations in the changes in the carbon sink in the study area. Previous research methods did not consider the impacts of forest scale and resources on the efficiency of FMI. Therefore, it was impossible to accurately identify high-efficiency investment areas, and it was difficult to improve the level of carbon sinks and the efficiency of FMI in a targeted manner, resulting in a waste of forestry funds. In this paper, the investment efficiency of forest management in the key SOFRs of Heilongjiang Province, divided according to the amount of carbon sink, was quite different. There were 21 forest regions with carbon sinks of less than 532,721.87 tons, and their FMI efficiency was 56.18% lower than that of forest regions with more than 532,721.87 tons.