## 2 Overview of Study Area, Data, and Methods
### Index Selection  
1. Explained variable: As the largest terrestrial carbon pool, forests play a major role in the goal of achieving \"carbon neutrality\". The management system of China's state-owned forest farms is relatively complete, the FMI is relatively high, and the forest quality is relatively good. Previous studies mostly used NPP as the basis for calculating carbon sinks [31; 32]. To measure the carbon sink level of 40 key SOFRs, this paper used vegetation NPP as the basis for calculation. The NPP of vegetation refers to the amount of organic matter accumulated by green plants per unit area and unit time, i.e., the remaining part after deducting autotrophic respiration (RA) from the gross primary productivity (GPP) fixed by plant photosynthesis. This indicator can measure forest quality to the greatest extent and can calculate the carbon sink amount based on basic data. The specific calculation method is explained in the next section.
2. Explanatory variables: To measure the investment efficiency in forest tending and management and the investment in various major forestry projects, this paper selected the total FMI (invest) as the explanatory variable. This measure includes forest tending investment, forest management and protection investment, forestry fixed asset investment, afforestation and renewal investment, Natural Forest Protection Program (NFPP) investment, and forest quality improvement investment.
3. Socioeconomic factors: Although the increase in the carbon sink amount requires a large amount of financial investment, it also creates many employment opportunities. Furthermore, as more become engaged in forest management, tending, and industrial development, it has a positive effect on increasing forest quality and increasing the  
Figure 1: Location map of key SOFRs in Heilongjiang Province.  
carbon sink amount. Therefore, the paper incorporated the number of employees (workpop) into the model. In addition, personnel wages play a positive role in stimulating forest management measures such as management and maintenance, and it is necessary to consider the indicator of total wages (wage) [33]. However, forest maintenance measures such as thinning have led to a large amount of timber output and income, which also promotes the development of downstream enterprises related to wood products. Forest maintenance will produce income from tourism, stimulate the economic development of forest regions, and generate income from the tertiary industry. Therefore, in the econometric model, the impact of SOFRs' gross domestic product (gdp) on the carbon sink should be examined [34]. In addition, there may be an inverted U-shaped relationship between the economic development level of the SOFRs and the ecological environment, following the path of the environmental Kuznets curve (EKC) [35]. Therefore, we put gdp and gdp\({}^{2}\) into the model at the same time as control variables.
4. Natural meteorological factors: The effect and efficiency of FMI are related to forest quality issues. The afforestation land, the growth of young and middle-aged trees, and the effect of forest tending are greatly affected by climatic factors [36; 37]. Climatic factors such as precipitation and temperature have greater impacts on forest quality and productivity [38; 39]. Additionally, temperature and soil moisture together affect the photosynthesis sensitivity of plants [40; 41]. Therefore, when constructing the model, precipitation and temperature need to be used as control variables. Furthermore, because the overall precipitation in the SOFRs of Heilongjiang Province has little difference, the temperature difference between summer and winter is large. Therefore, we used the annual average precipitation and the July average temperature data.