## 1 Introduction  
Faced with a series of issues such as climate change, frequent increases in extreme weather, and industrial structural innovation, China has made a serious commitment to \"strive to peak carbon dioxide emissions by 2030 and strive to achieve carbon neutrality by 2060\". Under the demand of mitigating climate change, carbon sinks have an important ecosystem regulation function [1; 2; 3]. Among them, the main ways to increase sinks are bioenergy with carbon capture and storage (BECCS) and increasing the carbon sink capacity of terrestrial vegetation [4]. The former method has higher costs for technological innovation, investment, and maintenance, and its universality and economy have yet to be considered. Nature-based policies are one of the most cost-effective ways to increase carbon sinks and simultaneously have large social and economic benefits [5]. Among all terrestrial vegetation types, forests are the most important carbon pools in terrestrial ecosystems, accounting for 70%-80% of the global amount of carbon storage [6; 7]; additionally, forestshave the best long-term effects. Therefore, an increase in the forest carbon sink will play a vital role in the process of carbon neutrality. State-owned forest regions (SOFRs) are experiencing conflicts between ecological and economic benefits in the process of reform, and they are undertaking the major goal of achieving \"carbon neutrality\" [8]. Therefore, it is necessary to measure the cost-effectiveness of forest management investment (FMI) in various forest regions and identify areas with high efficiency in forest management. Forest management measures mainly increase the carbon storage of forests by improving the forest growth environment, increasing the forest area, and improving the forest stand quality. SOFRs are large in scale, relatively standardized in their management, and have a high FMI, such as forest tending. The main task of SOFRs is to increase forest resources, improve forest quality, give full play to the production potential of SOFRs, and improve the ecological, social, and economic benefits of various forest regions. However, the improvement of forest quality is not only related to forest management measures, but is also affected by regional forest stand quality, natural climate conditions, and forest region size [9; 10]. In particular, forest management has scale effects, and large-scale management results are better [11]. Moreover, because forest tending and afforestation measures do not obtain immediate results, there may be a lag effect. Therefore, the effect of FMI on forest quality improvement is uncertain in time and space, and there may be differences in the level of investment efficiency among forest regions. Therefore, identifying high-efficiency investment areas can help alleviate the conflict between the ecological and economic benefits of SOFRs, and is of great significance for policymakers who wish to improve the efficiency of policy implementation [12]. Research on the ecological efficiency of SOFRs mainly adopts the methods of data envelopment analysis (DEA) and slacks-based measure-data envelopment analysis (SBM-DEA) to evaluate the ecological efficiency of key state-owned forestry enterprises [13; 14]. However, this research failed to link the FMI with the increase in the carbon sink amount and focused on the expected and undesired output of the overall input to the ecological environment. Most of the research on the measurement of the ecological effects of forest management has focused on measuring the impact of different forest management methods (natural forests, artificial forests) and forest tending measures on soil and tree diameter at breast height [15; 16; 17]. Similarly, most studies from the perspective of increasing carbon sinks in forests have focused on small-scale investigations.