Algorithm of Ecocompensation in Sloping Land Conversion Program Based on Heckman’s Two-Step Model

In this paper, we broadly generalize the assignment auction algorithm to solve linear minimum cost network flow problems. It is significant to establish a market-based compensation mechanism by way of conservation auctions based on peasant households’ willingness, which can promote the innovation of ecocompensation policies, green development, and balanced growth. Using the survey data collected from 453 households within 3 national pilot counties in ecologically fragile regions in northwest Liaoning for the Sloping Land Conversion Programme, measuring peasant households’ willingness to accept ecocompensation through sealed auctions, we built a database through cloud computing to realize information collation and query and applied the Heckman’s Two-Step Model to study the impact of risk preference, social capital, cognitive preference, land parcel characteristics, and family endowments on farmers’ willingness to participate in protection auctions and their bid prices. *e results reveal that the average bid price of peasant households in the ecologically fragile region in northwest Liaoning for the Sloping Land Conversion Programme is annually 274.5 yuan per mu and that risk preference and social capital have positive impacts on peasant households’ willingness to participate in conservation auctions and on their bid prices, cognitive preference has a positive impact on peasant households’ bid prices in conservation auctions, and land plot characteristics have a negative impact on peasant households’ bid prices in conservation auctions. It is suggested that ecocompensation policies should be optimized with such methods as lowering peasant households’ perception of high risks, setting role models for them to follow, and strengthening their perception of the environment, income, and property rights.


Introduction
Ecocompensation is a willingness-based transaction mechanism, where ecosystem service (ES) buyers/users/beneficiaries make direct and contractually agreed payments to ES providers [1]. Payment standards that influence incentive effects are always the core of policy design [2]. As a landmark project in the course of China's ecological conservation, research on ecocompensation standards for the Sloping Land Conversion Programme (SLCP) made by scholars with the ES value method [3,4], contingent valuation method (CVM) [5,6], choice experiment method (CE) [7], and opportunity cost approach (OCA) [8,9] has been running through all the phases of programme implementation. Nondiscriminatory compensation standards based on opportunity costs for the SLCP have the advantages of openness, transparency, and easy operation, but they also have the problem of information asymmetry between ES providers and users [2], which leads to either insufficient compensations lower than ES providers' opportunity costs or inefficient overcompensation transactions. What is worse, recultivation in major grain producing areas and reclamation in barren areas occur even more frequently due to hidden action caused by moral hazard [10].
In order to reduce informational rents generated by heterogeneity in opportunity costs, Ferraro proposed three solutions: gathering information relevant to opportunity costs, revealing peasant types by screening contracts, and using conservation auctions [11]. As an effective marketbased policy tool, the mechanism of conservation auction allows ES providers to express their opportunity costs actively through specific mechanism desig, and ultimately improve ES programs' fund use efficiency [12]. e mechanism of conservation auction was first used in ecocompensation practices in developed countries, including the BushTender Trial (BTT) in Australia and the Conservation Reserve Program (CRP) in the United States [13,14]. Several cases of peasant households' participation in conservation auctions were also found in developing countries such as Indonesia, Malawi, and Kenya [15][16][17].
An overview of key theoretical and laboratory studies on the mechanism of conservation auction by scholars at home and abroad reveals three problems that are worth noticing. First, there is a lack of theoretical research to reveal ES providers' opportunity costs. Second, there is currently little relevant research on unobservable factors featuring heterogeneity in ES providers [21]. ird, it still needs to be verified whether the mechanism of conservation auction can be used as an effective policy tool to solve environmental issues in developing countries.
To bridge the existing research gaps summarized above, this article takes the Sloping Land Conversion Programme, one of the biggest ecocompensation programs in the world at present, as an example to reveal peasant households' real opportunity costs through the mechanism of conservation auction, which is expected to provide a valuable reference for China's innovation of ecocompensation policies and its establishment of a long-term effective ecocompensation mechanism.
What makes this research innovative primarily lies in three aspects. First, the opportunity costs offered by peasant households for plots of land were taken as an essential indicator of ES provider heterogeneity to examine how peasant households' opportunity costs affect their participation in conservation auctions, which lays a foundation for the establishment of discriminatory ecocompensation standards. Second, based on Heckman's Two-Step Model, we study the impacts of unobservable factors including risk preference, cognitive preference, and social capital on peasant households' willingness to participate in conservation auctions, which is also innovative to some extent. ird, our study on SLCP ecocompensation with the conservation auction mechanism expands the range of applying the conservation auction mechanism in developing countries.

eories and Hypotheses.
In 1997, Latacz-Lohmann and Van der Hamsvoort developed a hypothetical program to verify that the conservation auction mechanism can significantly promote the program's cost-effectiveness [12]. ey concluded that an ES provider's bid price is formed based on a balance between net income and the probability of winning the bid, that the tender decision is made on the basis of the ES provider's expectation on the highest price acceptable to the government, and that the optimal bid price is the one that maximizes the expected utility or gain from the auction. Existing findings disclose several individual characteristics that affect an ES provider's tender decision, including his age, race, education, residence, etc. [21].
Risk preference is a key factor affecting SLCP peasant households' decision-making behavior [22]. When examining the issue of risk difference, Latacz-Lohmann and Van der Hamsvoort divided peasant bidders into two types: risk neutral and risk averse, arguing that risk averse bidders tend to lower their bids to increase the probability of winning the bid [12]. In reality, ES providers represented by peasant households are mostly the risk averse type, and there are even highly risk averse peasant households who refuse to participate in conservation auctions [23]. Cognitive preference also has impacts on SLCP peasant households [24]. When bidding in conservation auctions, those with relatively higher levels of environmental perception know better the importance of ecological services and therefore tend to increase their tender prices to earn informational rent [25]. According to e Rational Peasant by Schultz [26], peasant households' decision-making behavior is profit-driven, and the bid prices offered by peasant households in conservation auctions are positively correlated with their perception of income. As an important means to make external and public goods become internal and private, clarification of property rights is of positive significance to promote peasant households' management and conservation of natural resources [27]. Influenced by the endowment effect, peasant households having a better perception of property rights tend to offer higher tender prices [28]. As a sort of group characteristic, behavior, or outcome, social capital affects individual behavior or outcome [29]. Whether an individual possesses social capital or not decides his amount of right to speak or to make decisions. erefore, participants with rich social capital tend to be in a more advantageous position in conservation auctions [30,31]. Land is the most important means of production for peasant households, and plots of land are basic units for the SLCP. Peasant households make their bids based on the opportunity costs of land plots [25]. ey tend to offer higher bid prices for good-quality land plots with higher opportunity costs. In this article, four hypotheses are summed up and proposed as follows: e Sloping Land Conversion Program is a major policy decision made by China to improve the ecological environment and build an ecological civilization [32]. As one of the top ecologically sensitive zones in China, the ecologically fragile region in northwest Liaoning has finished one-fifth of Liaoning Province's SLCP work in the first round. e data of this article are sourced from the field survey made by the research team between 2019 and 2020 in 3 national SLCP pilot counties in the ecologically fragile region in northwest Liaoning, namely, Zhangwu, Beipiao, and Jianchang, involving 18 villages 6 townships. With the method of stratified sampling, the research team first selected 2 townships at random from each county and then selected 3 villages from each township at random for the survey. Ultimately, 480 households who participated in the first round of the SLCP were drawn as samples, and finally 453 valid questionnaires were sorted out, accounting for 94.4%.

Research Design.
How conservation auctions are designed directly affects the effect of implementing the SLCP, which is supposed to reveal peasant bidders' real opportunity costs and avoid possible moral hazard caused by fraud [33]. Referring to the study by Han Hongyun and Yu Yonghong [7], this research is designed to adopt a sealed bid procurement auction to give peasant households continuous compensation for the SLCP. e use of a single-round auction permits a direct observation of the field experiment results of the conservation auction, which helps relieve participants' tiredness and cognitive load in the survey and meanwhile reduce the management and transaction costs of the auction [34,35]. Auction payment rules mainly include discriminatory price auctions and uniform price auctions. Discriminatory pricing is closer to bidders' real costs, and its cost-effectiveness performs better on the whole [36,37]. Before each auction, the researchers explain in detail the auction process to avoid abnormal bidders. e auction design in this article is shown in Table 1.

Query of Farmers' Bidding Information under Cloud
Computing. According to the bidding information resources, cloud computing technology is used to divide the integrated information resources into multiple subsets according to the attributes of the information relationship. After the division is completed, the database construction is completed in a bottom-up manner.
Adopt SQL SERVER 2000 database management system, call the distributed information integration function in the database, and coordinate the management of the database through cloud computing technology. Design four query methods: (1) Uncertain query: In the database, there are two types.
One is that the query information is stored on a certain node. When the word "query completed" appears, the query ends; the other is that the query information is stored on multiple nodes. Based on the first query, I want to continue to query and obtain information.
(2) Combined query: Divide the query information in more detail, and define query D as shown in the following formula: In the formula, d 1 , d 2 , ...d n represent atomic queries. Atomic query is to store all query results on a node, that is, to obtain the data at that point. (3) Connect query: the connection query in the database is divided into two connection queries and multiple connection queries. In the first type, two connection queries, the query information is defined as follows: In the formula, ∞ represents the connection symbol. ere are three query results shown in the following formula: TD ≈ Td 1 ≈ Td 2 or TD ≈ Td 1 and TD > Td 2 . (3) In the formula, T represents the record information; TD, Td 1 , and Td 2 , respectively, represent the record number of D, d 1 , and d 2 . e second is multiconnection query; the query information is defined as follows: Reduce the redundant data in the database; at the same time, connect the atomic query with the node to complete the information query. (4) Compound query: e composite result of the merge and join query is shown in the following formula: In the formula, F represents the function composed of ∞ and ∪.
After completing the above steps, the database construction and information query can be realized.

Peasant Household Bidding Model.
Supposing there are N peasant households participating in the government's compensation for the SLCP, the bid price and opportunity cost of Peasant Household i are, respectively, b i and δ i . en, the objective function and the optimal strategy of Peasant Household i in the discriminatory auction are summed up as follows.
e objective function of Peasant Household i is e optimal strategy of Peasant Household i is  [38], the current study divides peasant households' bid decisionmaking process into two steps in the current study. e first step is that peasant households make decisions on whether to participate in bidding and their willingness to do that is defined as a binary choice variable between 0 and 1; the second step is that peasant households who are willing to participate in bidding make decisions on their bid price, which is a continuous variable. e model is set as follows: Formulas (1) and (2) constitute the selection model for Heckman's first step, and formula (3) is the result model of Heckman's second step. In formula (1), Z * i is the latent variable of peasant households' willingness to bid. If Z * i ≤ 0, then Z i � 0; otherwise, Z i � 1. In formula (2), X i is the core explanatory variable affecting peasant households' bidding, C i is the control variable, D i is the identification variable, and ε i is the error term. In formula (3), Y i is the peasant household's bid price, λ is the inverse Mills ratio, and μ i is the error term.

Variable Selection.
In accordance with the research objectives, a peasant household's willingness to bid and bid price are chosen as explained variables, while a peasant household's risk preference, social capital, cognitive preference, and land plot characteristics are chosen as the core explanatory variables. According to theoretical research on behavioral economics, a peasant household's risk preference can be measured directly [39]. In this research, 2 indicators of risk preference, namely, planting risk and investment risk, are selected through combining the management characteristics of peasant households involved in the SLCP. Referring to the study made by Liao Peiling and other scholars [40], perception of the environment, perception of income, and perception of property rights are selected as 3 indicators of cognitive preference. e variables description and descriptive statistics are shown in Table 2.

Analysis of Results.
Per capita income of household and income of the land plot before conversion are processed with logarithm to eliminate errors. en, due to VIF, the two variables, income of the land plot before conversion (after logarithm) and soil quality, fail the test for multicollinearity. e first step is to construct the Probit regression model and calculate the inverse Mills ratio λ; the second step is to put the inverse Mills ratio λ into the least squares regression model with bid price as the dependent variable. e results show that the inverse Mills ratio λ is statistically significant at the 10% level, which implies sample selection bias exists and Heckman's Two-Step Model is applicable. Pseudo-R 2 of the Probit model is 0.424, and R 2 of the OLS model is 0.505, which indicates a good fit between the two models. Results of the two regression models are shown in Table 3.
e estimated results of Heckman sample selection model are summarized as follows:  (1) Risk preference: Although only investment risk significantly affects the probability of peasant households' willingness to participate in the conservation auction, both planting risk and investment risk are positively correlated with peasant households' bid prices at 5% significance level. is suggests that more risky peasant households are more willing to participate in conservation auctions and choose higher bid prices at the cost of reducing the probability of winning the bid.
(2) Social capital: Social prestige is positively correlated with peasant households' willingness to make a bid in conservation auctions at 5% significance level, which indicates village cadres are more willing than common peasant households to accept the policy design of taking conservation auctions as a means of ecocompensation payment; social participation has a positive impact on peasant households' bid prices at 5% significance level, which suggests that rural capable people who participate more in social activities are willing to achieve higher bid prices by making use of the resources and information in hand.
(3) Cognitive preference: e perception of the environment, income, and property rights, passing the 5% level, 10% level, and 5% level significance test, respectively, is positively correlated with peasant households' bid prices, which indicates that peasant households' perception of the ecological and economic benefits of the SLCP significantly promotes their bid prices in the conversation auction and that peasant households are more willing to choose relatively high bid prices when engaging more in the management and conservation of land plots under conversion to forests due to the influence of their perception of property rights.
(4) Land plot characteristics: As an indicator with dual attributes of generating both ecological and economic profits attributes, slope, is negatively correlated with peasant households' bid prices at 5% significance level, which indicates the stronger the slope of an SLCP land plot is, the less income it generates from planting before the implementation of the SLCP and the lower bid prices peasant households tend to offer when considering its opportunity costs. (5) Control variables: e age of the head of household has a significantly negative impact on a peasant household's willingness to bid and bid prices, passing the 5% level and 1% level significance test, respectively. at suggests, with their ages growing and out of consideration for stable income, the peasants tend to lose their enthusiasm for participating in conservation auctions and choose relatively low bid prices for higher probabilities of winning the bid. e health and political status of the head of household are positively correlated with his willingness to bid, passing the 5% level significance test. e results indicate that a good health is the basic guarantee of peasants' participation in bid auctions and fulfillment of auction contracts and that peasant households with Party members are more active in participating in conservation auctions. e area of arable land has a negative impact on peasant households' willingness to bid but a positive impact on their bid prices, which suggests SLCP peasant households with rich arable land resources are not very willing to participate in conservation auctions but they are driven by economies of scale to choose relatively high bid prices. (6) Identification variables: e proportion of SLCP peasant households has a positive relationship with peasant households' willingness to bid, passing the 1% level significance test, which indicates peasant households in the villages with higher proportions of households engaged in the SLCP are more willing to participate in conservation auctions. But this ratio has no significant impact on bid prices, which suggests the identification variable has been selected appropriately.

Suggestions on Optimizing Ecological Compensation.
Strengthen the information publicity of ecological compensation policy, make the incentive policy open and transparent, reduce farmers' awareness of the high risk of ecological compensation, improve farmers' enthusiasm for participation through incentive policy, set up property right knowledge lectures, and enhance farmers' awareness of property rights. At the same time, it is best to establish ecological compensation projects in the surrounding areas, so that farmers can understand the relevant information of ecological compensation in the surrounding areas, deepen their understanding of ecological compensation, and enhance their willingness to participate in ecological compensation. e diversification of farmers' income sources will also promote the implementation of ecological compensation policy. With the development of information society, farmers' demand for labour transfer is increasing day by day. ey often struggle between continuing farming and going out to work. Generally speaking, the higher the education level, the faster the ability to accept new things. erefore, for farmers with higher education, their vision and thinking are also broader. ey are more able to look at the ecological compensation policy from an objective perspective, which can often play a role model and drive other farmers to participate. At the same time, the government should increase support for sideline and migrant work other than farming, based on the necessary help of farmers, which is also conducive to increasing farmers' confidence in the government, so as to improve farmers' participation in ecological compensation policies. In the process of implementing the ecological compensation policy, we can also vigorously support the development of organic agriculture, improve the protection of the ecological environment, develop low-carbon organic agriculture, fundamentally improve the agricultural economic benefits, and promote the sustainable development of economy and society through the ecological compensation policy.

Conclusion and Discussion
Our results show that the average bid price of peasant households in the ecologically fragile region in northwest Liaoning for the Sloping Land Conversion Programme is annually 274.5 yuan per mu, close to the net income of 309.1 yuan per mu before the SLCP and also close to the compensation standard of 300 yuan per mu for the new-round SLCP [32]. It is 3.05 times the subsidies for the consolidation period of the first-round SLCP. As the important subjects to implement and manage the SLCP, 78.6% of peasant households are willing to participate in conversation auctions, which indicates means of compensation based on the willingness of peasant households are easier to be accepted, among them, the query function constructed by cloud computing provides convenience for farmers to obtain information to a large extent. Risk preference and social capital have positive effect on peasant households' willingness to bid in conservation auctions as well as on their bid prices; cognitive preference has positive effect on bid prices in conservation auctions; land plot characteristics have negative effect on bid prices in conservation auctions; of the factors of family endowment, the age of the head of household has significantly negative effect on peasant households' willingness to bid and on their bid prices, the health and political status of the head of household has positive effect on the peasant household's willingness to bid, and the area of arable land has negative effect on peasant households' willingness to bid but positive effect on their bid prices. According to these findings, it is advised to improve ecocompensation policy design following peasant households' willingness, lower SLCP peasant households' risk perception, give play to the leading and exemplary role of the village Party branch, the village committee, village cadres, and active management participants, strengthen peasant households' perception that the SLCP helps improve the environment and income, and encourage peasant households' management and conversion of the converted land through the design of conservation auction contracts.
is paper uses protective auction mechanism to solve the problem of information asymmetry. At the same time, it is innovative to use cloud computing to establish a database, realize information query, facilitate farmers, and establish an ecological compensation standard based on farmers' real opportunity cost. However, this paper only selects the information of 453 farmers in three national pilot counties in western Liaoning as the data sample, which has limitations. erefore, in the next research, more data will be used for 3.89 * , * * , and * * * represent the estimated coefficient is statistically significant at the 1% level, at the 5% level, and at the 10% level, respectively.
Scientific Programming statistics and supplemented with more sample data for research and analysis, so as to make the application of distribution auction algorithm in the operation of ecological compensation more persuasive and referential, make the ecological compensation standard based on farmers' protection auction mechanism more perfect, and lay a good foundation for extensive promotion in the future.

Data Availability
Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Conflicts of Interest
e authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.