Chemical Fertilizer Abatement and Ecological Compensation in China’s Northeast Black Soil Region: An Assessment with a Fertilization Balance Equivalence Framework

Abstract

Overreliance on fiscal support policy instruments to improve cultivated land fertility poses a challenge to the sustainable supply capacity of government ecological compensation funds, especially given the limited scope for market-based implementation. To address this, it is necessary to further examine and optimize the effectiveness of existing ecological compensation schemes. Using field survey data from 612 rice farm households across three provinces in Northeast China’s black soil region, we constructed an equivalent ecological compensation framework for “chemical fertilizer (CF) abatement to fertilization balance (FB)” grounded in the logic of ecological increment and abatement processes, and evaluated the performance of China’s Cultivated Land Productivity Subsidies. The results reveal that the environmental cost per unit of CF input in this region is 40.6 CNY/kg, with a regional fertilization balance standard (FBS) of 20.04 kg/mu. Owing to the heterogeneity in farmers’ fertilization practices, the actual rate of excessive CF application (RECFA) (101.5%) is notably higher than the statistical estimate of 78%, indicating that the scale of overapplication has been systematically underestimated. Yet with its uniform per mu subsidy standard and a policy design that targets ecological compensation at landowners, the government directs a share of subsidy funds to land transferors who bear no CF abatement responsibilities. This, in turn, deepens the mismatch between farmers’ CF abatement efforts and the ecological compensation they receive. At the regional level, the current subsidy of 122.1 CNY/mu drives only a 13.42% abatement in CF application, while achieving full FB would require a subsidy of 552.7 CNY/mu. This points to a clear shortfall in aggregate support and an appreciable gap between current policy inputs and actual CF abatement demand. These findings provide empirical support for the ecological compensation assessment framework based on the equivalence between CF abatement and FB. The dual-level analysis across regional and household scales offers practical references for optimizing black soil conservation subsidy policies in Northeast China.

1. Introduction

Black soil is globally recognized as one of the most fertile and arable soil types [1]. The black soil region in Northeast China functions as the main grain-producing area and national commodity grain base, and plays a vital role in safeguarding national food security [2]. In recent years, however, an extensive management model defined by excessive inputs of chemical fertilizers (CF, specifically nitrogen, phosphorus, potassium fertilizers and their compound products) and pesticides, compounded by natural degradation processes, has pushed the black soil region into severe ecological decline [3,4]. Since large-scale reclamation in the 1950s, the plow layer thickness has decreased by 60–80%, and soil organic matter content has declined by 2% on average [5]. In 2020, the color of black soil had gradually changed from dark to light [6]. To deeply implement the “Storing Grain in the Land” strategy and address the public dilemma of insufficient supply of agricultural ecosystem services, China has established a multi-level policy system for black soil conservation, including the Black Soil Protection Law of the People’s Republic of China, the Northeast Black Soil Conservation Project, and a series of supporting fiscal incentive policies. Meanwhile, local governments have encouraged farmers to adopt black soil conservation tillage techniques [7] and have utilized economic incentive measures to stimulate farmers’ endogenous motivation and initiative in cultivated land conservation [8,9]. Over time, government-funded Payment for Ecosystem Services (PES) frameworks have gradually taken shape [10,11].

In China, such economic incentive-based ecological governance policies are generally referred to as ecological compensation mechanisms [12]. Based on funding sources and operating models, these mechanisms fall into two main categories [13,14,15]: (1) Government-led schemes: top-down fiscal payment systems that draw on dedicated public funds to compensate actors for ecological protection efforts [14]. (2) Market-oriented compensation: w frameworks aligned more closely with international PES models, where end consumers act as the source of payment [16,17,18]. As a crucial policy instrument, the Chinese ecological compensation mechanism significantly advanced environmental protection and sustainable development [19,20], with large-scale fiscal input in agricultural ecological conservation practices nationwide [21]. In agricultural ecological protection, government fiscal transfers remain the dominant incentive instrument. However, amid low agricultural comparative advantage and rising opportunity costs [22,23], sustaining agricultural ecosystem services through overreliance on government financial transfer payments has become increasingly challenging [24]. Although China’s ecological civilization concept and policy development direction support the development of market-oriented compensation schemes [10], pure market-oriented approaches have not been fully applied [15]. Before the ecological product market matures, public fiscal incentives remain an expedient measure to boost farmers’ motivation for cultivated land protection [25]. Therefore, while advancing market-oriented mechanisms, it is critical to evaluate and optimize the performance of government-led subsidy programs [26]. For the black soil region of Northeast China, cultivated land protection is the core task of ecological governance, and excessive CF input is a key driver of soil degradation [3,4,5,6]. As the core fiscal compensation policy for cultivated land protection, the Cultivated Land Productivity Subsidy is critical to promoting cuts in CF use, yet its targeted compensation effect and design rationality for CF abatement lack systematic evaluation.

Against this backdrop, our analysis centers on China’s Cultivated Land Productivity Subsidy, the core fiscal instrument for on-farm cultivated land protection nationwide. Evolved from earlier direct grain subsidies and comprehensive agricultural input subsidies, the scheme was formally incorporated into the national Agricultural Support and Protection Subsidy framework in 2016. Delivered as direct fiscal transfers to farmers holding contracted land use rights, the subsidy is disbursed conditional on farmers’ uptake of conservation practices—including subsoiling, straw incorporation, CF abatement, and organic fertilizer application—all oriented toward preserving cultivated land quality and sustaining soil fertility. In the black soil region of Northeast China, it serves as the primary policy lever to incentivize farmers to cut excess CF use and mitigate soil degradation. CF abatement is chosen as the core metric for assessing subsidy policy performance for three reasons. First, it is highly aligned with the core objectives of the Cultivated Land Productivity Subsidy: excessive CF input is the dominant driver of black soil fertility degradation, and curbing such overuse is the direct path to achieving cultivated land protection. Second, it fits subsidy accounting logic: the magnitude of CF cuts directly corresponds to farmers’ production opportunity costs, and the matching degree between subsidies and abatement costs can directly reflect the incentive effect of fiscal funds. Third, it ensures the validity of evaluation: as a quantifiable household production behavior variable, CF abatement can avoid interference from multiple confounding factors and more clearly identify the net effect of the policy. Accordingly, we adopted CF abatement as the primary indicator for policy assessment.

Existing research on agricultural incentive policies largely assesses welfare impacts and implementation efficiency [27,28], but most evaluations adopt a stock-based perspective that values existing ecological endowments. Few studies benchmark subsidy payments against the opportunity costs of generating incremental ecological improvement [25]. For the Northeast black soil region specifically, no quantitative framework yet exists that explicitly links CF abatement to payment levels. Therefore, we developed an equivalent incentive framework of “CF abatement to FB” to evaluate the performance of the Cultivated Land Productivity Subsidy in Northeast China’s black soil region, with a core focus on aligning farmers’ CF abatement costs with subsidy disbursements. The construction of this framework needs to clarify the following concepts: Fertilization balance (FB) refers to an equilibrium state where CF input matches regional agro-ecological endowments. It balances farm income security and the positive ecological externalities of CF abatement, and serves as the objective benchmark for quantifying abatement potential. The fertilization balance standard (FBS) is the quantified value corresponding to the FB state, serving as the quantitative benchmark for assessing fertilization levels and setting subsidy rates. For the purposes of this study, excessive CF application is defined as the amount by which a farmer’s actual CF input exceeds the regional FBS. On this basis, the rate of excessive CF application (RECFA) is calculated as the ratio of excess CF volume to the FBS, used to measure the degree of over-fertilization. Equivalent compensation is an incentive-based paradigm where subsidies are aligned with ecological protectors’ actual opportunity costs. For cultivated land CF abatement, it takes farmers’ net yield losses from cutting excess CF input to the FBS as the core accounting basis to sustain farmers’ green production incentives. This framework differs methodologically from existing studies in two dimensions. First is the innovation in evaluation logic. Taking FBS as an objective benchmark, the framework converts CF abatement into quantifiable subsidy equivalents, shifting from traditional ecological stock evaluation to incremental cost matching. Unlike composite index-based evaluation systems that often suffer from variable omission and subjective weighting, this design avoids subjective weight setting and, in turn, improves the objectivity and accuracy of evaluation results. Second is the optimization of analytical path and scale. Built on field survey data, it conducts a dynamic comparative analysis of subsidy receipts and CF abatement costs at both regional and household levels. In contrast to econometric approaches like DID that inherently require multi-group, multi-period data, this framework adapts to single-region cross-sectional scenarios. Meanwhile, it introduces RECFA to eliminate confounding factors and further enhance the reliability of policy effect assessment.

Based on the above analysis, this study attempts to address four research questions:

(1) How to construct the logical framework for equivalent ecological compensation oriented to CF abatement and FB? (2) Is the current subsidy standard sufficient to achieve the regional FB target at the aggregate level? (3) How does the subsidy perform at the household level, and what differences exist across different farmer groups? (4) What drives the gap between actual policy outcomes and theoretical objectives?

To address these questions, the study is structured around one overarching aim delivered through four specific objectives. The overarching aim is to develop an equivalent ecological compensation framework centered on CF abatement and FB, and systematically assess the incentive performance and design limitations of the Cultivated Land Productivity Subsidy in the study area, providing quantitative evidence and practical references for optimizing agricultural ecological subsidy policies. These questions are addressed through four specific objectives:

(1)

To establish the logical framework of equivalent ecological compensation for CF and FB. Grounded in the perspective of CF abatement and the rationale of ecological incremental compensation, we defined core concepts including FB, FBS and RECFA, and follow the logic of “excessive fertilization, CF abatement, incentive payments, FB”, framing FB attainment as a process of progressive CF cuts and incremental ecological incentives.

(2)

To estimate the total subsidy requirement for achieving regional FB and assess the sufficiency of the current official subsidy standard. We calculate RECFA at the household level to capture the actual scale of excessive fertilization, and incorporate farmers’ net income loss from CF cuts into the subsidy accounting framework for regional-level evaluation.

(3)

To analyze the match between subsidy payments and RECFA at the household level and quantify achievable CF abatement rates. We stratify households by RECFA to account for structural heterogeneity across farmer groups, evaluate whether the current subsidy payments enable farmers in different strata to reach the FB threshold, and analyze the variability of the ecological compensation effect.

(4)

To identify the root causes of deviation between actual policy outcomes and theoretical objectives and propose targeted policy recommendations. In reality, there are often scenarios such as underestimation of the RECFA, insufficient compensation amounts, and deviation from compensation objectives, which require us to analyze the root causes from a statistical perspective and put forward actionable suggestions for subsidy scheme optimization.

2. Review of Ecological Compensation Evaluation Methods

The primary objective of ecological compensation is to cover the opportunity costs borne by governments, entities and individuals within ecological conservation areas due to restricted economic development activities [29]. From a sustainable development perspective, the alignment between subsidy funds and actual opportunity costs is a key benchmark for policy performance evaluation and institutional optimizing. Existing evaluation methods for such incentive policies fall into four main categories.

The first consists of econometric approaches represented by the DID model, a quasi-natural experimental method built on panel data that estimates net policy impacts by comparing outcome changes between treatment and control groups. This method has been widely applied in regional compensation studies [11,28]. By design, it requires multi-group panel data and is thus unsuitable for the single-region cross-sectional setting of this study, and it also faces risks of external policy interference, selection bias and uneven policy implementation [30]. The second covers indicator-based evaluation systems, which generally follow the logical sequence of “indicator selection, weight determination, performance measurement”. Researchers establish indicator evaluation systems that align with policy priorities based on specific policy content, and then combine these systems with other quantitative methods to assess policy performance. Common methodological combinations include EWM-PSM [8], AHP-DEA [31,32] and EWM-CCD [33]. While flexible in design, these systems carry inherent subjectivity in indicator selection that can lead to variable omission and reduce the reliability of research results [27]. The third category refers to intuitive evaluation methods, which assess ecological improvement effects mainly through environmental monitoring and field surveys, including pre-post policy comparative analysis (tracking ecological changes before and after policy implementation) and field investigation evaluation. Relevant studies have verified their application in watershed water quality improvement and grassland ecological protection cases [34,35,36], but these methods are still limited by strong subjective judgment and may not accurately reflect the actual effects of such incentive schemes. The fourth category includes customized adaptive analytical frameworks, where scholars develop targeted analytical tools according to specific research objectives and practical needs [37], such as improved ecological footprint models and translog cost function analysis [30,38]. Such frameworks are highly context-specific and generally lack generalizability.

Overall, existing studies mostly conduct ex-post analyses based on the ecological stock compensation logic, neglecting the governance mechanism of providing economic incentives for ecological protectors to generate ecological increments. For clarity, ecological stock refers to the existing ecological value of natural resources and environmental elements at a given point in time, while ecological increment refers to the additional ecological value generated through targeted environmental governance over a specific period—the former is a stock concept and the latter a flow concept. Generating ecological increments incurs real costs, and as rational economic actors, farmers will adopt green production practices only when compensation matches these costs. Accordingly, this study constructs an equivalent ecological compensation framework of “CF abatement to FB” to assess the actual performance of the subsidy policy. Compared with existing methods, this framework addresses three core limitations: first, it adapts to single-region cross-sectional research designs, overcoming the applicability limitation of DID and similar econometric methods; second, it takes FBS as an objective benchmark to avoid the subjective weighting bias common in indicator-based systems; third, its incremental cost-matching logic more accurately captures farmers’ actual compensation requirements than intuitive evaluation and context-specific customized frameworks. Based on field survey data, this study evaluates compensation adequacy, analyses practical deviations and their root causes, and finally proposes targeted policy recommendations for optimizing agricultural ecological compensation policies.

3. Theoretical Analysis: Compensation Logic Deconstruction and Mathematical Model Construction

3.1. Logical Starting Point: A Compensation Framework Oriented to Ecological Increments and Abatement Process

Ecological compensation refers to financial compensation paid by the government to ecological protectors to offset income losses resulting from restrictions on economic activities [39]. Therefore, compensation standards should be formulated based on farmers’ net income losses from implementing ecological protection measures, rather than the value of ecosystem services they provide [25]. However, Lu et al. [40] take a different view: farmers engaged in farmland pollution remediation can benefit from the ecological value generated by their protection efforts. Thus, the value of ecosystem services should be incorporated into the accounting framework of such incentive schemes, a viewpoint supported by Xia et al. [41]. Obviously, the formulation of compensation standards for cultivated land productivity will vary with the design of compensation mechanisms. To establish scientific and reasonable compensation standards, it is first necessary to clarify the theoretical basis and fundamental principles of ecological compensation.

In fact, this study considers two approaches to ecological incentive design: one compensates farmers for income losses caused by CF abatement, and the other provides incentive compensation based on low fertilization thresholds. Due to differences in their underlying compensation mechanisms, the calculated compensation standards are bound to differ. This raises a core research question: should the government compensate farmers based on the ecological incremental value generated by cutting CF use, or on the existing ecological stock value? Li [25] argues that ecological compensation should target farmers’ new contributions to ecological improvement through CF abatement (or the corresponding increase in ecological increment), while also recognizing their historical contributions to maintaining low fertilization levels (or the corresponding ecological stock). Different from ecological stock, ecological increment refers to the additional ecological value created by farmers through proactive CF cuts, and farmers should receive equivalent incentive payments for the income losses arising from this behavior. Therefore, ecological increment serves as the core research perspective and guiding principle for subsidy design, rather than the calculation standard for compensation amount. To improve subsidy efficiency, limited financial funds should be targeted at farmers with excessive CF application to compensate them for the ecological increment they generate. At the same time, farmers who maintain low fertilization levels should be encouraged to obtain stock-based ecological compensation through market mechanisms.

When balancing soil fertility, food security goals and farm household income, CF application rates should not be minimized but maintained at a reasonable level to meet the FBS. At this point, another critical question arises: should the government disburse subsidies to farmers based on the process of CF abatement or based on the abatement target? In theory, due to the fact that current fertilization rates in the black soil region of Northeast China have exceeded the FBS, in order to achieve regional FB, excluding a few farmers who have already obtained ecological product value through market mechanisms, most farmers still need to cut their CF use to the FB level. Therefore, achieving FB can obtain ecological compensation; otherwise, compensation funds cannot be obtained. This subsidy eligibility should be closely related to whether the FB target is achieved. However, when rolling out such subsidy policies, the government cannot set payment levels based on each farmer’s opportunity cost. Therefore, the government can only implement a uniform subsidy scheme in specific regions. Statistics indicate that, given the fundamental principle of yield reduction from CF cuts, the current subsidy rate is 122.1 CNY/mu (All monetary values in this paper are expressed in Chinese Yuan (CNY). Based on the 2023 annual average exchange rate, 1 USD ≈ 7.0467 CNY. The mu is a conventional land area unit in rural China: one hectare = 15 mu, and 1 mu ≈ 666.67 m². Accordingly, the subsidy is insufficient to achieve regional FB.Based on the annual average exchange rate in 2023, 1 USD ≈ 7.0467 CNY (mu is a conventional unit of land area in rural China. One hectare = 15 mu; 1 mu = 666.67 m²), the subsidy is insufficient to achieve regional FB. From this perspective, attainment of FB is a long-term and dynamic adjustment process. It requires the government to use its institutional credibility to underwrite the agricultural income losses of farmers, and to guide farmer households to gradually lower their CF use until the FB is met. Therefore, for farmers to access subsidy funds, they must shift their fertilization behavior from excessive application to meeting the FB standard. The core of this shift lies in the gradual abatement of CF inputs. Since such CF abatement will result in economic losses for farmers, commensurate incentive payments are essential to maintain producer motivation. Otherwise, farmers will lack the motivation to voluntarily reduce CF application. In short, subsidy provision should be linked to the process of CF abatement, rather than merely the achievement of the FB goal.

Based on this logic, the “CF abatement to FB” equivalence ecological compensation framework constructed in this study includes two core components. The first is the establishment of the FB standard for the Northeast black soil region. The determination of this standard must fully consider both the guarantee of national food security and the stability of farmers’ income. Given the severe situation of excessive fertilization in this region, it is crucial to effectively curb excess CF inputs and the supply of ecological benefits. Therefore, it is necessary to scientifically determine the FBS level that considers both economic returns and ecological benefits. Second is the assessment of the equivalent incentive effects of the Cultivated Land Productivity Subsidy policy. Based on the concept of ecological compensation rooted in opportunity cost principles, mathematical statistical analysis provides a more intuitive and precise analytical framework than econometric methods for assessing subsidy outcomes across regions and households. However, the fundamental premise of the research is to clarify the actual RECFA and verify whether the statistical RECFA has been underestimated relative to the FBS. On this basis, the study examines, at the macro level, whether the total subsidy is sufficient relative to the regional total. If insufficient, what is the funding gap? In fact, farmers are the ultimate beneficiaries of the subsidy program. However, variations in CF use among various farmer groups mean that implementing fixed, uniform subsidy rates by the government will inevitably lead to payment mismatches and target bias. Thus, it is necessary to further explore the equivalent incentive relationship between “CF abatement and FB” at the household level and verify whether subsidy provision is sufficient at this level. If it is insufficient or surpluses exist, at which level? And to what extent? Finally, this study analyzed achievable CF abatement rates under current subsidy rates and conducted a variability analysis across different subsidy standards and agricultural net income losses.

3.2. Logical Mechanism: Constructing an Equivalent Ecological Compensation Model for “CF Abatement–FB”

(1) Fertilization Balance Standard (FBS). The FBS refers to the minimum CF application rate determined based on a region’s resource endowment conditions, while considering the positive externalities of CF abatement and safeguarding farmers’ agricultural production income. Based on this definition, this study integrates the methodological frameworks proposed by Erin and Michael [42], Xiang et al. [43], and Bai et al. [44] to determine the FBS in the black soil region of Northeast China.

(a) External Cost of CF Application. This study employs the Dose–Impact Method to quantify the external costs of CF application across three dimensions: atmospheric pollution, soil contamination, and water pollution. First, we construct a CF pollutant Dose–Impact Formula:

$$Dos{e}_i=M\times C_{ei}\times (W_c/W_f)$$

(1)

In Formula (1), Dose_i denotes the dose of CF pollutant i (unit: kg); M represents the pure nutrient content of CF; C_ei stands for the nutrient cycling coefficient; W_c and W_f indicate the molecular weights of the pollutant and CF, respectively. Data on CF nutrient cycling were obtained from Bai, Xu, Chen, Chen, Duan and Li [44].

Second, the Disability-Adjusted Life Year (DALY) method is applied to develop a hazard coefficient formula for CF pollution:

$$DAL{Y}_i=C_{di}\times Dos{e}_i$$

(2)

In Formula (2), DALY_i refers to the Cumulative Years of Life Lost (CYLL) caused by CF pollution (unit: years, abbreviated as “a”). C_di denotes the Years of Life Lost per unit dose of the pollutant (unit: a/kg), with values referenced from Bai, Xu, Chen, Chen, Duan and Li [44].

Third, based on the CYLL and unit labor emergy consumption, we constructed the emergy cost formula for CF pollution:

$$U={\displaystyle {\displaystyle \sum _{i=1}^n}Emerg{y}_i}={\displaystyle {\displaystyle \sum _{i=1}^n}(DAL{Y}_i\times C_m)}$$

(3)

In Formula (3), U represents the total energy cost of the environmental impact of CF application (unit: sej); Emergy_i denotes the emergy cost of pollutant i; and C_m signifies unit labor emergy consumption, with a value of 9.35 × 10¹³ sej [45].

Finally, incorporating China’s annual emergy-to-money ratios, the comprehensive formula for calculating the environmental cost of CF applications is derived as follows:

$$Emdollar=U/C_g$$

(4)

In Formula (4), Emdollar represents the macroeconomic economic value of pollution from CF applications (i.e., total comprehensive environmental cost, in CNY); C_g denotes the emergy intensity of unit macroeconomic value, defined as the ratio of emergy consumption to GDP during a specific period, with a value of 5.26 × 10¹¹ J/CNY [46].

On this basis, the comprehensive environmental cost per unit of CF (N(P), unit: CNY/kg) is calculated by dividing the total comprehensive environmental cost by the pure nutrient content of the CF (M):

$$N(P)=Emdollar/M$$

(5)

In this study, CF covers nitrogen, phosphorus, and potassium fertilizers and their compound products, and field surveys confirm that rice-specific NPK compound fertilizers are the main type applied by local farmers. All CF application rates are converted into total pure nutrient content following the standard convention in Chinese agricultural economic research [43,44,45,46]: nitrogen is calculated as elemental N, phosphorus as P₂O₅, and potassium as K₂O. The application amount of compound fertilizers is converted based on the labeled nutrient content of commercial fertilizer products to ensure a unified statistical caliber.

(b) Optimal CF Application Rate. For any given combination of input factors, the maximum achievable output is finite. Assuming other conditions remain constant, as the variable factor CF is continuously increased, grain output initially rises steadily. However, once CF input exceeds a critical threshold, grain output begins to exhibit diminishing marginal returns. Therefore, the inflection point in the relationship between CF input and grain output can be modeled using an opening downward quadratic production function. This specification is fundamentally consistent with the well-documented inverted-U pattern of crop yield response to nutrient input, following the law of diminishing marginal returns and reflecting the biological reality that excessive CF delivers no further yield gains and may even suppress production. It is also the standard empirical paradigm in research on optimal fertilization and agricultural non-point source pollution control, widely adopted across comparable studies. For the purposes of this work, it offers the practical advantage of allowing straightforward derivation of the optimal fertilization rate via first-order conditions, which underpins our calculation of the FBS benchmark for ecological compensation. Of course, our empirical results further confirm a statistically significant negative quadratic term, verifying a strong fit to the study area data.

$$y=a+bx-c{x}^2$$

(6)

In Formula (6), y represents grain yield, x denotes CF application rate, and a, b, and c are constants to be determined. According to the rational economic agent hypothesis, farmers pursue profit maximization in actual production, based on the principle that marginal cost equals marginal revenue (MC = MR). The CF application rate at the intersection point represents the optimal rate for grain production. When considering the negative externalities of excessive fertilization, the environmental costs of excessive CF application must be incorporated into the framework for calculating total social costs. At this point, the marginal social cost (MSC) of CF application comprises the marginal production cost (MPC), marginal use cost (MUC), and marginal external cost (MEC). The CF application rate corresponding to MR = SMC represents the optimal rate that balances both production and ecological benefits.

The total value of grain production (V) is calculated as the product of grain yield (y) and its average market price (P_r):

$$V=y{P}_r$$

(7)

From a social welfare perspective, the calculation of factor costs must incorporate external costs associated with CF application. Therefore, MSC is regarded as the shadow price of CF. The previously mentioned CF price P_f represents only the marginal private cost and should be replaced by MSC. Thus, the shadow price of food (MSB) equals the sum of P_r, MUB, and MEB. To simplify analysis, we assumed P_r = MSB. Under this assumption, total cost (T) and economic welfare (W) are expressed as follows:

$$T=K+xMSC$$

(8)

$$W=V-T$$

(9)

Here, K represents fixed costs, and x denotes the amount of CF applied. Based on the above formula, Formula (9) can be rewritten as:

$$W=(a+bx-c{x}^2)P_r-K-x(P_f+MUC+MEC)$$

(10)

Marginal profit is the derivative of the profit function with respect to the variable resource. By setting marginal profit to zero, one can obtain the maximum profit:

$$dW/dx=b{P}_r-2cx{P}_r-P_f-MUC-MEC=0$$

(11)

The optimal CF application rate that balances production and ecological benefits (X’) is determined as follows:

$$X^{\prime }=b/2c-(P_f+MUC+MEC)/2c{P}_r$$

(12)

(2) Evaluating the Effectiveness of Equivalent Ecological Compensation Under the Cultivated Land Productivity Subsidy. The standard for cultivated land productivity subsidy is determined by the income differential generated when individual farmers gradually transition from excessive CF application to FB. If compensation levels fail to offset farmers’ net income losses from CF abatement, they will lack incentives to reduce CF application; instead, they are likely to maintain current fertilization rates. Farmers’ CF abatement behavior and its magnitude depend on the balance between net income losses incurred by reduced CF application and government-provided compensation. Therefore, this study draws on the research ideas of Hu [47] on “Livestock reduction by herders and rewards for grassland-livestock balance” for analysis.

(a) Compensation Standards for Cultivated Land Productivity by Farmers. Assuming the FBS for the Northeast black soil region is n kg/mu; the actual CF application rate by farmers is u kg/mu; the desirable compensation standard is the compensation amount (S₁ CNY/kg) corresponding to the abatement of per kilogram of CF. The RECFA per mu based on FBS is x. The agricultural net income loss per mu due to CF abatement is t CNY. For analytical convenience, we assumed that the marginal return on CF inputs remains constant. The desirable ecological compensation formula for CF abatement is derived as follows:

$$\left(u-n\right)S_1=tx$$

(13)

$$S_1=tx/\left(u-n\right)$$

(14)

Here, the ecological compensation standard required to achieve FB exhibits a positive correlation with three factors: the agricultural net income loss from CF abatement, the RECFA, and the FBS. Conversely, it shows a negative correlation with farmers’ actual CF application rate.

(b) Statistical vs. Actual RECFA. Within a given region, RECFA (denoted x) across farm households follows a defined probability distribution function F(x), with a corresponding probability density function f(x). Here, f(x) represents the ratio of cultivated area with an RECFA x to the total cultivated area; μ and σ² denote the expected value and variance of x, respectively. The statistical RECFA is then expressed as follows:

$${\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx$$

(15)

When x ∈ (−∞,0), the actual RECFA is defined as:

$${\displaystyle {\int }_{-\infty }^{0}xf(x)}dx$$

(16)

When x ∈ (0,+∞), the actual RECFA is defined as:

$${\displaystyle {\int }_0^{+\infty }xf(x)}dx$$

(17)

Since ${\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx={\displaystyle {\int }_{-\infty }^{0}xf(x)}dx+{\displaystyle {\int }_0^{+\infty }xf(x)}dx$, and given that ${\displaystyle {\int }_{-\infty }^{0}xf(x)}dx\le 0$, it follows that:

$${\displaystyle {\int }_0^{+\infty }xf(x)}dx\ge {\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx$$

(18)

When this equality holds, it can be concluded that ${\displaystyle {\int }_{-\infty }^{0}xf(x)}dx=0$, which implies that all farmers are engaging in excessive CF application.

If some farmers do not overapply CF, the actual RECFA will exceed the statistically estimated RECFA. This indicates that the actual extent of excessive fertilization has been underestimated. The underlying reason is that the statistical calculation fails to distinguish between farmers who overapply CF and those who do not, leading to an offset between the residual fertilization quota of non-overapplying farmers and the excessive application amounts of overapplying farmers. In practice, even if some farmers apply CF below the FBS, their residual fertilization quota should not be used to offset the excessive CF application of others.

(c) Actual vs. Desired Ecological Compensation. To better analyze how the RECFA influences the desired ecological compensation, this study introduces two simplifying assumptions. First, the FBS is uniform across the black soil region in Northeast China. Second, based on the aforementioned assumption of constant marginal returns to CF inputs, the agricultural net income per unit of CF input is identical across the Northeast black soil region. In theory, compensation standards can be formulated based on the net income loss for each farmer resulting from the CF abatement. However, the government can only implement a uniform compensation standard within a given administrative region, which inevitably leads to a mismatch between the net agricultural income loss incurred by individual farmers due to CF abatement and the ecological compensation they actually receive.

Let k be the cultivated land productivity compensation standard, and g(x) be the desirable ecological compensation standard. Under this framework: if x < 0, then g(x) = 0; if x > 0, then g(x) = tx/(u − n).

Assume the gap between the actual compensation standard and the desired compensation standard is h(x); thus, the net compensation amount is expressed as h(x) = k − g(x). Specifically: if x < 0, then h(x) = k; if x > 0, then h(x) = k − tx(u − n).

(d) Aggregate vs. Structural Ecological Compensation. Aggregate ecological compensation aims to verify whether the cultivated land productivity subsidy in Northeast China’s black soil region is sufficient at the regional aggregate level. When the regional compensation standard offsets farmers’ net income loss, h(x) = k − g(x) = 0, i.e., k = g(x). At this equilibrium point, the RECFA is x^∗ = k(u − n)/t.

When $x^{*}=k(u-n)/t>{\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx$ holds, the cultivated land productivity compensation standard required to achieve FB is sufficient at the regional aggregate level.

When $x^{*}=k(u-n)/t<{\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx$ holds, the cultivated land productivity compensation standard required to achieve FB is insufficient at the regional aggregate level.

Structural ecological compensation aims to assess whether the cultivated land productivity compensation in Northeast China’s black soil region is sufficient at the farm household level. It further aims to determine at which household levels and across what percentage of cultivated land, the compensation is surplus, equivalent, or insufficient, as well as to quantify the magnitude of these discrepancies.

Building on the above findings, this study classifies the RECFA into three intervals: (−∞, 0], (0, k(u − n)/t], and (k(u − n)/t, +∞). It further analyzes the corresponding situation regarding excessive CF application, CF abatement, the proportion of ecological compensation funds, and the CF abatement ratio (

Table 1. Structural Ecological Compensation for CF Abatement.

RECFA:x	(−∞, 0] 1	(0, k(u − n)/t] 2	(k(u − n)/t, +∞) 3
Excessive CF Application Status	No Excessive CF Application	Excessive CF Application	Excessive CF Application
CF Abatement Status	No CF Abatement Required	Capable of Complete CF Abatement	Capable of Partial CF Abatement Only
Proportion of Ecological Compensation Funds	${\displaystyle {\int }_{-\infty }^{0}f(x)}dx$	${\displaystyle {\int }_0^{k(u-n)/t}f(x)}dx$	${\displaystyle {\int }_{k(u-n)/t}^{+\infty }f(x)}dx$
CF Abatement Ratio (With reference to actual RECFA)	0	${\displaystyle \frac{{\displaystyle {\int }_0^{k(u-n)/t}xf(x)}dx}{{\displaystyle {\int }_0^{+\infty }xf(x)}dx}}$	${\displaystyle \frac{{\displaystyle {\int }_{k(u-n)/t}^{+\infty }xf(x)}dx}{{\displaystyle {\int }_0^{+\infty }xf(x)}dx}}$
CF Abatement Ratio (With reference to statistical RECFA)	0	${\displaystyle \frac{{\displaystyle {\int }_0^{k(u-n)/t}xf(x)}dx}{{\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx}}$	${\displaystyle \frac{{\displaystyle {\int }_{k(u-n)/t}^{+\infty }xf(x)}dx}{{\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx}}$

Note: x = RECFA, defined as the ratio of excess CF application to the FBS. The threshold k(u − n)/t (denoted as x* in the text) is the RECFA level at which full FB is achievable under the current compensation standard. At this equilibrium point, the current subsidy per mu exactly offsets the net income loss incurred by reducing CF inputs to the FBS level. The three columns correspond to three distinct economic outcomes: ¹ Column 1 (x ≤ 0): Farmers apply CF at or below the FBS. They have no CF abatement obligation but still receive the area-based subsidy, representing “surplus compensation with zero abatement contribution”. ² Column 2 (0 < x ≤ x*): Farmers have moderate excess CF. The subsidy fully covers farmers’ opportunity cost of reducing CF inputs to the FBS, representing “full and adequate compensation that enables complete abatement”. ³ Column 3 (x > x*): Farmers apply CF at severely excessive levels. The subsidy only covers part of the income loss from full abatement, representing “insufficient compensation that only enables partial abatement”.

).

(e) Expected Achievable CF Abatement Ratio. Based on the analysis results in Table 1 and the total volume of ecological compensation funds, two key proportions can be defined: (1) the proportion of CF abatement that farmers are expected to achieve to reach FB, denoted as ${\displaystyle \frac{{\displaystyle {\int }_0^{k(u-n)/t}xf(x)}dx}{{\displaystyle {\int }_0^{+\infty }xf(x)}dx}}$; (2) the proportion of CF abatement that is not expected to be achieved to reach FB, denoted as ${\displaystyle \frac{{\displaystyle {\int }_{k(u-n)/t}^{+\infty }xf(x)}dx}{{\displaystyle {\int }_0^{+\infty }xf(x)}dx}}$.

If ecological compensation is provided exclusively to farmers who overapply CF, the expected achievable CF abatement proportion is given by:

$${\displaystyle \frac{{\displaystyle {\int }_0^{k(u-n)/t}xf(x)dx}}{{\displaystyle {\int }_0^{+\infty }xf(x)dx}}}+{\displaystyle \frac{{\displaystyle {\int }_{k(u-n)/t}^{+\infty }k(u-n)/tf(x)dx}}{{\displaystyle {\int }_0^{+\infty }xf(x)dx}}}$$

(19)

Obviously, the expected CF abatement ratio is positively correlated with three factors: the probability density function of the RECFA, the ecological compensation standards, and the RECFA. In contrast, it is negatively correlated with the agricultural net income loss per mu.

3.3. Model Assumptions and Robustness Discussion

The equivalence compensation framework developed above rests on a set of simplifying assumptions to facilitate regional and household-level analysis. This section clarifies the rationale behind each key assumption and discusses its potential implications for the estimation results.

(1)

The marginal return to CF inputs is held constant. This premise is introduced when deriving the formula for desired compensation, and serves as the basis for quantifying farmers’ opportunity costs of CF abatement. This assumption substantially simplifies the characterization of heterogeneous farmer production behaviors in opportunity cost accounting. Its rationality rests first on the relatively narrow adjustment range studied—from the regional average of 35.6 kg/mu to the FBS of 20.04 kg/mu—where the marginal product of rice varies only modestly per our estimated quadratic production function, keeping approximation error well controlled. It also offers practical advantages by simplifying opportunity cost calculations across heterogeneous farm households and improving the operability of regional aggregate analysis. In addition, this treatment is widely adopted in studies of equivalent ecological compensation for agricultural resource conservation [47]. If diminishing marginal returns were fully incorporated, the average yield loss per unit of CF abatement across the full interval would be smaller than our current estimate, and the total subsidy required to achieve full FB would be slightly lower than 552.7 CNY/mu. In other words, our estimate of the regional compensation gap is relatively conservative. Even so, the required subsidy level is still far higher than the current 122.1 CNY/mu, so the core finding of insufficient aggregate compensation remains valid.

(2)

A uniform FBS applies across the entire Northeast black soil region. This assumption is laid out at the start of the actual and desired compensation analysis, and allows a consistent benchmark for calculating RECFA across all farm households. The study area lies within a contiguous black soil belt with highly homogeneous soil properties, hydrothermal conditions and single-season rice farming systems. Since this study focuses on the aggregate effect of province-level subsidy policies, a unified average FBS aligns with the actual implementation caliber of China’s provincial unified subsidies and has more direct policy reference value. Disaggregating FBS to the county level would reveal spatial heterogeneity in compensation adequacy. Nonetheless, the regional aggregate estimate remains a valid benchmark for provincial policy design, and the broad conclusion of insufficient aggregate subsidy intensity holds.

(3)

Per-unit net income from CF input is identical across the region. This assumption complements the uniform FBS premise and supports the calculation of a unified regional compensation standard. Markets for CF, rice and agricultural machinery services are highly integrated across the three northeastern provinces, so per-unit net returns from CF use show minimal inter-provincial variation. Households with higher production costs or lower output prices would face a larger compensation gap than the average estimate, while low-cost, high-return households would face a smaller gap. The average result nonetheless reliably captures the aggregate adequacy of regional compensation funds.

(4)

One additional technical simplification is adopted when deriving the social welfare function: grain market price equals marginal social benefit (P_r = MSB). This allows the analysis to focus on the negative externalities of excessive CF application. As a staple commodity, rice’s market price already internalizes most of its food security value under China’s minimum grain purchase policy, and this treatment is standard in optimal fertilization research [43]. If the full positive externality of food security were accounted for, MSB would exceed the market price and the calculated FBS would be slightly higher, leading to a marginal increase in the required compensation standard. Again, this does not alter the core finding of insufficient current subsidies.

Taken together, these key assumptions are adopted primarily for analytical simplification, and they are appropriate for the study context and align with established research conventions in the field. Relaxing these assumptions would produce only modest, non-substantive fluctuations in key estimated values, and would not overturn the central findings of insufficient aggregate compensation and structural targeting bias.

4. Study Area and Data Sources

4.1. Study Area

The black soil region in Northeast China, one of the world’s three major black soil belts [48], covers approximately 1.03 million square kilometers. It is mainly distributed across Jilin, Liaoning, and Heilongjiang provinces and eastern Inner Mongolia [49], with the most contiguous and fertile core zones concentrated in the three northeastern provinces. As a critical national grain production and commercial grain hub, the three provinces account for over 20% of China’s total grain output with an 87.2% commodity rate (the ratio of commercially marketed grain to total grain output), leading the country in both commercial grain output and inter-provincial transfer volume. Since the 1980s, China has implemented one of the world’s strictest cultivated land protection regimes [50]. Initially centered on quantitative preservation—enforced via administrative restrictions on arable land conversion to non-agricultural uses and the requisition-compensation balance rule requiring equivalent replacement of occupied cultivated land—the system gradually shifted to a dual mandate of quantity and quality in the 2000s, when grain subsidies and comprehensive agricultural input subsidies were introduced to incentivize on-farm productivity maintenance. Since 2016, it has further developed into an integrated framework covering quantity, quality and ecological protection. The Cultivated Land Productivity Subsidy, the core policy examined in this paper, was formally established under this evolving framework as a targeted fiscal instrument to promote soil fertility conservation and reduce excessive CF application [51,52,53]. However, practical compensation still faces prominent issues such as insufficient funding and imprecise beneficiary targeting, making it necessary to further evaluate and optimize the existing compensation mechanism.

This study focuses on core rice-growing black soil areas across Heilongjiang, Jilin and Liaoning provinces, covering the three key sub-zones of the region: the Sanjiang Plain, Songnen Plain and northern Liaohe Plain. All sites lie within the world’s golden rice cultivation belt, with well-coupled sunlight, heat and rainfall conditions. The area has a temperate continental monsoon climate, with annual accumulated temperature (≥10 °C) of 1600 °C–3600 °C and annual precipitation of 400 mm–1100 mm [54]. The dominant soil types are typical black soil, meadow black soil and albic black soil with thick humus layers and high inherent fertility. Early-maturing single-season rice with one harvest per year is the dominant cropping pattern, aligned with the mainstream farming system of the broader Northeast black soil region. First, the natural and agronomic characteristics outlined above reflect the general zonal features of the region. Second, local CF input intensity, rice yield levels and production patterns match the regional average for rice farming. Third, the key issues addressed—excessive CF application, black soil degradation and agricultural non-point source pollution—are prevalent challenges across the entire region. When combined with the uniformly implemented cultivated land productivity subsidy policy across the three provinces, the research conclusions hold generalizability and can provide empirical reference for formulating regional CF abatement and ecological compensation policies.

4.2. Data Sources

(1) Regional sample design. From March 2022 to August 2023, the research team conducted five rounds of field surveys among rice farmers in the three northeastern provinces. Rice farmers were selected as the research subjects because early-maturing single-season rice cultivation areas in Northeast China are important national grain production bases, where excessive CF application is widespread and thus offers great potential for CF abatement. Concurrently, the cultivated land productivity subsidy policy offers broad coverage and strong targeting. Therefore, it is reasonable for this study to explore the policy effectiveness of cultivated land productivity subsidies for rice growers from the perspective of CF abatement.

This study adopted a stratified multi-stage sampling design combined with simple random sampling, with clear selection criteria at each level to ensure sample representativeness. At the provincial level, Heilongjiang, Jilin and Liaoning provinces were selected as the study scope. They cover more than 90% of the contiguous black soil arable land and core rice-producing areas in the Northeast black soil region, and are the key implementation zones of the cultivated land productivity subsidy policy, with representative agricultural production characteristics. At the prefectural level, 12 prefecture-level administrative units were selected hierarchically according to the principle of “large inter-group differences and small intra-group differences”, based on black soil distribution, rice planting scale and agricultural development level. Specifically, 6 units from Jilin Province, 3 from Liaoning Province and 3 from Heilongjiang at the county level were selected; two county-level units with well-developed rice industries were selected within each prefecture, prioritizing major rice-producing counties with a high proportion of black soil and stable policy implementation, and covering both plain and semi-mountainous areas to retain production diversity. At the village level, two villages with concentrated rice cultivation and complete agricultural production records were chosen in each county, excluding remote mountain villages and non-core rice-growing areas to ensure data quality. At the farmer level, 10–15 rice growers were randomly selected from each village for face-to-face interviews. Eligible respondents were local rural households with years of continuous rice farming experience, excluding households with extremely high off-farm income and short-term land lessees, to ensure the samples represent the core production subjects targeted by the policy. The detailed geographical distribution of samples at the prefectural, county and village levels is shown in

Table 2. Sample distribution.

Province	Prefecture-Level Division	County-Level Division	Town/Village	Valid Questionnaires	Proportion (%)
Jilin Province (290 questionnaires)	Baicheng City	Taonan City	Xingfu Village, Chunhua Village	25	47.39%
		Taobei District	Liming Village, Shuguang Village	26
	Changchun City	Jiutai District	Qiangang Village, Hongguang Village	27
		Gongzhuling City	Bawu Town, Nanwaizi Village	23
	Jilin City	Yongji County	Wujia Village, Xinxing Village	25
		Shulan City	Ping’an Town, Shuanghe Village	30
	Tonghua City	Meihekou City	Tongxin Village, Xitaiping Village	22
		Tonghua County	Xijiang Town, Xinmin Village	21
	Yanbian Korean Autonomous Prefecture	Yanji City	Pinggang Village, Badao Village	24
		Longjing City	Xinhua Village, Dongsheng Village	22
	Songyuan City	Changling County	Wanghai Village, Wangjiahu Village	25
		Qianguo County	Daliba Village, Zuojia Village	20
Liaoning Province (157 questionnaires)	Panjin City	Dawa District	Yejia Village, Xiaoqing Village	24	25.65%
		Panshan County	Zhangjia Village, Lala Village	30
	Dalian City	Zhuanghe City	Shaxi Village, Zhanglu Village	27
		Wafangdian City	Xianyuwan Town, Songshu Town	26
	Shenyang City	Sujiatun District	Wanzhuang Village, Beihong Village	23
		Liaozhong District	Wangjiagang Village, Manghou Village	27
Heilongjiang Province (165 questionnaires)	Shuangyashan City	Raohe County	Lintong Village, Changbei Village	30	26.96%
		Baoqing County	Fuxing Village, Xingye Village	30
	Qitaihe City	Qiezihe District	Xinmingshan Village, Xinshan Village	29
		Boli County	Xinhua Village, Xinqi Village	26
	Wuchang City	Anjia Town	Changfa Village, Minzhu Village	28
		Xiaoshanzi Town	Shengfeng Village, Yong’an Village	22
Total	12	24	48	612	100%

Data source: Compiled from field survey results.

.

During the field surveys, the research team distributed 628 questionnaires and ultimately obtained 612 valid responses, with a validity rate of 97.5%. Descriptive statistics of sample household characteristics are presented in

Table 3. Basic information of sample farmers.

Variable		Jilin Province		Liaoning Province		Heilongjiang Province		Total
		Household Count	Proportion (%)	Household Count	Proportion (%)	Household Count	Proportion (%)	Household Count	Proportion (%)
Gender	Male	179	61.7	82	52.2	107	64.8	368	60.1
	Female	111	38.3	75	47.8	58	35.2	244	39.9
Age (years)	<50	31	10.7	14	8.9	23	13.9	68	11.1
	[50, 59]	113	38.9	64	40.8	47	28.5	224	36.6
	[60, 69]	127	43.8	67	42.7	91	55.2	285	46.6
	≥70	19	6.6	12	7.6	4	2.4	35	5.7
Education Level	Illiterate	45	15.5	26	16.6	33	20.0	104	17.0
	Primary	119	41.1	68	43.3	56	33.9	243	39.7
	Junior High	72	24.8	37	23.5	46	27.9	155	25.3
	Senior/Technical Secondary	34	11.7	13	8.3	24	14.5	71	11.6
	College and Above	20	6.9	13	8.3	6	3.7	39	6.4
Cultivated Land Area (mu)	[0, 20]	122	42.1	73	46.5	61	37.0	256	41.8
	(20, 60]	125	43.1	62	39.5	58	35.2	245	40.0
	(60, 100]	30	10.3	14	8.9	33	20.0	77	12.6
	>100	13	4.5	8	5.1	13	7.8	34	5.6
CF Application Rate (kg/mu)	[0, 20]	36	12.4	22	14.0	31	18.8	89	14.6
	(20, 40]	131	45.2	72	45.9	83	50.3	286	46.7
	(40, 60]	108	37.2	52	33.1	39	23.6	199	32.5
	>60	15	5.2	11	7.0	12	7.3	38	6.2

Data source: Compiled from field survey results.

.

(2) Potential Selection Bias. Regarding potential selection bias in the sampling process, this study evaluates its possible impact on the estimation results as follows: First, the sample is concentrated in core rice-growing black soil areas, with limited coverage of scattered rice-growing areas at the regional edge. However, since this study focuses explicitly on core black soil zones, this scope delimitation falls within an acceptable range, and the core conclusions remain robust for the target study area. Second, the age and education structure of the sample is highly consistent with the actual labor structure of rural rice production in Northeast China, and does not constitute a systematic bias. Its impact on the overall estimation is negligible. Third, excluding households with extremely high off-farm income and short-term land lessees may slightly overestimate farmers’ sensitivity to the policy. Nevertheless, the sampled professional grain farmers are more aligned with the target group of the cultivated land productivity subsidy policy, and can more accurately reflect the actual policy response of core production subjects.

Overall, the sampling design minimizes major systematic biases, and the sample offers reasonable representativeness for the study’s target population.

(3) Representativeness and Reliability Assessment. The final sample size was determined by balancing three sets of considerations: prevailing empirical norms, model statistical requirements, and fieldwork feasibility. For farm household studies in Northeast China’s black soil belt, 500–800 valid responses are widely accepted as an appropriate scale [55,56], and our 612 valid samples fall well within this range. This sample size provides sufficient statistical power for the econometric analyses used, and reduces the risk of small-sample estimation bias. At the operational level, a sampling quota of 10–15 farmers per village was chosen to fit the stratified multi-stage design, balancing survey costs, fieldwork logistics and representativeness at the local level.

On this basis, we formally assessed the sample’s representativeness and analytical reliability. On the one hand, we compared sample characteristics with official provincial statistics and published benchmark data on rice farmers in the three northeastern provinces. Basic demographic features of the sample align well with the regional rural labor structure. More importantly, core analytical variables—including cultivated land scale, CF application intensity and per-unit rice yield—are highly consistent with the overall regional level, which verifies the representativeness of the sample for the core analysis of CF use and ecological compensation. On the other hand, we evaluated the statistical reliability of the study. Table 7 Based on the stratified distribution analysis of our survey data, farmers are ranked by CF application rate from highest to lowest, with relevant indicators computed for each over-application gradient.presents a stratified distribution analysis, where farmers are ranked by CF application from highest to lowest, with relevant indicators computed for each overapplication gradient. With adequate sample coverage across all gradients, we minimized the estimation bias that typically arises from sparse observations at the distribution tails. For the OLS regression used to estimate the yield impact of CF application, rice yield per mu is specified as the dependent variable and CF application rate as the core explanatory variable. Post hoc statistical power analysis was performed using G*Power3.1 software. Applying the conventional significance level of α = 0.05 and a moderate effect size of f² = 0.15, the model with 612 valid observations returns statistical power above 0.8. This meets the standard threshold for empirical analysis and supports reliable statistical inference.

4.3. Questionnaire Design and Data Quality Control

Data for this study were collected through face-to-face semi-structured interviews with rice farmers, with a questionnaire designed to examine CF overapplication and ecological compensation in Northeast China’s black soil regions. The questionnaire was organized into five interrelated sections. The first section captures individual farmer characteristics, including demographics, farming experience, risk preferences, organizational membership, and knowledge of agricultural policies. The second covers household and production profiles, such as labor structure, income composition, rice input costs and returns, and subsidy uptake. The third and most substantive section documents detailed CF purchase and application practices, including product types, purchase channels, application rates, timing, and operational methods for each fertilization event across the full growing season. The fourth section examines farmers’ perceptions of fertilization, their decision-making logic, and views on the environmental and agronomic impacts of CF use. The final section explores awareness and acceptance of market-based ecological compensation, expected risks and returns, and preferred compensation mechanisms. Each interview lasted 50 to 60 min on average.

We implemented a three-stage validation process to refine the questionnaire before formal fieldwork. The initial draft drew on established survey instruments from peer-reviewed farm household studies in the region and was adapted to include granular data on split CF applications and ecological compensation preferences tailored to our research questions. The draft was then reviewed by researchers in agricultural economics and soil science to assess content validity, and technical terminology was adjusted to align with local farming terminology and ensure comprehensibility for farmers. Finally, we piloted the questionnaire with 30 rice farmers in Changchun, Jilin Province. Pilot feedback informed refinements to question wording, simplified explanations of abstract concepts such as market-based compensation, and the removal of redundant items to finalize the instrument.

All interviewers were graduate students with backgrounds in agricultural economics and management, and completed standardized training prior to fieldwork. Training covered the study’s objectives, uniform definitions of key metrics, neutral questioning techniques, and strategies for addressing sensitive topics. Trainees passed practice interview assessments before joining the field team, and daily debrief meetings were held throughout the survey period to ensure consistent data recording across interviewers.

We incorporated multiple design features and field protocols to minimize recall and response bias. To limit recall bias, all questions on production inputs and outputs referenced the most recent full rice growing season, and respondents were encouraged to consult purchase receipts and subsidy records for accuracy. The questionnaire included built-in cross-checks to verify total CF use against per mu application rates and planted area, with inconsistencies clarified and corrected on site. To mitigate response bias, interviewers opened each interview by stating the survey’s exclusive academic purpose and assuring full anonymity and confidentiality. Questions were read verbatim, with only neutral clarification provided as needed. Sensitive topics such as over-fertilization and policy attitudes were framed around common local farming practices to reduce respondent defensiveness. Following fieldwork, all completed questionnaires were screened for logical consistency after fieldwork, and invalid or contradictory responses were excluded from the final sample.

5. Results

5.1. Calculation of FBS

For this study, total CF input is calculated as total pure nutrient (N, P₂O₅, K₂O) applied per mu over the full growing season, combining both basal dressings and topdressings. This is a standard metric widely used across agricultural policy evaluation and CF-focused environmental impact research [44,45,46].

Field observations show that local rice farmers follow a staged fertilization schedule aligned with crop growth. As a basal dressing before transplanting, most apply a conventional NPK compound fertilizer at 35 kg/mu, typically with a nutrient ratio of N:P₂O₅:K₂O = 1:1.1–1.5:1–1.2. For topdressings at the tillering (mid-June) and grain-filling (mid-July) stages, practices differ across households: some use straight nitrogen and potassium sources (urea, ammonium sulfate, potassium sulfate), while others apply compound fertilizers tailored to each specific growth phase. Given this variation in topdressing products, and in keeping with both standard practice in the literature and the core focus of this policy evaluation, we used total growing-season nutrient input as the unified metric for all statistical analysis and impact estimation.

(1) Estimating the External Costs of CF Application. Drawing on mathematical model formulas and relevant data indicators, this study estimated the pollutant generation dosage, pollutant impact intensity, and CYLL resulting from CF inputs in the black soil region, from three dimensions: atmosphere, soil, and water (

Table 4. Assessment of Pollutant Information from CF Application in Black Soil Region of Northeast China.

Categorized Accounts		Generation Dosage (kg)	Impact Intensity (a/kg)	CYLL(a)
Atmosphere	NH3	1.44595	5.10 × 10−5	7.37 × 10−5
	N2O	0.502808	4.15 × 10−3	2.09 × 10−3
	NOx	0.323845	2.67 × 10−3	8.65 × 10−4
	NO3−	59.7261	6.90 × 10−2	4.12 × 1000
Soil	PO43−	25.63275	4.75 × 10−2	1.22 × 1000
	Cd	0.017925	1.06 × 10−4	1.90 × 10−6
	NO3−-N	7.093759	1.32 × 10−4	9.36 × 10−2
Water	NH4+-N	1.017423	6.50 × 10−3	6.61 × 10−3
	PO43−	3.351975	6.21 × 10−3	2.08 × 10−2

Note: Pollutant generation dosages, impact intensities and CYLL are calculated via the Dose–Impact Method and DALY approach detailed in Section 3.2. All values are estimated for per-unit CF input in the study area. Units: generation dosage (kg), impact intensity (a/kg), CYLL (a, years).

).

Based on this, by incorporating relevant parameter values and applying formulas (3)–(5), the following results were calculated: the total pollution emergy cost (U) of CF application is 5.11 × 10¹⁴ sej, the total economic value (Emdollar) of CF pollution is 971 CNY/kg, and the environmental cost per unit of CF input (N(P)) is 40.6 CNY/kg (see

Table 5. Assessment of Environmental Impact Costs of CF Application in the Black Soil Region of Northeast China.

Categorized Accounts		Total Pollution Emergy Cost (sej)	Total Economic Value (CNY/kg)	Environmental Cost per Unit (CNY/kg)
Atmosphere	NH3	6.90 × 109	1.31 × 10−2	5.48 × 10−4
	N2O	1.95 × 1011	3.71 × 10−1	1.55 × 10−2
	NOx	8.08 × 1010	1.54 × 10−1	6.43 × 10−3
	NO3−	3.85 × 1014	7.32 × 102	3.07 × 101
Soil	PO43−	1.14 × 1014	2.16 × 102	9.06 × 100
	Cd	1.78 × 108	3.38 × 10−4	1.41 × 10−5
	NO3−-N	8.76 × 1012	1.66 × 101	6.96 × 10−1
Water	NH4+-N	6.18 × 1011	1.18 × 1000	4.92 × 10−2
	PO43−	1.95 × 1012	3.70 × 1000	1.55 × 10−1
Total	-	5.11 × 1014	971	40.6

Note. Environmental cost indicators are calculated following Formulas (3)–(5) in Section 3.2. Units: total pollution emergy cost (sej), total economic value (CNY/kg), environmental cost per unit (CNY/kg). For unit conversion: 1 kg/mu = 15 kg/ha (1 hectare = 15 mu).

for specific indicators).

(2) Optimal CF Application Rate. As indicated by the preceding analysis, the environmental cost per unit of CF input is 40.6 CNY/kg. Based on Formula (18), and assuming that CF is treated as an inexhaustible resource with MUC set to 0, the formula can be further simplified as follows:

$$X^{\prime }=b/2c-(P_f+40.6)/2c{P}_r$$

(20)

We estimated the quadratic relationship between rice yield per unit area and CF application rate in the black soil region from 2006 to 2022. The OLS regression is specified as:

$$y=a+bx-c{x}^2+\epsilon$$

(21)

where y is rice yield (kg/mu), x is CF application rate (kg/mu), a is the intercept term, b and c are the linear and quadratic coefficients of CF input, respectively, and ε is the stochastic error term. The overall model is statistically significant at the 5% level (F (2, 14) = 4.96, p = 0.0235), with an R² of 0.4148 and adjusted R² of 0.3312. This level of explanatory power is reasonable for a univariate production function based on regional time-series data, as rice yield is also shaped by climatic conditions, agronomic practices and technological progress not captured in the model. The linear CF coefficient (b = 134.841, p = 0.072) and quadratic coefficient (c = 0.196, p = 0.087) are both significant at the 10% level, and the negative quadratic term aligns with the standard law of diminishing marginal returns to CF input. Residual diagnostics confirm no significant first-order serial correlation (Durbin-Watson d = 1.607), normally distributed residuals (joint p = 0.157), and homoskedasticity (White’s test p = 0.213), verifying the reliability of the estimates. The resulting quadratic production function is: y = −0.196x² + 134.841x − 15446.44. Based on price data from the BRIC Agricultural Database, the market purchase price of rice (Pᵣ) is 2.85 CNY/kg, and the average market price of CF (P_f) is 7.89 CNY/kg. Substituting the above parameters into Formula (20) yielded the optimal fertilization level that balances production and ecological benefits, namely the FBS of 300.58 kg/ha, equivalent to 20.04 kg/mu. For the convenience of calculation, this value was rounded off to 20 kg/mu.

On this basis, one-way sensitivity analyses were conducted to evaluate the robustness of the FBS estimates. Each of the five core parameters was adjusted by ±10% and ±20% from its baseline value, with all other parameters held constant. Full results are reported in Table 6.

Table 6. Sensitivity analysis of parameter changes.

Parameter	Parameter Variation Amplitude
	−20%	−10%	10%	20%
Marginal yield coefficient (b)	107.87 (15.45)	121.36 (17.75)	148.33 (22.33)	161.81 (24.63)
Quadratic coefficient (c)	0.157 (25.05)	0.176 (22.27)	0.216 (18.22)	0.235 (16.70)
CF price (Pf)	6.31 (20.13)	7.10 (20.09)	8.68 (19.99)	9.47 (19.94)
Rice price (Pr)	2.28 (19.32)	2.57 (19.72)	3.14 (20.30)	3.42 (20.52)
Unit environmental cost (E)	32.48 (20.52)	36.54 (20.28)	44.66 (19.80)	48.72 (19.55)

Note. Values outside parentheses indicate adjusted parameter values under each perturbation; values inside parentheses are corresponding FBS estimates in kg/mu. Baseline parameters: b = 134.841, c = 0.196, P_f = 7.89 CNY/kg, P_r = 2.85 CNY/kg, E = 40.60 CNY/kg; FBS = 20.04 kg/mu. All FBS can be converted to kg/ha by multiplying by 15.

Table 6. Sensitivity analysis of parameter changes.

Parameter	Parameter Variation Amplitude
	−20%	−10%	10%	20%
Marginal yield coefficient (b)	107.87 (15.45)	121.36 (17.75)	148.33 (22.33)	161.81 (24.63)
Quadratic coefficient (c)	0.157 (25.05)	0.176 (22.27)	0.216 (18.22)	0.235 (16.70)
CF price (Pf)	6.31 (20.13)	7.10 (20.09)	8.68 (19.99)	9.47 (19.94)
Rice price (Pr)	2.28 (19.32)	2.57 (19.72)	3.14 (20.30)	3.42 (20.52)
Unit environmental cost (E)	32.48 (20.52)	36.54 (20.28)	44.66 (19.80)	48.72 (19.55)

Note. Values outside parentheses indicate adjusted parameter values under each perturbation; values inside parentheses are corresponding FBS estimates in kg/mu. Baseline parameters: b = 134.841, c = 0.196, P_f = 7.89 CNY/kg, P_r = 2.85 CNY/kg, E = 40.60 CNY/kg; FBS = 20.04 kg/mu. All FBS can be converted to kg/ha by multiplying by 15.

As shown in Table 6, the FBS was most responsive to shifts in the production function coefficients. It rose alongside the marginal yield coefficient b, as a higher marginal product of CF pushes up the socially optimal application rate. By contrast, larger absolute values of the quadratic coefficient c—reflecting a faster decline in marginal returns—reduced FBS. These two coefficients accounted for the majority of variation in the estimates.

Market prices and environmental costs had far more modest effects. Rice price (P_r) showed a mild positive association with FBS, driven by the higher value of the marginal product of CF at higher output price. Unit environmental cost (E) exerted a small negative influence, as higher external costs raise marginal social cost and lower the optimal fertilization threshold. CF price (P_f) had the weakest impact overall, with a ±20% perturbation shifting FBS by less than 1%.

Across all ±20% scenarios, FBS estimates ranged from 15.45 to 25.05 kg/mu; the ±10% adjustments yielded a tighter range of 17.75 to 22.33 kg/mu. Even the upper bound of the ±20% range (25.05 kg/mu) remained well below the observed average application rate of 35.6 kg/mu in the sample, confirming that the core finding of widespread excessive CF use is robust to reasonable parameter uncertainty. Consistently, the ecological compensation required to achieve regional FB exceeded the current subsidy level across all scenarios, supporting the conclusion of insufficient aggregate compensation at the regional scale.

5.2. Evaluating the Effectiveness of Equivalent Ecological Compensation Under the Cultivated Land Productivity Subsidy

By integrating the FBS of the black soil region with individual farmers’ fertilization levels, the RECFA, desired compensation standard, and net compensation amount for each farmer can be calculated. For the convenience of statistical analysis and computation, this study sorts the 612 sample farm households in descending order of their fertilization levels, followed by corresponding statistical analyses (Table 7).

Table 7. Statistical information of sample farmers.

Serial No.	Cultivated Land Area (mu)	Net Rented-In Area (mu)	Cumulative Rented-In Area (mu)	Cumulative Rented-In Ratio (%)	Yield (kg/mu)	Actual CF Application (kg/mu)	Excessive CF Amount (kg/mu)	Cumulative Average Excessive CF per mu (kg)	RECFA (%)	Cumulative Average RECFA (%) ${\displaystyle {\int }_0^{\mathit{x}}\mathit{x}\mathit{f}(\mathit{x})}\mathit{d}\mathit{x}$	Desired Ecological Compensation Standard (CNY/kg/mu)	Desired Ecological Compensation Amount (CNY)	Actual Ecological Compensation Amount (CNY)	Compensation Standard Gap (CNY)	Cumulative Cultivated Area Ratio (%)	Cumulative Net Cultivated Area (mu)	Cumulative Net Cultivated Area Ratio (%) ${\displaystyle {\int }_0^{\mathit{x}}\mathit{f}(\mathit{x})}\mathit{d}\mathit{x}$
1	1	0	0	0	613.3	89	69	69	345	345	6.1	421	122.1	−289.9	0	1.0	0
20	24	4	104	0.4	600	66	46	1045.7	230	261.4	9.2	8420	2442	−5978	1.4	294	1.6
40	240	52	415.6	1.5	600	60	40	1897.8	200	237.2	10.5	79,148	22,954.8	−56,193.2	5.4	1142.6	6.1
60	6	0	507.6	1.9	640	56.7	36.7	2656.1	183.3	221.3	11.5	2526	732.6	−1793.4	7.2	1558.6	8.4
80	23	10	661.6	2.5	573.3	52.7	32.7	3327.5	163.3	208	12.9	5473	1587.3	−3885.7	8.8	1879.6	10.1
100	23	3	709.6	2.6	593.3	50.7	30.7	3949.5	153.3	197.5	13.7	8420	2442	−5978	9.8	2103.1	11.3
120	33	8	944.1	3.5	580	49.3	29.3	4547.1	146.7	189.5	14.4	10,525	3052.5	−7472.5	13.3	2920.3	15.7
140	25	0	1095.1	4.1	600	47.7	27.7	5117.1	138.3	182.8	15.2	10,525	3052.5	−7472.5	15.9	3501.3	18.8
160	56	6	1233.1	4.6	566.7	46	26	5653.9	130	176.7	16.2	21,050	6105	−14,945	19	4239.3	22.8
180	67	17	1713.1	6.3	560	44.7	24.7	6159.3	123.3	171.1	17.1	21,050	6105	−14,945	24.1	5329.3	28.6
200	12	2	2044.1	7.6	620	43.3	23.3	6634.6	116.7	165.9	18	4210	1221	−2989	27.8	6107.3	32.8
220	15	0	2115.1	7.8	633.3	41.7	21.7	7082.8	108.7	161	19.4	6315	1831.5	−4483.5	29.1	6427.4	34.5
240	10	0	2653.1	9.8	633.3	40	20	7500.5	100	156.3	21.1	4210	1221	−2989	34.6	7777.9	41.7
260	5	2	2732.1	10.1	593.3	39.3	19.3	7893.3	96.7	151.8	21.8	1263	366.3	−896.7	36	8080.9	43.4
280	72	18	2948.6	10.9	566.7	38	18	8264	90	147.6	23.4	22,734	6593.4	−14,140.6	38.8	8687.9	46.6
300	47	17	3398.6	12.6	566.7	36.3	16.3	8606.9	81.7	143.4	25.8	12,630	3663	−8967	43.4	9625.9	51.7
320	57	10	3519.6	13.0	546.7	35.1	15.1	8917	75.3	139.3	27.9	19,787	5738.7	−14,048.3	45.5	10,118.4	54.3
340	31	17	3860.6	14.3	520	33.9	13.9	9204	69.7	135.4	30.2	5894	1709.4	−4184.6	48.5	10,717.4	57.5
360	41	4	4109.6	15.2	540	33.3	13.3	9471.9	66.7	131.6	31.6	15,577	4517.7	−11,059.3	50.8	11,235.4	60.3
380	73	11	4335.6	16.1	580	31.3	11.3	9722.6	56.7	127.9	37.1	26,102	7570.2	−18,531.8	54	11,967.4	64.2
400	5	0	4643.6	17.2	533.3	30	10	9935.3	50	124.2	42.1	2105	610.5	−1494.5	57.3	12,647.8	67.9
420	20	8	4714.6	17.5	506.7	28.7	8.7	10,125.7	43.3	120.5	48.6	5052	1465.2	−3586.8	58.3	12,849.3	69
440	13	5	4827.6	17.9	526.7	27.7	7.7	10,291	38.3	116.9	54.9	3368	976.8	−2391.2	59.5	13,085.8	70.2
460	21.5	2	4950.6	18.3	453.3	26.7	6.7	10,431	33.3	113.4	63.2	8209.5	2381	−5828.6	60.9	13,368.3	71.7
480	40	22	5238.1	19.4	460	23.6	3.6	10,536.5	18	109.8	116.9	7578	2197.8	−5380.2	63	13,711.4	73.6
481	20	8	5246.1	19.4	453.3	23.3	3.3	10,539.8	16.7	109.6	126.3	5052	1465.2	−3586.8	63.1	13,723.4	73.7
500	59	9	5507.6	20.4	366.7	22.0	2	10,594.1	10	105.9	210.5	21,050	6105	−14,945	66.6	14,514.3	77.9
520	2.5	0	5747.6	21.3	300	20.3	0.3	10,614.3	1.7	102.1	1263	1052.5	305.3	−747.3	69.2	15,046.6	80.8
523	99	3	5773.6	21.4	280	20.3	0.3	10,615.3	1.7	101.5	1263	40,416	11,721.6	−28,694.4	69.6	15,148.6	81.3
524	92	33	5821.6	21.6	306.7	20	0	10,615.3	0	101.3	0	0	7203.9	7203.9	69.9	15,207.6	81.6
540	59	12	6096	22.6	213.3	14.7	−5.3	10,569.3	−26.7	97.9	0	0	5738.7	5738.7	71.9	15,615.8	83.8
560	66	38	6597	24.5	246.7	8.7	−11.3	10,412	−56.7	93	0	0	3418.8	3418.8	77.4	16,835.8	90.4
580	259	120	7696	28.5	220	6	−14	10,159	−70	87.6	0	0	16,971.9	16,971.9	83.8	17,767.3	95.4
600	162	123	11,005	40.8	126.7	0	−20	9781.2	−100	81.5	0	0	4761.9	4761.9	97.6	18,601.3	99.8
612	3.3	0	11,634	43.1	146.7	0	−20	9541.2	−100	78	0	0	402.9	402.9	100	18,632.6	100

Data source: Compiled and calculated from field survey results. Note: The serial numbers are sorted in descending order by the actual CF application rate for each rice-growing household. Due to space constraints, only partial data are presented.

Table 7. Statistical information of sample farmers.

Serial No.	Cultivated Land Area (mu)	Net Rented-In Area (mu)	Cumulative Rented-In Area (mu)	Cumulative Rented-In Ratio (%)	Yield (kg/mu)	Actual CF Application (kg/mu)	Excessive CF Amount (kg/mu)	Cumulative Average Excessive CF per mu (kg)	RECFA (%)	Cumulative Average RECFA (%) ${\displaystyle {\int }_0^{\mathit{x}}\mathit{x}\mathit{f}(\mathit{x})}\mathit{d}\mathit{x}$	Desired Ecological Compensation Standard (CNY/kg/mu)	Desired Ecological Compensation Amount (CNY)	Actual Ecological Compensation Amount (CNY)	Compensation Standard Gap (CNY)	Cumulative Cultivated Area Ratio (%)	Cumulative Net Cultivated Area (mu)	Cumulative Net Cultivated Area Ratio (%) ${\displaystyle {\int }_0^{\mathit{x}}\mathit{f}(\mathit{x})}\mathit{d}\mathit{x}$
1	1	0	0	0	613.3	89	69	69	345	345	6.1	421	122.1	−289.9	0	1.0	0
20	24	4	104	0.4	600	66	46	1045.7	230	261.4	9.2	8420	2442	−5978	1.4	294	1.6
40	240	52	415.6	1.5	600	60	40	1897.8	200	237.2	10.5	79,148	22,954.8	−56,193.2	5.4	1142.6	6.1
60	6	0	507.6	1.9	640	56.7	36.7	2656.1	183.3	221.3	11.5	2526	732.6	−1793.4	7.2	1558.6	8.4
80	23	10	661.6	2.5	573.3	52.7	32.7	3327.5	163.3	208	12.9	5473	1587.3	−3885.7	8.8	1879.6	10.1
100	23	3	709.6	2.6	593.3	50.7	30.7	3949.5	153.3	197.5	13.7	8420	2442	−5978	9.8	2103.1	11.3
120	33	8	944.1	3.5	580	49.3	29.3	4547.1	146.7	189.5	14.4	10,525	3052.5	−7472.5	13.3	2920.3	15.7
140	25	0	1095.1	4.1	600	47.7	27.7	5117.1	138.3	182.8	15.2	10,525	3052.5	−7472.5	15.9	3501.3	18.8
160	56	6	1233.1	4.6	566.7	46	26	5653.9	130	176.7	16.2	21,050	6105	−14,945	19	4239.3	22.8
180	67	17	1713.1	6.3	560	44.7	24.7	6159.3	123.3	171.1	17.1	21,050	6105	−14,945	24.1	5329.3	28.6
200	12	2	2044.1	7.6	620	43.3	23.3	6634.6	116.7	165.9	18	4210	1221	−2989	27.8	6107.3	32.8
220	15	0	2115.1	7.8	633.3	41.7	21.7	7082.8	108.7	161	19.4	6315	1831.5	−4483.5	29.1	6427.4	34.5
240	10	0	2653.1	9.8	633.3	40	20	7500.5	100	156.3	21.1	4210	1221	−2989	34.6	7777.9	41.7
260	5	2	2732.1	10.1	593.3	39.3	19.3	7893.3	96.7	151.8	21.8	1263	366.3	−896.7	36	8080.9	43.4
280	72	18	2948.6	10.9	566.7	38	18	8264	90	147.6	23.4	22,734	6593.4	−14,140.6	38.8	8687.9	46.6
300	47	17	3398.6	12.6	566.7	36.3	16.3	8606.9	81.7	143.4	25.8	12,630	3663	−8967	43.4	9625.9	51.7
320	57	10	3519.6	13.0	546.7	35.1	15.1	8917	75.3	139.3	27.9	19,787	5738.7	−14,048.3	45.5	10,118.4	54.3
340	31	17	3860.6	14.3	520	33.9	13.9	9204	69.7	135.4	30.2	5894	1709.4	−4184.6	48.5	10,717.4	57.5
360	41	4	4109.6	15.2	540	33.3	13.3	9471.9	66.7	131.6	31.6	15,577	4517.7	−11,059.3	50.8	11,235.4	60.3
380	73	11	4335.6	16.1	580	31.3	11.3	9722.6	56.7	127.9	37.1	26,102	7570.2	−18,531.8	54	11,967.4	64.2
400	5	0	4643.6	17.2	533.3	30	10	9935.3	50	124.2	42.1	2105	610.5	−1494.5	57.3	12,647.8	67.9
420	20	8	4714.6	17.5	506.7	28.7	8.7	10,125.7	43.3	120.5	48.6	5052	1465.2	−3586.8	58.3	12,849.3	69
440	13	5	4827.6	17.9	526.7	27.7	7.7	10,291	38.3	116.9	54.9	3368	976.8	−2391.2	59.5	13,085.8	70.2
460	21.5	2	4950.6	18.3	453.3	26.7	6.7	10,431	33.3	113.4	63.2	8209.5	2381	−5828.6	60.9	13,368.3	71.7
480	40	22	5238.1	19.4	460	23.6	3.6	10,536.5	18	109.8	116.9	7578	2197.8	−5380.2	63	13,711.4	73.6
481	20	8	5246.1	19.4	453.3	23.3	3.3	10,539.8	16.7	109.6	126.3	5052	1465.2	−3586.8	63.1	13,723.4	73.7
500	59	9	5507.6	20.4	366.7	22.0	2	10,594.1	10	105.9	210.5	21,050	6105	−14,945	66.6	14,514.3	77.9
520	2.5	0	5747.6	21.3	300	20.3	0.3	10,614.3	1.7	102.1	1263	1052.5	305.3	−747.3	69.2	15,046.6	80.8
523	99	3	5773.6	21.4	280	20.3	0.3	10,615.3	1.7	101.5	1263	40,416	11,721.6	−28,694.4	69.6	15,148.6	81.3
524	92	33	5821.6	21.6	306.7	20	0	10,615.3	0	101.3	0	0	7203.9	7203.9	69.9	15,207.6	81.6
540	59	12	6096	22.6	213.3	14.7	−5.3	10,569.3	−26.7	97.9	0	0	5738.7	5738.7	71.9	15,615.8	83.8
560	66	38	6597	24.5	246.7	8.7	−11.3	10,412	−56.7	93	0	0	3418.8	3418.8	77.4	16,835.8	90.4
580	259	120	7696	28.5	220	6	−14	10,159	−70	87.6	0	0	16,971.9	16,971.9	83.8	17,767.3	95.4
600	162	123	11,005	40.8	126.7	0	−20	9781.2	−100	81.5	0	0	4761.9	4761.9	97.6	18,601.3	99.8
612	3.3	0	11,634	43.1	146.7	0	−20	9541.2	−100	78	0	0	402.9	402.9	100	18,632.6	100

Data source: Compiled and calculated from field survey results. Note: The serial numbers are sorted in descending order by the actual CF application rate for each rice-growing household. Due to space constraints, only partial data are presented.

(1) Statistical vs. Actual RECFA. According to theoretical analysis, both the statistical and actual RECFA depend on the probability distribution of RECFA. Calculations show that the expected value of RECFA is 78%, with a standard deviation of 82.17%.

Thus, the statistically calculated RECFA can be calculated as follows: the total cultivated land area of the 612 sample households is 26,981.5 mu, with an average CF application rate of 35.6 kg/mu, the FBS is 20 kg/mu, and the calculated RECFA is 78%. An analysis of the actual RECFA reveals that among the 612 sample households, 523 households (covering a total cultivated land area of 18,768.1 mu) are overapplying CF, with an average application rate of 40.3 kg/mu and an RECFA of 101.5%. In contrast, the remaining 89 farmer households (with 8213.4 mu of cultivated land) are not overapplying CF, with an average application rate of 7.9 kg/mu and an average excessive application level of −60.35%.

The analysis above demonstrates that the statistically excessive CF application situation is underestimated due to the 89 farm households that do not overapply. In fact, even though some farmers do not overapply CF, their residual fertilization amount, the gap between actual application and the FBS, should not be used to offset the excessive CF application amounts of others. According to the survey data, the actual CF application rate in the black soil region of Northeast China is 40.3 kg/mu, with an RECFA of 101.5%, rather than the statistically fertilization level of 35.6 kg/mu and the statistically RECFA of 78%.

On this basis, building on the ±20% sensitivity bounds for the FBS derived in the preceding section, we further assessed the corresponding uncertainty in both aggregate statistical RECFA and actual RECFA calculations. At the upper end of the FBS range (25.05 kg/mu), the corresponding aggregate statistical RECFA across all sample households is 42.1%, and the actual RECFA computed for overapplying farmers is 69%. At the lower end of the range (15.45 kg/mu), the aggregate RECFA stands at 130.4%, and the actual RECFA for overapplying farmers reaches 156.7%. As expected, RECFA estimates move inversely with the FBS threshold: a higher FBS reduces the calculated relative excess application rate, and vice versa.

These values delineate the full plausible range of RECFA estimates driven by parameter uncertainty in the underlying production function and price inputs. The baseline estimates—78% for the full sample and 101.5% for overapplying farmers— fall within this range, and the core finding of widespread excessive fertilization holds across all sensitivity scenarios.

(2) Aggregate Ecological Compensation and Compensation Standard. Based on the theoretical analysis above, the aggregate ecological compensation focuses on examining two core issues at the regional level: first, whether the total amount of cultivated land productivity compensation is sufficient to facilitate the achievement of the FB target; second, if the existing total compensation is insufficient, what the appropriate ecological compensation standard should be.

To address the above questions, it is necessary to compare the RECFA (x* = k(u − n)/t) that enables the achievement of FB under the current compensation standard with the statistically derived RECFA ${\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx$ in the black soil region of Northeast China.

Based on the calculated findings, ${\displaystyle {\int }_{-\infty }^{+\infty }xf(x)}dx=78\%$, the RECFA in the black soil region of Northeast China is 78%.

Based on intuitive survey data. For the black soil region in Northeast China, the CF application rate (u) is 35.6 kg/mu, and the FBS (n) is 20 kg/mu. According to the survey, the ecological compensation standard for CF abatement in this region is 122.1 CNY/mu. An assumption can thus be made: the government aims to reduce the CF application rate to the FBS, indicating it intends to adopt a compensation standard of 122.1 CNY/mu to incentivize a 15.6 kg/mu abatement in CF. Consequently, the ecological compensation amount provided by the government for each kilogram of CF abatement, denoted as k, is 7.83 CNY/kg.

The estimation of farmers’ net income loss under the fertilization equilibrium scenario is built on four explicit premises to ensure clear calculation boundaries and consistent caliber: ① Yield effect assumption. Only the direct yield impact of reducing CF inputs from current conventional levels to the FBS is considered. All other production factors, including rice variety, climatic conditions, field management practices, and pest and disease control, are held constant to exclude the interference from non-fertilizer factors. ② Cost rigidity assumption. CF abatement only changes the purchase cost of CF and the corresponding fertilization operation cost. Other production costs (machinery operation, labor, seeds, pesticides, irrigation, land rent, etc.) remain unchanged, as these inputs have no direct linear correlation with fertilization rate within the adjustment range studied. ③ Price stability assumption. Both rice market purchase price and CF market price adopt the regional average level in the survey year, assuming short-term price stability and excluding the impact of price fluctuations on income loss accounting. ④ Scenario boundary assumption. The FB scenario refers to adjusting CF input to the regional optimal nutrient balance level (20.04 kg/mu) rather than complete elimination of CF application. The yield decrease is measured relative to farmers’ current conventional fertilization level, not the theoretical maximum yield.

Let t represent the agricultural net income loss per mu resulting from CF abatement in the black soil region of Northeast China. As a core parameter that determines the level of the calculated compensation standard, the yield reduction estimate is fully grounded in field-level farmer evidence. Based on the basic pattern that CF abatement induces a sharp decline in yield, achieving FB in this region will reduce rice yield by about 50%. So, we adopted a 53.9% abatement rate. It should be noted that the baseline yield reduction of 53.9% under the FB scenario is calibrated entirely based on field-level producer survey evidence. Most farmers in the study area have engaged in rice production for more than ten years, and some even for several decades. Long-term on-farm practice has given them highly sensitive, experience-based perceptions of how CF input changes translate to rice yield responses. Our field interviews consistently found that the vast majority of local growers believe that reducing CF inputs from current conventional levels to the FBS would lead to a roughly 50% drop in rice yields. We used the average value of farmers’ self-reported yield reduction expectations as our final baseline figure, i.e., 53.9%, and we considered this value reasonable and representative of typical on-farm production outcomes in the study region. The average rice yield in this region stands at 502.3 kg/mu. When FB is achieved (corresponding to a CF application rate of 15.6 kg/mu), the resulting rice yield loss is 270.7 kg/mu, leaving a residual yield of 231.6 kg/mu. Based on the average purchase price of rice (3.07 CNY/kg), the total revenue from rice production under conventional fertilization is 1542.1 CNY/mu, while that under the FBS is 711 CNY/mu. In terms of production costs, the costs of rice production under conventional fertilization include machinery operating costs and input costs for production factors. Specifically, the breakdown and respective expenses of machinery operation costs are as follows: soil turnover operation cost at 33 CNY/mu, subsoiling operation cost at 26.7 CNY/mu, fertilization operation cost at 15.3 CNY/mu per application (totaling 61.2 CNY/mu for four applications), rice transplanter operation cost at 160 CNY/mu, rice harvesting operation cost at 153 CNY/mu, and straw incorporation operation cost at 23 CNY/mu. Therefore, the total machinery operation costs amount to 456.9 CNY/mu. The detailed items and expenses for production factor inputs are as follows: the average cost of herbicides and insecticides is 33 CNY/mu, and hired labor costs 29 CNY/mu, bringing the total expenditure for weed and pest control to 62 CNY/mu. Basal fertilizer averages 90 CNY/mu, and topdressing fertilizer averages 67 CNY/mu, resulting in a total CF purchase cost of 157 CNY/mu. Additionally, there are costs for seedling cultivation (16.7 CNY/mu), agricultural film (23.3 CNY/mu), water extraction and irrigation (66.7 CNY/mu), management fees (40 CNY/mu), and land rent (122 CNY/mu). The total production factor input cost for rice production thus amounts to 487.7 CNY/mu. In summary, the total production cost of rice is approximately 944.6 CNY/mu (sum of machinery operation costs and production factor input costs), and the net income from rice production under conventional fertilization is 597.5 CNY/mu; after CF abatement, changes in production costs are primarily reflected in the decrease in CF input quantity and its associated expenses, while other cost outlays remain unchanged. According to the statistics, the CF purchase cost under the FB scenario is 34.5 CNY/mu. Consequently, the total production cost after CF abatement amounts to 822.1 CNY/mu, and the resulting net income from rice production drops to −111.1 CNY/mu. Therefore, the net agricultural income loss per mu from reducing CF inputs to the FB level is 708.6 CNY.

Based on the above analysis, we have calculated that under the cultivated land productivity compensation standard of 122.1 CNY/mu, the RECFA corresponding to the achievement of CF abatement to the level of FB is x* = 17.23%, which is lower than the region’s existing RECFA of 78%. In fact, the required ecological compensation standard for reducing RECFA from 78% to the FB level is 552.7 CNY/mu. Therefore, the current compensation standard of 122.1 CNY/mu is insufficient at the regional level to support achieving regional FB.

Building on the ±20% sensitivity bounds for the FBS derived in the preceding section, we further examined the corresponding uncertainty in both RECFA estimates and the desired ecological compensation standard. At the upper bound of the FBS range (25.05 kg/mu), the statistical RECFA across all sample households is 42.1%; at the lower bound (15.45 kg/mu), the aggregate RECFA reaches 130.4%. We then derived the desired ecological compensation standard for each extreme scenario, defined as the per mu net income loss incurred when farmers reduce CF inputs to the corresponding FBS level: at the upper FBS bound, the smaller required CF abatement translates to a lower income loss, yielding a corresponding ecological compensation standard of 298.3 CNY/mu; at the lower FBS bound, the larger required CF cut drives a greater net income loss, raising the desired compensation standard to 924 CNY/mu. The baseline estimates—a 78% RECFA and a corresponding 552.7 CNY/mu desired compensation standard—fall centrally within this range, and the compensation standard scales consistently with RECFA across scenarios, which aligns with the analytical framework applied earlier in the paper. Across all sensitivity scenarios, the prevailing official compensation standard of 122.1 CNY/mu remains well below the theoretically required level, confirming the robustness of the core finding that current compensation is insufficient.

On this basis, we conducted a sensitivity analysis to examine how changes in the magnitude of rice yield reduction affect the estimated desirable ecological compensation standard. Applying the 78% RECFA uniformly across all scenarios, we specified five gradient yield reduction trajectories while holding all other production and price parameters constant. We assumed that rice yield declines by 30%, 40%, 50%, 53.9% (our baseline estimate), and 60%, respectively, when moving from conventional fertilization to the fertilization equilibrium state. For each scenario, we calculated the desirable ecological compensation standard based on the corresponding net agricultural income loss per mu. Full results are reported in

Table 8. Desirable ecological compensation standards under different yield reduction scenarios.

Yield Reduction Rate	Net Income Loss (CNY/mu)	Desired Compensation Standard (CNY/mu)	Ratio to Current Subsidy
30% (Mild)	340.2	265.4	2.17
40% (Moderate)	494.4	385.6	3.16
50% (Moderately high)	648.6	505.9	4.14
53.9% (Baseline)	708.6	552.7	4.53
60% (Relatively high)	802.8	626.2	5.13

Note: All production and price parameters are held constant.

.

The estimation results indicate that the desirable compensation standard scales almost linearly with the yield reduction rate. Even under the mildest 30% yield reduction scenario, the required ecological compensation standard reaches 265.36 CNY/mu, which remains substantially higher than the current official subsidy level. This verifies that our core finding of insufficient aggregate ecological compensation support is not contingent on the specific baseline yield reduction assumption, and holds robustly across the entire plausible range of yield outcomes.

(3) Structural Ecological Compensation and Its Equivalence Relationship. Based on theoretical analysis, structural ecological compensation focuses on examining the equivalence relationship between cultivated land productivity compensation and farmers’ CF abatement targets at the heterogeneous farm household level. In other words, three core questions arise: first, whether compensation is excessive, equivalent or insufficient; second, the share of cultivated land falling into each of these three categories; third, the magnitude of any surplus, equivalent or shortfall.

Based on intuitive data, the FBS for the black soil region of Northeast China is 20 kg/mu, the average CF application rate is 35.6 kg/mu, the cultivated land productivity compensation standard for CF abatement is 7.83 CNY/kg, and the agricultural net income loss under the FB scenario is 708.6 CNY/mu. Based on these parameters, the RECFA that matches ecological compensation with CF abatement is calculated to be 17.23%. In view of this, the RECFA is divided into three intervals: (−∞, 0], (0, 17.23%], and (17.23%, +∞). Further statistical analysis of the structural compensation status across these three intervals is shown in Table 8, with the results presented in

Table 9. Structural Compensation Status of CF Abatement.

RECFA:x	(−∞, 0]	(0, k(u − n)/t]	(k(u − n)/t, +∞)
Excessive CF Application Status	No Excessive CF Application	Excessive CF Application	Excessive CF Application
CF Abatement Status	No CF Abatement Required	Capable of reducing CF application to FBS	CF application can be reduced, but not to the FBS
Proportion of Ecological Compensation Funds	${\displaystyle {\int }_{-\infty }^{0}f(x)}dx$ = 18.7%	${\displaystyle {\int }_0^{17.23\%}f(x)}dx$ = 7.7%	${\displaystyle {\int }_{17.23\%}^{+\infty }f(x)}dx$ = 73.6%
CF Abatement Ratio (With reference to actual RECFA)	0%	0.74%	99.26%
CF Abatement Ratio (With reference to statistical RECFA)	0%	0.83%	110.43%

Data source: Compiled and calculated according to Table 7. Note: This table presents the structural ecological compensation status of cultivated land productivity based on CF abatement. Farmers without excessive CF application receive 18.7% of total compensation funds but contribute 0% to CF abatement. Among overapplying farmers, 7.7% of the compensation funds go to those capable of reducing CF inputs to the FBS, accounting for 0.74% of total abatement; 73.6% of the funds flow to those unable to reach the FBS, contributing 99.26% of total CF abatement.

.

Table 9 estimates the status of structural ecological compensation for cultivated land productivity based on CF abatement. The results indicate that farmers who do not overapply CF receive 18.7% of the total ecological compensation funds. However, as they have no obligation to reduce CF application, their contribution to total CF abatement is 0%. Regarding farmers who overapply CF, the government allocates 7.7% of the compensation funds to those capable of reducing CF application to the FBS level, and this portion of funds contributes 0.74% of total CF abatement. Meanwhile, 73.6% of the ecological compensation funds are allocated to farmers who overapply CF but cannot achieve the FB, and the CF abatement driven by this fund portion accounts for 99.26% of the total abatement. However, the survey revealed that cultivated land productivity subsidies are only disbursed to land contractors. Consequently, land transferees (those who rent land) are required to fulfill the obligations of CF abatement and soil conservation without receiving corresponding government subsidies. According to the calculations, this group receives only 54.2% of total compensation funds but bears 99.26% of the abatement obligation. Meanwhile, the remaining 19.4% of the subsidy funds are allocated to land transferors (those who rent out land), who are not required to bear the obligations of CF abatement and cultivated land protection.

It should be noted that this notable discrepancy stems from the institutional mismatch between CF abatement obligations and subsidy allocation rules. Among the 612 sampled farm households, the vast majority have an actual RECFA that exceeds the threshold required to achieve FB under the current compensation standard. To expand their operation scale and consolidate fragmented parcels into contiguous farmland, most of these producers have restructured their land holdings through land rental (both leasing in and out) or land exchange arrangements. As the dominant source of excessive CF input across the study area, they shoulder 99.26% of the total required CF abatement. For the parcels operated by these households, the government earmarks 73.6% of total compensation funds. Yet these subsidies are disbursed to land contractors by statutory entitlement, not to the on-farm operators who actually carry out CF abatement. For producers who both lease in and lease out land, the subsidy payments they receive for the parcels they rent out do offset a portion of the subsidy losses on the parcels they rent in. Still, this partial cross-offset does not resolve the fundamental misalignment between cost bearers and fund recipients. The end result is an inefficient allocation of compensation resources: the actual cultivators who bear nearly all the cost of CF abatement receive only 54.2% of total available funds.

Based on the parameters in Table 7, a model-based calculation is further conducted to assess the degree of inequality between farmers’ CF abatement and cultivated land productivity compensation. For the 89 farmers without excessive fertilization, they can always obtain 18.7% of the total ecological compensation funds, regardless of the compensation standard, with each farmer’s average income increasing by 4779.73 CNY. For the 43 farmers capable of reducing CF application to the FB level, combined with their land circulation area and taking compensation for achieving FB as the goal, the average income of each farmer will increase by 4081 CNY. For the 480 farm households with an RECFA exceeding 17.23%, their actual cumulative RECFA is 109.8%, corresponding to a total desired ecological compensation amount of 5.772 million CNY. However, the current total ecological compensation provided by the government is only 1.674 million CNY, accounting for 29% of the total desired ecological compensation amount. If the current compensation standard is evaluated against the goal of achieving the FBS in the black soil region of Northeast China, these 480 households would experience an average reduction in compensation income of 8538.2 CNY.

(4) Expected Achievable CF Abatement Ratio. Based on Formula (19) and Table 9, the expected achievable CF abatement ratio is further calculated as follows:

$${\displaystyle \frac{{\displaystyle {\int }_0^{17.23\%}xf(x)}dx}{{\displaystyle {\int }_0^{+\infty }xf(x)}dx}}+{\displaystyle \frac{{\displaystyle {\int }_{17.23\%}^{+\infty }17.23\%f(x)}dx}{{\displaystyle {\int }_0^{+\infty }xf(x)}dx}} = 0.74\% + 17.23\% \times 73.6\% = 13.42\%$$

In summary, under the ecological compensation standard of 122.1 CNY/mu, the expected achievable CF abatement ratio is 13.42%, corresponding to a CF application reduction of 4.78 kg/mu.

(5) Variability Analysis. Among the influencing factors of the expected achievable CF abatement ratio, the following characteristics and relationships exist: ① the distribution of RECFA is fixed. ② The actual cultivated land productivity compensation standard is determined with reference to the average compensation standard in the region, and the annual compensation amount is relatively stable. ③ Ecological compensation is determined and disbursed by the government. ④ The agricultural net income loss per mu caused by CF abatement is associated with rice yield, market prices, and production costs.

Building on this foundation, a further analysis examines the impacts of different compensation standards (k) and agricultural net income losses per mu (t) on the RECFA (x) and the expected achievable CF abatement ratio, while holding other conditions constant (

Table 10. Variability Analysis of the Expected Achievable CF Abatement Ratio.

k(CNY/kg)	6.41	7.83	12.82	19.23	25.64	32.05
k(u − n)/t	100	122.1	200	300	400	500
t	708.6	708.6	708.6	708.6	708.6	708.6
x*	14.11%	17.23%	28.22%	42.34%	56.45%	70.56%
CF Abatement Ratio	11.12%	13.42%	21.62%	33.31%	44.85%	54.06%
t(CNY/mu)	400	500	600	708.6	800	900
k(u − n)/t	122.1	122.1	122.1	122.1	122.1	122.1
x*	30.53%	24.42%	20.35%	17.23%	15.26%	13.57%
CF Abatement Ratio	23.40%	18.80%	15.79%	13.42%	12.03%	10.71%

Data Source: Calculated based on Table 7. Note: The analysis quantifies how the RECFA threshold (x*) and achievable CF abatement ratio respond to changes in the unit compensation rate (k) and per mu net income loss from CF abatement (t). Baseline values: k = 7.83 CNY/kg (equivalent to 122.1 CNY/mu), t = 708.6 CNY/mu. Units: k (CNY/kg), t (CNY/mu), x* and abatement ratios (%).

).

Table 10 reports a one-way sensitivity analysis characterizing uncertainty in estimated CF abatement outcomes. It examines how the RECFA threshold for achieving FB (x*) and the corresponding CF abatement ratio respond to changes in the unit ecological compensation rate (k) and agricultural net income loss from CF abatement (t). Holding net income loss constant at the baseline of 708.6 CNY/mu, a higher compensation standard strengthens farmers’ incentives to cut CF use, raising both the equilibrium RECFA threshold and the achievable abatement ratio; on average, each 100 CNY/mu increase in total compensation corresponds to a 10.74% rise in the abatement ratio. When the compensation standard is held fixed, by contrast, a larger net agricultural income loss erodes the incentive effect of the subsidy, with each 100 CNY/mu increase in net agricultural income loss reducing the achievable CF abatement ratio by an average of 2.54%. This analysis maps out the full plausible range of policy outcomes under parameter uncertainty, and confirms that raising compensation standards is a more effective lever for advancing CF abatement than mitigating farm production losses.

6. Discussion

6.1. Key Empirical Findings

To frame the discussion that follows, we first summarize the core empirical estimates from our survey data and incentive evaluation framework.

Based on farm-level survey data from 612 rice growers in the Northeast black soil region, we estimated the FBS for rice production at 20.04 kg/mu. At the aggregate sample level, the statistical RECFA stands at 78%; when calculated only for households that apply CF above the FBS, the actual RECFA reaches 101.5%, confirming that aggregate statistics systematically underestimate the true scale of excessive fertilization. At the regional level, the total subsidy requirement to achieve full FB is 552.7 CNY/mu, roughly 4.5 times the current official cultivated land productivity subsidy of 122.1 CNY/mu. Under the existing subsidy standard, farmers only have an incentive to reduce CF inputs to an equilibrium RECFA of 17.23%, translating to an expected overall CF abatement ratio of 13.42%. Our structural analysis further identifies clear targeting bias in current policy: 18.7% of subsidy funds flow to farmers with no excess CF application, while farmers who bear 99.26% of the actual abatement obligation receive only 54.2% of total compensation payments. Sensitivity analysis shows that each 100 CNY/mu increase in the subsidy rate raises the achievable CF abatement ratio by an average of 10.74%, while each 100 CNY/mu increase in net agricultural income loss reduces the ratio by an average of 2.54%.

6.2. Economic and Policy Mechanisms Underlying the Results

(1) Reexamining Compensation Standards: An Exploration of Rationality Issues. The persistent overapplication of CF and the limited performance of existing subsidy schemes stem from both microeconomic incentive structures and inherent flaws in current policy design.

At the microeconomic level, excessive fertilization is fundamentally driven by the externality of agricultural environmental costs. For individual farm households, the marginal yield return of CF remains positive across a wide range above the FBS, while the full ecological costs of soil degradation, non-point source pollution and greenhouse gas emissions are externalized and not incorporated into private production decisions. This is why rational farmers continue to apply CF beyond the socially optimal level even when they are aware of the associated environmental risks.

At this point, it is necessary to discuss a key research question: why does this study estimate compensation rates based on net income loss rather than total income loss? Assuming that market prices remain constant, the total income loss to farmers is determined solely by the changes in rice yield before and after the CF abatement. Payment standards calculated by this method cannot accurately reflect farmers’ actual net income, creating a mismatch between government transfers and real production. Therefore, when calculating farmers’ income losses from CF reductions, it is necessary to fully account for changes in production costs before and after the reduction. Only a subsidy standard based on net income loss can accurately reflect farmers’ surplus income, thereby improving the accuracy of payment rate calculation. This research perspective is consistent with Yuan [57]. According to statistics, to achieve FB, the subsidy level calculated based on total income loss suffered by farmers is 601.5 CNY/mu, whereas that based on net income loss is 552.7 CNY/mu. Thus, if the government determines payment standards based on gross income losses, it will overestimate the subsidy amount for cultivated land productivity under the FB target, inevitably leading to inefficient use of subsidy funds. Yuan [57] calculated the subsidy standard for rice production under a zero-fertilization scenario based on net income loss at 9967.35 CNY/ha, equivalent to 664.5 CNY/mu. In this study, reducing the RECFA by 78% requires an average compensation of CNY 552.7 per mu. Considering the positive correlation between the CF abatement rate and the subsidy rate, the payment level estimated in this study is reasonable.

According to the calculations, the net income from rice production before CF abatement is 597.5 CNY/mu, while the subsidy amount under the FBS is 552.7 CNY/mu. Although the difference is small, this does not imply that the proximity of the subsidy standard to the net income from rice production justifies deeming our estimated payment level unreasonable on the grounds that “farmers receive subsidies for abandoning rice production”. The reason lies in the fact that previous studies have shown that if FB is achieved in the black soil region of Northeast China, the total income from rice production will decrease by 50% compared with a year earlier. Due to the relative fixity of the rice production process and its factor inputs, the production cost of CF abatement is mainly reflected in changes in the cost of CF factors. Therefore, apart from changes in factor purchase costs, other cost expenditures remain almost unchanged. Therefore, following the production principle that “reducing CF application leads to a sharp decline in rice yield”, the per mu net income from rice production after CF abatement falls to CNY −111.1. Therefore, when determining subsidy rates, it is crucial to consider that CF abatement pushes net agricultural income into negative territory. This methodology yields a subsidy standard of 552.7 CNY/mu under the FB target. However, excessively high payment levels may encourage speculative behavior among farmers, such as abandoning or leaving land fallow to obtain ecological subsidy funds, thus necessitating strict government oversight.

(2) Reexamining the Compensation Logic: Incentive Compensation or Punitive Compensation? From a policy design perspective, the limited performance of current subsidy programs stems largely from the equivalence bias embedded in stock-oriented subsidy models. Most existing agricultural environmental subsidies are allocated uniformly by planted area, regardless of actual CF abatement or incremental ecological improvement. This flat-rate allocation creates no differential incentive for heavy CF users to cut application, and decouples subsidy payments from actual ecological contributions.

Incentive-oriented subsidies include both ecological incremental compensation and ecological stock compensation. As mentioned earlier, the focus should be on providing incremental incentive payments to farmers who apply excessive CF. However, in the context of market failures and insufficient fiscal resources, this approach may inadvertently undermine the fairness of remuneration for farmers who maintain low fertilization levels, potentially encouraging them to increase CF application. Undoubtedly, the ecological compensation policy is an incentive-based institutional arrangement through which the government compensates those who protect the ecological environment for their income losses. Its purpose is to incentivize, not to penalize. However, from a managerial perspective, environmental management policies were initially designed on the basis of the “polluter pays” principle. According to the Land Administration Law of the People’s Republic of China, “where land development causes desertification or salinization of land, the relevant authorities shall order rectification or remediation within a prescribed period, and may impose fines”. Existing research argues that cultivated land conservation subsidies should incorporate ecological value into the total value of cultivated land to internalize externalities, strengthen protection of cultivated land ecosystems, and simultaneously curb destructive behaviors by stakeholders [58]. Therefore, farmers who overapply CF and damage the ecological environment of cultivated land should be penalized.

Based on the above reasoning, this study proposes a subsidy framework that follows the logic of “penalizing excessive fertilization and rewarding ecological stock”. This policy framework emphasizes that the government should impose punitive measures on farmers based on the degree of their excessive CF application to urge them to reduce CF inputs and achieve the FBS. Fines collected through punitive measures will be used to compensate farmers with low fertilization levels for their ecological contributions. Through this “penalty and reward” mechanism, the regional FB goal can be achieved while black soil fertility is effectively protected. The advantage of this policy design lies in its dual reinforcement mechanism: on the one hand, administrative penalties imposed by the government can force farmers with excessive CF application to reduce their CF inputs. On the other hand, the transfer of fine income provides an additional funding source for subsidy programs, creating sustainable incentives for farmers who maintain low CF application practices. The interaction of these two aspects forms a self-reinforcing cycle that can drive the region toward FB.

However, when examining the trajectory of agricultural development in China, the current state of excessive CF application among farmers stems from the historical context of “the imperative to extract maximum grain output from the land”. The practice of applying high CF rates developed over long-term production processes [59]. Moreover, fertilization behavior is often more influenced by factors such as gender, health status, risk attitudes, household size, and farm scale, and farmers have no malicious motive for excessive fertilization [60]. Therefore, farmers’ excessive CF application is “rational” in the sense that it is an inevitable outcome of the traditional production practice of “emphasizing base fertilizer while neglecting topdressing” [61]. Consequently, from the standpoint of the current new era of ecological civilization construction, we should not simplistically blame farmers for overapplying CF or attribute the responsibility for cultivated land pollution to them. Furthermore, the survey indicates that the majority of farmers apply excessive CF. Under normal fertilization conditions, the average net income from rice production is 597.5 CNY/mu. However, when fertilization is reduced to the FBS, the net income drops to CNY −111.1 per mu. Imposing penalties on farmers for excessive CF application may lead to widespread abandonment of cultivated land, further affecting national food security and social stability. At the same time, farmers with low fertilization levels usually have established market channels for ecological agricultural products and can realize the economic value of ecological products through market mechanisms. If the fine income is used to compensate these farmers, it will result in double subsidies and thus lead to inefficient subsidy allocation.

Therefore, given the current state of agricultural production in China, it is not feasible to use penalty funds from excessive fertilization to fund ecological stock compensation. Instead, the subsidy model should be shifted from the traditional “polluter pays, compliant parties rewarded” to the scientific “beneficiary pays, protectors compensated”, which better aligns with the scientific essence and original intention of ecological compensation.

6.3. Comparison with International PES and Agri-Environmental Subsidy Literature

These findings align closely with broader international evidence on payment for ecosystem services (PES) and agri-environmental policies, and contribute to the international literature on environmental governance and subsidy design in several ways.

First, our focus on ecological increment and additionality aligns with a broad consensus in international PES research. Existing studies show that action-based payments compensate farmers for adopting pre-set management practices rather than delivering tangible environmental gains, and are widely recognized for their low cost-effectiveness. Results-based payments, by contrast, reward producers for measurable improvements in environmental outcomes instead of requiring specific practices [62,63]. Other studies have also documented that results-based payment designs are more effective at achieving ecological objectives [64]. Consistent with this rationale, our research emphasized that payments tied to incremental environmental improvements deliver stronger ecological outcomes than stock-based subsidies that reward pre-existing conservation practices. Our framework addresses this gap by tying subsidy payments directly to the volume of CF abated, rather than to baseline land quality or pre-existing farming practices.

Second, our finding of a large gap between required subsidy levels and actual subsidy levels is consistent with widespread evidence from PES implementation research. Related literature indicates that subsidies supporting productivity enhancement or direct income payments for cultivated land generally increase the opportunity costs of adopting environmentally friendly farming practices [65]. When PES payment rates fall below these elevated opportunity costs, they consistently result in low program participation and limited environmental impacts [66]. Evidence from subsistence-oriented rural PES programs further confirms this pattern: when payments fall short of foregone production income and participation carries high transaction costs, farmers hold mixed perceptions of program value [67]. Our estimate that the official subsidy standard covers only about 22% of the required incentive level mirrors this documented pattern of underfunded agri-environmental subsidies across different national contexts.

Third, our analysis of CF abatement incentives adds to the global evidence base on agricultural environmental governance. International experience shows that voluntary subsidy programs alone rarely deliver substantial pollution abatement [68,69], and that effective strategies typically combine performance-based payments with regulatory constraints or nutrient pricing instruments [67,69]. Our sensitivity result—that subsidy levels have a larger marginal effect on abatement than income loss mitigation—supports the relevant research that well-calibrated incentive structures are central to effective nutrient pollution control.

Finally, our discussion of targeting excess CF users engages with a broad literature on PES targeting and distributional trade-offs. International studies widely note that concentrating payments on high-emission or high-input producers can maximize ecological return per unit of funding, but also raises equity concerns and potential behavioral distortions [70,71,72]. Our study quantifies the potential efficiency gains from such targeting in the Chinese black soil context, while also detailing the associated risks, which we elaborated in the following section.

6.4. Policy Implications and Associated Risks

From a pure efficiency perspective, reallocating subsidy funds toward farmers with higher CF application rates would improve the ecological return on public spending. Our calculations suggest that redirecting all subsidies currently going to non-overapplying farmers to the overapplying group would raise the equilibrium RECFA from 17.23% to 23.42%, and increase the achievable CF abatement ratio from 13.42% to 18.1%. Targeting high-input producers aligns with the incremental logic of performance-based subsidies, where payments are tied to actual pollution reductions rather than uniform land-area allocations. Beyond inter-household allocation, further efficiency gains can be unlocked by correcting the vertical mismatch between subsidy recipients and actual reduction implementers. Currently, subsidies are disbursed to land contractors by statutory entitlement rather than to on-farm producers who bear the real cost of CF abatement. On leased parcels, a substantial share of the environmental incentive passively accrues to landowners who take no part in cultivation decisions, which dilutes the effective incentive for lessees to adjust fertilization practices. Directing subsidy payments to the actual producers who deliver CF abatement on the ground would reduce this policy leakage and is a key priority for mechanism optimization.

Nevertheless, this policy orientation carries notable risks that warrant careful consideration. First, there are clear distributional and equity concerns. Farmers who already apply CF at or near the FBS have made greater contributions to ecological protection through more sustainable practices, yet would receive little or no support under a scheme focused on high-input producers. This creates a situation where less environmentally responsible farmers capture most of the subsidy resources, which runs counter to the polluter pays principle and may erode public acceptance of the policy. Second, and more critically, subsidies focused heavily on excess CF users can generate moral hazard and strategic overapplication incentives. If subsidy eligibility and payment levels are linked to current CF application rates, farmers may engage in strategic baseline inflation—intentionally raising CF application rates before policy implementation to raise their reference level and qualify for larger payments. This type of ex ante moral hazard has partially or even fully offset the intended CF abatement effects. Third, over the long term, sustained preferential subsidies for high-input farmers may create distorted expectations, weakening incentives for all farmers to proactively optimize CF management. Farmers may delay adopting efficient fertilization technologies in anticipation of future subsidy programs targeted at excess application.

Another associated risk is potential land abandonment and speculative behavior. Notably, this risk is conditional rather than a universal outcome: it primarily arises when the ecological compensation standard is set close to or even exceeds the net income from conventional rice cultivation, which would weaken the relative economic incentive for farmers to maintain normal production. Under a reasonable compensation range calibrated to actual yield loss, the risk of land abandonment remains limited and controllable. To stop compensation funds flowing to farmers who leave land fallow, a layered system of monitoring and enforcement can be built into the subsidy delivery process. Before any payments are issued, actual planted area and crop type are cross-validated against village-level production records and satellite remote sensing data to confirm that all subsidized plots are being actively farmed. Payments are then rolled out in phases. A base amount is released once planting is confirmed, while the remaining performance-linked share is only disbursed after mid-season field checks confirm that standard crop management practices are being followed. Alongside these checks, a dynamic inspection and clawback rule remains in place throughout the growing cycle. If any parcel is found to be fallow at any stage, all corresponding compensation payments are subject to full recovery.

To mitigate these risks, any targeted subsidy scheme should be designed with several safeguards. Baseline CF application rates should be determined using multiple years of historical data rather than a single survey year, to limit opportunities for strategic manipulation. Payment caps should be imposed to prevent excessive rents for heavy CF users. The scheme should also be paired with independent monitoring of CF application and a phased payment schedule tied to verified CF abatement outcomes. Finally, complementary support for low-fertilizer farmers, such as technical extension and green certification, should be maintained to address equity concerns and reinforce long-term sustainable practices.

It is also worth noting that a punitive subsidy model—fining overapplying farmers to fund subsidies for low-fertilizer producers—is not practically feasible in the current Chinese context. Given that excessive fertilization is a long-established practice driven by historical yield priorities rather than intentional misconduct, imposing penalties would risk widespread land abandonment and threaten food security. Instead, policy should follow the beneficiary-pays, protector-compensated logic that is core to ecological compensation principles.

6.5. Research Limitations and Future Directions

This study examines the ecological compensation effectiveness of the cultivated land productivity subsidy in Northeast China’s black soil region from the perspective of CF abatement. At its core, it investigates whether the compensation standard achieves equivalent ecological compensation for the “CF abatement to FB”. In fact, following the research logic of equivalent ecological compensation, assessing the effectiveness of ecological compensation for the cultivated land productivity subsidy in the black soil region of Northeast China should first involve estimating the regional FBS. Subsequently, it is necessary to determine the ecological increment that each farmer should improve and set the compensation standard based on the opportunity cost of increasing the ecological increment, while examining the compensation effect. However, the Cultivated Land Productivity Subsidy policy lacks a concrete research framework to underpin its design. The current policy encourages farmers to improve cultivated land fertility through a variety of measures, including “promoting CF and pesticide reduction and efficiency improvement, increasing organic fertilizer application, and adopting green production technologies”. However, different production methods have distinct mechanisms for improving soil fertility and ecological compensation. As a result, the current research framework cannot yet evaluate the effects of ecological compensation based on multiple production methods. To unify research criteria and avoid duplicate subsidies, this study focuses exclusively on the CF abatement measure. In addition, this study draws on field survey data from 612 farming households, and our findings are primarily root in the conditions of the sampled households. Our sample spans major grain-producing counties and typical farming operations in the black soil region, so the core findings and policy takeaways carry broader relevance for the region as a whole. That said, the specific quantitative estimates align most closely with conditions in the sampled areas. Extending these figures directly across the full geographic scope of the Northeast black soil region would require additional localized empirical support.

Beyond sample representativeness, there are additional contextual boundaries to the analysis that are worth noting. The survey data are cross-sectional, collected at a single point in time, and as such only capture farmers’ fertilization practices and cost-revenue conditions at that specific moment. They cannot fully trace dynamic adjustments in farmers’ fertilization decisions over time, capture long-term learning effects, or control for time-invariant individual fixed effects. In addition, core indicators including CF application rates, rice yields and production costs are self-reported by survey respondents, which may introduce a degree of recall bias and reporting inaccuracy. While we implemented consistency checks and sample verification during fieldwork to mitigate this issue, measurement error cannot be entirely removed. In terms of calculation premises, our estimates of the FBS and desired compensation standards are derived under static assumptions of stable agricultural input and output prices and constant production technology. Fluctuations in CF or commodity prices, as well as incremental advances in agronomic practices, would shift the marginal product of CF and thus affect the precision of our baseline estimates to some extent.

In terms of indicator measurement and environmental cost accounting, all fertilizer-related estimates are anchored to total pure nutrient (N, P₂O₅, K₂O) input across the full growing season, and the corresponding external environmental costs are derived on this same basis. We do not further disentangle the differing pollution intensities of individual nutrient elements, nor variations in environmental load across the basal, tillering topdressing and grain-filling topdressing stages. This level of granularity is consistent with the study’s core focus on policy evaluation, but cannot support fine-grained agronomic guidance for targeted pollution mitigation.

With regard to analytical design, this study adopts a production function estimation approach paired with scenario simulation. We did not employ quasi-experimental methods for formal causal identification, meaning the estimated policy effects and CF abatement potentials presented are theoretical equilibrium projections, rather than causal impacts empirically identified from actual policy shocks.

That said, these contextual boundaries shape the scope and precision of the findings rather than undermining their core validity. The core conclusions of the study remain robust within the established analytical framework, and the quantitative estimates provide a meaningful reference for optimizing regional cultivated land subsidy policies. Therefore, future research should further optimize research methods, expand the scope of field surveys, and construct a theoretical analysis framework for evaluating the effectiveness of diversified ecological compensation mechanisms. Specifically, expanding the scope of field surveys and supplementing location-specific empirical data would support broader regional generalization of the findings; panel datasets would enable tracking of dynamic behavioral adjustments among farmers; linkage with administrative records could reduce measurement bias; multi-scenario analyses that relax static economic assumptions would strengthen result robustness; quasi-experimental designs could help isolate the causal effects of subsidy policies, and disaggregated data on CF nutrient composition and stage-specific application would support more accurate assessment of the environmental outcomes of different fertilization practices. This will provide a more scientific theoretical basis for the formulation and optimization of regional agricultural subsidy policies.

7. Conclusions

This study constructs a theoretical framework for “CF abatement to FB” equivalent ecological compensation and empirically evaluates the ecological compensation effect of cultivated land productivity subsidies using survey data from 612 rice farmers in the Northeast black soil region. The evaluation is conducted from five dimensions: FBS, RECFA, aggregate ecological compensation, structural ecological compensation, and the expected achievable CF abatement ratio.

Our findings fall into two broad categories: empirical patterns observed directly from the survey sample, and quantitative estimates generated by the equivalence framework. Items (1) and (2) reflect empirical statistics and structural patterns from the sampled households, while items (3), (4) and (5) are model-derived estimates based on sample data and theoretical premises.

(1) Because of the spatial heterogeneity and group differences in the application of CF by farmers, the actual RECFA (101.5%) is underestimated compared with the statistical RECFA (78%). (2) The cultivated land productivity subsidy exhibits clear targeting bias at the farm household level, creating a mismatch between abatement efforts and compensation received. According to the statistics, 18.7% of the compensation funds are allocated to farmers who do not need to reduce CF application; 7.7% are allocated to farmers who overapply CF but are capable of reducing to the FBS level; and 73.6% are allocated to farmers who overapply CF and cannot achieve the FBS. However, because the compensation model that disburses subsidies solely to land contractors overlooks the fact that land transferees (those who rent land) are the actual agricultural producers, the group bearing 99.26% of the abatement obligation receives only 54.2% of the compensation funds, while the remaining 19.4% is allocated to land transferors (those who rent out land) who bear no CF abatement responsibility. (3) The FBS for the black soil region in Northeast China is 300.58 kg/ha, equivalent to 20.04 kg/mu. (4) Based on our sample data and model assumptions, the cultivated land productivity subsidy appears insufficient in aggregate at the regional level. The current compensation standard of 122.1 CNY/mu can only promote the RECFA of 17.23% to meet the FB, whereas the required subsidy standard to achieve FB across the black soil region of Northeast China should be 552.7 CNY/mu. (5) The expected achievable CF abatement ratio under the current compensation standard is 13.42%, which corresponds to an abatement in CF application of 4.78 kg/mu. As the cultivated land productivity compensation standard gradually increases or the per mu agricultural net income loss gradually decreases, the expected achievable CF abatement ratio rises accordingly.

Based on the research findings and the above conclusions, the following policy implications are derived: (1) The current cultivated land productivity subsidy is insufficient at the regional level. Therefore, subject to fiscal feasibility, the government should raise compensation amounts to broadly improve the excessive CF application situation. (2) Refine the regional distribution, calculate the regional FBS, and formulate differentiated ecological compensation policies for different regions and different fertilization groups to improve the efficiency of ecological compensation. (3) Enhancing cultivated land productivity by advancing regional FB cannot be achieved overnight; it should be pursued gradually and progressively. In this process, relying solely on government efforts is entirely insufficient. We should promote the ecologicalization of the agricultural industry, realize the value of agricultural ecological products through the construction of an ecological product market mechanism, and take it as the dominant compensation mode for CF abatement to make collaborative compensation with the government. On the one hand, market-based compensation mechanisms can enhance farmers’ ecological income, thereby incentivizing farmers’ pro-environmental behavior, while simultaneously alleviating fiscal pressure on the government. On the other hand, given the inherent fluctuation of markets, government compensation funds can complement market mechanisms when market failures occur or when consumer groups cannot afford the market price of farmers’ ecological products, thereby enhancing overall compensation effectiveness. (4) The current household management objectives of farmers practicing FB mainly fall into two categories: meeting daily household grain needs and capturing the eco-economic value of agricultural production, both of which inherently drive CF abatement. However, small and medium-sized growers, whose household management goal remains yield maximization, constitute the dominant share of agricultural production. Therefore, the focus of ecological compensation policies should shift to medium- and small-sized rice farmers. (5) To realign subsidy recipients with actual production operators, the compensation mechanism should be restructured to channel funds directly to on-farm producers who deliver CF abatement, rather than disbursing payments to land contractors by statutory entitlement. (6) The subsidy program should be closely integrated with grassroots agricultural advisory services. Agricultural advisors play a critical role in raising farmers’ awareness that excessive mineral fertilizer application erodes the long-term productive capacity of black soil, and in delivering targeted technical guidance on optimized nutrient ratios and stage-specific fertilization schedules. This combination of economic incentives and educational support bridges the gap between aggregate policy goals and specific on-farm practices, and typically yields more durable outcomes than policy instruments alone.

Overall, this study develops and empirically applies an equivalent ecological compensation framework for CF abatement aligned with the FSB. It provides a practical, quantifiable approach for assessing the ecological compensation effectiveness of cultivated land productivity subsidy policies. For broader application, this framework still needs further validation using independent samples, longitudinal panel data, and evidence from other agricultural regions.