The effectiveness of OFA improved by the soil-testing formula

As a form of precise fertilization technology, soil-testing formulas, vigorously promoted by the Chinese government, help farmers enhance the accuracy of OFA (Sun and Li, Reference Sun and Li2021; Zheng et al., Reference Zheng, Li, Zhao and Qian2023). Based on soil test field experiments, these formulas can be made by local fertilizer stations or cooperatives, utilizing soil nutrient content measurements to precisely replenish missing nutrients in the soil (Zhang et al., Reference Zhang, Antonangelo, Grove, Osmond, Slaton, Alford, Florence, Huluka, Hardy, Lessl, Maguire, Mylavarapu, Oldham, Pena-Yewtukhiw, Provin, Sonon, Sotomayor and Wang2021). Consequently, the application of soil-testing formulas not only determines precise fertilizer inputs, leading to improved crop yields, but also reduces fertilizer residue, thereby enhancing crop quality (Li et al., Reference Li, Zhang, Song, Ren, Jin, Fang, Yan, Li, Wang and Cao2022b). Theoretically, the economic benefits of OFA can be realized through the use of soil-testing formulas, and this article proposes the following hypothesis:

The effectiveness of OFA improved by outsourcing services

Outsourcing services help alleviate the inefficiencies of OFA resulting from farmers' limitations in accessing information, machinery, and technical support. Firstly, professional organizations have stronger market negotiation skills than farmers, enabling them to purchase fertilizers at lower prices (Rutsaert et al., Reference Rutsaert, Chamberlin, Oluoch, Kitoto and Donovan2021). In addition, these organizations can mitigate the information asymmetry regarding fertilizer quality that often hinders farmers, thus ensuring the acquisition of high-quality fertilizers (Li et al., Reference Li, Yang, Shi, Zang and Liu2021). Secondly, professional organizations employ mechanized fertilization, facilitating the delivery of fertilizers to deep soil layers and thus enhancing operational efficiency (Chen, Zhong, and Lu Reference Chen, Zhong and Lu2023). Thirdly, professional organizations have better access to government-provided technical support compared to individual farmers (Mattila et al., Reference Mattila, Hagelberg, Söderlund and Joona2021). In theory, the economic effects of OFA can be enhanced through the implementation of outsourcing services, and this article proposes the following hypothesis:

Empirical model

The dependent variable in this paper is farmers' income, measured by the variable ‘net income of wheat (Triticum aestivum L.) per hectare of land’ (NIW). This variable is calculated by subtracting total costs, including the cost of seedlings, fertilizers, pesticides, irrigation, machinery, labor, and land rent, from total revenue. The key independent variables represent farmers' behaviors regarding OFA, encompassing several choices: applying no organic fertilizers, OFA with soil-testing formula, OFA without soil-testing formula, OFA with outsourcing service, and OFA without outsourcing service, with farmers applying no organic fertilizers considered the control group. The two key independent variables are ‘whether organic fertilizer is applied with soil-testing formula (OSF)’ and ‘whether organic fertilizer is applied with outsourcing service (OUS)’. Farmers' selections of OFA are not random behaviors. They are influenced by various factors, such as technical training, which may also impact farmers' income, potentially leading to self-selection bias (Ma and Abdulai, Reference Ma and Abdulai2016). Reliable estimates of OFA's effect on farmers' income cannot be obtained without addressing self-selection bias (Vigani et al., Reference Vigani, Kathage, Khanna, Roe, Vercammen and Wu2019). The Propensity Score Matching Model (PSM) cannot correct for self-selection bias resulting from unobservable factors (Abdulai, Reference Abdulai2016), and the Difference-in-Difference Model (DID) cannot be applied to cross-sectional data (Pan, Lu, and Kong, Reference Pan, Lu and Kong2022). Therefore, the Multinomial Endogenous Switching Regression Model (MESR) is chosen to address the self-selection bias issue (Deb and Trivedi, Reference Deb and Trivedi2006), and the IV-2sls method is selected to test the robustness of the results.

The MESR comprises three stages. In the first stage, a Multinomial Logit Model (Mlogit) is used to estimate the probability of farmers choosing various behaviors related to OFA. This article assumes that there are k selections in total.

(1)$$S = \left\{{{\rm \;}\matrix{ {1\;\;\;if\;U_{i1}^{\rm \ast } \;< \;\;\;\mathop {\max }\limits_{n\ne k} ( {U_{{\rm in}}^{\rm \ast } } ) \;\;} \hfill \cr \cdots \hfill \cr {k\;{\rm if}\;U_{ik}^{\rm \ast } \;\;> \;\;\mathop {\max }\limits_{n\ne k} ( {U_{{\rm in}}^{\rm \ast } } ) } \hfill \cr } } \right.\quad n\ne k$$

S represents all the k selections made by famers. ‘S = 1’ represents the absence of OFA, serving as the control group, while ‘S = 2, 3■■■k’ represents the other selections, including OFA with soil-testing formula, OFA without soil-testing formula, OFA with outsourcing service, and OFA without outsourcing service. $U_{ik}^{\rm \ast } {\rm \;}$represents the utility attained by farmers from the kth selection. The selection equation can be represented by Equation (2).

(2)$$U_{ik}^{\rm \ast } = \beta _kX_{ik}{\rm \;} + \varepsilon _{ik}$$

X _ik represents the observable factors that may influence farmers' selection, including the characteristics of the household head and family (Lee, Reference Lee2005). Household head characteristics that may impact OFA include the ‘age of the household head (AGE)’ (Oyetunde-Usman, Olagunju, and Ogunpaimo, Reference Oyetunde-Usman, Olagunju and Ogunpaimo2021), ‘gender of the household head (GEN)’ (Makate and Mutenje, Reference Makate and Mutenje2021), ‘years of education of the household head (EDU)’ (Ojo and Baiyegunhi, Reference Ojo and Baiyegunhi2021), ‘risk preference of the household head (RPH)’ (Qiao and Huang, Reference Qiao and Huang2021), ‘whether the household head has received technical training (HRT)’ (Maertens, Michelson, and Nourani, Reference Maertens, Michelson and Nourani2021), ‘whether the household head is a village cadre (HVC)’ (Li et al., Reference Li, Tang, Che, Shi and Ma2022a), and ‘whether the household head is a member of a cooperative (HMC)’ (Zhang et al., Reference Zhang, Yang, Zhao and Kong2023). Family characteristics include ‘per capita household income (PHI)’ (Setsoafia, Ma, and Renwick, Reference Setsoafia, Ma and Renwick2022), ‘number of household labor force (NHL)’ (Qian et al., Reference Qian, Lu, Gao and Lu2022), ‘size of farm (SOF)’ (Hu et al., Reference Hu, Li, Zhang and Wang2022), and ‘proportion of non-farm income to total household income (PNT)’ (Wesenbeeck et al., Reference Wesenbeeck, Keyzer, Veen and Qiu2021). Additionally, the instrumental variable ‘distance between farmers and the nearest store selling organic fertilizers (WOV)’ is included in Equation (2). This variable reduces transaction costs associated with accessing organic fertilizer by allowing farmers to purchase it from nearby stores (Jiang et al., Reference Jiang, Zhang, Zhang, Su, Cong and Deng2022b), which also provide farmers with information related to OFA, aiding in the rational use of organic fertilizers (Li et al., Reference Li, Tang, Che, Shi and Ma2022a). Therefore, ‘WOV’ and OFA are highly correlated, but ‘WOV’ does not directly impact farmers' income, making it a suitable instrumental variable for this article.

β _k is the estimated coefficient of X _ik. $\varepsilon _{ik}$ represents unobservable variables assumed to follow an independent and identical Gumbel distribution. Thus, the probability of the kth selection by the farmer, characterized by X _i can be calculated by Equation (3) (McFadden, Reference McFadden1974).

(3)$$P_{ik} = P{\rm r}\left({U_{ik}^{\rm \ast } > \mathop {\max }\limits_{n\ne k} ( {U_{{\rm in}}^{\rm \ast } {\rm \vert }X_i} ) } \right) = \displaystyle{{{\rm exp}( {X_i\beta_k} ) } \over {\mathop \sum \nolimits_{n = 1}^k {\rm exp}( {X_i\beta_n} ) }}$$

In the second stage, an income determination equation is constructed to estimate the effects of various OFA selections on farmers' income. In this article, farmers have k different selections, with each corresponding to its own income determination equation.

(4)$$\eqalign{& S = 1\colon {\rm \;}NIW_{i1} = \alpha _1Z_{i1} + \mu _{i1} \cr & \cdots } $$

(5)$$S = K\colon NIW_{ik} = \alpha _kZ_{ik} + \mu _{ik}$$

S = 1 represents the condition where farmers do not apply organic fertilizers, considered the control group. NIW _i1 represents the income of those farmers who do not use organic fertilizer, while NIW _ik represents the income of farmers employing the kth selection of OFA methods. Z represents all factors that may impact farmers' income. The variable μ _ik satisfies the equation E(μ _ik|X, Z) = 0 and ${\rm var}( {\mu_{ik}{\rm \vert }X, \;Z} ) = \sigma _k^2$. If OLS is used to estimate equation (5), biased results may be obtained (Teklewold et al., Reference Teklewold, Kassie, Shiferaw and Köhlin2013). Therefore, a correction item is added to equation (5) to replace the selection of OFA (Kumar et al., Reference Kumar, Mishra, Saroj and Joshi2019). This article assumes that μ _ik is highly correlated with farmers' selections, leading to the modification of Equations (4) and (5) into Equations (6) and (7).

(6)$$\eqalign{& S = 1{\rm \;}NIW_{i1} = \alpha _1Z_{i1} + \sigma _1{\hat{\lambda }}_{i1} + \omega _{i1} \cr & \cdots } $$

(7)$$S = k\;NIW_{ik} = \alpha _kZ_{ik} + \sigma _k\hat{\lambda }_{ik} + \omega _{ik}$$

σ _k represents the covariance of $\varepsilon _{ik}$ and μ _ik, and unbiased estimates of σ _k can be obtained. ω _ik represents the error term with an expected value of zero. $\hat{\lambda }_{ik}$ represents the Inverse Mills Ratio, which is calculated based on the probability of the kth selection by farmers.

(8)$$\hat{\lambda }_{ik} = \mathop \sum \limits_{n\ne k}^k \rho _k\left[{\displaystyle{{{\hat{\rho }}_{ni{\rm \;}}{\rm ln}( {{\hat{\rho }}_{ni{\rm \;}}} ) } \over {1-{\hat{\rho }}_{ni{\rm \;}}}} + {\rm ln}( {{\hat{\rho }}_{ik{\rm \;}}} ) } \right]$$

ρ represents the correlation coefficient of $\varepsilon _{ik}$ and μ _ik. The standard error in Equation (6) can be obtained using the bootstrap method to account for the heteroscedasticity that arises when generating $\hat{\lambda }_{ik}$.

In the third stage, the average treatment effects (ATT) of different OFA methods on farmers' income are estimated by comparing their income under factual and counterfactual scenarios.

The expected income value of farmers who made the kth selection can be calculated using Equation (9).

(9)$$E( {NIW_{ik}{\rm \vert }U = k, \;Z_{ik}, \;{\hat{\lambda }}_{ik}} ) = \alpha _kZ_{ik} + \sigma _k\hat{\lambda }_{ik}$$

The expected income value of farmers making the kth selection in the counterfactual state can be calculated using Equation (10).

(10)$$E( {NIW_{i1}{\rm \vert }U = k, \;Z_{ik}, \;{\hat{\lambda }}_{ik}} ) = \alpha _1Z_{ik} + \sigma _1\hat{\lambda }_{ik}$$

The unbiased estimation results of the ATT can be calculated using Equation (11).

(11)$${\rm ATT} = E( {NIW_{ik}{\rm \vert }U = k, \;Z_{ik}, \;{\hat{\lambda }}_{ik}} ) -E( {NIW_{i1}{\rm \vert }U = k, \;Z_{ik}, \;{\hat{\lambda }}_{ik}} ) = Z_{ik}( {\alpha_k-\alpha_1} ) + \hat{\lambda }_{ik}( {\sigma_k-\sigma_1} ) $$

When examining the influencing mechanism, the variable ‘yield of wheat on per ha of land (YWH)’ is chosen to assess the impact of ‘OSF’ and ‘OUS’ on crop yield, while the variable ‘proportion of wheat price exceeding the village's average wheat price (PWA)’ is selected to evaluate the effects of ‘OSF’ and ‘OUS’ on wheat price. We do not use wheat price as a dependent variable due to its significant regional variation (Langridge and Reynolds, Reference Langridge and Reynolds2021).

Study site

The study was conducted in Anhui Province, China, in 2021. Anhui is one of the most important grain-producing provinces in eastern China, encompassing the production of cereals, legumes, and tuber within its grain production sector. Data from the China Statistical Yearbook indicates that Anhui Province's grain production in 2022 reached 411,001 million kg, ranking fourth among all provinces in China. Firstly, 18 counties with the highest grain output in Anhui Province in 2022 were selected as our sample sources. Second, these 18 counties were ranked based on their grain output in 2022. From this ranking, 6 counties were chosen as sample counties in this paper using equidistant sampling method. Among these 6 sample counties, 3 are situated north of the Huai River, comprising Funan County, Lixin County, and Yongqiao County, where wheat and maize are the primary crops. The remaining 3 counties are located south of the Huai River and north of the Long River, namely Feixi County, Mingguang County, and Dingyuan County, where rice (Oryza sativa L.) and wheat are the predominant crops. Figure 2 depicts the geographic locations of the sample counties.

Figure 2. Location of Anhui Province and the province's 6 grain-producing counties that are the study sites.

Data

Data were collected through a survey of grain-growing households located in the county study sites in 2021. The survey involved face-to-face questionnaires with household heads. A multi-stage clustered random sampling strategy was employed to derive the household sample. Specifically, within each sample county, high-, middle-, and low-income towns were identified based on the index of per capita disposable income, with one town of each income level selected. Subsequently, all villages within each selected town were categorized into high- and low-income villages, from which one village of each type was chosen. Within each village, rural households were further divided into large-scale farmers managing at least 3.33 hectares of land and smallholders managing less than 3.33 ha (Note. Anhui province belongs to the region of two-harvest-a-year. According to the standard set by Ministry of Agriculture and Rural Affairs of the People's Republic of China, farmers who operate on at least 3.33ha of farmland in the region of two-harvest-a-year are classed as large-scale farmers (Guo, Zhong, and Ji, Reference Guo, Zhong and Ji2019)). 10 large-scale farmers and 10 smallholders were then selected from each village. This sampling strategy resulted in 720 households being selected for the survey (36 villages in 18 towns across 6 counties). Among them, 104 surveyed households did not grow wheat and were therefore excluded from the total sample, leaving 616 effective samples.