The data used for statistical analysis were obtained from a farm survey conducted in the North China Plain in 2020. The surveyed provinces included Henan, Hebei, and Shandong, which are the core components of the North China Plain. Household-level data on agricultural production and family characteristics were also collected. This survey focuses on farmers' adoption of agricultural machinery and its influence.

In terms of survey methodology, we conducted an eight-wave farm survey. We used stratified random sampling to select household farms. We selected Jing, Wuqiang, Gaocheng, Wenshang, Guan, Yucheng, Xingyang, and Sui counties as the sample areas, which are located in the core area of the North China Plain and are China's major food-producing counties. We conducted a farm survey in each county, leading to a total of eight farm surveys. The sampling process consists of three steps: First, 3–4 townships in each county were randomly selected based on their level of economic development; second, 2–3 villages from each township were randomly selected based on their level of economic development; and third, 15–20 household heads from each were randomly selected. The eight-wave survey included 840 observations. As 19 farm households contained missing values and 26 farm households did not plant grain, their data were removed, and a sample of 795 grain farmers was used in this study. Moreover, the same survey methodology was used to collect data on AMS suppliers. Because 12 AMS suppliers contained missing values and 10 AMS suppliers quit the AMS market for the first time, their data were removed, and a sample of 338 AMS suppliers was used in this study.

The dependent variable in this study is food productivity. The literature uses land output (or output value) to indicate food productivity, such as the average yield of crops, the natural logarithm of total yield, and the net output value (Muyanga and Jayne, 2019; Sheng et al., 2019; Qiu et al., 2020). However, higher levels of land output (or output value) may not be the most effective measure of food productivity (Yan et al., 2019). Drawing on the methods of existing research, this study uses the input and output of agricultural production factors to calculate the inefficiency of technology and uses technical efficiency and input efficiency for agricultural machinery to represent food productivity.

Technical efficiency is the decision-making unit's ability to maximize the output under the premise that the input does not change. Data envelopment analysis (DEA) and stochastic frontier analysis (SFA) are the commonly used methods for measuring technical efficiency, but neither incorporates relaxation improvement into the efficiency measurement process. As the bias of DEA and SFA poses problems in our estimates, the super-efficient slack variable slack-based model (SBM) proposed by Tone (2001, 2002) was used to measure farm technical efficiency. Introducing relaxation variables into the objective function and subdividing the effective decision-making units are the advantages of the SBM. The linear programming formula for farm technical efficiency is as follows:

The constraint conditions are follows:

where Equation (1) is the objective function, and Equation (2) is the constraint condition, μ denotes farm technical efficiency of the j-th farmer, X_ik represents the i-th input of the j-th farmer, Y_sj represents the s-th output of the j-th farmer, γ_j denotes the weight, X¯ represents the amount of adjustment of the input indicator, and Y¯ represents the amount of adjustment for the output indicator. The input factors for grain production include seeds, pesticides, fertilizers, irrigation, agricultural machinery, and labor (Yan et al., 2019; Yi et al., 2019). Therefore, we selected them as the input variables for wheat and corn crops per mu. The yield is inaccurate when measuring output owing to differences in grain quality (Yan et al., 2019). We selected the grain (wheat and corn) output value per mu as the output variable. There were differences in the values of grains of different qualities. For example, the value of the first-class wheat was higher than that of the second-class wheat. If only grain yield is used to measure output, it will not reflect differences in grain quality. The output value can be used to measure the differences in both yield and quality. Table 1 describes the input–output variables and summary statistics.

Factor input efficiency refers to the gap between the possible optimal input quantity and the actual input quantity when the total output and other factor inputs remain unchanged. We used the methods by Kaneko et al. (2004) and Hu et al. (2006) to measure factor input efficiency. The input efficiency of the agricultural machinery is determined according to Equation (3):

where MachinIE_j denotes the agricultural machinery input efficiency for the j-th farmer, Minput_j represents the actual input amount of agricultural machinery of the j-th farmer, and Xj¯ is the slack amount in the agricultural machinery's input of the j-th farmer calculated from the super-efficient slack variable model. From Equation (3), it can be observed that MachinIE satisfies 0 ≤ MachinIE ≤ 1; the lesser slack, the closer the input efficiency of agricultural machinery is to 1, and the higher the input efficiency.

The primary focus of this study is to analyze the influence of agricultural machinery adoption modes on food productivity. The North China Plain is a two-cropping area per year, where wheat and corn are alternately planted, and there are six tasks of agricultural machinery. Wheat production tasks include machine farming, machine sowing, and machine harvesting. Corn is exempt from arable land in the North China Plain, and its tasks include machine sowing, machine harvesting, and straw return. This dummy variable is commonly used in the literature (i.e., outsourcing or non-outsourcing) (Yi et al., 2019; Xue et al., 2022). However, the continuous/count version (the number of tasks for SP) was more informative than the dummy (outsourcing or non-outsourcing). The utilization rate of agricultural machinery for the six tasks in the 795 households in the survey is 100%. Therefore, the sum of tasks for service outsourcing (SO) and self-purchase (SP) is six. The number of tasks for SP is used as a characterization variable for the farm's adoption mode of agricultural machinery. The greater the SP's task number, the lower the SO's task number.

The characteristic variables of an individual, family, and location affect their food productivity. First, age, gender, education, health, and job affect food productivity (Newman et al., 2015; Amare and Shiferaw, 2017; Deng et al., 2020); therefore, we controlled for householder characteristics [e.g., age, gender, education, self-identified health, working experience, agricultural training, Communist Party of China (CPC) identity, and village cadre identity]. Second, land size, off-farm employment, cooperative membership, and income affect food productivity (Rozelle et al., 1999; Alene and Manyong, 2007; Qiu et al., 2020); therefore, we controlled for the variables of household characteristics (e.g., land size, land fragmentation, labor structure, cooperative membership, and family income). Third, Newman et al. (2015) and Alves and Kato (2018) found that distance and regional conditions affect food productivity; thus, we controlled for distance and region dummy variables. Table 2 presents the model variables and summary statistics.

First, we assess the relationship between the mode of adoption of agricultural machinery and food productivity. The model is expressed as follows:

where Apefficien_i denotes food productivity, which is measured by the super-efficient slack variables SBM and Equation (3). Mode_i represents the adoption mode of agricultural machinery, which takes the value of the task number of an SP. X_ij are the control variables, including age, gender, education, and health. α₀ is a constant term. α₁ and β_j are the regression coefficients to be estimated. ϵ_i is the random error, which is assumed to be independent and normally distributed.

Omitting important variables and reverse causality may confound our parameter estimations, and hence, the statistical inference. To some extent, reverse causality of the adoption mode of agricultural machinery on food productivity exists. Farmers with higher agricultural productivity are more likely to own agricultural machinery and become SP-based specialists. In addition, although we controlled for variables, such as land and income, which might affect food productivity, we may have missed some unobservable variables, such as the household head's production preferences.

We use the instrumental variable (IV) method to solve the above endogenous issues. The average service acreage per horsepower of AMS suppliers at the town level was utilized to serve as the IV. Regarding the exogeneity and exclusion restrictions of the IV, first, the average service acreage per horsepower of AMS suppliers is a town-level variable, which means that the dependent variable cannot inversely affect the IV, and the IV is exogenous to the dependent variable considerably. Second, the service radius of the Chinese AMS market continues to shrink, and the proportion of long-distance inter-provincial services continues to decline (Qiu and Luo, 2021). Of the 338 AMS providers surveyed, 266 offered AMSs within their town limits. Therefore, the supply of agricultural machinery to towns is insufficient. In this case, farmers will adopt the SO model more frequently. Conversely, farmers adopted the SP model. The average service acreage per horsepower of AMS suppliers at the town level can affect food productivity only by affecting farm households' adoption mode of agricultural machinery, i.e., the IV exclusion restriction. The two-stage least squares method is suitable for situations where the endogenous variable is a continuous variable.

The endogenous variable is an ordinal index, and the two-stage least squares method cannot be used to estimate the model parameters. Instead, we used a conditional mixed process (CMP). The CMP allows for continuous, binary, and ordered endogenous variables.

To test why farms with different agricultural machinery adoption modes have different food productivity levels, we assessed the mediating effect of the operation quality and input of agricultural machinery. The four models were as follows:

where Quality_i represents the farmer's evaluation of the operational quality of agricultural machinery. Indicators such as the depth of cultivated land, the density of sowing, and the cleaning loss during harvesting are used as technical indicators to measure the quality of agricultural machinery operations (Banerjee and Punekar, 2020). However, in the questionnaire survey, technical indicators are difficult to observe. Previous studies have used subjective evaluation indicators to measure objectively existing transaction costs (Abd Latif and Kadhim, 2018; Mugwagwa et al., 2020). Therefore, the subjective evaluation of the quality of agricultural machinery operation by farmers is used as a measure of the quality of agricultural machinery operation, which takes a value of 1–5 (1 = very bad, 2 = bad, 3 = central, 4 = good, and 5 = very good). Minput_i denotes the cost of machinery input per mu (yuan), which we deal with logarithmically as follows: The cost of the SO is the price of AMS per mu, and the cost of SP includes mechanical depreciation, fuel, labor, and maintenance costs per mu. δ₀ and μ₀ are constant terms. δ₁, θ_j, μ₁, and ρ_j are the estimated parameters.

The causal step method was first used to test the mediating effect (Baron and Kenny, 1986). However, when the mediating effect is small, the applicability of the causal-step method is weakened. The Sobel and bootstrap methods were used to replace the causal-step method (Mackinnon et al., 2007; Hayes, 2009). In contrast to the causal step method, the Sobel and bootstrap methods directly test the mediating effect. Due to the limitations of a single test method, this study employed the causal step, Sobel, and bootstrap methods simultaneously to test the mediating effect. The number of repeated samples in the bootstrap method was set to 1,000.

In recent decades, with the development of the AMS market, China has rapidly realized agricultural mechanization based on smallholder farmers. China has blazed a special path toward achieving agricultural mechanization (Yang et al., 2013; Zhang et al., 2017). However, the AMS market capacity began to decline. First, according to the China Agricultural Machinery Industry Yearbook, AMS revenue continued to decline after reaching its peak in 2015, and the profit margin of agricultural mechanization in 2019 was nearly 5% lower than that in 2015. Second, the number of AMS practitioners decreased from 55.715 million in 2015 to 53.412 million in 2019. The number of AMS professionals annually decreased from 5.2508 million in 2014 to 4.243 million in 2019. Third, the cross-regional harvested areas of wheat, rice, and corn peaked in 2013 but showed a downward trend after 2013. The cross-regional harvested area of wheat decreased from 14.426 million ha in 2013 to 6.035 million ha in 2019, indicating a decrease of 58.17%. The cross-regional harvested area of rice decreased from 7.696 million ha in 2013 to 4.473 million ha in 2019, indicating a decrease of 41.88%. The cross-regional harvested area of corn decreased from 3.251 million ha in 2013 to 2.57 million ha in 2019, indicating a decrease of 20.95%. Many studies have discussed the impact of the rapid development of the AMS market on farmer behavior, food production, and agricultural efficiency (Sheng and Chancellor, 2019; Yi et al., 2019; Zheng et al., 2021; Qiu and Luo, 2021). They focused on discussing the positive effects of AMS. Existing theories cannot explain the transition from prosperity to decline in the AMS market (Wei and Lu, 2023). However, the conclusions of this study provide a new perspective to explain this phenomenon. Compared to SP, SO improves the input efficiency of agricultural machinery but reduces technical efficiency. With the development of China's land transfer market, moderate-scale operations have been regarded as an important goal of the Chinese government to promote agricultural production. An increasing number of farmers are shifting from the SO mode to the SP mode, which has led to a recession in the AMS market.

Farmers are involved in the division of the labor economy through the SO model, and economies of scale of agricultural machinery are obtained by farmers without bearing the sunk costs of agricultural machinery (Yang et al., 2013). Developing an AMS is conducive to reducing farmers' sunk costs incurred from self-owned machinery assets and labor costs (Wang et al., 2016). Previous studies have shown that AMS solves the capital and labor constraints faced by farmers, thereby improving food efficiency (Zheng et al., 2021; Huan et al., 2022; Zhou and Ma, 2022). Although agricultural machinery services can enable small farmers to achieve the same technological progress as large farmers (Sheng and Chancellor, 2019), the results of this study show that agricultural machinery services cannot perfectly replace their own agricultural machinery. By comparing with SP, SO reduces the technical efficiency of agricultural production. The reason behind this is that SO has increased the transaction costs of outsourcing AMS. The opportunistic behavior of AMS suppliers reduces the quality of agricultural machinery, which poses a threat to technical efficiency. Unfortunately, existing literature has paid little attention to the issue of moral hazard for AMS suppliers.

Government should not be overly obsessed with the positive effects of AMS on agricultural production. They should be aware that farmers adopt AMS at the expense of technical efficiency in exchange for saving production costs, which is a manifestation of efficiency loss for a country's agricultural production. Notably, the Chinese government is currently cultivating family farms. It can be predicted that the AMS will decline in China with an increase in the number of large-scale operating farms. Therefore, the Chinese government's policies must be adjusted in a timely manner. Instead of blindly pursuing the development of the AMS market, the loss of technical efficiency in agricultural production caused by AMS should be corrected. The most effective way is to suppress the opportunistic behavior of AMS suppliers and reduce the information asymmetry of AMSs. Based on the results, this study puts forward two suggestions. First, the government should maintain a flexible subsidy policy for the purchase of agricultural machinery. According to the saturation state of agricultural machinery in the regional market, the scope and proportion of agricultural machinery subsidies need to be adjusted at any time. For example, in areas where the number of agricultural machinery is saturated, the government needs to reduce subsidies and encourage farmers to exchange old agricultural machinery for new ones. In areas where the number of agricultural machinery is insufficient, the government needs to increase subsidies. Second, the skill training of agricultural machinery hands is used to improve the proficiency of agricultural machinery hands. The government should regularly carry out business training for AMS suppliers, improve the quality of agricultural machinery operations, and reduce the transaction costs of service outsourcing.

A few studies have compared the relationship between AMS and the food productivity of farmers of different sizes. However, the underlying mechanisms remain unclear. Some studies have found that small farms can obtain more benefits from AMS (Yi et al., 2019; Zhou and Ma, 2022), whereas others have shown that AMS has a greater positive impact on medium-sized farms (Qiu and Luo, 2021). The results of this study provide a new perspective for understanding AMS preferences of farms of different sizes. Compared to large farms, small farms have obtained greater efficiency improvements from SO. However, compared with small farms, large farms have obtained greater efficiency improvements from SP. The impact of adopting agricultural machinery on food productivity is asymmetrical among farmers of different sizes. Therefore, the Chinese government should not encourage AMS to be used by all farms but should encourage small farms to purchase AMS and large farms to purchase agricultural machinery for self-operation. Non-farm employed farmers can obtain more benefits from AMS (Ji et al., 2012; Yang et al., 2016), which is supported by the conclusions of this study. However, the results of this study indicate that professional farmers can obtain greater benefits from SP. Therefore, the behaviors of professional farmers purchasing agricultural machinery and that of non-farm employed farmers purchasing AMS should be supported.

Our study has some limitations. We examined the differences in food productivity between the SO and SP. However, apart from SO and SP, farmers also lease agricultural machinery in the North China Plain, although the leasing model is restricted to relatives, friends, and neighbors, and it accounts for very little market share. Owing to data limitations, we could not test the impact of leasing agricultural machinery on food productivity. Moreover, we concede that our measure of the quality of agricultural machinery operations may fail to fully capture the opportunistic behaviors of AMS suppliers. Therefore, information from interviews inevitably suffers from bias. In conclusion, we call for more detailed studies, given the differences between leasing agricultural machinery and AMS. There are two ways to mitigate these limitations in future studies: First, the technical indicators of agricultural machinery operation quality can be used to evaluate the transaction cost of AMS outsourcing. The technical indicators include the depth of cultivated land, planting density, and the loss of cleaning in harvest. The use of objective indicators helps to improve the accuracy of estimation. Second, on the basis of collecting data on agricultural machinery leasing, we call for more literature to discuss the impact of farmers' behavior of leasing agricultural machinery on food productivity.

The results indicate that, compared with service outsourcing (SO), self-purchase (SP) improves the technical efficiency of farms; however, it reduces the input efficiency of agricultural machinery. The channel of the effect is that, although SO can reduce the redundancy of agricultural machinery's input, the opportunistic behavior of AMS suppliers and labor supervision problems lead to a decline in agricultural machinery's operation quality. The impact of the adoption mode of agricultural machinery on food productivity is asymmetrical among different types of farmers. Large-scale and professional farmers benefit more from SP, whereas small-scale and part-time farmers benefit more from SO. The AMS is not perfect, and the Chinese government should pay close attention to the loss of technical efficiency in agricultural production caused by the opportunistic behavior of AMS suppliers.