Does a higher minimum wage accelerate labour division in agricultural production? Evidence from the main rice-planting area in China

Abstract Agricultural production outsourcing, a new means of agricultural production, can optimise the allocation of resources, reduce agricultural production costs, and improve agricultural productivity. However, farmers' outsourcing behaviours are strongly interfered with by many factors such as economics, technology and institutions. Using a farmer-level data set from 2014 to 2018 in China, we examine the effects of the minimum wage increase on rice farmers' production outsourcing behaviours. Our study relies on a Logit regression framework and uses the control function (C.F.) approach to address potential endogeneity concerns. Results show that the minimum wage increase significantly reduces the probability of farmers conducting production outsourcing. We also examine the heterogeneous effects of the minimum wage increase, and find that compared with other outsourcing services, the adverse effects on harvesting outsourcing are the strongest; the negative effects on production outsourcing are stronger for rice farmers with higher education. Our results provide new insights into understanding how labour regulation affects labour division in agricultural production.


Introduction
Agricultural production outsourcing refers to transfer some or all stages of agricultural production to some service providers or hire others to complete some production tasks (Mi et al., 2020). Existing literatures have concluded that agricultural production outsourcing is one of the most efficient measures to address the labour shortage in agricultural production (Igata et al., 2008;Picazo-Tadeo & Reig-Mart ınez, 2006;Wolf, 2003), improve agricultural productivity (Gillespie et al., 2010), reduce agricultural production costs (Zhang et al., 2017), and enhance the welfare of small farmers (Gillespie et al., 2010;Mi et al., 2020;Picazo-Tadeo & Reig-Mart ınez, 2006). At present, more and more farmers begin to outsource their production tasks to others in China (Ji et al., 2017;Zhang et al., 2017). Previous research documents some evidence on the question: what are the factors that affect agricultural production outsourcing? Using the data on rice farmers in Zhejiang province, Ji et al. (2017) established an econometrics model to explore the factors affecting agricultural outsourcing, and found that labour force, government subsidies, planting area, and the number of farm machines owned by farmers are the main determinants of agricultural production outsourcing. Vernimmen et al. (2000) suggested that some critical factors affect agricultural production outsourcing, including the age of farmers, agricultural production scale and institutional environment. Importantly, it is found that non-farm income had a significant and positive effect on production outsourcing (Baiyegunhi et al., 2019;Zhang et al., 2017).
While various factors could affect farmers' decisions on agricultural production outsourcing, whether minimum wage could play a role in this process remains unclear. Some studies have concluded that a rise in the minimum wage increases the income expectations of migrant workers (Sun & Shu, 2011;Zhang & Yang, 2019), so that the opportunity cost of farmers engaged in agricultural production increases. However, other existing literature shows that an increase in the minimum wage would lead to a significant increase in the unemployment rate (Bhaskar & To, 1999;Burkhauser et al., 2000;Katz & Krueger, 1992;Kohen et al., 1982;Neumark & Wascher, 2002), especially for low-skilled workers (Stigler, 1946), thereby reducing the opportunities for farmers to go out to work, forcing most farmers to engage in local agricultural production, reducing farmers' demand for outsourcing agricultural production. Therefore, based on the existing theory, we cannot accurately judge the net impact of the minimum wage on agricultural production outsourcing. However, there has been little discussion about how the minimum wage increase affects agricultural production outsourcing. This article attempts to bridge this research gap.
Rice is one of the three major food crops in the world, as well as one of the most important food crops in China. With less than 7% of the world's arable land, China needs to support 22% of the world's population (Bryan et al., 2018;Deng et al., 2015;Jin et al., 2019). With rapid progress in urbanisation, the labour shortage in rural has become one of the most urgent issues threatening China's food security. Understanding how and to which extent minimum wage could affect agricultural production outsourcing has significant implications not only for farmers' welfare but also for sustainable agriculture production to ensure food security.
Using a farmer-level data set from 2014 to 2018 in China, this article focuses on the effects of the minimum wage increase on rice farmers' production outsourcing behaviours. Given that the rapid improvement of mechanisation and organisation sets up a solid foundation on the division of labour in small-scale farming, our results contribute to the literature on the relationship between labour market regulation and division of labour, and help differentiate changes in labour division due to technical factors, market reasons, institution factors as well as labour market regulation. With an increase in wages, large-scale farmers use more hired-in machines through machine rental or specialised mechanisation service providers, which contributes to the mechanisation of agricultural production (Qiao, 2017;Wang et al., 2016;Yamauchi, 2016), and induces a division of labour between farmers and mechanisation service providers to take place (Zhang et al., 2017). Our results present an opposite perspective toward this view: raising the minimum wage would serve to retard the labour division in agricultural production, and this put farmers at a disadvantage. Second, the article has further deepened the understanding of labour division in small-scale agricultural production (a farming production form with one household as the production unit formed under the household contract responsibility system). Our results show that as minimum wage increases, agricultural production with limited resources and scale in a household cannot be as divisible as industrial production. The results are consistent with the traditional ideas about the division of labour, which means that even if some steps in the agricultural production process can be outsourced, the restriction of resources and scale on labour division will still not be erased due to the change of labour market institution. Although our article is about China's rice production, the research results may shed some light on how the labour market regulation affects division of labour and help us understand how to create the conditions for labour division in agricultural production from the perspective of the minimum wage system. Finally, understanding the role of minimum wages in improving the outsourcing of agricultural production is essential for policymaking. Compared with other countries in the world, China's agricultural production efficiency has been low (Cao & Zhu, 2019;Gao, 2015), which seriously limits the development of agriculture and threatens food security in China (Bale zentis et al., 2021;Guo et al., 2020;Zhang et al., 2021). So the Chinese-related government has been working hard to improve the efficiency of agricultural production. In recent years, the population bonus has gradually disappeared, labour costs have continued to rise (Li et al., 2019;Qiao, 2017;Zhang et al., 2017;Zhang & Yang, 2019), also the minimum wage has been continuously raised in China (Du & Wang, 2020;Fan et al., 2018;Howell, 2020). At the same time, the level of agricultural mechanisation and organisation in China is relatively low (Jiang et al., 2020;Wang et al., 2016). In this context, does the increase in the minimum wage encourage farmers to adopt production outsourcing, thereby accelerating the division of labour in agricultural production, improving agricultural production efficiency? The existing literature does not provide a clear answer to this question. Therefore, our article attempts to fill this research gap and provide inspiration for further research and policymakers.
The rest of this study is organised as follows. Section 2 addresses the institutional background, Section 3 introduces data collection, and Section 4 explains the empirical strategy. Section 5 results analysis and discussion and robustness tests, while conclusions and policy implication of the study are furnished in Section 6.

Institutional background and hypothesis development
The minimum wage institution is a special provision made by the state to protect the fundamental interests of low-income groups and avoid excessive infringement of workers' rights by enterprises. In 1993, the minimum wage institution was officially introduced as the former Chinese Ministry of Labour issued 'Enterprise Minimum wage Standards'. The 1994 Labour Law authorised that municipal governments could set their minimum wage standards according to local specific conditions. In 2004, the Ministry of Labour and Social Security issued a new 'Minimum Wage Standards Regulations', which made amendments and supplements to the old regulations. In 2008, the new Labour Contract Law strengthened the enforcement of minimum wage regulations, also further guaranteed the implementation of minimum wage institutions. In the second quarter of 2017, the Human Resources and Social Work Report, the Ministry of Human Resources and Social Affairs stated that by the end of July 2017, and minimum wage also increased by up to 10.8% in 11 regions. In China, the monthly minimum wage in Shanghai is the highest at 2,300 yuan, which is 3.7 times lower than its monthly average wage of employees; the monthly minimum wage in Beijing is 1890 yuan, which is five times lower than its monthly average wage of employees.
The relationship between migrant workers and minimum wage originated from the dual economic structure in China. Since the Reform and Opening-up, the state has concentrated its efforts on developing urban industrial departments, and a lot of resources have been transferred to the urban. Meanwhile, the government has carried out the urban-rural household registration system to restrict a massive migration of rural residents to the cities. Eventually, the labour market was divided, forming a dual labour market (Piore, 1978), the primary and the secondary labour market. Most jobs in the primary labour market belong to some core departments with high technology, efficiency and welfare, mainly local urban labour forces. On the contrary, the secondary labour market includes those labour-intensive, unstable and inefficient secondary departments, where most migrant workers are employed in low-skilled occupations. In general, the minimum wage institution mainly plays a role in the secondary labour market. When the state raises the minimum wage standard, the labour cost of enterprises increases (Gindling & Terrell, 2009;Riley & Bondibene, 2017). To make up for the shortfall in its pay arising from the increment of minimum wage, enterprises may increase the prices of produced goods and services to transfer higher costs, extend workers' working hours, or use machinery to replace the labour force. However, according to the actual situation in China, the secondary labour market is dominated by labour-intensive enterprises, and the products or services produced by these enterprises are usually in a perfectly competitive market. In this kind of market, enterprises can only passively accept prices, and once they increase the prices of products or services, their market share will drop significantly. Therefore, these enterprises usually do not transfer the higher costs to the consumers by raising prices. In addition, we believe that these companies rarely alleviate the dilemma of rising labour costs by extending workers' working hours and increasing labour intensity. The reason is that such behaviour will not only reduce workers' motivation and productivity but also violate the labour law. Therefore, we consider that in the short term, enterprises mainly directly decide to lay off low-skilled workers, etc. In the long term, they mainly replace workers with machinery to reduce the cost of labour (Stigler, 1946), or improve labour productivity to earn more benefits to relieve the pressure of labour cost (Mayneris et al., 2018). In the end, the employment opportunities for low-skilled migrant workers decrease (Fang & Lin, 2015;Jia, 2014;Sun et al., 2015). Under this condition, farmers continue to engage in agricultural production rather than search for a non-farm job in the labour market. Therefore, the demand for production outsourcing decreases. Based on the above discussion, we propose Hypothesis 1 as follows: H1. The increase in minimum wage can reduce farmers' probability of conducting production outsourcing.
According to the theory of human capital, the education level of the employees usually affects their employment by affecting labour productivity and human capital. As discussed above, the secondary labour market can almost be called a competitive market of rural surplus labour, where higher-educated farmers are more likely to work in the formal sector, while less-educated farmers are more likely to be employed in the informal sector (Bose et al., 2017;Wu et al., 2020;Zhang et al., 2002). The existing literature indicates that formal sector employment suffers more negative effects when the minimum wage increases, while informal sector employment is less negatively affected. Gindling and Terrell (2007) find minor adverse employment effects in the formal sector but not in the informal one. Ham (2018) finds that employment in the formal sector falls and wages rise due to a minimum wage increase, while the opposite happens in the informal sector. Neumark and Mungu ıa Corella (2021) suggest that when minimum wages are binding and enforced, it could reduce employment in the formal sector. Thus, compared with less-educated farmers who work in the informal sector, higher-educated farmers who participate in the formal sector are hit the hardest when minimum wage increases. The decrease in employment opportunities for the formal sector arising from a rise in the minimum wage could make higher-educated farmers allocate more time to engage in agricultural production, reducing the probability of outsourcing agricultural production. Therefore, we propose Hypothesis 2 as follows: H2. The higher the education level of farmers is, the stronger the negative effect on their outsourcing behaviour is.
Based on the analysis of the above theoretical background, we then conduct empirical testing for these hypotheses in this article.

Outsourcing data
We use data from an annual survey of Chinese rice farmers conducted by the Rural Economic Research Centre of Agriculture Ministry, and the period from November to December each year, the Rural Economic Research Centre of Agriculture Ministry conducts the surveys on farmers, and randomly selects 20-25 farmers from each village. A total of 5,403 observations were collected from Chinese main rice-planting areas involved in 70 counties of 30 cities belonging to 12 provinces during 2014-2018 ( Figure 1). The collected data included information on rice production and management (e.g., input use, costs, output and technology adoption), marketing (e.g., price, sale channel and policy), as well as characteristics at the household and village levels (e.g., gender, health, incomes).
According to the process of rice production, we divide rice production outsourcing into five stages: farming outsourcing, planting outsourcing, field management outsourcing, harvesting outsourcing and drying outsourcing. Rice farmers make outsourcing choices based on their family conditions and external socio-economic factors. Figure 2 presents the average ratio of rice outsourcing from 2014 to 2018. As the figure shows, the annual percentage of outsourcing is about 60%$70% from 2014 to 2018. The ratio of rice production outsourcing in China indicates a trend of rising  Note: Outsourcing data in this figure refers to no less than one stage of outsourcing in the process of rice production. Source: Authors' estimation using the survey data from 2014 to 2018. and then falling, but the overall level does not change much. The average ratio of outsourcing in 2016 is the highest, with about 65.6% of sample farmers choosing to outsource some or all stages of rice production. Figure 3 shows the ratio of rice outsourcing by region from 2014 to 2018. As indicated in Figure 3, there are regional differences in the proportion of rice production outsourcing in China. In the central, western and eastern regions, at least half of farmers choose to outsource some or all stages of rice production. The outsourcing ratio in the eastern region is 73.4%, which is significantly higher than that in the central and western regions. Compared with the western region, the percentage of outsourcing in the central region is lower, about 52%.

Minimum wage data
We manually collect the minimum wage data at the city level from the websites of local labour security departments and other relevant governments. Then, taking 2014 as the base year, we obtain a real minimum wage data set after removing the effect of the price level. 1 Figure 4 shows the average monthly real minimum wage across sample districts from 2014 to 2018. As presented in Figure 4, the average monthly real minimum wage increases from 943 yuan in 2014 to 1,170 yuan in 2018, an increase of 24%. Figure 5 presents the average hourly real minimum wage across sample districts from 2014 to 2018. As indicated in Figure 5, the average hourly real minimum wage increases from 9.4 yuan per hour in 2014 to 11.4 yuan per hour in 2018, an increase of 21%.

Empirical model
To investigate the effects of a minimum wage increase on rice production outsourcing at the micro-farm level, we establish the model as follows: Note: Outsourcing data in this figure refers to no less than one stage of outsourcing in the process of rice production. Source: Authors' estimation using the survey data from 2014 to 2018.
where y it is a dummy variable that takes a value of 1 if farmer i outsources any stage of rice production in year t, and takes a value of 0 otherwise. wage it is the real minimum wage in the district where farmer i is located in year t, X it is the control variables at the household level including the characteristics of household head (e.g., gender, age, education level, health level, rice-planting experience, rice planting preference, whether to join a farmer cooperative), family factors (e.g., whether to lease the land, the family population, the labour force population, the total area of rice field, the number of plots) and policy factors (e.g., the implementation of the agricultural technician system), area r is the region fixed effects variable, u t is the year fixed effects variable, and e it is a random error term. For the binary dependent variable  (outsourcing dummy) model, we use the logit estimators. In Eq.(1), the main coefficient is b 1 , which measures the impact of minimum wage standard on rice production outsourcing. However, due to unobservable heterogeneity, reverse causality, or measurement errors, there may be a correlation between minimum wage (wage it ) and the random error term e it , which results in a biased estimate of b 1 : We use the control function (C.F.) approach to address endogenous bias, as described below.

Control function approach
Although the control variables affecting farmers' production outsourcing behaviour are added, there still exist endogenous problems due to omitted variables, such as cultural factors and other unobservable variables. We use a C.F. approach (Rivers & Vuong, 1988;Smith & Blundell, 1986;Wooldridge, 2015) to explore the impacts of the minimum wage increase on rice production outsourcing. In the C.F. approach, we could use instrument variables (I.V.) to correctly identify the causal effects. Compared with ordinary I.V. approaches, the C.F. approach is more flexible in terms of functional form and can efficiently address the endogenous explanatory variable in a relatively complex non-linear model (Wooldridge, 2015). To efficiently deal with the endogenous problem of core explanatory variable (wage it ) in the non-linear model, we choose the C.F. approach (Verkaart et al., 2017;Wooldridge, 2015).
Using a C.F. approach, we must find at least one instrument variable. To obtain the residual prediction value, we first use the I.V. to make the first-stage regression estimation of our model. The first-stage equation is as follows: where Z is the instrument variable vector of wage it , and d it satisfies e it ¼ hd it þ l it . Subsequently, we introduce the residual prediction b d it in the second stage of regression, where l it follows a normal distribution and is independent of wage it and d it : If the residual coefficient h is statistically significant, which means that the minimum wage variable is endogenous. The regression with the residual term can make our estimation of the coefficient b 1 more effective. In theory, a valid instrument variable should be related to the target variable and not correlated to the random error term. Therefore, we use two instrumental variables, namely the urban registered unemployment rate with a lag of one period and the average wage of employees at the city level in 1992 (Howell, 2020).
The first instrumental variable is the urban registered unemployment rate with a lag of one period. According to the 'Minimum Wage Regulations' issued by the Ministry of Labour and Social Security in 2003, the determination and adjustment of minimum wage standard should refer to local employment conditions. The government generally decides whether to increase the minimum wage based on the unemployment rate in previous years. Therefore, there is a correlation between the urban registered unemployment rates with a lag of one period with minimum wage standards, which satisfies the correlation of the instrument variable. On the other hand, the urban registered unemployment rate with a lag of one period does not directly affect farmers' outsourcing decisions, so the exogenous of instrumental variable is satisfied. This instrumental variable is valid.
The second instrumental variable is the average wage of employees at the city level in 1992 because of the origins of minimum wage institutions. The Labour Law promulgated a formally minimum wage institution in 1994. On December 30, 2003, China issued the 'Minimum Wage Regulations' and carried it out nationwide from March 1, 2004. All areas in China Mainland are authorised to adjust minimum wage standards according to their situation. The average wage of employees in 1992 shows the difference in wage levels of various regions, which is an essential basis for determining the starting point of minimum wage. Thus, there is a correlation between the average wage of employees at the city level in 1992 and the city-level minimum wage standard, which satisfies the correlation of instrumental variable. On the other hand, the average wage of employees at the city level in 1992 does not directly affect farmers' rice production outsourcing decisions, so the exogeneity of instrumental variables is satisfied. This instrumental variable is also valid. Table 1 shows the three-step test for endogeneity and addressed by the instruments. The test results in Table 1 show that the instrumental variables we selected are valid. Table 2 presents the statistical characters of the main variables. In our sample, farmers' probability of choosing to outsource farming, planting, field management,

Descriptive statistics
Test for the endogeneity of monthly minimum wage; H0：Variables are exogenous. harvesting, and drying is 44.3%, 34.7%, 28.1%, 46.0%, and 8.7%, respectively. Farmers' probability of conducting harvesting outsourcing is the greatest, and the least that is drying outsourcing. About 64.0% of farmers outsource at least one production stage. The average hourly minimum wage is 10.78 yuan, while the average monthly minimum wage is 1,092 yuan. Due to the differences in economic development levels, there is a large gap in minimum wage levels between different districts. The minimum wage of the highest district is about twice that of the lowest district. From 2014 to 2018, the average unemployment rate in the districts of sample farmers is 2.382%, and the average worker's salary in 1992 is 2,775 yuan. In our sample, most of the respondents are male, accounting for 91.2%. Sample farmers are about 53years-old on average. About 30.2% of respondents have a primary school education; 44.7% of respondents have a junior school education; 21.7% of respondents have a high school education or above. 97.4% of sample farmers are healthy. The average rice planting experience of sample farmers is about 27 years, with the highest even reaching 60 years. 88.2% of farmers prefer to grow rice, and only 19.2% of sample farmers join the rice cooperative. According to our statistical results, there are only 28.4% of farmers choosing to rent in land. The average family size of rice farmers is about 4.5 people, among whom the average labour force is only two people. The logarithmic value of the average rice planting area in our sample peasant households is 2.32, and the logarithmic value of the average number of households owned plots is 1.68. 73.3% of sample farmers are in rural areas where the rural technical staff institution is practised.

Impact of hourly minimum wage
In China, most migrant workers are low-skilled labour forces. They are usually parttime workers rather than full-time workers. Compared with the monthly minimum wage, migrant workers are more sensitive to the adjustment of the hourly minimum wage. Therefore, we use the hourly minimum wage as an independent variable in our benchmark regression. Table 3 indicates the estimation results of the effects on production outsourcing behaviours of farmers in equation (1). As Table 3 shows, the estimated coefficients on hourly minimum wage are negative and significant, indicating that the increase in the minimum wage reduces the probability of farmer's participation in rice production outsourcing. As the second column of Table 3 shows, farmers have a 3.5 percentage point lower probability of participation in rice production outsourcing after increasing each unit of standard deviation in the hourly minimum wage. Table 4 presents the estimated results using a C.F. approach. The signs of the C.F. estimated coefficients are consistent with our baseline regression results. Also, the estimated coefficients on the hourly minimum wage are significant. As presented in the second column of Table 4, farmers' probability of participation in rice production outsourcing is 7.9 percentage points lower after each additional standard deviation unit in the hourly minimum wage. Meanwhile, the estimated coefficients on residual term are significant, so we could argue that variable (wage ct ) is endogenous. The estimated coefficients of the Logit regression b 1 are endogenously biased (Wooldridge, 2015). As indicated in Tables 3 and 4, compared with the Logit estimation results, the absolute values of estimates are larger when we use a C.F. approach. It means that the endogenous problem of minimum wage makes us underestimate its adverse effects on rice production outsourcing. Therefore, the C.F. estimates are more precise. Overall, Hypothesis 1 is supported by empirical evidence.

Impact of other variables
In addition to minimum wage, farmers' age, gender, physical health, planting experience, planting preference, whether to join the rice cooperative, the planting scale and the number of rice cultivated land plots, and whether to implement the rural technical staff institution in the village also significantly affect farmers' production outsourcing behaviours. The estimated coefficient on farmers' age is negative and significant at 1% level. The older farmers have less competitive advantages in the urban-rural dual labour market, so they are less likely to engage in non-agricultural works, which led to a lower probability of participation in agricultural outsourcing. Compared with female farmers, male farmers are more likely to outsource because male farmers have more opportunities to find off-farm jobs. The estimated coefficient on physical health is positive and significant at 1% level. The healthier farmers are, the more likely they are to outsource. The estimated coefficient on rice-planting experience is negative and significant at 5% level. The more experienced rice farmers are, the less likely they are to outsource their production. The dummy variable of planting preference has a significantly negative effect on rice production outsourcing. Farmers who prefer to grow rice are more reluctant to outsource the production process because they are experienced in rice farming. The dummy variable of whether or not to join a farmers' cooperative has a significantly positive effect on rice production outsourcing. Farmers who become cooperative memberships have more channels to learn about agricultural production outsourcing, and they trust the agricultural outsourcing service organisations more and are more enlightened. Hence, they are more likely to choose to outsource agricultural production. The planting area has a negative and significant effect on rice production outsourcing. This finding contradicts the previous study which suggested that limited by the labour force, farmers with large planting areas are more likely to outsource (Zhang et al., 2017). The reason for this may be that farmers with larger operation areas usually choose to buy machines such as ploughs, rice transplanters and reapers to achieve economies of scale. They are less likely to outsource. The number of cultivated land plots positively affects rice production outsourcing. The number of cultivated land plots measures land fragmentation level. The more cultivated land plots are, the greater the land fragmentation level is. A greater degree of fragmentation can reduce rice production efficiency. In order to give full play to their comparative advantages and improve productivity, farmers maybe search for individuals with higher productivity in the market to realise the externalisation of internal production. The dummy variable of whether or not to implement the farm technical staff institution in the village has a negative and significant effect on rice production outsourcing. In the areas where the farm technical staff institution is practised, technicians provide technical training and door-to-door guidance to promote local specialised production and improve farmers' production efficiency. Farmers are less willing to outsource rice production.

Impacts on the production outsourcing in different stages
To test the robustness of our study results, regression analysis is carried out on the production outsourcing in various stages. Tables 5 and 6 demonstrate the impacts of the hourly minimum wage increase on production outsourcing in different stages. As Table 5 presents, for farming, field management, harvesting and drying, the coefficients on hourly minimum wage are negative and significant at 1% level. It means that a rise in the hourly minimum wage reduces farmers' probabilities of conducting farming outsourcing, field management outsourcing, harvesting outsourcing and drying outsourcing. Hourly minimum wage does not significantly affect planting outsourcing. We use a C.F. approach to address the endogenous problem of hourly minimum wage, and the results are presented in Table 6. For farming, planting outsourcing, field management, harvesting and drying, the coefficients on hourly minimum wage are negative and significant at 1% level, which means that the hourly minimum wage increase can reduce farmers' probability of conducting the production outsourcing in any links. The estimated results suggest that after an increase of each unit of standard deviation in the hourly minimum wage, farmers' probabilities of conducting farming outsourcing, planting outsourcing, field management outsourcing, harvesting outsourcing and drying outsourcing decrease by 11.6%, 6.4%, 4.6%, 16.8%, and 5.0%, respectively. Among them, the average marginal effect of hourly minimum wage on harvesting outsourcing is the strongest.

The effect of monthly minimum wage
Although migrant workers are more sensitive to the hourly minimum wage, we cannot rule out the impact of the monthly minimum wage on some migrant workers who are engaged in full-time jobs. In order to ensure the robustness of our results, this article replaces the hourly minimum wage with the monthly minimum wage to explore whether the increase in the monthly minimum wage has a negative impact on farmers' outsourcing behaviours. The results are shown in Tables 7 and 8. The results show that the increase in monthly minimum wage will significantly reduce the probability of farmers conducting production outsourcing. The impacts of the monthly minimum wage rise on production outsourcing in different stages are reported in Tables 9 and 10. As evident from Table 9, the monthly minimum wage has a negative and significant impact on farming outsourcing. But it has a significantly positive effect on planting and drying outsourcing, yet not on field management outsourcing and harvesting outsourcing. We also used a C.F. approach to control the endogeneity of monthly minimum wage, and the estimated results are   given in Table 10. The increase in the monthly minimum wage significantly affects farming outsourcing, planting outsourcing, harvesting outsourcing and drying outsourcing, but it has no significant impact on field management outsourcing. After each additional unit of standard deviation in the monthly minimum wage, farmers' probabilities of conducting farming outsourcing, planting outsourcing, field management outsourcing, harvesting outsourcing and drying outsourcing decrease by 24.1%, 6.4%, 0.2%, 36.7% and 13.2%, respectively. Our results are not affected by the difference between the hourly minimum wage and the monthly minimum wage. It underlines the robustness of our study results.

The effect of minimum wage on the number of outsourced rice production stages of farmers
We use a Zero-inflated Poisson regression model 2 to explore the relationship between the minimum wage and the number of outsourced rice production stages of farmers, 3 and the estimated results are shown in Table 11 below. As Table 11 indicates, both monthly minimum wage and hourly minimum wage have a significant negative correlation with the number of outsourced rice production stages of farmers. After each additional unit of standard deviation in the monthly minimum wage, the number of outsourced rice production stages of farmers will decrease by 39.6%; After each additional unit of standard deviation in the hourly minimum wage, the number of outsourced rice production stages of farmers will reduce by 22.2%. This once again confirms the robustness of our conclusions.

Heterogenous effect of minimum wage by education
Other complex factors might influence the relationship between minimum wage and production outsourcing. An examination of heterogeneous effects caused by the minimum wage increase will be carried out in this section. Hypothesis 2 predicts the negative effects of the minimum wage increase on production outsourcing to be stronger for farmers with higher education. To analyze the heterogeneous effects of   education, we include interactions between minimum wage and education dummies in both the logit model and the C.F. approach. The estimation results are shown in Table 12. As Table 12 indicates, compared with illiterate farmers, educated farmers' production outsourcing behaviour is more significantly and negatively affected by the minimum wage increase. The margin treatment effects (M.T.E.s) on the outsourcing behaviour of farmers with different education levels are presented graphically in Figures 6 and 7. As the figures show, the M.T.E. of the minimum wage rise on the outsourcing behaviour of illiterate farmers is insignificant, but the negative M.T.E. on the outsourcing behaviour of farmers with Primary school or above education becomes significant. And the negative impact of the minimum wage increase on the rice production outsourcing probability of farmers with higher education is stronger. This result applies to both the monthly minimum wage and the hourly minimum wage. Thus, it is true that the increase in the minimum wage has different effects on farmers with varying levels of education. These results provide evidence to certify Hypothesis 2.
In conclusion, we find that the lower possibility of rice production outsourcing is related to a rise in the city-level minimum wage. This finding is consistent with that of He (2019), who found the increase in minimum wage can affect farmers' grain production behaviours by affecting their employment and income status. Also, our research results are in line with the expected theory of the labour market in China. According to the demand for labour model of Stigler (1946), in the competitive labour market, the minimum wage set above the equilibrium price will reduce the demand for labour, due to the output effect (a rise in labour costs increases the price of the product, and the demand for the product will lessen, finally causing the demand for labour to decrease) and the substitution effect (enterprise will increase the input in other factors of production, thereby replacing the demand for labour). Some studies on the employment effect of minimum wages (Fang & Lin, 2015;Jia,  2014; Sun et al., 2015) are consistent with this theory. In addition to the adverse impact on employment, Sun et al. (2015) also found that a rise in the minimum wage can lessen the working hours of workers. The above analysis confirms that the minimum wage increase might reduce employment opportunities. The employment effect  of the minimum wage mainly occurs in the secondary labour market dominated by migrant workers (Sun et al., 2015). The rise in the minimum wage causes employment opportunities of migrant workers to decrease, so they have more time and energy to engage in agricultural production, reducing outsourcing in agricultural production. Our study results are in line with China's current situation that uses machines to replace labour forces to make up for the shortage of funds caused by rising labour costs.

Conclusion
Agriculture development is crucial for all countries, especially for China, a traditional farming country. However, the high degree of fragmentation and small land, and small-scale household farming methods limit the efficiency of agricultural production. Agricultural production outsourcing, a new means of agricultural production, not only benefits agricultural productivity growth, but also optimises the allocation of agricultural production resources, which indicated that agricultural production outsourcing is a crucial way to promote agricultural scale management and modern agricultural development. This research of rice farmers in China examines whether and how a rise in the minimum wage can affect farmers' probability of conducting production outsourcing. The Baseline results indicate that increasing each unit of standard deviation in the hourly minimum wage can reduce farmers' probability of conducting production outsourcing by 3.5%. We then use the C.F. approach to address potential endogeneity concerns, and the results indicate that an increase of each unit of standard deviation in the hourly minimum wage can reduce farmers' probability of conducting production outsourcing by 7.9%. We prefer the estimated results using a C.F. approach because of their more efficient estimates. In a word, the increase in the minimum wage reduces farmers' probability of conducting production outsourcing. One possible reason is that a rise in the minimum wage raises enterprises' labour costs and forces enterprises to downsize their low-skilled staff in response to rising production costs. Hence, employment opportunities for migrant workers decrease, causing more farmers to undertake agricultural production on their own, reducing production outsourcing. Finally, we also notice that as the education level of farmers improves, the negative impacts of the minimum wage increase on agricultural production outsourcing by farmers is also increasing; the effect of the minimum wage increase on harvesting outsourcing is the strongest. Our research results provide empirical evidence for exploring a connection between labour market regulation and the division of labour. From the perspective of the minimum wage system, it provides inspiration for how to promote labour division in agricultural production. In reality, policymakers often worry that the minimum wage rise attracts more farmers to work in the city, which may be aggravated by rural ageing and abandoned land. But according to our findings, this concern is unnecessary. In order to weaken the negative impact of higher minimum wages on labour division in agricultural production, policymakers need to fully consider its impact on agricultural production when raising the minimum wage standard, and should not raise the minimum wage excessively first; Second, while increasing the minimum wage, it is necessary to create other employment opportunities for them to promote the reemployment of migrant workers. As one of the new models of modern agricultural production, more future studies should focus on agricultural production outsourcing.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
Funding for this research from National Natural Science Foundation of China with ratification number 71603177, and National Social Science Foundation of China with ratification number 20CMZ037.

Variable Definition
Farming outsourcing Equals 1 if the HH head outsources farming task, and equals 0 otherwise Planting outsourcing Equals 1 if the HH head outsources planting task, and equals 0 otherwise Field management outsourcing Equals 1 if the HH head outsources field management task, and equals 0 otherwise Harvesting outsourcing Equals 1 if the HH head outsources harvesting task, and equals 0 otherwise Drying outsourcing Equals 1 if the HH head outsources drying task, and equals 0 otherwise outsourcing Outsourcing at any task：equals 1 if the HH head outsources any rice production task, and equals 0 otherwise rhwage Taking 2014 as the base year, real hourly minimum wage in the district where the HH head is located (RMB) rmwage Taking 2014 as the base year, real monthly minimum wage in the district where the HH head is located (100RMB) unemployment Urban registered unemployment rate in the district where the HH head is located (%) asalary92 The average wage of employees in 1992 in the district where the HH head is located (RMB) gender The gender of the HH head：equals 1 if the HH head is male 0 if it is female age The age of the HH head (years) agesq The square of the HH head's age illiteracy Equals 1 if the highest school level achieved by the HH head is illiteracy, and equals 0 otherwise primary school Equals 1 if the highest school level achieved by the HH head is primary school, and equals 0 otherwise junior school Equals 1 if the highest school level achieved by the HH head is junior school, and equals 0 otherwise high school or above Equals 1 if the highest school level achieved by the HH head is high school or above, and equals 0 otherwise health The health level of the HH head：equals 1 if the HH head is healthy 0 if it is unhealthy experience The rice-planting experience of the HH head (years of planting rice) preference The rice planting preference of the HH head：equals 1 if the HH head love planting rice, and equals 0 otherwise membership Whether the HH head joins the farmers' cooperative: Equals 1 if it is yes, and equals 0 otherwise rentin Whether the HH head rents his land: Equals 1 if it is yes, and equals 0 otherwise hhsize The total family population of the HH head (number) rlabour The labour force population of the HH household (number) lnarea Natural logarithm of the total area of rice field in the HH household lnplots Natural logarithm of the number of plots operated by the HH household vtechnician Whether to implement the system of 'one agricultural technician to one village': equals 1 if it is yes , and equals 0 otherwise