Spatial variation of technical efficiency of cereal production in China at the farm level

ZHOU Wen-bin,WANG Huai-yu,HU Xi,DUAN Feng-ying

1 Institute of Crop Sciences,Chinese Academy of Agricultural Sciences,Beijing 100081,P.R.China

2 School of Management and Economics,Beijing Institute of Technology,Beijing 100081,P.R.China

3 Agricultural Genomics Institute at Shenzhen,Chinese Academy of Agricultural Sciences,Shenzhen 518108,P.R.China

Abstract Rice,wheat and maize are the main staple food crops to ensure the food security in China with diversified climate condition,cropping system and environmental and socio-economic factors across provinces. Spatial variation of technical efficiency in farmers’ field is helpful to understand the potential to improve farmers’ yield given the inputs level and reduce the yield gap. The study is based on a large-scale farm household survey which covered 1 218 rice farmers,3 566 wheat farmers and 2 111 maize farmers in the main producing areas. The results indicate that rice farmers are with very high technical efficiency level,nearly 0.9 on average,with little room to improve the efficiency of agricultural inputs. Similar results have been found in wheat and maize farmers’ fields,although the technical efficiency levels are lower than that of rice farmers while still at a high level with obvious variation across regions. Farmers with higher yield level also achieve better technical efficiency in most locations. Both local environmental and socio-economic factors significantly affect farmers’ technical efficiency. In the context of urbanization and economic development,improved and new agricultural technologies need to be prioritized and facilitated to improve cereal yield at farm level.

Keywords:technical efficiency,spatial variation,rice,wheat,maize

1.lntroduction

China is the most populous country with peak population in 2030 which will have additional 60 million people to be fed(UN 2019). China’s food security is an important worldwide issue in the context of globalization (Godfrayet al.2010;Luet al.2015). Grain self-sufficiency,especially absolute self-sufficiency in cereals supply,is prioritized in China’s food security strategy associated with a series of policies support to ensure sufficient food supply (Ito and Ni 2013; Luet al.2015). Various efforts,such as agricultural investment on technology development and farming conditions improvement,training program on improved technology adoption and extension,have been made to increase the grain production continuously to satisfy the increasing food demand (Huanget al.2010; Wanget al.2014,2018; Caoet al.2018).

The yields of rice,wheat and maize have stagnated with decreasing cropland in most main producing area in China(Weiet al.2015). The yield potential of staple food crops has reached the ceiling (Cassmanet al.2003; Lickeret al.2010;Neumannet al.2010; van Wartet al.2013),closing the yield gap between actual yield and yield potential consequently should be prioritized to improve the productivity (Grassiniet al.2013; van Ittersum and Cassman 2013; van Ittersumet al.2013; Denget al.2019). It is needed to find out where the improvement needs mostly and its potential for the improvement given the limited land and water resources(Grassiniet al.2013; Fischer 2015; Longet al.2015).

Yield potential defines the ideal yield level to be achieved with perfection in the management of all production factors determining the yield (Lobellet al.2009). Although the yields of crops in many regions reached the 80% of the maximum yield,there are still some areas to have the potential (Neumannet al.2010; Weiet al.2015). Yield at farm level is vital for the productivity analysis as it decides the crop area and production (Fischer 2015),their maximum yield level can be taken as the indicator to measure the yield potential. The efficiency is in turn important to maximize the production at farm level given the climate change and environmental pressure (Tilmanet al.2011; Luet al.2015).

Technical efficiency has been applied widely to investigate the difference between farmer’s practice and“frontier” production level. It,as a part of household economic efficiency,is typically used to evaluate how well a producer is utilizing an underlying technology including a set of inputs and technology to produce maximum output(Farrell 1957; Thiamet al.2001; Chavaset al.2005). By making full use of the inputs and reducing the yield variation across farms,the improvement of technical efficiency is helpful to mitigate the overuse of chemical inputs. It is also considered as a critical approach to increase agricultural production in developing countries since many empirical studies indicated that most small-scale rice farmers were inefficient (Haji 2006; FAO 2012).

The yield gap based on actual grain yield data given the inputs level can be estimated by the stochastic frontier production function (Neumannet al.2010). Previous studies are based on the farm level,region and country level data(Lobellet al.2009; Van Wartet al.2013). China is a country with diversified cropping patterns,geographic characters and farming conditions. Land use and the cropping pattern are gradually changed due to the climate change,economic development and urbanization (Weiet al.2015).To understand the spatial variation of technical efficiencies in the production of individual crops could provide useful information to understand the grain supply and demand as well as to achieve the sustainable development of food production (Tian and Wan 2000; Rayet al.2012; Weiet al.2015).

Various methods have been applied to estimate the yield potential,and farmers’ validation is necessary to reduce the yield gaps between the maximum,experiment and average yields (Lobellet al.2009; Affholderet al.2013; Challinoret al.2014; Taoet al.2015; Denget al.2019). Farmers are motivated to gain profit and reduce uncertainty to engage in cereal crop farming,however,their performance varied greatly associated with the diversified geographic characteristics as well as socio-economic factors (Chenet al.2014; Xuet al.2020). Different from the assumption by the agronomists that the environmental and biophysical factors (i.e.,weather,soil,water and so on),socio-economic factors also contribute to the yield loss in farmers’ field in the economics’ perspective and are subsequently required to be introduced into the models for the analysis (Lobellet al.2009). A large-scale farm survey is required for the technical efficiency analysis of crops,however,it is costly and time-consuming (Affholderet al.2013). Little studies have been implemented to describe the spatial variation across locations in the country to provide the details of China’s grain production potential at farm level.

The paper is to investigate the technical efficiency and yield difference of rice,wheat and maize across main areas using farm level data in 2016. The purposes of the study are not only to analyze the spatial variation of Chinese cereal production at farm level but also to discuss the areas for potential grain output improvement associated with technology development and agricultural policies. The contribution of the study is as follows. First,the yields of food crops at farm level,technology adoption and agricultural inputs of farmers are essential to provide the actual picture of food production in the field and such detail information is necessary to understand the actual yields in the field and farmers’ practice properly. This provides the information for the extension specialists and policy makers to find the target farmers and apply the appropriate agricultural technology intervention for yield improvement; second,the spatial distribution of farmers’ technical efficiency is needed to estimate the yield gaps of food crops between farmers’ actual and potential yields to identify the productive areas. Improving the efficiency can minimize the waste of agricultural inputs and reduce the expense of environment by reducing the chemical inputs; third,farmers’ average yield is affected by the demographic characteristics,land and water resources,inputs,cropping pattern,and farming activities as well as non-farm activities (Chavaset al.2005; Silvaet al.2017). To investigate the determinants affecting the technical efficiency with primary data could be reference to rethink the current support policies and farmland protection systems (Wanget al.2018).

The paper is organized as follows:data and methods were presented in the second section; the main results and discussion were subsequently presented; the last section provided conclusion.

2.Data and methods

2.1.Survey sites

The data collected were funded by the project of“Differentiation on the output and efficiency of grain production and its mechanisms of improvement in China”led by the Institute of Crop Sciences,Chinese Academy of Agricultural Science. A total of 6 535 respondents participated in the survey which was implemented in 2016 including 1 218 rice farmers covering 615 inbred rice farmers and 603 hybrid rice farmers,respectively,and 3 279 wheat farmers1There are spring and winter wheat in China. The area and production of winter wheat account for 94% of national wheat area and 95% of national wheat production,respectively. In the study,wheat mainly refers to the winter wheat.as well as 2 038 maize farmers. The respondents were farmers who manage the farming. The survey included information on farmers’ resource endowment,varieties grown,grain yield,production,and agricultural inputs.

The survey sites for rice include seven rice producing areas including Heilongjiang,Guangxi,Guangdong,Zhejiang,Jiangxi,Hunan,and Hubei. The total rice sown area and rice production in the seven areas account for 59%of national rice area and 56% of rice production,respectively.The survey sites for wheat covered major producing areas in China including Jiangsu,Anhui,Hubei,Sichuan,Henan,Hebei,Shandong,and Xinjiang. The total wheat area and production in the eight producing areas account for 87% of national wheat area and 92% of wheat production,respectively. For maize,there are eight producing areas including Jiangsu,Hunan,Sichuan,Shandong,Jilin,Gansu,Liaoning,and Inner Mongolia. The total maize area and production in the eight locations account for 41% of national maize area and 44% of maize production,respectively.The farm-level data were collected by Chinese Academy of Agricultural Sciences in collaboration with provincial research institutes and local authorities. A stratified random sampling technique was used to select the households.Counties selected represented variation in geographic features (such as location and remoteness) and climate features. Villages were first selected on the basis of proportionate area and households from those villages were selected randomly.

2.2.Methods

The methods to estimate farm household technical efficiency include parametric and nonparametric methods,i.e.,stochastic frontier analysis (SFA) introduced by Farrell(1957) and data envelopment analysis (DEA) introduced by Charneset al.(1978). There are debates on which approach is more appropriate for technical efficiency estimation. In this study,we apply the SFA for our data set,which is a one-step approach using the maximum likelihood method to estimate the parameters of the production function equation and the technical efficiency model. This may be more appropriate than separately estimating these two equations (i.e.,estimate the production function first to calculate the technical efficiency scores and then use these scores to estimate the parameters of the efficiency equation) because it is more reasonable to assume that technical inefficiency is not independent of production outcomes. The one-step approach is thus applied in this study,i.e.,a stochastic production frontier based on the factors of production was estimated simultaneously with the determinants of inefficiency using the maximum likelihood estimation (Battese and Coelli 1995).

Both descriptive and inferential statistics were used to analyze the pattern of input use and the socioeconomic characteristics of the farm households. To verify which model specification fits the stochastic frontier best,a generalized likelihood-ratio test is conducted where a Cobb-Douglas production function (H0) is nested in the transcendental logarithmic (TRANSLOG) production function (H1). Based on the likelihood ratio test,where the test statistic is–79.56 with aP-value of 1.000,a Cobb-Douglas production function is the appropriate model for hybrid rice production in 2016 and TRANSLOG production function is for the rest of stochastic frontier. The empirical specification used in this study is the Cobb-Douglas functional form:

wherejindex represents thejth observation,since one parcel was selected from one household,thejth parcel is also thejth household;Yjrepresents rice production yield in tons per hectare on thejth parcel;αandβjare parameter vectors to be estimated;Vjis purely random error term;Xiis a vector ofiproduction inputs (i.e.,fertilizer,pesticide,herbicide,and labor) and indicator variables (i.e.,the irrigation) for thejth farmer;Ujis a non-negative random variable and named as inefficiency component to capture inefficiency effects relative to the stochastic frontier by truncating the normal distribution at zero.

While the technical inefficiency model is given as:whereUjrepresents technical inefficiency of thejth household to be estimated in the stochastic production function;δjare parameters to be estimated;Zijis theith socio-economic determinant at household level affecting inefficiency onjth farm.

In the production function,zero values were also observed in cases where farmers did not apply organic fertilizer and pesticides. As proposed by Battese and Broca(1997),the following methodology was applied to account for the zero values:

The model in eq.(3) implies thatX2j＊=X2jis true forX2j>0 but ifX2j=0,thenX2j＊=1. This methodology allows the homogeneity of error variances between farmers who did and did not apply organic fertilizer and pesticides under the assumption that the elasticities of output with respect to inputs of production were the same across farmers.Additional dummy variables were also included in the production function to control for the type of ecosystem and farm ownership.

2.3.Variables and specification

In this study,the household-specific factors in the inefficiency model include gender,age and education of household head,and household size or labor size. The effect of age on efficiency is expected to be positive since older respondents tend to have more farming experience(Chenet al.2009; Tanget al.2015). Farmers’ education is expected to affect technical efficiency positively (Chenet al.2009). Farm households that produce grains tend to satisfy the family members’ consumption requirement and income. Hence,we expect that households with bigger farm size tend to have lower technical inefficiency. The effect of farm size is expected to be positive. Dummy variables for cropping pattern were used to be the proxy to show the land use preference of farmers. Irrigation is important for rice farming and the dummy variable of traditional irrigation method was used. We hypothesize that farmers with traditional irrigation method will negatively affect technical efficiency.

The specification for the Cobb-Douglas production function is as follows:

Following the previous literature,the common agricultural inputs,i.e.,seed,organic and chemical fertilizer,pesticides input,and labor were defined in the function (for instance,Haji 2006; Yao and Shively 2007; Takahashi and Otsuka 2009). In addition,the variables in eq.(6) have been widely used in the study on agriculture production in developing countries (Haji 2006).

3.Results and discussion

3.1.Demographic and farm characteristics of cereal crop farming across regions

The majorities of the household head are males for both inbred and hybrid rice production. For the inbred rice production,the average age of household head is nearly in their 50s with an average household size of four persons.The age of household head in the less developed areas of Heilongjiang and Guangxi is younger than that in developed areas. The household size ranges from three to five persons while the number of agricultural labors is similar across regions (Table 1). Compared to the inbred rice production,age of household head in hybrid rice production is older and on average it is older than 55-year-old with lower education level. There is no significant difference across provinces in terms of the demographic characteristics in hybrid rice production.

For the wheat farming,similar with the household growing rice,most of the household heads are males with an average age of 51-year-old. Their education level is at the level of high school and below. The average household size is four persons with two labors.

Most household heads in the areas for maize production are males,except in Liaoning. The percentage of female head is 32% in Liaoning Province and it is much higher than that in other provinces. The average age of the maize farmers was 53-year-old. Farmers in Inner Mongolia and Jilin are relatively younger,with an average age of 48 years old. The average household size in maize farming is similar with that in rice and wheat farming,being four persons with two labors in one household. Basically there is not much difference among different locations in terms of demographic characteristics.

3.2.Variation of cereal crop yield associated with cropping pattern

Both single rice cropping pattern and double rice cropping pattern were implemented by the farmers while most of them grew single rice (Table 1). Rice pattern in China has changed to single rice due to lack of labors which is affected by the increasing non-farm opportunities and income in the context of urbanization (Chenet al.2013). Heilongjiang is an exception as it is used to be the area for single rice cropping pattern and with inbred rice production,so 100%of rice farmers adopt both inbred rice variety associated with single rice pattern. In most cases,the situation is a kind of mixed adoption of cropping pattern depending on the type of rice variety being grown. The cropping pattern varies across different provinces,but it is quite uniform within the same producing area.

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The yield of hybrid rice is significantly higher than that of inbred rice,which still indicates the yield advantage of hybrid rice production,but yield gap between hybrid and inbred rice is less than 4% on average. The average yield of hybrid rice is 7.94 t ha–1ranging from 9.58 to 5.89 t ha–1in the survey areas. Similarly,the average yield of inbred rice is 7.64 t ha–1with significant variation across different regions. It ranges from 5.43 t ha–1in Guangdong Province to 8.26 t ha–1in Zhejiang Province and the difference accounts for over 50% of the yield level in Guangdong Province.

In 2016,the average wheat yield was 6.84 t ha–1,while the highest yield was 8.0 t ha–1in Shandong Province and thelowest yield at 5.36 t ha–1in Hubei Province. The difference between the highest and lowest yield levels,2.65 t ha–1,is substantial and accounts for nearly 50% of the yield in Hubei Province. The average wheat sown area per household in the survey sites is 2.7 ha and varies greatly across locations.Less than 10% of wheat farmers have more than 6.7 ha growing wheat (i.e.,100 mu in Chinese). Most farmers are still with small-scale wheat farming.

Table 1 Statistics of demographic characteristics and inbred rice production in 2016

In 2016,the average maize area per household was 1.2 ha ranging from 0.3 to 4.4 ha per household. The average maize yield was 8.13 t ha–1,of which Jilin Province has the highest yield at 9.63 t ha–1and this is more than 40% higher than that in Hunan Province.

3.3.Technology adoption and agricultural inputs of cereal crops across locations

For the technology adoption,only less than 10% of farmers adopt mechanical transplanting for rice seedlings and most of them locate in Heilongjiang and Guangxi for inbred rice production. The adoption of organic fertilizer is very limited and it only accounts for 4% of rice farmers.

For the hybrid rice farming,in 2016,the average inputs of fertilizer and pesticide were 445 kg ha–1and 1 409 CNY ha–1,respectively. The highest input level of fertilizer was nearly twice more than the average level in Zhejiang Province.It is also the place that farmers invest the highest cost of pesticide for hybrid rice production than other locations.The lowest input of fertilizer was 279 kg ha–1in Sichuan Province,less than 2/3 of the average level. And the lowest input of pesticide was 848 CNY ha–1in Jiangxi Province. The average input of labors for the hybrid rice farming in 2016 is 6 687 CNY ha–1,while the lowest input was 3 488 CNY ha–1in Hubei Province and the highest was 11 864 CNY ha–1in Guangdong Province. Agricultural inputs varied investigate locations in terms of either quantity or value measurement.

For the wheat farming,all farmers in the survey applied organic fertilizer and over 70% of them with monoculture.In terms of the input,both the quantity of fertilizer and pesticide cost are with significant differences across locations. Chemical fertilizer used in the wheat farming includes nitrogen,phosphate and compound fertilizer.Chemical fertilizer used by farmers in Jiangsu Province exceeds nearly 80% of national average level and is more than three times than that in Anhui Province. Farmers in Anhui Province with the largest wheat sown area had the lowest chemical fertilizer input,which is 443 kg ha–1,less than the half of the average level. Similar with the fertilizer input,pesticide input across locations varied greatly. The average pesticide input was 618 CNY ha–1,while the highest was 908 CNY ha–1in Sichuan Province and the lowest was 411 CNY ha–1in Hebei Province.

For maize farming,yield level is not consistent with the agriculture input,i.e.,farmers produce high yield of maize are not always with high inputs. The average nitrogen fertilizer of maize production was 157 kg ha–1,ranging from 289 kg ha–1in Jiangsu Province to 112 kg ha–1in Hunan Province. For the phosphate and potassium fertilizer,the average inputs were 29 and 26 kg ha–1,respectively. Gansu Province had the highest phosphate fertilizer input,with an average level of 83 kg ha–1and Jiangsu Province has the highest potassium fertilizer input of 63 kg ha–1. Pesticide input in Liaoning Province was at the highest level,which is 3 717 CNY ha–1,exceeding the lowest level of pesticide input in Gansu Province. The pesticide input in Liaoning Province was five times higher than that of national average level. In addition,the seed input in Liaoning Province was 14 562 CNY ha–1,which was also at the highest level. The labor input also varied significantly across provinces,which was affected by the amount and price of labor input as well as mechanical input cost.

3.4.Distribution and variation of technical efficiency across locations

The average technical efficiencies of inbred rice,hybrid rice,wheat,and maize were 0.91,0.89,0.84,and 0.77,respectively (Table 2). Our estimation of technical efficiency scores for rice,wheat and maize farmers is in line with Tian and Wan (2000),with lower level of technical efficiency.The distribution of technical efficiency of food crops varied across locations.

A total of 80% of yield potential was taken as the ceiling yield that can be achieved by farmers (Lobellet al.2009;Denget al.2019). Taking 80% as the threshold level of measurement,inbred rice farmers could be called as efficient in general because over 89% of farmers’ efficiency is higher than 0.8. The average level of technical efficiency of inbred rice farmers from Heilongjiang Province was the highest level of 0.93,while that from Guangdong Province being the lowest with the level of 0.76. As shown in the Fig.1,the technical efficiency of inbred rice production in Guangdong Province is relatively dispersed. In contrast,the variation of individual farmers’ practice in Guangxi,Zhejiang and Heilongjiang is much less. Although inbred rice farmers mostly achieved 80% of the maximum yield given the current agriculture input,it is still possible to find the areas with potential (Neumannet al.2010; Weiet al.2015). Considering its variation of technical efficiency,Guangdong Province is the area with more potential for yield improvement to reduce the yield gap comparing to other locations.

The average level of technical efficiency of hybrid rice farmers is 0.89,with Jiangxi and Zhejiang provinces havingthe highest level of 0.94 and Hubei Province having the lowest level of 0.84. Compared with inbred rice farmers,the technical efficiency level of hybrid rice farmers is less dispersed in the same location than that of inbred rice farmers (Fig.2). The distribution of technical efficiency of farmers in Hubei and Hunan provinces is more dispersed,and farmers’ technical efficiency within the province is with variation.

Table 2 Distribution of yield and technical efficiency of cereal crops across different locations

On average,farmers’ technical efficiencies in both wheat and maize production are lower than that in rice farming and show significant variation across locations(Fig.2). The distribution of technical efficiency within each province showed different trends. On average,the technical efficiency of wheat farmers was 0.84 ranging from 0.90 in Xinjiang to 0.78 in Jiangsu. Although there was not substantial difference across locations in terms of the mean value of technical efficiency,the variation of technical efficiency within the producing area was significant. The distribution of technical efficiency in Anhui,Shandong and Jiangsu is relatively scattered,and some farmers’ technical efficiencies are even less than 0.4. The similar trend has been showed in maize production. That is,the mean value of technical efficiency at provincial level is similar across locations,while the difference within the location is significant across individual farmers.

In total,the average technical efficiencies of inbred rice,hybrid rice and maize in 2016 all exceeded 0.80,which was at a relatively high level,while the technical efficiency of wheat production was lower than 0.80,indicating that there is still a potential to improve the agricultural input efficiency by improving farmers’ practice. In general,farmers at higher level of cereal yields achieved higher technical efficiency which means they were more efficient than others. Chenet al.(2009) showed that farmers in Northeast and North China were more efficient than those in east and southwest regions which is inconsistent with our results,however,their study did not identify the specific product. For each individual crop,the spatial distribution of technical efficiency varied across different geographic locations.

3.5.Comparison on the determinants of technical efficiencies

According to the frontier production function result (Table 3),the amount of chemical fertilizer input significantly affected the yield of hybrid rice. But the effect of chemical fertilizer input on the yield of inbred rice is negative. The fertilizer input of inbred rice (680 kg ha–1) was much higher than that of hybrid rice (445 kg ha–1). Overuse or the improper usage of chemical fertilizer can negatively affect rice yield (Wanget al.2017). Pesticide input showed a significant negative impact on the yield of the inbred rice,but the effect of pesticide on the yield of wheat is positive. However,inbred rice and wheat are grown in different geographic locations associated with different management technologies,farmers’ practice on pesticide input is different. Thus,the effect of pesticide on farmers’ technical efficiency should be related to the specific crop and technology adoption.Seed input significantly affected the yields of hybrid rice and wheat,and 1% increase in seed input would increase the yields of the hybrid rice and wheat at 0.03 and 0.52%,respectively.

Fig.1 Distribution of technical efficiency of cereal production across the locations.

Based on the technical efficiency model,the adoption of irrigation technology will significantly reduce the technical efficiency of inbred rice farmers. In contrast,it is not consistent for hybrid rice production. Inbred rice and hybrid rice are two different technologies and traditional irrigation may influence the production differently. Maize and wheat farmers with monoculture pattern will have higher efficiency than those with other cropping patterns like rotation or intercropping. The kind of technology in agriculture would affect farmers’ technical efficiency (Zhuet al.2016; Tavvaet al.2017).

In addition,female farmers engaged in both maize and wheat production have significantly lower efficiency level than male farmers. Inbred rice farmers with a high education level or above have a lower inefficiency than that of farmers with a primary education level or below.It is different from Pedeet al.(2018),but consistent with Yao and Shively (2007) that showed farmers with higher formal education tended to engage in non-farm activities and were less efficient in rice production.

Older farmers were less efficient than young farmers in inbred rice and wheat farmers,which was inconsistent with the results of Chenet al.(2009),however,their study using the dummy variable to divide farmers into different age groups. Farmers were mostly in their 50-year-old and those growing inbred rice in Guangdong Province were nearly 60-year-old on average. In the context of urbanization and mechanization,older farmers may have physical limitations that hinder productivity improvements and access to modern agricultural technology. Household labors significantly contribute to farmers’ technical efficiency. This is in line with Yao and Shively (2007) that farmers are more technical efficiency with more family labors helping in rice production.

Fig.2 Distribution of technical efficiency of cereal production by crops.

Farm size affected farmers’ technical efficiency differently in rice,wheat and maize production. The results in previous studies were mixed as well. For instance,Zhanget al.(2016) showed that farmers with bigger farm size were not more efficient to achieve the economies of scale of farm production,but it was inconsistent with others. Our results indicated that the effect of farm size need to be investigated further for the specific cereal crops production.

3.6.Hypothesis test

To further validate the result of the frontier regression,tests of hypotheses were conducted. First,the test of hypothesis that technical inefficiency is not present in the model. Based on the test statistics in Table 4,the null hypothesis,i.e.,technical inefficiency not present in the model is rejected.In other words,the test proves statistically that the production frontier model should have an inefficiency component.Second,the test of hypothesis that observed parameters of the inefficiency model has no random component. If this is true,an ordinary least square (OLS) regression model combining production frontier and inefficiency components will be appropriate to conduct the analysis. However,the test statistics show that the hypothesis is rejected; hence,the parameters of the inefficiency model should have random components (i.e.,it is stochastic). Third,we test the hypothesis that the selected inefficiency variables have no significant effect on technical inefficiency. In this case,the inefficiency variables should be replaced in the technical inefficiency model. This hypothesis is also rejected based on test statistics. This means that the explanatory variables significantly affect the technical inefficiency model.

4.Conclusion

Our results showed the Chinese farmers in cereal production were efficient and farmers’ technical efficiency was varied across locations. Given the current inputs in the survey,the efficiency levels of most regions are nearly and over 90% is high and very close to the ceiling of best yield level.When farmer’s yield close to the potential threshold given the certain socio-economic and ecological environment,the overall technology improvement or new agriculture technology including new varieties associated withcultivation management is urgently needed in the main production areas to change or improve the trajectory of farmers’ practices.

Table 3 Estimation results of production function and efficiency function in stochastic frontier analysis (SFA)

Table 4 Results of hypothesis tests

Individual farmers’ technical efficiency ranged from 66 to 94%.It showed the potential to improve the yield through fining tuning the management of farmers’ practices by training and technical support in Guangdong Province for inbred rice,Hubei and Hunan provinces for hybrid rice,Jiangsu and Hubei provinces for wheat,and Inner Mongolia,Sichuan and Jilin for maize. Many of the locations are not in the developed areas,capital required for agricultural development may be helpful to facilitate the improved agricultural technology development and adoption.

The yield levels of the three major crops vary greatly from place to place as well. Farmers being investigated in the survey with higher yield level are also with better technical efficiency. Farmers’ agricultural inputs,demographic characteristics and technology adoption have different effects on farmers’ crop production and efficiency. In the survey,farmers for three crops are generally older and the age of above 50-year-old with similar trend across locations.Older farmers are less efficient than young generation.It is challenging for the aged farmers to adopt the new agricultural technology. The number of young farmers has sharply been reduced in the grain production. Shortage of labor supply associated with the increasing labor cost become the constraint of grain production development.The technology to save labor is critical and needs to be prioritized in the future research.

Currently,the Chinese agriculture is under transition in the context of rapid industrialization and urbanization. While non-farm employment has increased farmers’ income and changed their income structure,it has also triggered fierce competition for labor resources between farm and non-farm activities. While in the long run,the availability of non-farm opportunities may contribute to farmers’ yield improvement and this would be helpful for the resources allocation within the household,which helps in bridging the gap between farming and non-farm activities. This may affect the technology adopted and needed by Chinese farmers.However,the historical record shows that such integration takes a long time. An analysis using panel data with longer time periods will produce more convincing results.

Acknowledgements

Financial support for this research was funded by the grants from the National Key Research and Development Program China (2016YFD0300100). We thank Dr.Hou Peng (Chinese Academy of Agricultural Sciences),Dr.Li Congfeng (Chinese Academy of Agricultural Sciences),Dr.Liu Peng (Shandong Agricultural University,China),Dr.Lu Dalei (Yangzhou University,China),Dr.Lu Weiping(Yangzhou University,China),Dr.Zhang Yinghua (China Agricultural University),Dr.Wang Xiao (Nanjing Agricultural University,China),Dr.Wang Danying (China National Rice Research Institute),and Dr.Wang Shu (Shenyang Agricultural University,China) for their efforts to organize the household survey. We also thank Dr.Chen Chuanbo(Renmin University of China) for his valuable discussion and comments.