Measurement,of,Grain,Production,Efficiency,in,Main,Grain-producing,Areas,and,Analysis,of,Inter-provincial,Differences——,A,Study,Based,on,Super-SBM,Model,and,Malmquist,Index

Qi Heng, and Su Jing-yan

Department of Academic Theory Research, Northeast Agricultural University, Harbin 150030, China

Abstract: China"s food security mainly depends on the core areas of food production. Under the dual constraints of resource scarcity and environmental degradation, improving the grain production efficiency of the main grain-producing areas has become the fundamental way to strengthen the grain production capacity and improve the national food security capability, and to improve the efficiency of grain production in major grain-producing areas requires empirical support. This paper used the Super SBM model and the Malmquist index to measure the grain production efficiency of the main grain-producing areas from 2001 to 2020 from both static and dynamic perspectives, and compared the differences in grain production efficiency among different soil types and different provinces (autonomous regions) in the main grain-producing areas. The results showed that from 2001 to 2020, the grain production in the main grain-producing areas was in a relatively ineffective state, and the differences in grain production efficiency among different soil types and different provinces (autonomous regions) in the main grain-producing areas were obvious. The order of grain production efficiency in different soil types was black soil region>red-yellow soil region>paddy soil region>fluvo-aquic soil region, and the order of grain production efficiency of the provinces (autonomous regions) in the main grain-producing areas was Jilin>Heilongjiang>Inner Mongolia>Jiangxi>Hunan>Sichuan>Hubei>Jiangsu>Liaoning>Henan>Anhui>Shandong>Hebei.From 2001 to 2020, the total factor productivity of grain in the main grain-producing areas increased, but due to the trade-off between the technological progress and the growth of technical efficiency, the increase in the total factor productivity of grain in the main grain-producing areas was small, and the growth mainly came from the increase of input factors in this period. The total factor productivity of grain in Hebei, Heilongjiang, Liaoning, Jilin, Inner Mongolia, Shandong, Jiangsu, Henan and Anhui increased,but the increase was small, while the total factor productivity of grain in Jiangxi, Sichuan, Hunan and Hubei provinces declined.

Key words: main grain-producing area, grain production efficiency, inter-provincial difference

Food is related to the national destiny and people"s livelihood, and food security is an important foundation for national security. China relies on its own strength to guarantee its food security, and has achieved a historic change from "not enough to eat"to "to eat enough" and "to eat well". However, many factors, such as the increasingly intensified resource and environmental constraints make the grain production capacity gradually approach the limit, and the space to increase grain output by increasing factor input is getting smaller and smaller (Yanget al., 2022).Production efficiency refers to the ratio between the actual output and the optimal output under a certain input factor (Gaoet al., 2017). Therefore, under the dual constraints of resource scarcity and environmental degradation, improving grain production efficiency has become the fundamental way to strengthen grain production capacity and improve the country"s ability to ensure food security. Some scholars have measured and analyzed grain production efficiency,for example, Gao and Song (2014) measured the technical efficiency value of grain production in China"s provinces and regions from 1978 to 2012 and the technical efficiency differences among the main grain production areas, main sale areas and balance areas, Tang and Vila (2016) estimated the technical efficiency and its changing trend of grain production in China"s provinces from 1990 to 2013, Yanget al.(2022) calculated the grain production efficiency and its dynamic evolution trend in 30 provinces and three functional areas in China from 2001 to 2018, Luet al. (2020) measured and analyzed the ecological efficiency of grain production in China from 2000 to 2018. From the current literature, the researches on grain production efficiency have matured, but there still remains some limitations. First, there are few studies on the measurement of grain production efficiency for major grain-producing areas. China"s food security mainly depends on the core areas of food production,and the fundamental way is to improve the efficiency of food production in the main food production areas(Min, 2012). However, the existing researches mainly analyze the differences in grain production efficiency among the main grain production areas, the main grain sale areas, and the grain production and sale balance areas, and there are few studies on the grain production efficiency in the main grain production areas. Second, there is a lack of difference analysis in grain production efficiency in different soil types. The quality of cultivated land has an important impact on the efficiency of grain production, so it"s a problem worthy of in-depth study to fully excavate and improve the efficiency of grain production in different soil types. In view of this, this paper used the Super SBM model and the Malmquist index to measure the grain production efficiency of the main grain-producing areas from 2001 to 2020 from both static and dynamic perspectives, and analyzed the differences in grain production efficiency among different soil types and different provinces (autonomous regions) in the main grain-producing areas, and attempted to provide a basis for formulating and implementing differentiated regional grain production policies.

Methods

Super-SBM modelThe data envelopment analysis (DEA) model was proposed by Charneset al. (1978), based on the concept of"relative efficiency evaluation", it used a linear programming method to build a non-parametric segmented surface(or leading edge) of the observed data, and then calculated the efficiency relative to this leading edge (Xiao and Wang, 2012). The DEA model included the traditional Chames, Cooper and Rhodes (CCR) model and Banker,Charnes and Cooper (BCC) model (Bankeret al.,1984), it was used to measure the degree to which the input (output) of the decision-making unit needed to be improved proportionally when it reached the production frontier, but it did not consider the "relaxation" influence of the elements, so its efficiency measure might produce bias (Xuet al., 2021). Based on this, a non-radial and non-oriented DEA analysis method based on the slacks-based measure was proposed, namely the SBM model, but the calculated efficiency value decreased strictly monotonically with the change of input and output slack, but there would be cases where multiple decision-making units were all completely effective,and it was impossible to evaluate and sort these decision-making units effectively. Therefore, the Super-SBM model based on the modified slack variables was further proposed, which effectively solved the discrimination and sorting problem when the efficiency value of multiple decision units was 1 (Huanget al.,2020). This paper selected the Super-SBM model to measure the grain production efficiency of 13 provinces(autonomous regions) in the main grain-producing areas. The model was defined as shown in formula (1).Where,mandswere the number of input and output,indicatorsSi-≥0,Sr+≥0 represented the slack variables of input and output, respectively,xandyrepresented the input and output variables, respectively，λj≥0(j=1, 2, ...,n) represented the weight vector.

Malmquist index

The Malmquist index method was proposed on the basis of the DEA method. This method could not only calculate the total factor productivity (TFP), but also decompose it into efficiency changes (catch-up effect)and technological changes (frontier shift), where efficiency changes reflected the degree of efficiency improvement or deterioration of the decision-making unit (DMU), while technological changes reflected the changes in the efficiency frontier in the two periods, so that the composition of productivity and its dynamics could be better understood. From periodsttot+1, the Malmquist index could be represented as:

The Malmquist total factor productivity change index could be further decomposed into the technical efficiency change index (Effch) and the technology progress index (Techch), the calculation formula was as the followings:

The technical efficiency change index could be decomposed into the pure technical efficiency change index (Pech) and the scale efficiency change index (Sech), and the calculation formula was as the followings:

Index selection and data sources

Index selection

When using the Super SBM model and the Malmquist index, the determination of input and output indicators was the primary issue. In this paper, the total grain output was used to measure the output level of grain production in each province in the main grainproducing areas. Six types of input indicators,including cultivated land input, labor input, capital input, fertilizer input, pesticide input and agricultural film input, were selected to measure the input of grain production in each province in the main grainproducing areas. Grain production is a resourceconstrained production, and cultivated land was the most important material basis for grain production(Nie, 2015). In addition, the multiple cropping index also had an important impact on grain output.Therefore, this paper measured the input of cultivated land by the sown area of grain crops. Labor force was a necessary input factor in grain production. Due to the lack of direct statistics on the number of workers in grain planting industry, the weight coefficientαwas constructed by Min and Li (2013), Yanget al. (2022)and Luet al. (2020), so that the number of laborers used for food production could be stripped from the number of employees in the primary industry, the weight coefficientα=(agricultural output value/total output value of agriculture, forestry, animal husbandry and fishery)×(sown area of grain crops/total sown area of crops).

With the popularization of agricultural machinery and the outflow of rural labor, agricultural machinery played an increasing role in modern grain production;and with the popularization of petroleum agricultural technology, pesticides, fertilizers and agricultural film became important input elements of modern grain production. This paper measured the capital input of grain production by the total power of agricultural machinery, the pesticide input of grain production by the use of pesticide, the chemical fertilizer input of grain production by the current scalar quantity for fertilizer application, and the agricultural film input of grain production by the use of agricultural plastic film. Due to the lack of data on the total power of agricultural machinery, pesticide use, fertilizer application and agricultural plastic film were used directly for grain production in the official statistical yearbook, with reference to Minet al. (2013) and Yanget al. (2022), this paper constructed a weight coefficientβ=(grain crop sown area/crop sown area)to strip out the factor inputs for food production in generalized agriculture.

Data sources

The index data of 13 provinces (autonomous regions)in the main grain-producing areas from 2001 to 2020 were selected to measure and evaluate the grain production efficiency of the 13 provinces(autonomous regions) in the main grain-producing regions. The total grain output, the sown area of grain crops, the agricultural output value, the total output value of agriculture, forestry, animal husbandry and fishery, the total sown area of crops, the total power of agricultural machinery, the amount of pesticides used, the pure amount of chemical fertilizers applied and the amount of agricultural plastic film used were from China Rural Statistical Yearbook (2000-2021);the data of primary industry employees from 2001 to 2019 of each province (autonomens region) in the main grain-producing areas were from the statistical yearbooks of each province over the years, and the primary industry employees in 2020 were from China Statistical Yearbook (2021). There were individual missing values in the indicators of individual provinces(autonomous regions), referring to the method of Huanget al. (2020), the imputation method was used for the indicators showing a time trend.

Static efficiency analysis: based on Super-SBM Model

Aiming at the input-output data of 13 decision-making units (DMU), based on the Super SBM model, the DEA SOLVER Pro5.0 software was used to calculate the grain production efficiency of each province (autonomous region) in the main grain-producing areas from 2001 to 2020.

Changes in grain production efficiency in major grain-producing areas

The calculated grain production efficiency of each province (autonomous region) in the main grainproducing areas was statistically analyzed, and the statistical analysis results are shown in Table 1.According to the principle of the Super-SBM model,when the production efficiency value was greater than or equal to 1, the evaluated decision-making unit was relatively effective; when the production efficiency value was less than 1, the evaluated decision-making unit was relatively ineffective (Huanget al., 2020).A specific analysis of the grain production efficiency in the main grain-producing areas from the vertical and lateral perspectives was made. It could be seen from Table 1 that from a vertical perspective, from 2001 to 2020, the average value of grain production efficiency in the main grain-producing areas did not exceed 1, indicating that grain production in the main grain-producing areas was relatively ineffective. From 2001 to 2020, the grain production efficiency of the main grain-producing areas fluctuated continuously,and the grain production efficiency of the main grainproducing areas reached the highest value (0.965) in 2009. In addition, the grain production efficiency of the main grain-producing areas in 2001, 2004, 2007 and 2020 also exceeded 0.9, while the grain production efficiency values of the main grain-producing areas in the rest of the years were between 0.6 and 0.9,which indicated that the grain production efficiency of the main grain-producing areas did not rise steadily,but had a downward trend. The possible reason was that, although continuous and high-intensity farming through the introduction of petroleum agricultural technology could increase the total grain output, this energy and resource input-based grain production method led to the destruction of the nutrient cycle of cultivated land, so that even if the input was greatly increased, it was also difficult to achieve a rapid increase in output. From the lateral perspective, the grain production efficiency of the provinces (autonomous regions) in the main grain-producing areas was quite different. The grain production efficiency of some provinces (autonomous regions) exceeded 1, which was a relatively efficient state of grain production, while the grain production efficiency of some provinces was much lower than 1, which was a relatively inefficient state of grain production. From 2001 to 2020, the coefficient of variation of grain production efficiency in the main grain-producing areas was relatively high,above 20% in most years. For example, in 2005, the coefficient of variation of grain production efficiency in the main grain-producing areas reached 31.65%, which indicated that the grain production efficiency among the provinces (autonomous regions) within the main grainproducing areas was quite different.

Table 1 Statistical analysis of grain production efficiency in major grain-producing areas from 2001 to 2020

Differences in grain production efficiency of different soil types

According to the main soil types, the quality of cultivated land and the distribution characteristics of the major crops such as grains, the "Plan for Rehabilitation of Cultivated Land, Grassland, Rivers and Lakes (2016-2030)" divided China into five major areas including black soil in northeast China, fluvoaquic region in north China and Huanghuai Plain,paddy soil region in the middle and lower reaches of the Yangtze River, red-yellow soil region in the hilly and downland areas in the south, irrigation and loess type dry farming areas in the northwest. According to this division, this paper divided the main grainproducing areas into four regions as black soil region(Heilongjiang, Jilin, Liaoning and Inner Mongolia),fluvo-aquic region (Hebei, Henan, Shandong and Anhui), paddy soil region (Jiangsu and Hubei), redyellow soil region (Sichuan, Hunan and Jiangxi),and then compared the grain production efficiency differences of different soil types in the main grainproducing areas. From 2001 to 2020, the average grain production efficiency in the main grain-producing areas was 0.863, the average grain production efficiency in the black soil region was 1.021, the average grain production efficiency in the fluvoaquic region was 0.628, the average grain production efficiency in the paddy soil region was 0.867, and the average value of grain production efficiency in the red-yellow soil region was 0.965. Judging from the ranking of the mean value of grain production efficiency, the order of grain production efficiency was black soil region> red-yellow soil region>paddy soil region>fluvo-aquic region. Next, the spatial pattern evolution characteristics of grain production efficiency in major grain-producing areas were further analyzed from the time dimension (Fig. 1). As shown in Fig. 1, from 2001 to 2020, the grain production efficiency values in some years in the black soil region were slightly lower than 1, and the grain production efficiency values in most years were higher than 1.Especially since 2017, the grain production efficiency in the black soil region was on the rise. The cultivated land in the black soil region of northeast China had good characters, high fertility and was suitable for farming. According to the data of the second national land survey and the evaluation results of county-level cultivated land quality survey, the cultivated land area of the typical black soil region in northeast China was about 18.53 million hectares, of which 1.67 million hectares were in Inner Mongolia Autonomous Region,1.86 million hectares in Liaoning Province, 4.6 million hectares in Jilin Province and 10.4 million hectares in Heilongjiang Province. Compared with other soil types, the quality of cultivated land in the black soil region was higher, so it was relatively efficient in grain production. In view of the importance of black land,China had issued the "Outline of the Northeast Black Land Protection Plan (2017-2030)" to increase the protection of black land, which might be an important policy boost to increase the efficiency of grain production in the black soil region since 2017. From 2001 to 2020, the grain production efficiency in fluvoaquic region was far below the average level, and grain production was in an ineffective state. Henan,Hebei and Shandong in the fluvo-aquic soil region are located in the North China Plain. The contradiction between supply and demand of water resources in the North China Plain is prominent, the spring drought is severe, and agricultural production is restricted by the lack of agricultural irrigation water sources. The North China Plain is mainly planted with winter wheat and summer corn. The irrigation period for winter wheat is in spring, due to the lack of irrigation water resources, even if other input factors increase, the grain production efficiency is also restricted. From 2001 to 2020, the grain production efficiency in the red-yellow soil region was higher than the average level, and the grain production efficiency fluctuated greatly, in some years, the grain production efficiency was higher than 1, and the grain production was in a relatively efficient state, but in some years, the grain production efficiency was lower than 1, and the grain production was in a relatively ineffective state. From 2001 to 2020, there were only a few years in the paddy soil region where the grain production efficiency was greater than 1, and the grain production efficiency was lower than 1 in most years. In general, among the main grain-producing areas, the grain production efficiency in the black soil region was relatively high and stable; the grain production efficiency in the fluvoaquic soil region was the lowest, and the value of grain production efficiency had remained around 0.6 in recent years; the grain production efficiency in the red-yellow soil region was on average above the level,the grain production efficiency fluctuated greatly;grain production in paddy soil region was relatively ineffective.

Fig. 1 Differences in grain production efficiency of different soil types in major grain-producing areas

Comparison of grain production efficiency at interprovincial level

What the Super-SBM model provided was essentially only a relative efficiency evaluation status, that was,the efficiency status of the provinces (autonomous regions) in the main grain-producing areas was relative to the production frontier constructed by the best practitioners. Therefore, the ranking of the grain production efficiency of the provinces (autonomous regions) in the main grain-producing areas was the focus of the super-efficiency analysis in this paper.Table 2 showed the grain production efficiency and its ranking by periods of each province (autonomous region) in the main grain-producing areas from 2001 to 2020 and each sub-period. From 2001 to 2020, the order of grain production efficiency of the provinces(autonomous regions) in the main grain-producing areas was as the following: Jilin> Heilongjiang>Inner Mongolia>Jiangxi>Hunan> Sichuan>Hubei>Jiangsu>Liaoning>Henan>Anhui>Shandong>Hebei. From 2001 to 2020, the average grain production efficiency of Jilin, Heilongjiang and Inner Mongolia was greater than 1, the grain production of these provinces(autonomous regions) was in a relatively efficient state;the average grain production efficiency of Jiangxi,Hunan and Sichuan was between 0.9 and 1, the grain production in these three provinces was on the verge of being relatively efficient; while other provinces(autonomous regions) had lower grain production efficiency and were in a relatively ineffective state of grain production. Judging from the dynamic changes in the ranking of grain production efficiency by stages, the ranking of grain production efficiency of some provinces (autonomous regions) had increased significantly. For example, Heilongjiang Province ranked the 3rd in grain production efficiency during the"10th Five-Year Plan" and the "11th Five-Year Plan"periods, while the ranking rose to the 1st during the"12th Five-Year Plan" and the "13th Five-Year Plan"periods; Jiangxi Province"s grain production efficiency ranked the 7th during the "10th Five-Year Plan" period,and the ranking rose to the 4th during the "13th Five-Year Plan" period. The ranking of grain production efficiency in some provinces (autonomous regions) had dropped significantly. For example, Hubei Province ranked the 6th during the "10th Five-Year Plan" and the"11th Five-Year Plan" periods, but dropped to the 10th during the "13th Five-Year Plan" period.

Table 2 Grain production efficiency by stages of each province (autonomous region) in main grain-producing areas from 2001 to 2020 and each sub-period

Dynamic efficiency analysis: based on Malmquist index

Using the Malmquist index and the DEAP2.1 software,the total grain productivity (TGP) of the 13 provinces(autonomous regions) in the main grain-producing areas from 2001 to 2020 were calculated and the structural efficiency was obtained by decomposition from the time and space dimensions.

Time dimension

From the perspective of the time dimension, it could be seen from Table 3 that from 2001 to 2020, the average grain total factor productivity in the main grain-producing areas was greater than 1. In general,the grain total factor productivity in the main grainproducing areas increased during this time period,but the range was small, with an increase of only 0.9%, which showed that the growth of grain output in the main grain-producing areas was mainly driven by the input of factors. Before 2014, the total factor productivity of grain in the main grain-producing areas fluctuated significantly, the total factor productivity of grain in the main grain-producing areas was only 0.945 from 2008 to 2009 and from 2004 to 2007, the total factor productivity of grain was less than 1; the total factor productivity of grain in the main grainproducing areas was relatively stable after 2014,all greater than 1, indicating that the total factor productivity of grain in the main grain-producing areas had steadily increased after 2014. Since the total factor productivity could be decomposed into the product of technical efficiency and technological progress,the changes in technical efficiency and technological progress of grain production and their impact on the total factor productivity in major grain-producing areas were next analyzed. From 2001 to 2020, the technical efficiency of grain production in the main grainproducing areas fluctuated around 1, with an average value of 1.002, which indicated that there was a slight improvement in the technical efficiency of grain production in the main grain-producing areas. From 2001 to 2020, the average value of the technological progress index in the main grain-producing areas was 1.007, and the technological progress index of grain production in the main grain-producing areas showed an upward trend, but the technological progress index fluctuated greatly. The gap between the minimum value and the maximum value was 0.156.In some years, the technological progress index rose more obviously, while the technological progress index declined more obviously. From 2003 to 2004 and from 2014 to 2015, the technical efficiency and technological progress indexes were both greater than 1, and from 2002 to 2003, the technical efficiency and technological progress indexes were both less than 1,in the rest of the period, the technological progress and the growth of technical efficiency had traded off the other (showing opposite trends). But the total factor productivity was greater than 1 in most periods, which indicated that the party greater than 1 had a relatively greater containment force, and this effect still kept the change in the total factor productivity above 1. From 2001 to 2020, the change direction of the change index of pure technical efficiency and the change index of scale efficiency of grain production in major grainproducing areas were consistent in most periods, either pure technical efficiency and scale efficiency increased simultaneously, or pure technical efficiency and scale efficiency decreased simultaneously.

Table 3 Malmquist index of grain production in major grain-producing areas and its decomposition from 2001 to 2020

Space dimension

Table 4 showed the Malmquist index and the decomposition results of grain production in each province(autonomous region) in the main grain-producing areas. From the perspective of space, from 2001 to 2020, nine of the 13 major grain-producing provinces(autonomous regions) had improved their grain total factor productivity, namely Hebei, Heilongjiang,Liaoning, Jilin, Inner Mongolia, Shandong, Jiangsu,Henan and Anhui, which were mainly located in the black soil region and fluvo-aquic region, but the growth rate of the total factor productivity in these provinces (autonomous regions) was relatively small,and Hebei, which had the highest growth rate, only increased by 2.9%; the total factor productivity of grain in the four provinces of Jiangxi, Sichuan, Hunan and Hubei declined, respectively, which were mainly located in the red-yellow soil region. From 2001 to 2020, the technical efficiency of grain production in the provinces (autonomous regions) in the main grainproducing areas changed little, and the changes in grain total factor productivity were mainly caused by changes in the technological progress index, and the decline in the total factor production efficiency of grain was also mainly caused by the decline in the technological progress index.

Table 4 Malmquist index and decomposition of provinces(autonomous regions) in major grain-producing areas

The improvement of grain production efficiency in major grain-producing areas faces serious resource constraints. The grain production efficiency in the black soil region is relatively high, but the further improving of the grain production efficiency in the black soil region faces obvious constraints, such as the decline in the quality of the black soil cultivated land. The black soil in northeast China has a deep humus layer and high organic matter content, which provides excellent soil conditions for grain production.However, due to years of development and utilization,the cultivated land resources in the black soil region had been overdrawn for a long time, and the organic matter content of the black soil had decreased year by year (Wang and Yang, 2021). The quality of black soil cultivated land had declined, and the improvement of grain production efficiency in the black soil region would inevitably be limited. The grain production efficiency in fluvo-aquic region was low, and with the continuous advancement of industrialization and urbanization, the shortage of agricultural irrigation water in fluvo-aquic region would become increasingly serious (Huanget al., 2019), which would significantly restrict the improvement of grain production efficiency in fluvo-aquic region. In addition, the cultivated land in the red-yellow soil region and paddy soil region also faces the problems of acidification and degradation.Therefore, it was necessary to improve the quality of cultivated land in the main grain-producing areas to lay a good resource foundation for the improvement of grain production efficiency.

From the static analysis results, in general, from 2001 to 2020, the grain production in the main grainproducing areas was relatively ineffective. There were obvious differences in grain production efficiency among different soil types and different provinces(autonomous regions) in main grain-producing areas.The order of grain production efficiency in different soil type areas was black soil region>red-yellow soil region>paddy soil region>fluvo-aquic region. Among them, the grain production in the black soil region was relatively effective, while the grain production in the red-yellow soil region, paddy soil region and fluvoaquic region was relatively ineffective. Judging from the inter-provincial differences in grain production efficiency, the grain production in some major grainproducing provinces (autonomous regions) was relatively efficient, the grain production in some major grain-producing provinces (autonomous regions) was on the verge of being relatively effective, and the grain production in some major grain-producing provinces(autonomous regions) was relatively ineffective.Judging from the dynamic changes in the ranking of grain production efficiency by periods, the grain produ-ction efficiency rankings of some major grainproducing provinces (autonomous regions) had risen considerably, and the grain production efficiency rankings of some major grain-producing provinces(autonomous regions) had significantly regressed.

From the dynamic analysis results, the total factor productivity of grain in the main grain-producing areas increased in 2001-2020, but due to the tradeoff between the technological progress and the growth of technical efficiency, the increase in grain total factor productivity in the main grain-producing areas was small, so the increase in grain output during this period was mainly due to the increase in input factors. The total factor productivity of grain in Hebei, Heilongjiang, Liaoning, Jilin, Inner Mongolia,Shandong, Jiangsu, Henan and Anhui increased,but the increase was small, while the total factor productivity of grain in Jiangxi, Sichuan, Hunan and Hubei declined. The technical efficiency of grain production in the main grain-producing areas had little change, and the change in grain total factor productivity was mainly caused by the change in the technological progress indexes.