The low and slowly increasing soybean yield restricts the development of soybean production. Accurate measures of total factor productivity (TFP) for soybean production can be helpful in identifying conditions, institutions or policies that promote soybean production development in China. In this paper, TFP growth for soybean production was estimated for a panel data of 10 major soybean producing provinces from 2005 to 2017. Results reveal that TFP grew at an average rate of 1.3% over the whole period, with technical progress contributing 2.3% and efficiency change providing the other -1.0%. The change of TFP for soybean production over that time, whether increase or decline, was mainly derived by technical change except in three years (2005-2007). Positive TFP growth in the provinces of Liaoning and Inner Mongolia, and negative TFP growth in Hebei and Anhui were mainly driven by efficiency change, specifically scale efficiency change except pure technical efficiency in Liaoning.
China is the original country of soybean. Once, it was the largest producer and exporter of soybean in the world. However, with the development of Chinese economy and the change of consumption structure, soybean demand continues to grow in China and soybean imports continue to increase, which has accounted for 80% of the total soybean supply. The soybean planted area in China has declined since 2005 due to its disadvantage of price compared with imported soybean and low benefit compared with other competitive crops. The contribution rate of planting area to total soybean production showed a downward trend due to the limited arable land resource in China. Therefore, soybean production in China will mainly depend on the increase of soybean yield. We estimate the total factor productivity (TFP) of soybean and analyze the contributing factors, so that effective measures will be taken to improve soybean yield to further promote the development of soybean production in China.
TFP is an important variable to measure the contribution of factor input efficiency to production growth and also an important index to reflect whether the economy may achieve sustainable development. Since J. Tinbergen, the Dutch economist, first proposed the concept in 1942 [
There are still differences in the definition of the connotation of TFP in academic circles at present from the existing theoretical research. TFP in the traditional sense, refers to an increase in output resulting from technical advances and capacity realization other than inputs of various elements (such as capital and labor, etc.). These elements are the residuals of the exclusion of factor input contributions, also known as “Solow residual” [
Method and data are the keys to the research in the process of TFP estimation from the existing empirical research. Generally speaking, there are two main types of assessing methods, parametric method and nonparametric method. Parametric method mainly includes production function (e.g. C-D production function, Transcendental Logarithmic production function, Constant Elasticity of Substitution production function) and Stochastic Frontier Model, etc. Nonparametric method mainly includes Data Envelopment Analysis (DEA) and index method (e.g. Fisher, Tornqvist, Hicks-Moorsteen TFP index and Malmquist index), etc. The hypothesis condition of production function is strict (e.g. Solow residual), which is often difficult to realize in a real economy. Although the Stochastic Frontier Model allows technical inefficiency and separates TFP into technical change and technical efficiency change, strictly speaking, this method is more applicable to measure efficiency [
Scholars have also begun to pay attention to soybean production efficiency, and carried out special research in recent years, such as the use of Stochastic Frontier production function to analyze technical efficiency [
DEA-Malmquist index is a common method for calculating TFP in the present application, which was constructed in 1994 by Rolf Fare, Grosskopf, Norris and others on the basis of Malmquist index and DEA. This approach uses Malmquist index to construct the distance function, and uses DEA to measure the distance function, then estimates TFP according to distance function value.
Malmquist index was developed based on the concept of Malmquist quantity index and distance function by Caves, Christensen and Diewert [
The essence of DEA is a nonparametric statistical analysis to evaluate the relative efficiency of each decision unit by comparing the degree of the ineffective decision unit deviating from DEA effective production frontier surface. The advantage of DEA is to avoid the subjectivity of the evaluation results by using the linear programming method, which need not consider the function relation of input-output, need not estimate the parameters in advance and any weight hypothesis. At the same time, there is no requirement for the unit of measurement of input-output variables, and there is no need for data consistency, homogenization and other preprocessing.
1) The first step of constructing Malmquist productivity index is to define the distance function. The distance function of the output indicator variable is defined as follows:
D o = { δ ( x , y / δ ) ∈ P ( x ) }
where x and y denote matrices of input variables and output variables, respectively. δ denotes a directional output efficiency indicator, and P ( x ) is defined as a possible production set. If y is the component of P ( x ) , then the value of the function will be less than or equal to 1. If y is on the external frontier surface of a possible production set, then the function value will be equal to 1, and conversely, if y is located outside of P ( x ) , then the function value will be greater than 1 (Li et al., 2008).
2) Define Malmquist productivity index based on output indicator variables:
M o t = D o c t ( x t + 1 , y t + 1 ) D o c t ( x t , y t ) (1)
M o t + 1 = D o c t + 1 ( x t + 1 , y t + 1 ) D o c t + 1 ( x t , y t ) (2)
where subscript c denotes technology under constant return to scale (CRS); ( x t , y t ) and ( x t + 1 , y t + 1 ) denote input and output vector in t period and t + 1 period, respectively. D o c t ( x t , y t ) and D o c t + 1 ( x t + 1 , y t + 1 ) denote the output distance function obtained by comparing the production point with the frontier surface technology at the same period (t and t + 1 periods), respectively. D o c t ( x t + 1 , y t + 1 ) and D o c t + 1 ( x t , y t ) denote the output distance function obtained by comparing the production point with the frontier surface technology at the mixing period, respectively. M o t and M o t + 1 denote the technical efficiency change from t to t + 1 period using technology in t and t + 1 period as reference, respectively.
In order to avoid constraints or arbitrariness due to choosing reference technology, Malmquist index generally is calculated by the geometric mean of both, that is,
M o ( x t , y t , x t + 1 , y t + 1 ) = [ D o c t ( x t + 1 , y t + 1 ) D o c t ( x t , y t ) × D o c t + 1 ( x t + 1 , y t + 1 ) D o c t + 1 ( x t , y t ) ] 1 2 (3)
If M o ( x t , y t , x t + 1 , y t + 1 ) > 1 , it denotes that TFP grows from t to t + 1 period, and conversely, if M 0 ( x t , y t , x t + 1 , y t + 1 ) < 1 , then it declines.
The Equation (3) is further separated, that is:
M o ( x t , y t , x t + 1 , y t + 1 ) = D o c t + 1 ( x t + 1 , y t + 1 ) D o c t ( x t , y t ) [ D o c t ( x t + 1 , y t + 1 ) D o c t + 1 ( x t + 1 , y t + 1 ) × D o c t ( x t , y t ) D o c t + 1 ( x t , y t ) ] 1 2 (4)
3) Under the assumption of CRS, separate (4) into technical change (TECH) and efficiency change (EFFCH).
TECH = [ D o c t ( x t + 1 , y t + 1 ) D o c t + 1 ( x t + 1 , y t + 1 ) × D o c t ( x t , y t ) D o c t + 1 ( x t , y t ) ] 1 2 (5)
EFFCH = D o c t + 1 ( x t + 1 , y t + 1 ) D o c t ( x t , y t ) (6)
4) Under the assumption of variable return to scale (VRS), efficiency changes (EFFCH) is further separated into pure efficiency change (PECH) and scale efficiency change (SECH).
PECH = D o v t + 1 ( x t + 1 , y t + 1 ) D o v t ( x t , y t ) (7)
SECH = D o v t ( x t , y y ) / D o c t ( x t , y t ) D o v t + 1 ( x t + 1 , y t + 1 ) / D o c t + 1 ( x t + 1 , y t + 1 ) (8)
where subscript v denotes technology under VRS.
Therefore, TFP change may be written as follows:
TFPCH = M o ( x t , y t , x t + 1 , y t + 1 ) = TECH × EFFCH = TECH × PECH × SECH (9)
5) Calculate these four distance functions: D o c t ( x t , y t ) , D o c t + 1 ( x t + 1 , y t + 1 ) , D o c t ( x t + 1 , y t + 1 ) , D o c t + 1 ( x t , y t ) using DEA linear programming method of CRS output-oriented.2 At the same time, the constraint, ∑ i λ i t = 1 , is added to the following linear programming and the distance functions under the condition of VRS, D o v t + 1 ( x t + 1 , y t + 1 ) and D o v t ( x t , y t ) , can be obtained.
[ D o c t ( x t , y t ) ] − 1 = max ϕ , λ ϕ s . t . − ϕ y i t + Y t λ ≥ 0 x i t − X t λ ≥ 0 λ ≥ 0 [ D o c t + 1 ( x t + 1 , y t + 1 ) ] − 1 = max ϕ , λ ϕ s . t . − ϕ y i , t + 1 + Y t + 1 λ ≥ 0 x i , t + 1 − X t + 1 λ ≥ 0 λ ≥ 0
[ D o c t ( x t + 1 , y t + 1 ) ] − 1 = max ϕ , λ ϕ s . t . − ϕ y i , t + 1 + Y t + 1 λ ≥ 0 x i , t + 1 − X t λ ≥ 0 λ ≥ 0 [ D o c t + 1 ( x t , y t ) ] − 1 = max ϕ , λ ϕ s . t . − ϕ y i t + Y t + 1 λ ≥ 0 x i t − X t + 1 λ ≥ 0 λ ≥ 0
6) By inserting the distance functions calculated by DEA into (5)-(9), TFP and its components can be obtained.
Based on the input and output of soybean, we selected soybean yield as output variable and 6 indicators (land cost, seed fee, pesticide and fertilizer fee, labor cost, mechanical fee, other direct and indirect cost) as input variables considering the characteristics of soybean production and the actual composition of production costs, as well as the availability of sample data. The unit of output variable is “kg/mu”, and the unit of each input variable is “Yuan/mu”. In order to eliminate the impact of inflation on price data, input indicators were converted according to the corresponding Price Indexes in each province.
Soybean yield: the variable of soybean yield is substituted by output of main product, since National Bureau of Statistics of China has adjusted the data of food production since 2018, soybean production data are included in beans and no longer counted separately.
Land cost: This variable covers rent of circulation land and opportunity cost of land. Land cost was converted according to the Price Index of Agricultural Means of Production (AMPI) [
Seed fee: This variable is converted according to the Price Index of AMPI.
Labor cost: This variable covers hired labor and the opportunity cost of unpaid labor. Labor cost is converted according to Consumer Price Index (CPI) of rural residents.
Pesticide and fertilizer fee: This variable covers the fee of pesticide, organic fertilizer and chemical fertilizer. Pesticide and fertilizer fee is converted according to the Price Index of Chemical Fertilizer.
Mechanical fee: This variable covers the fee of fuel, lube, electricity, repairs, tool, mechanical operations, irrigation and drainage, and technical service. Mechanical fee is converted according to the Price Index of Mechanized Agricultural Tools.
Other direct and indirect costs: This variable covers the other direct fee, with the exception of the above fees and the indirect fees, which cover depreciation for plant assets, insurance, administration expenses, sales charge, and financial charge. Other direct and indirect cost is converted according to the Price Index of AMPI.
The input-output data from 2004 to 2017 in the main 10 soybean producing provinces (including Hebei, Shanxi, Inner Mongolia, Liaoning, Jilin, Heilongjiang, Anhui, Shandong, Henan and Shaanxi) were used as samples on the basis of variables and the availability of data. The output of main production and the soybean cost data of each province are derived from National Compilation of Agricultural Products Cost and Income. The various Price Indexes in each province are derived from China Statistical Yearbook.
Distance functions were calculated by using DEAP2.1 software, and selecting output orientation of constant return to scale (CRS)3 as parameter according to DEA-Malmquist index model established previous and related input-output statistics data. Then, Malmquist index and its components can be obtained according to the distance functions.
Then, we consider the annual change of cumulative TFP and its components in
Year | TFPCH | TECHCH | EFFCH | PECH | SECH |
---|---|---|---|---|---|
2005 | 1.595 | 1.235 | 1.291 | 1.227 | 1.052 |
2006 | 1.022 | 1.108 | 0.922 | 0.945 | 0.976 |
2007 | 0.922 | 0.846 | 1.089 | 1.086 | 1.003 |
2008 | 1.186 | 1.157 | 1.025 | 0.989 | 1.037 |
2009 | 0.752 | 0.751 | 1.001 | 0.997 | 1.004 |
2010 | 1.176 | 1.163 | 1.011 | 1.012 | 0.999 |
2011 | 0.932 | 0.934 | 0.998 | 0.996 | 1.001 |
2012 | 0.946 | 0.943 | 1.004 | 1.006 | 0.998 |
2013 | 0.881 | 0.887 | 0.993 | 1.000 | 0.993 |
2014 | 0.900 | 0.905 | 0.995 | 1.000 | 0.995 |
2015 | 1.019 | 1.020 | 0.998 | 1.000 | 0.998 |
2016 | 0.915 | 0.905 | 1.010 | 1.000 | 1.010 |
2017 | 1.147 | 1.150 | 0.997 | 1.000 | 0.997 |
Average | 1.013 | 0.990 | 1.023 | 1.018 | 1.005 |
Lastly, efficiency change was volatile and stemmed from the change of pure efficiency from 2005 to 2007. It was relatively stable and stems from the change of scale efficiency from 2008 to 2017 (
The other seven provinces showed negative TFP growth ranging between −6.5% and −0.6%. The highest negative TFP growth was achieved by Anhui with −6.5%, followed by Hebei with −6.3%, Heilongjiang with −4.2%, Jilin with −3.7%, Shandong with −3.2%, Shanxi with -0.6%, and Shaanxi with −0.5% in turn. Technical regress was the main driver of negative TFP growth. All seven provinces experienced technical change ranging between −6.2% and −0.6%. Hebei and Anhui were the only two provinces that experienced negative efficiency change with −0.1% and −0.5%, respectively, which were driven by scale efficiency change (−0.1% and −0.5%, respectively).
Province | TFPCH | TECHCH | EFFCH | PECH | SECH |
---|---|---|---|---|---|
Hebei | 0.937 | 0.938 | 0.999 | 1.000 | 0.999 |
Shanxi | 0.994 | 0.994 | 1.000 | 1.000 | 1.000 |
Inner Mongolia | 1.065 | 1.011 | 1.054 | 1.000 | 1.054 |
Liaoning | 1.180 | 0.988 | 1.194 | 1.194 | 1.000 |
Jilin | 0.963 | 0.963 | 1.000 | 1.000 | 1.000 |
Heilongjiang | 0.958 | 0.958 | 1.000 | 1.000 | 1.000 |
Anhui | 0.935 | 0.940 | 0.995 | 1.000 | 0.995 |
Shandong | 0.968 | 0.968 | 1.000 | 1.000 | 1.000 |
Henan | 1.167 | 1.167 | 1.000 | 1.000 | 1.000 |
Shaanxi | 0.995 | 0.994 | 1.001 | 1.000 | 1.001 |
Figures 3-5 depict the annual change of TFP and its components for every province over time. The change of TFP was characterized by fluctuation in the ten provinces, especially in Henan, Liaoning and Inner Mongolia. The highest positive and negative TFP growth were achieved by Henan with 94.9% in 2012 and Inner Mongolia with −51.8% in 2009, respectively (
Although technical progress (regress) plays an important role in the change of TFP growth (positive or negative), there were diverging trends among the different provinces. Positive (negative) technical change indicates progress (regress) in terms of soybean production technology (Ang et al., 2017). The trend of technical progress (regress) and TFP growth was roughly coincident except for individual provinces and years, such as Inner Mongolia in 2006. The highest technical progress and regress were achieved by Henan in 2012 (94.9%) and Inner Mongolia in 2009 (−51.8%), respectively (
Technical efficiency change plays a minor role in TFP growth. Positive (negative) technical efficiency change indicates that the distance to the frontier decreases (increases) over the whole time period (Ang et al., 2017). Negative technical efficiency change is quickly followed by positive changes. These spikes were visible in Inner Mongolia, Liaoning and Hebei. The highest technical efficiency was achieved by Inner Mongolia with 51.3% in 2005 and −37.5% in 2006, respectively. There was no change only in Shanxi, Shandong and Henan (
Positive (negative) scale efficiency change indicates that the provinces operate at a more (less) optimal scale over the whole time period (Ang et al., 2017). There were no changes of scale efficiency in Shanxi, Jilin, Shandong, Henan and Shaanxi over the whole period. This means that the scale of production was optimal in the five provinces. The highest scale efficiency and scale inefficiency were achieved by Inner Mongolia with 96% in 2005 and −18% in 2007, respectively (
This paper discusses the change of TFP indicator and its components for soybean production in China. TFP index was separated into technical change and efficiency change, and efficiency change was further separated into pure efficiency change and scale efficiency change over the period 2005 to 2017. The results show annual growth in TFP of 1.3%, with technical change contributing 2.3% and efficiency change providing the other −1.0%. The change of TFP for soybean production over that time, whether increase or decline, mainly was derived by technical change except for typical technology propulsion or efficiency driven characteristics from 2005 to 2007. In terms of each province performance, positive TFP growth was achieved by Liaoning, Henan and Inner Mongolia with 18%, 16.7% and 6.5% over the study period, respectively, which was mainly derived by efficiency change in Liaoning and Inner Mongolia and derived by technical change in Henan. The other seven provinces showed negative TFP growth driven by technical regress except Hebei and Anhui, in which TFP growth was driven by inefficiency, properly speaking scale inefficiency in addition to technical regress.
According to the conclusions, in order to promote the growth of TFP for soybean production in China, first of all, soybean production technology should be improved by research and popularization in order to continuously promote the process of high quality of varieties to adapt to different soil environments and to resist the influence of uncertain factors (e.g. drought and waterlogging natural disasters) on soybean yield. This technology includes excellent variety breeding technology, cultivation techniques closely combined with agricultural machinery and agronomy, technology of fertilizer application and pest detection, prediction, scientific prevention and controlling etc. Secondly, it should be considered to optimize soybean planting scale promotion in terms of local conditions except focusing on technology in Anhui and Hebei. At the same time, reasonable allocation of input elements to improve soybean production is necessary. Lastly, government should continue to strengthen agricultural policy support to ensure the optimization and application of good seeds, agricultural machinery, etc., to encourage the enthusiasm of soybean farmers.
Though the results are quite plausible and meaningful, the authors are quite conscious of the data limitations (only 10 provinces), and investigation of soybean input factors is necessary in more soybean planting provinces for further work in this area.
Postdoctoral Foundation of Heilongjiang Province (CN) (Award Number: LBH-Z15026).
Philosophy and Social Science Foundation of Heilongjiang Province (CN) (Award Number: 16JYB16).
Heilongjiang Bayi Agricultural University (CN) (Award Number: XDB2015-06).
The authors declare no conflicts of interest regarding the publication of this paper.
Yang, S.G., Malaga, J. and Guo, X.Y. (2020) Assessing Total Factor Productivity for Soybean Production in China Based on DEA-Malmquist Index: 2005-2017. American Journal of Plant Sciences, 11, 24-39. https://doi.org/10.4236/ajps.2020.111003