Assessing Total Factor Productivity for Soybean Production in China Based on DEA-Malmquist Index: 2005-2017

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.


Introduction
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 ac-counted 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 [1], it has attracted wide attention in academia. Some literature focused more on the basic theory and methodology of TFP, such as the Production Function analysis of R. Solow [2], E. Denison [3] and Jorgenson [4] et al., the Production Frontier Theory of Farrell [5], the Stochastic Frontier Model of Aigner [6], DEA Method of Charnes [7], Malmquist Index Method of Caves [8], proposed by Malmquist in 1953 [9], Hicks-Moorsteen TFP Index Method of Briec and Kerstens [10], and so on. Abundant empirical studies have been carried out in various fields, especially in agriculture [11]- [20], and Coelli et al. listed 17 studies in agriculture that have been conducted from 1993 to 2003, which provide a reference for our study [21].
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" [2], meaning TFP is an alternative metric for technical progress. With the deepening of the research, the connotation of the concept of TFP has been further expanded. Productivity growth was originated from four factors, namely technical change, efficiency change, scale efficiency change and mixed output effect. In the case of yield, the mixing effect of output is equal to 1 [21]. Therefore, in this paper, TFP growth is separated into components of technical change, efficiency change (efficiency improvements due to labor proficiency and management improvements) and scale efficiency change (productivity gains due to economies of scale).
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 in-American Journal of Plant Sciences dex 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 [22]. Data required by Transcendental Logarithmic production function, Constant Elasticity of Substitution production function, Fisher index and Tornqvist index are not available [23]. It can be seen that each method has its own specific applied environment, which should be selected according to the characteristics of the sample data. The DEA-Malmquist index effectively avoids the problems caused by the selection of specific production functions in the parametric method and has been proved by Caves and others to be superior to Tornqvist index and Fisher index under certain conditions [24] and applied widely [2] [13] [25] [26].
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 [27] and to analyze the technical progress and technical efficiency [28] [29] for soybean in China.
However, due to the limitations of the research methods, these studies only analyzed technical efficiency or separated the TFP for soybean production into technical progress and technical efficiency. Although Tian (2009) used Malmquist index and DEA to separate the TFP for soybean into technical progress, pure efficiency and scale efficiency, his conclusions are questionable due to unscientific selection in variable (one output variable, two input variables) [30].
Therefore, DEA-Malmquist index model is used in this paper, which is suitable for panel data, and we considered as far as possible a variety of input factors to estimate TFP for soybean in 10 provinces from 2005 to 2017. The TFP for soybean is separated into technical change and efficiency change, and efficiency change is further decomposed into pure efficiency change and scale efficiency change to judge the drivers of productivity growth for soybean in China.

Methodology
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 [23]. The basic principle is to construct productivity index by the ratio of distance functions, namely, to measure TFP growth of two digits through the distance ratio of each data point relative to the ordinary technology, and to separate TFP into three Therefore, calculating distance function is the key of Malmquist index. At present, the calculation methods include DEA and Stochastic Frontier Analysis (SFA). As mentioned previously, DEA has been widely used because it effectively avoids selection of boundary production functions caused by using SFA. 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.

Model Establishment
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: 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: where subscript c denotes technology under constant return to scale (CRS); ( )  The scale efficiency reflects the gap between the actual scale and the optimal production scale; the pure efficiency reflects the production efficiency of the input elements at a certain scale (optimal scale). The scale efficiency and the pure efficiency constitute the efficiency, which is the comprehensive measurement and evaluation of the ability of resource allocation, resource use efficiency and so on. American Journal of Plant Sciences by comparing the production point with the frontier surface technology at the mixing period, respectively. M + 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, > , it denotes that TFP grows from t to t + 1 period, and conversely, if The Equation (3) is further separated, that is: 3) Under the assumption of CRS, separate (4) into technical change (TECH) and efficiency change (EFFCH).
where subscript v denotes technology under VRS.
Therefore, TFP change may be written as follows: 5) Calculate these four distance functions: For a macroeconomic body, its input factor endowment is given and the scale is unlikely to be determined by itself, so input orientation or output orientation has no effect on the measurement results under the assumption of constant scale compensation [31]. American Journal of Plant Sciences By inserting the distance functions calculated by DEA into (5)-(9), TFP and its components can be obtained.

Variables
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 con-

Data Sources
The   Table 1 shows the average change of TFP and its components for soybean pro-   Figure 1. The cumulative change rate of TFPCH, TECHCH and EFFCH for soybean production.  (Figure 2). It can be judged that the change of TFP stems from technical change and pure efficiency change from 2005 to 2007. This may be because different soybean producing regions were limited by natural resources and production conditions. There were great differences in soybean production technology, such as breeding, fertilization, dense planting, irrigation and other cultivation techniques, as well as technology application and management. The gap between regional soybean production and various factor input is large, and the annual fluctuation is large, which led to large annual fluctuation of soybean yield in China.

Change and Analysis of TFP and Its Components in Soybean
Producing Regions Table 2 shows the average TFP and its components for every province from 2005 to 2017. The highest positive TFP growth was achieved by Liaoning province with 18%. It was followed by Henan and Inner Mongolia provinces with 16.7% and 6.5%, respectively. The sources of TFP growth were diverging among different provinces. Technical progress (16.7%) played an important role in Henan. Inner Mongolia experienced technical progress with 1.1% and the efficiency change with 5.4%, and scale efficiency change (5.4%) was the main source of efficiency change. Efficiency change (19.4%) is the major source of TFP growth in Liaoning and pure efficiency change (19.4%) is the major source of efficiency change.
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).

Conclusions
This paper discusses the change of TFP indicator and its components for soy- 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