Analysis on the Trend and Factors of Total Factor Productivity of Agricultural Export Enterprises in China

There is an “export productivity paradox” in Chinese enterprises, which has been confirmed in agricultural enterprises. This paper attempts to explain this phenomenon from the perspective of the components of TFP. This paper uses the SFA-Malmquist method to decompose and compare the TFP of China’s agricultural export enterprises based on the data of the state-level leading agricultural enterprises from 2016 to 2017. The conclusions are as follows: firstly, China’s agricultural TFP shows a negative growth trend, and the growth rate of TFP of agricultural export enterprises is less than that of agricultural non-exported enterprises; secondly, the growth rate of TFP of grain and animal husbandry export enterprises is less than that of non-export enterprises; the growth rate of TFP of private agricultural export enterprises is lower than that of non-export enterprises of the same type; the growth rate of TFP of export enterprises in eastern and western regions is lower than that of non-export enterprises; and thirdly, technical progress is an important reason for the change of TFP of China’s agricultural enterprises. However, compared with agricultural non-exported enterprises, improving the technical efficiency of enterprises can more promote the TFP of agricultural export enterprises.


Introduction
Export is the main means by which agricultural enterprises participate in the international market. As a major agricultural trader, China ranks among the top agricultural exporting and importing countries in the world. China's agricultural trade shows a continuous increasing trend, which has increased from $26.94 billion in 2000 to $201.39 billion USD in 2017, with an average annual growth rate of 12.56%, of which the agricultural export has continued to increase. Since 2004, China's agricultural trade deficit had expanded, and it was −$50.32 billion. Agricultural enterprises, as an important trade body of China's agricultural export, make outstanding contributions. The state-level agricultural enterprise export sector accounts for a large share of agricultural exports; the export value of these enterprises accounts for more than 80% of the total export value of China's agricultural enterprises. Indeed, the export value of agricultural enterprises accounted for 20-25% of the total export value of China's agricultural enterprises from 2013 to 2017.Total factor productivity (TFP) is the core of a country's economic growth and the main factor of enterprise development. Enterprise export and productivity increase promote each other. However, there is an "export-productivity paradox" in Chinese agricultural enterprises [1], that is, the productivity of agricultural enterprises that export is lower than that of non-exporting agricultural enterprises. What is the difference in TFP between Chinese agricultural export and non-export enterprises, and what leads to this difference? In exploring these questions, this paper has important theoretical and practical significance for adjusting the export from the level of agricultural enterprises, only Liu et al. (2018) and Jia et al. (2018) measure and compare the TFP of agricultural enterprises [1,41], and there is a lack of the comparison of TFP to specific agricultural industries. Second, from the perspective of the relationship between export and productivity, although some studies have confirmed the existence of the "export productivity paradox" in China's agricultural enterprises and analyze the reasons for the existence of this "export productivity paradox", they have not undertaken this analysis from the perspective of the composition of TFP. What is the difference of TFP between agricultural export and non-export enterprises, and is there a gap between agricultural enterprises in different regions and industries?
What causes the change in TFP? This paper focuses on whether there are differences in TFP among agricultural enterprises in different industries in China, and if so, what causes these differences. It also analyzes the TFP of agricultural exporting and non-exporting enterprises and the impact of the components of TFP on the TFP of agricultural exporting and non-exporting enterprises.
The structure of this paper is as follows: first, we introduce the research methods and data sources; second, we measure the TFP of agricultural enterprises and compare TFP across industries, regions, and enterprise properties; third, we present the conclusions, shortcomings, and policy suggestions arising from this research.

Methodology
This paper decomposed the TFP into the technical efficiency change (TEC), technical change (TC), scale efficiency change, and distribution efficiency, on the basis of the research of Si and Wang [18]. The price of products is an important factor in calculating TFP, but our data does not include price statistics, so, it is difficult to calculate scale efficiency and distribution efficiency based on our data. Therefore, this paper decomposes TFP into technical progress and technical efficiency, namely the TFP index (TFPC t,t+1 i ) is the product of the technical progress index (TC t,t+1 i ) and the efficiency improvement index (TEC t,t+1 i ), as shown in Equation (1), It can be seen from Equation (1) that measuring technical efficiency is the key. In general, technical efficiency needs to set a stochastic frontier production function, and the parameter form of the production function, the equation structure, and the setting of the error term have strict requirements, and the remaining growth except the part that can be explained by the factor contribution is regarded as the productivity. It is believed that the main reason why individual economic decision-making units cannot fall to the frontier production is the loss of technical efficiency.
According to Aigner et al. [42], and Battese and Coelli [43], the basic expression of stochastic frontier production function is as follows: where i = 1, 2, I; t = 1,2, . . . , T; y it is the output of the i enterprise in t period, X it is the input vector of the i enterprise in t corresponding to y it , t is the time trend, β is the parameter vector of stochastic frontier production function to be estimated. V it is a random disturbance term, which is assumed to obey the normal distribution of N(0,σ 2 v ), and is independent of U it , which represents the loss of technical efficiency caused by uncontrollable factors; U it is the non-negative random variable of technical efficiency loss per unit t year, which is assumed to obey N(m it ,σ 2 u ), represent the influence of controllable factors on technical efficiency.
Combined with the empirical study of Coelli and Prasada [44], the stochastic frontier production function is as follows: where, y it is the level of sales revenue of i enterprise in t period, x 1it , x 2it , x 3it are the capital input, labor input, and raw material input of i enterprise in t period, t is the time trend of technical progress change, β is the estimated parameter, v it , u it are the random error term and the technical inefficiency term respectively, v it and u it is independent of each other. Stata is a kind of statistical software, scholars use the software to write the corresponding program language for the measurement and analysis of TFP. This paper use Stata15.0 software) to measure the technical efficiency, namely where, TE it represents the technical efficiency of i enterprise in the period t; E() is the expected value of the mathematical formula in parentheses; when the logarithm of actual output is used as the dependent variable, y it * is equal to EXP(y it ). The technical efficiency change value is the ratio of the technical efficiency value between the t + 1 and t, as shown in Equation (5): The change of technological progress is derived from Equation (2), The technological progress index is: where, Formula (7) TC it , TC t,t+1 i respectively represents the technological progress rate and technological progress index in t period.

Data
The relevant index data of agricultural enterprises used in this paper come from the data of 1145 state-level leading agricultural enterprises from 2016 to 2017, and a total of 2290 enterprise samples of annual data are obtained. The sample is representative for the following reasons: first, the export of sample enterprises is an important part of the export of China's agricultural enterprises. The data showed, the number of agricultural exporting enterprises accounts for 37.5% of the total number of agricultural leading enterprises, and the export volume of 1145 agricultural enterprises accounts for 18.7% of China's agricultural export. Second, the productivity of sample enterprises is high. Leading agricultural enterprises have become the leader in the development of agricultural enterprises. At present, there are more than 90,000 agricultural enterprises in China, including 1542 agricultural leading enterprises, the sample enterprises account for 74% of the total number of agricultural leading enterprises. We discuss agricultural leading enterprises from the regional perspective, China's eastern region includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, and Guangdong. China's central region includes Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, and Hunan. China's western region includes Chongqing, Sichuan, Guizhou, Yunnan, Xizang, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang Guangxi, Inner Mongolia, and Hainan.According to the regional division, Hainan should belong to the eastern region. However, in the evaluation process of national leading enterprises in agricultural industrialization, Hainan is included in the western region with reference to the standards of national leading enterprises in the western region.The number of agricultural leading enterprises in the eastern, central, and western regions is 441, 348, and 356, respectively) We discuss agricultural leading enterprises from the perspective of enterprise properties, agricultural enterprises are divided into three types: collective, private, and foreign enterprises, the number of collective, private, and foreign-owned agricultural leading enterprises is 156, 940, and 49, respectively. We discuss agricultural leading enterprises from the perspective of industry distribution, agricultural enterprises include 15 categories, such as grain (including feed), eggs, milk, meat, tea, flowers, forestry, cotton, flax and silk, furriery, vegetables, aquatic products, fruits, sugar, oil and medicinal materials. Egg, milk, and meat enterprises are classified as animal husbandry enterprises. In terms of sample distribution, the number of grain and animal husbandry enterprises is large, and the number of all kinds of agricultural enterprises except grain and animal husbandry enterprises is small. They are merged into other types of enterprises. Therefore, this paper forms the sample of grain, animal husbandry, and other types of enterprises, the number of animal husbandry, grain, and other agricultural leading enterprises is 271, 274, and 600, respectively.
From the comparison of whether agricultural enterprises export or not (see Table 1), the number of grain and animal husbandry exporting enterprises account for 23.36% and 31.00% of the total number of sample enterprises, respectively, while the proportion of other exporting enterprises is higher, which is 46.83%; and the proportion of exports to sales is 2.94%, 2.75%, and 13.5%, respectively. The export of private enterprises is an important part of the export of China's agricultural leading enterprises. There are about 339 private enterprises that export, accounting for 36% of the total number of private agricultural leading enterprises, and their export volume accounts for 73.3% of the total export of agricultural leading enterprises. The number of foreign-funded agricultural export enterprises accounts for the highest proportion of the total number of agricultural enterprises, but due to the small number of foreign-funded agricultural exporting enterprises, the proportion of their exports is the lowest. In terms of the proportion of export and domestic sales of agricultural enterprises, most of their products are sold in China's domestic market. The export of leading agricultural enterprises accounts for only 5.61% of their sales revenue, and that of private enterprises in their sales revenue is the highest, which is 9.33%, while that of collective enterprises is relatively low. The export volume of grain and animal husbandry enterprises accounts for 2.94% and 2.75% of the sales revenue of similar enterprises, respectively. Note: The data was compiled by the author. N1 and N2 respectively represent the number of various types of agricultural export enterprises and non-export enterprises. P1 and P3 were the ratio of the number of agricultural export and non-export enterprises to the total agricultural enterprises, respectively. P2 is the ratio of agricultural enterprise exports to sales revenue.

Index Selection and Measurement
This paper refers to the research results of Wang and Wang (2017) [34,[45][46][47], and regards the output index as the sales income of enterprises, which reflect the production and operating conditions of enterprises and their scale. The input index includes capital, labor, and intermediate inputs, which reflect the enterprise scale and resource utilization. Capital, labor, and intermediate inputs are presented by total assets, number of employees, and raw material inputs of the enterprise, enterprise employment is divided into two parts: perennial employment and seasonal employment. This paper mainly considers perennial employment. Different from Gai et al.
(2011) and Yang (2015)'s literature, the sales revenue of enterprises is not deflated by price index. The reason is that the sample time sequence used in this paper is short, and there are many kinds of agricultural industries, thus, it is not appropriate to use a unified price index of agricultural products. The statistical description of each index is shown in Table 2. Note: The units of sales income, total assets, and purchasing-amount of raw materials of enterprises are ten thousand yuan, and the units of the number of employees of enterprises are people and have been calculated using logarithm.
Using the maximum likelihood ratio test, the adoption of the translog production function can better reflect the input-output relationship of agricultural leading enterprises, and agricultural leading enterprises have losses of technical efficiency. Table 3 presents the estimation results of the production function model generated using Stata15.0 software. From the estimation results of the stochastic frontier production function model, we see that capital have a positive impact on the output of agricultural leading enterprises and pass the 1% significance level test; labor input has no significant impact on the output of agricultural leading enterprises; and raw material input has a positive impact on the output of agricultural leading enterprises, passing the 5% significance level test. The maximum likelihood ratio test results show that the translog production function can better reflect the input-output relationship of agricultural leading enterprises than other types of production function. Lambda has passed the 1% significance level test, which shows that there is a loss of technical efficiency in the production process.

Measurement and Comparison of TFP
Using the estimation results of the stochastic frontier production function and Equations (1), (5), and (7), we calculate the technical efficiency index, technical progress index, and TFP index of 2290 sample enterprises from 2016 to 2017.

Overall Perspective Comparison
The TFP and technical progress of agricultural enterprises show a downward trend, technical efficiency shows improvement, and technical progress shows a downward trend. The degree of improvement in technical efficiency is less than the degree of technology regression; the technical progress rate of agricultural enterprises decreases by 1.9% and the rate of technical efficiency improvement increases by 0.1% (see Table 4). The root of the decline of the TFP of agricultural enterprises is the regression of enterprise technology. This is similar to Zhao et al.'s (2008) research conclusion, that is, the TFP of China's agricultural processing industry is mainly driven by technical progress [48]. Mizobuchi (2015) also points out that technical progress is an important source of TFP growth [49]. Considering different industries, we see that the change of the TFP of agricultural enterprises is the same. The TFP index of animal husbandry enterprises is higher than that of grain and other enterprises. The technological progress rate and technical efficiency of grain and animal husbandry enterprises shows the opposite trend, while the changing direction of the technological progress rate and the technical efficiency of other types of agricultural enterprises is the same. The technological progress rate of grain, animal husbandry, and other enterprises decreased by 2.3%, 2.0%, and 1.6%, respectively, and the technological efficiency of grain, animal husbandry, and other enterprises increased by 0.3%, 0.6%, and −0.3%, respectively.
Considering different enterprise properties, the TFP is in a declining state. The TFP index of foreign-funded agricultural enterprises is higher than that of collective and private enterprises, which also shows that TFP fluctuations are more obvious for collective and private agricultural enterprises. Yang (2015) also draws a similar conclusion based on the data of industrial enterprises, which is that the technical efficiency of collective and private enterprises is relatively low [50]. As for collective agricultural enterprises, aside from the technical progress index, which is higher than the average level by 0.6 percentage points, the other indexes are below average. As for private agricultural enterprises, aside from the technical efficiency index, which is equal to the average level, the other indexes are below average. For foreign-funded agricultural enterprises, the technical efficiency index, technical progress index, and TFP index are above the average level of all agricultural leading enterprises.

Comparison between Agricultural Exporting Enterprises and Non-Exporting Enterprises
The TFP of agricultural exporting and non-exporting enterprises shows a downward trend, and the TFP of exporting enterprises shows a significant downturn: the TFP of exporting enterprises and non-exporting enterprises decreases by 2% and 1.7%, respectively. The TFP, technical progress, and technical efficiency indices of agricultural exporting enterprises are 0.980, 0.983, and 0.997, respectively. For non-exporting enterprises, technical efficiency increases by 0.3% and the TFP and technological progress rate show a downward trend (see Table 5). According to the existing research on the relationship between the export of Chinese enterprises and TFP, export is not an important factor to promote the growth of enterprises' TFP [51]; and even export has a negative impact on the productivity of Chinese enterprises [52,53]. From the industry point of view, the TFP of all kinds of exporting enterprises is lower than that of the same type of non-exporting enterprises. Agricultural exporting and non-exporting enterprises show a downward trend in technological progress, with the technological progress rate of grain, animal husbandry, and other agricultural exporting enterprises decreasing by 1.9%, 1.9%, and 1.6%, respectively, while that of grain, animal husbandry, and other agricultural non-exporting enterprises decreases by 2.5%, 2.1%, and 1.6%, respectively. The technical efficiency of grain, animal husbandry, and other agricultural exporting enterprises is deteriorating by 0.5%, 0.2%, and 0.2%, respectively. For agricultural non-exporting enterprises, aside from the deterioration of the other agricultural non-exporting enterprises, the technical efficiency of grain and animal husbandry enterprises is on the rise, with an increase of 0.6% and 1.0%, respectively.
From the perspective of enterprise properties, the TFP growth rate of collective and foreign-funded agricultural exporting enterprises is greater than that of non-exporting enterprises, and the TFP growth rate of private agricultural exporting enterprises is less than that of non-exporting enterprises. The TFP index of foreign-funded agricultural exporting enterprises is higher than that of foreign-funded agricultural non-exporting enterprises, and the TFP of foreign-funded agricultural exporting enterprises is increasing. Foreign-funded agricultural enterprise exporters show an increasing trend in technical efficiency and a decrease in technical progress. The technical efficiency of agricultural exporting and non-exporting enterprises increases by 2.2% and 0.3%, respectively, and the technical progress rates decrease by 2.0% and 1.6%, respectively.
The overall TE of agricultural enterprises is high, and the sample size of agricultural leading enterprises with TE greater than 0.700 is 1031, accounting for 90.04% of the total sample size (see Table 6). The difference between the TFP index of agricultural exporting and non-exporting enterprises decreases with the increase of the average TE of enterprises, and even the growth rate of the TFP of exporting enterprises is higher than that of nonexporting enterprises. The direction and degree of the effect of technical efficiency of agricultural exporting and non-exporting enterprises on TFP change with the change of average TE levels. Bao et al. (2003) argue that the influence of export on TFP comes from the improvement of production effect of exporting sector and technology spillover to non-exporting sector, which also implies that technical efficiency is an important factor to improve TFP of exporting enterprises [54]. Finicelli et al. (2010) argue that the increase in TFP is usually associated with knowledge accumulation in technological innovation and R&D investment, from the viewpoint of innovation [55]. When the TE of enterprises is less than 0.6, the technical efficiency of both exporting and non-exporting enterprises deteriorates, and the deterioration degree of technical efficiency of agricultural exporting enterprises is greater than that of non-exporting enterprises. When the TE of enterprises [0.6,0.7), TE of agricultural exporting enterprises decreases by 0.9%. Conversely, the TE of agricultural no-exporting enterprises increases by 0.8%. When the TE of enterprises [0.7,0.8), the TE of agricultural exporting and non-exporting enterprises improve by 0.3% and 1.0%, respectively. When the TE of agricultural enterprises is greater than 0.8, the TE of agricultural exporting enterprises and non-exporting enterprises increase, but improvements in the TE of agricultural exporting enterprises is less than that of non-exporting enterprises, and the average value of the technical efficiency of agricultural exporting enterprises increase. When the TE of agricultural enterprises is greater than 0.9, the TFP growth rate of agricultural exporting enterprises is 0.1%.

Comparison of Agricultural Exporting and Non-Exporting Enterprises in Different Provinces
The TFP index of agricultural exporting enterprises in the eastern and western regions is less than that of agricultural non-exporting enterprises, while the central region is the opposite. The results show that the trend of TFP of agricultural enterprises is similar to that of technical efficiency. The gap between the TFP index, the technical efficiency index, and the technical progress index of exporting and non-exporting enterprises in central China is the smallest. Therefore, the difference of TFP changes between exporting enterprises and non-exporting enterprises is mainly due to the change of technical efficiency. The gap between the TFP index, the technical efficiency index, and the technical progress index of exporting and non-exporting enterprises is the largest in the western region, followed by the eastern region, and the smallest in the central region.
In the eastern region, the TFP index of agricultural exporting enterprises in Shandong, Zhejiang, Guangdong, and Liaoning is higher than that of agricultural non-exporting enterprises, while in other provinces it is lower than that of agricultural non-exporting enterprises (see Figure 1). In Shandong, Zhejiang, Guangdong, and Liaoning, the technical efficiency index of agricultural exporting enterprises is higher than that of agricultural non-exporting enterprises, while in other provinces it is lower than that of agricultural non-exporting enterprises (see Figure 2). Except in Guangdong, the technological progress index of agricultural exporting enterprises is lower than that of agricultural non-exporting enterprises. In all other provinces and cities the technological progress index of exporting enterprises is higher than that of non-exporting enterprises (see Figure 3). The key to the comparison of the TFP index between agricultural exporting and non-exporting enterprises lies in the comparison of the technical efficiency index. Changes in technical efficiency are the main factor affecting the change of TFP of agricultural enterprises.

Robustness Test
A single simple additive weighting (SAW) will lead to different calculation results. Referring to Yang's (2016) TFP calculation method [50], this paper measures the TFP index, technical efficiency index, and technical progress index of enterprises with sales income of agricultural enterprises as the weight. On the whole (see Table 7), although the value has changed, the basic conclusion remains the same. In general, the TFP of exporting enterprises is growing, and the growth rate of the TFP of exporting enterprises is higher than that of non-exporting enterprises. In different industries, the growth rate of TFP of grain and other exporting enterprises is higher than that of non-exporting enterprises, and that of animal husbandry exporting enterprises is lower than that of S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g TEC of export enterprises TEC of non-export enterprise 0.950 1.000

1.050
S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g TC of export enter prises TC of non-export enterpri se

Robustness Test
A single simple additive weighting (SAW) will lead to different calculation results. Referring to Yang's (2016) TFP calculation method [50], this paper measures the TFP index, technical efficiency index, and technical progress index of enterprises with sales income of agricultural enterprises as the weight. On the whole (see Table 7), although the value has changed, the basic conclusion remains the same. In general, the TFP of exporting enterprises is growing, and the growth rate of the TFP of exporting enterprises is higher than that of non-exporting enterprises. In different industries, the growth rate of TFP of grain and other exporting enterprises is higher than that of non-exporting enterprises, and that of animal husbandry exporting enterprises is lower than that of S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g TEC of export enterprises TEC of non-export enterprise 0.950 1.000

1.050
S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g TC of export enter prises TC of non-export enterpri se

Robustness Test
A single simple additive weighting (SAW) will lead to different calculation results. Referring to Yang's (2016) TFP calculation method [50], this paper measures the TFP index, technical efficiency index, and technical progress index of enterprises with sales income of agricultural enterprises as the weight. On the whole (see Table 7), although the value has changed, the basic conclusion remains the same. In general, the TFP of exporting enterprises is growing, and the growth rate of the TFP of exporting enterprises is higher than that of non-exporting enterprises. In different industries, the growth rate of TFP of grain and other exporting enterprises is higher than that of non-exporting enterprises, and that of animal husbandry exporting enterprises is lower than that of S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g TEC of export enterprises TEC of non-export enterprise 0.950 1.000

1.050
S h a n d o n g J ia n g s u F u ji a n H e b e i Z h e j ia n g G u a n g d o n g B e ij in g L ia o n in g S h a n g h a i T ia n j in H u b e i A n h u i H e n a n J ia n g x i H u n a n S h a n x i J il in H e il o n g ji a n g G u a n g x i S ic h u a n Y u n n a n C h o n g q in g S h a a n x i N in g x ia In n e r M o n g o li a X in j ia n g G a n s u G u iz h o u Q in g h a i H a in a n X iz a n g TC of export enter prises TC of non-export enterpri se In the central region, the TFP index of agricultural exporting enterprises in Hubei, Anhui, Henan, Hunan, Shanxi, and Jilin is higher than that of agricultural non-exporting enterprises, while in other provinces it is lower than that of agricultural non-exporting enterprises (see Figure 1). The technical efficiency index of agricultural exporting enterprises in Anhui, Henan, Hunan, Shanxi, and Jilin is higher than that of agricultural non-exporting enterprises, while in other provinces and cities it is lower than that of agricultural non-exporting enterprises (see Figure 2). Except for Jiangxi and Jilin, the technological progress index of agricultural exporting enterprises is lower than that of nonexporting enterprises, and in other provinces and cities it is higher than that of agricultural non-exporting enterprises (see Figure 3).
In the western region, the TFP index of agricultural exporting enterprises in Sichuan, Chongqing, Shaanxi, Ningxia, and Gansu is higher than that of agricultural non-exporting enterprises, while the TFP index of other provinces is lower than that of agricultural nonexporting enterprises (see Figure 1). At the same time, the technical efficiency index of agricultural exporting enterprises in Sichuan, Chongqing, Shaanxi, Ningxia, and Gansu is higher than that of agricultural non-exporting enterprises, while in other provinces and cities it is lower than that of agricultural non-exporting enterprises (see Figure 2). Except Ningxia, Gansu, and Guizhou, the technological progress index of agricultural exporting enterprises is lower than that of agricultural non-exporting enterprises, and in other provinces and cities it is higher than that of agricultural non-exporting enterprises (see Figure 3).

Robustness Test
A single simple additive weighting (SAW) will lead to different calculation results. Referring to Yang's (2016) TFP calculation method [50], this paper measures the TFP index, technical efficiency index, and technical progress index of enterprises with sales income of agricultural enterprises as the weight. On the whole (see Table 7), although the value has changed, the basic conclusion remains the same. In general, the TFP of exporting enterprises is growing, and the growth rate of the TFP of exporting enterprises is higher than that of non-exporting enterprises. In different industries, the growth rate of TFP of grain and other exporting enterprises is higher than that of non-exporting enterprises, and that of animal husbandry exporting enterprises is lower than that of non-exporting enterprises. From the perspective of different enterprise properties, the TFP growth rate of collective exporting enterprises is higher than that of non-exporting enterprises, while the TFP growth rate of foreign-funded and private exporting enterprises is lower than that of non-exporting enterprises.

Conclusions and Policy Recommendations
Based on the data of state-level leading agricultural enterprises from 2016 to 2017, this paper uses the SFA-Malmquist method to decompose and compare the TFP of China's agricultural exporting enterprises and obtains the following conclusions. First, China's agricultural TFP shows a negative growth trend, and the growth rate of the TFP of agricultural exporting enterprises is less than that of agricultural non-exporting enterprises. The technical progress rate of agricultural enterprises shows a downward trend, therefore, the fundamental reason for the change of China's agricultural TFP lies in the change of enterprise technical progress. Second, the TFP growth rates of agricultural exporting enterprises and non-exporting enterprises in different industries and enterprise property are significantly different. The growth rate of TFP of grain and animal husbandry exporting enterprises is lower than that of non-exporting enterprises. The TFP growth rates of collective exporting enterprises is higher than that of non-exporting enterprises. The TFP growth rates of private exporting enterprises is lower than that of non-exporting enterprises. The TFP growth rate of foreign-funded enterprises is positive, which is higher than that of nonexporting enterprises. Third, the TFP growth rate of exporting enterprises in the eastern and western regions is lower than that of non-exporting enterprises, and that of exporting enterprises in the central region is higher than that of non-exporting enterprises. The gap between the TFP index, the technical efficiency index, and the technical progress index of exporting and non-exporting enterprises in the central region is the smallest, whether or not the enterprises in these three regions are exporting. However, the gap between the TFP index and technical efficiency index of exporting enterprises and non-exporting enterprises is the largest in the western region.
Further discussion is presented as follows. First, there are limitations to this study's sample of agricultural enterprises. Our sample data has a short time sequence that cannot analyze the trends of TFP growth rate. With the change of economic cycle, the growth rate of productivity may accelerate [56], and it may take longer for technology to spread and develop its potential, which may have a certain impact on the research conclusions of this paper. In addition, the data on state-level leading agricultural enterprises may not represent the overall characteristics of changes in agricultural enterprises. However, our data has certain representativeness for agricultural exporting enterprises. Therefore, this paper focuses on the comparison of TFP of different industries, regions, and enterprise property of agricultural exporting enterprises, and judges the contribution of technical progress and technical efficiency to the change of TFP of agricultural enterprises. Second, many scholars have found that there is an "exporting productivity paradox" in Chinese enterprises, which still exists in agricultural enterprises. This paper focuses on the growth rate and decomposition of TFP, which is different from previous research that uses more data from the China Statistical Yearbook. This paper uses the sample of agricultural enterprises as an emphasis point sample, which allows us to analyze China's agricultural TFP from another level and provide other evidence.
At last, policy implications are discussed in the last part of this paper. First, it is needed to increase the R&D investment of enterprises, to improve the agricultural scientific and technical level, and the technical progress rate of agricultural enterprises. In addition, agricultural enterprises should strengthen cooperation with research institutions to improve the conversion rate of agricultural scientific achievements. Second, the change of technical efficiency is an important factor in the change of TFP, especially agricultural export enterprises, so it is necessary to further optimize the allocation of enterprise factors, especially to improve the substitute elasticity of labor, capital, and raw materials. Third, private enterprises are an important part of China's agricultural enterprises, and the export of private enterprises is also an important part of the export of agricultural products. However, the TFP of private enterprises is low. Therefore, it is needed to increase support policies and investment from government. From the regional level, the government should support the development of agricultural enterprises in the western region of China, and the central region and the western region should actively dock with the technology transfer in the eastern region. Fourth, China's domestic market segmentation and high productivity are the important causes of the "export productivity paradox". The government should try to take measures to eliminate the segmentation, encourage agricultural enterprises with competitive advantages and high productivity to export, especially those with high technology and high value-added products, and improve the competitiveness of China's agricultural trade.
Author Contributions: Q.F. and W.J. were responsible for the research methods. Q.F. and W.J. are responsible for data investigation and data sorting; Q.F., T.M. and W.J. completed the first draft of the paper; Q.F. and W.J. were in charge of proofreading manuscripts. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement:
The specific data of the survey samples cannot be made public.