The total factor productivity index of freshwater aquaculture in China: based on regional heterogeneity

Continuously improving freshwater aquaculture efficiency will promote the sustainable development of freshwater aquaculture, which is crucial to ensure aquatic food supply. In particular, measuring the total factor productivity (TFP) of freshwater aquaculture to find ways to improve its efficiency is of great significance to sustainable development of freshwater aquaculture industry. Therefore, based on directional distance function, this paper constructs a meta-frontier Malmquist index (MMI) model by considering the regional heterogeneity to evaluate the TFP of freshwater aquaculture of China from 2004 to 2019. The results show that (1) from the perspective of time, TFP fluctuated significantly from 2004 to 2012, while after 2013, TFP remained around 1 with small fluctuation. In other words, freshwater aquaculture in China began to maintain a relatively negative state of development. (2) From a regional point of view, this study found that freshwater aquaculture TFP of inland region is better than the TFP of coastal region. (3) From the decomposition index, the variation of freshwater aquaculture TFP was driven by the combined effect of technology change (TC) and technical efficiency change (EC). In addition, the decomposition index efficiency shows that the technical efficiency decreases and the management efficiency changes little. (4) The gap of freshwater aquaculture technology in coastal areas is very small, and close to the optimal technical level. While in inland region, on the contrary, there is more room for improvement. According to the above empirical results, this paper finally gives some policy suggestions to improve the TFP to ensure the sustainable development of freshwater aquaculture.


Introduction
Food shortage is a major problem faced by many developing countries. In view of the severe food security situation, the development of fishery will become one of the important ways to fill the gap between food supply and demand (Jennings et al. 2016). From the perspective of the world development situation, most of the natural fishery resources have been fully utilized or over utilized. In the future, the development of fishery and the supply of aquatic products will mainly rely on aquaculture. From 2007 to 2018, the average annual growth rate of global aquaculture was 4.6%, higher than that of other food crops (FAO 2020). FAO predicts that aquaculture will continue to be the driving force of global food production growth in the future. Thus, the importance of aquaculture food in global food supply cannot be ignored. It is an important means to meet the food demand of population growth (Troell et al. 2014). China is the main producer of farmed edible fish, and the number of edible fish produced in China each year has exceeded the rest of the world put together since 1991 (FAO 2018). According to the Chinese Academy of Fishery Sciences (2020), the production of freshwater aquaculture accounts for 59% of aquaculture production, which shows that freshwater aquaculture has become an important production mode of aquaculture. Therefore, the continuous improvement of freshwater aquaculture efficiency is very important to ensure the supply of aquatic products. In view of China's status as a large aquatic country and its representativeness in freshwater aquaculture, if China can explore a sustainable development path of aquaculture, it will be applicable to the sustainable and coordinated development of fisheries in the world, especially in Southeast Asian countries. Thus, this paper will measure the total factor productivity of freshwater aquaculture of China. Then, this paper will obtain the sustainable development strategy of freshwater aquaculture through the analysis of efficiency, trying to provide a certain degree of support for solving the problem of food security.
There are significant differences in the development of freshwater aquaculture between coastal region and inland region. Firstly, no matter economic level or science and technology, the development of coastal region is more advanced than the development of inland region. Therefore, the coastal region and inland region exist significant differences in freshwater aquaculture training intensity, technical level, and technology promotion (Ji and Wang 2015). Moreover, the coastal region and inland region also have obvious differences in the level of human capital, fishery infrastructure, resource endowment, and aquaculture scale, which will affect freshwater aquaculture efficiency. Secondly, due to abundant sea water resources, coastal region has been taking marine aquaculture as an important way of operation for a long time. This may lead to marine aquaculture has a technical spillover effect on freshwater aquaculture in coastal regions. However, few studies have shown that the development of marine aquaculture in coastal region has an impact on the efficiency of freshwater aquaculture. Only when Ji and Wang (2015) evaluated the efficiency of aquaculture, considering the regional heterogeneity of coastal and inland regions. They compared the marine aquaculture efficiency of eight coastal provinces with the freshwater culture of eight inland provinces. Obviously, incorporating regional heterogeneity into aquaculture research can effectively reduce the deviation of aquaculture efficiency measurement. Based on the above analysis, this paper uses directional distance function (DDF) and MMI model to analyze the TFP of freshwater aquaculture in China under the condition of considering regional heterogeneity. It will provide a powerful reference for the sustainable and coordinated development of freshwater aquaculture to China.
The research of this paper has both theoretical and practical significance. Firstly, in terms of theoretical significance, there are a lot of academic research literatures on aquatic products production, but there is a lack of research on freshwater aquaculture, which plays a very important role in aquaculture. This paper constructs the production efficiency index system of freshwater aquaculture, and then analyzes and evaluates the efficiency of freshwater aquaculture in China by using quantitative methods, DEA, and meta-frontier Malmquist index method. Based on the evaluation results, this paper will optimize and adjust the efficiency level of freshwater aquaculture. A new research perspective of freshwater aquaculture efficiency evaluation will be provided in this paper. Secondly, from the perspective of practical significance, the contribution rate of freshwater aquaculture to the total output of global aquaculture food is very large. The contribution rate was 57.9% in 2000 and increased to 64.2% in 2016 (FAO 2018). Freshwater aquaculture has long been an indispensable part of global aquatic product production, and the sustainability of aquaculture level is particularly important. In order to further improve the efficiency of freshwater aquaculture, we need to evaluate the current input-output conversion rate of freshwater aquaculture and accurately understand the corresponding situation of freshwater aquaculture to adjust the future development direction. In addition, areas with good aquaculture conditions should drive poor areas forward, so that aquaculture can develop better in more areas. In view of the large proportion of freshwater aquaculture in China, taking China's freshwater aquaculture efficiency and development strategy as an example has certain guiding significance for the sustainable development of freshwater aquaculture in other countries and regions, especially Southeast Asian countries.
The remainder of this study is as follows: The next section introduces the related literature. "Methodology" section describes the designed methodology applied in the study, the input-output variables, and data sources. The presentation of empirical analysis is elaborated in "Empirical analysis" section. This section makes two modeling analysis. The first three parts of this section analyze the results of the first model. Considering the intermediate consumption cost, that is, the expenses of feed, fertilizer, drugs, and fuel in the process of aquaculture, this paper optimizes the input variable system in "Further discussion" section, increasing intermediate consumption cost, and analyzes the results of the secondary model. And the "Comparative analysis and discussion" section compared the results of the two models. The general discussion is in the "Discussion" section. The main conclusions and policy suggestions are provided in the last section. And there are many abbreviations showed in Table 1.

Literature reviewed
TFP refers to the part from output that is not explained by input, which is a representative index to measure production efficiency (Lin and Ge 2019). Squire (1992) first applied TFP to the field of fishery, which made fishery research method and system more scientific and provided strong support for many scholars in the study of fishery development. By combing the existing literature, it can be found that the common methods of measuring TFP are stochastic frontier analysis (SFA) and data envelopment analysis (DEA). SFA which was introduced by Aigner et al. (1977) and Meeusen and Van den Broeck (1977), uses the metrology method to measure the growth structure. It needed to preset the production function and separate statistical errors and technical inefficiencies during the measurement process (Battese and Coelli 1995;Kumbhakar and Lovell 2000). Jamnia et al. (2013) employed Cobb-Douglas stochastic production frontier model to measure the technical efficiency of fishery in Chabahar region in southern Iran, and discussed the output elasticity and return to scale. At the same time, their research also found that the translog function cannot be used as an appropriate representation of data. Iliyasu et al. (2016) used SFA model to study the technical efficiency of cage fish culture in Malaysia peninsula. The results showed that the value of technical efficiency was 0.79, which had great room for improvement. Sarker et al. (2016) used stochastic frontier model to assess technical efficiency in Thai koi farming. They found that feed is the most important input to production. Yin et al. (2017) applied SFA model to estimate the efficiency of crucian carp culture in Jiangsu, China. They used Cobb-Douglasfunction and translog specification to analyze the data of 144 farmers in 2012, and concluded that the technical efficiency of crucian carp breeding was low. Kumaran et al. (2017) used the SFA method to evaluate the efficiency of Pacific white shrimp culture in India, and found that these farms achieved 90% of the maximum possible output of a given input. However, SFA has some defects. It cannot reasonably control the input-output variables and endogenous problems, and has high requirements for the setting of production function. Once the production function is set unreasonably, the result will be biased (Simar and Wilson 1998).
DEA model constructs nonparametric piecewise surface of data by linear programming, and then it calculates the relative effectiveness of multiple input-output decision-making units (DMUs) (Charnes et al. 1978;Coelli 1998). Compared with SFA model, the function forms related to inputs and outputs are not necessary to be calculated in DEA (Song and Zheng 2016), which can avoid strong hypothesis bias such as production function setting and random interference normal distribution (Färe et al. 1989). For these reasons, DEA model has more advantages in evaluating efficiency. Ji and Wang (2015) evaluated aquaculture efficiency of 16 provinces in China with SBM-DEAmodel, and they found that technology expansion and improvement of technology level have obvious positive effects on aquaculture. Iliyasu and Mohamed (2016) applied DEA model to measure pond culture efficiency. Result indicates that the technical efficiency of pond culture is 0.86, that is, the fish farmers could reduce 14% of input usage at the current technology level to achieve full technical efficiency. Song and Zheng (2016) used the Malmquist productivity index method to calculate the TFP and its decomposition index of marine fishery in China's coastal provinces, and they analyzed the temporal trend and spatial distribution of marine fishery efficiency. Wang and Ji (2017) built a DEA model to estimate mariculture efficiency in China's 10 coastal provinces using Seiford's linear converting method. Pipitone and Colloca (2018) used Malmquist index method to decompose TFP of Italian trawl fishery. The results showed that overfishing had a negative effect on fishery efficiency, and capital accumulation and pricing strategy had a positive effect on fishery efficiency. Mitra et al. (2020) used a Fisher quantity index and DEA method to study the TFP of 580 culture farms in Bangladesh. They concluded that the TFP is significantly affected by environmental characteristics. Yu et al. (2020) applied the global Malmquist index to measure the mariculture efficiency and their changes in China's nine coastal provinces from 2004 to 2016, and they concluded that technological progress is the main driving force to improve mariculture efficiency. Xu (2020) measured the TFP of mariculture in nine coastal provinces of China based on DEA Malmquist method, and pointed out that the growth of mariculture efficiency belongs to technology-induced growth.
From the above studies, it can be seen that most of the existing research on fishery efficiency focuses on single species breeding, fishing, mariculture, and overall fishery production efficiency, while few on the freshwater aquaculture efficiency. Moreover, no studies have considered the importance of regional heterogeneity for freshwater aquaculture efficiency by the meta-frontier. In terms of research methods, it is very common to use SFA function method, traditional DEA method, and traditional Malmquist index method. As for the analysis of the results, most of the existing studies are based directly on a frontier to analyze the overall situation. Therefore, in order to make up for the defects of the existing research, this paper uses the meta-frontier method to measure the TFP of freshwater aquaculture in China based on the regional heterogeneity. The inherent assumption of meta-frontier method is that the technological progress of different groups is heterogeneous, so DMUs should be divided into different groups. Previous studies have suggested that geographical proximity and self-characteristics are the decisive factors for grouping (Oh and Lee 2010). Considering the characteristics of freshwater aquaculture, this paper divides the areas into coastal regions and inland regions, which follows this principle.
In summary, there are three innovations in this paper. First, in the research of fishery production, there are few researches on freshwater aquaculture. This paper studies freshwater aquaculture in China, which is innovative. Moreover, compared with the previous studies that mainly focused on coastal provinces, the research area of this paper is most of the provinces in China, which can more accurately reflect the contemporary freshwater aquaculture TFP in China. Second, few studies use grouping model in aquaculture research. By considering the regional heterogeneity of coastal and inland regions, this paper uses DDF-MMI model to analyze the TFP of freshwater aquaculture. Third, this paper analyzes the TFP under the two conditions of overall and cluster group, and discusses the freshwater aquaculture technology gap rate (TGR) in coastal and inland regions, which is the first application in aquaculture.

DDF model
DDF was proposed by Chung et al. (1997) who proposed to measure the production efficiency. DDF can actually reflect the economic effect (Yang et al. 2020), which is suitable for the measurement of freshwater aquaculture efficiency. This paper takes provinces as DMUs. Assuming that the number of DMUs is K, and the number of inputs and outputs for each DMU is M and N, respectively, then the production possibility set of the current period can be expressed as follows: The definition of output oriented DDF is as follows: where x represents the input vector and y represents the output of the production; g is the direction vector, where the output expansion direction is denoted by (0, y). β is the value of DDF and represents the ratio of output expansion.
The specific process of using DDF to evaluate freshwater aquaculture efficiency is as follows: Max D ! x; y; g ð Þ¼β s:t: The closer each DMU is to the meta-front curve, the greater the efficiency of DMU is. The efficiency index of DMU is 1/(1 + β).
The double-hierarchy meta-frontier DDF-DEA model Hayami and Ruttan (1971) proposed the concept of metafrontier when considering heterogeneity. After the development of this method, it has been widely used by scholars in the measurement of efficiency (O'Donnell et al. 2008). On the basis of DDF, this paper adds regional factors to the model by considering the meta-frontier and regional frontier. The regional frontier includes coastal regional frontier and inland regional frontier. As shown in Fig. 1, there are two regional fronts under the envelope of the meta-frontier.
First, the DDF function model based on the meta-frontier is shown in Eq. (4).
where, β M is the proportion of output expansion under the meta-frontier. M, N, and T are the number of inputs, the number of outputs, and the number of periods respectively. μ is the intensity variable under the meta-frontier. K M is the number of DMUs in the meta-frontier;K M =28.
Second, the DDF function model at the regional frontier is shown in Eq. (5). where, β R is the proportion of output expansion under the regional frontier. θ is the intensity variable under the regional frontier. K R is the number of DMUs in the regional frontier. In coastal region, K R = 11, and in the inland region, K R =17.

The double-hierarchy meta-frontier Malmquist index
This paper aims to measure the TFP of freshwater aquaculture. Färe et al. (1994) proposed to apply Malmquist index (MI) method to measure TFP. The concept of MI was first proposed by Malmquist (1953) to analyze the cost change in different periods. However, the traditional MI is based on the relative change in the production frontier in the calculation process, rather than the absolute technical changes (Zhong et al. 2020). In addition, the traditional MI has some limitations, such as no feasible solution for linear programming, lack of transitivity, and technical regression (Pastor and Lovell 2005). Oh and Lee (2010) applied the method of meta-frontier to the global reference Malmquist model, and they constructed the metafrontier Malmquist index (MMI) model, and then further decomposed it. This method includes all the evaluated DMUs in the global reference set, which overcomes the shortcomings of the traditional MI. It is obvious that MMI can measure TFP more accurately. The global production possibilities can be expressed as Eq. (6). where, The calculation formulas of TFP of freshwater aquaculture at different frontiers are as follows: MMI M t−1;t ; MMI R t−1;t represent the TFP of freshwater aquaculture under the meta-frontier and regional frontier respectively. If the value of MMI is greater than 1, it indicates that the productivity will increase from the previous period to this period. MMI can be further decomposed into EC and TC, its decomposition is shown in Eq. (10): A key index of meta-frontier approach is technology gap ratio (TGR), which is the ratio of the meta-frontier efficiency value to the group frontier efficiency value. It can be used to measure the gap between the actual technology level and the potential optimal technology level of a group. Taking point A under group 1 as an example (combined with Fig. 1), TGR can be expressed as: TGR t = (BA/BD)/(BA/BC) = BC/BD. The value range of TGR is [0, 1], and the closer the value is to 1, the closer the actual technology level is to the potential optimal technology level.

Variables and sources of data
The accuracy of DEA in measuring TFP is closely related to the choice of input-output variables. Based on the characteristics of freshwater aquaculture and the existing literature (Asche et al. 2013;Ji and Wang 2015), this paper selects the appropriate variables to construct the input-output variable system, and it conducts two modeling analysis to obtain more reasonable results. In the first modeling, three variables are selected to construct the input variable system, which are freshwater aquaculture area, freshwater aquaculture professionals, and freshwater seedling quantity. As for the selection of output variables, it is usually to use gross economic value of fishery to reflect the total scale and total achievements of fishery production in a period of time at fishery application (Zheng et al. 2019). Based on the actual situation of freshwater aquaculture, the output variable of this paper is the fishery output value of freshwater aquaculture. In order to further verify the accuracy of the results, this paper attempts to introduce the intermediate consumption cost based on the first modeling index selection. This is the input variable. Thus, in the second modeling, this paper constructs the evaluation index system of freshwater aquaculture TFP to perform a modeling analysis. The variables are explained specifically as follows: (1) Freshwater aquaculture area: The water surface area of aquaculture products in freshwater areas, including pond culture area, lake culture area, river aquaculture area and reservoir aquaculture area, etc. The unit of measurement is hectare.
(2) Freshwater aquaculture professionals: Fishery practitioners who have been engaged in freshwater aquaculture for more than 6 months or more than 50% of their livelihood sources depend on freshwater fishery activities throughout the year. Compared with the part-time and temporary employees of freshwater aquaculture, the professionals from industry are more representative. The unit of measurement is person.
(3) Freshwater seedling quantity: including fry and fingerlings. The unit of measurement is tail.
(4) The fishery production value of freshwater aquaculture: It refers to the output and outcomes of freshwater aquaculture fishery activities in the accounting period in the form of currency. The unit of measurement is 10000 yuan. (5) Intermediate consumption cost: It includes the cost of feed, fertilizer, drugs and fuel. The unit of measurement is 10000 yuan.
The input-output variable system is listed in Table 2. The variables expressed in currency are bound to be affected by inflation, which will lead to the lack of objectivity and accuracy of data. For this reason, this paper selects 2003 as the base year to deal with the output variables, so as to eliminate the impact of inflation. The data of the aquaculture area, professionals, seedling quantity, and the fishery production value are derived from the "China Fisheries Statistical Yearbook." The data of the intermediate cost of aquaculture are derived from the "China Rural Statistical Yearbook." For the missing data, linear regression method is used to calculate the fitting value.

Study area
The paper aims to study freshwater aquaculture efficiency in China. The relevant data of some provinces are missing, and the output of freshwater fishery in Tibet, Gansu, and Qinghai provinces is small, which is lack of research value. For the sake of the truthful reliability of the research results, this paper selects 28 provinces with abundant freshwater aquaculture as samples, and divides them into coastal region and inland region. As shown in Fig. 2, there are 11 provinces in the coastal region. They are Fujian, Guangdong, Guangxi, Hainan, Hebei, Jiangsu, Liaoning, Shandong, Shanghai, Tianjin, and Zhejiang. Furthermore, there are 17 provinces in inland region, including Anhui, Beijing, Chongqing, Guizhou, Henan, Heilongjiang, Hubei, Hunan, Jilin, Jiangxi, Inner Mongolia, Ningxia, Shanxi, Shaanxi, Sichuan, Xinjiang, and Yunnan.

Empirical analysis
This work uses MaxDEA software to calculate the TFP and its decomposition index values of freshwater aquaculture in 11 coastal provinces and 17 inland provinces from 2004 to 2019. According to the calculation results, this part analyzes the development trend and regional characteristics of China's freshwater aquaculture.

Temporal and spatial characteristics of TFP in freshwater aquaculture
The overall fluctuation trend of TFP, EC, and TC in China's freshwater aquaculture is basically the same at the metafrontier and group frontier (Fig. 3). Whether under the metafrontier or the group frontier, the average annual TFP of freshwater aquaculture basically reached more than 1, except in 2009 and 2011. From 2004 to 2013, TFP fluctuated dramatically. After 2013, TFP is relatively stable. Specifically, TFP was the lowest in 2011 and the highest in 2012. Between these 2 years, TFP fluctuated the most, with meta-frontier of 0.811 and group frontier of 0.827. This is mainly because in 2012, the central government attached great importance to the development of fisheries. According to Ministry of Agriculture of the PRC (2013), the central government gave the highest amount of funding in the history of fisheries finance with 8.933 billion yuan in fishery infrastructure construction in 2012. Driven by the strong central investment, the level of fishery infrastructure has been significantly improved. In addition, the technological system of modern fishery industry was further improved in 2012. Seven key fishery technology research projects have been included in the national public welfare agricultural industry research special plan, with funding support of 106 million yuan. One hundred eightyfour patents were invented in fishery in the whole year, with a year-on-year increase of 142.11%. At the same time, the promotion of aquatic technology has been steadily promoted. In 2012, a total of 2.9534 million fishermen were trained, which effectively promoted the improvement of fishermen's quality and the popularization of aquaculture technology and management technology (Ministry of Agriculture of the PRC 2013). From 2012 to 2013, TFP fell the most, with the metafrontier of 0.617 and the group frontier of 0.619. From 2013 to 2019, the trend of TFP is moderate. It shows that the development of China's freshwater aquaculture has begun to stabilize after 2013, which is also a negative performance. The input of resource elements, technical level, and management level has developed to a relatively saturated level. All these factors put freshwater aquaculture in a slow state of development. On the whole, intensification and organization of China's fishery production are still low, and the quality of aquaculture practitioners is not good enough as well. These factors will restrict the sustainable development of freshwater aquaculture industry, and then make the efficiency of freshwater aquaculture at a relatively negative level. As shown in No matter under the meta-frontier or group frontier, the changing trend of TFP is roughly the same as the trend of EC and TC (Fig. 3). This suggests that the changes of TFP in China's freshwater aquaculture are driven by the combined effect of EC and TC. Especially under the meta-frontier, the changing trends of TFP and TC are more suitable. It should Fig. 2 Spatial distribution sampling in freshwater aquaculture areas Fig. 3 The trends of TFP, EC, and TC at two frontiers note that, in 2007, TC only changed slightly, while TFP increased significantly, which increased by 53.6% and 45% compared to the previous year in meta-frontier and group frontier respectively. It is mainly driven by the substantial increase of EC. The value of EC increased by 38.2% under the meta-frontier, and increased by 28.4%t under the group frontier. In 2008, the value of TC increased both under the meta-frontier and the group frontier, while MI decreased. This is mainly dominated by the decline in EC, and its value directly dropped below 1. This means that the management level of freshwater aquaculture in China had declined in 2008. This may be caused by the following two factors. On the one hand, in 2008, the impact of the global financial crisis began to appear to China. On the other hand, many key freshwater aquaculture provinces of China suffered rare freezing rain and snow disasters in 2008. Faced with the more severe fishery production situation, it is difficult for fishery production management to keep up in a short time. From 2013 to 2019, both EC and TC maintained a relatively stable level, and fluctuated closely around 1 slightly. This showed that after 2013, the management level and technical level of China's freshwater aquaculture were at a relatively stable level of development. In general, the development of freshwater aquaculture in China has management advantages. The technology level has also reached a stable and good level. However, there is still no breakthrough. Therefore, it is very necessary to cultivate professional management and technical personnel. At the same time, China should pay attention to the construction of freshwater aquaculture technology system, increase investment in fishery technology elements, continue to carry out technological innovation, and strive to achieve technological breakthroughs as soon as possible. This will effectively promote the improvement of freshwater aquaculture TFP and contribute to the sustainable development of freshwater aquaculture. Fig. 4 shows the spatial distribution characteristics of freshwater aquaculture TFP under the two frontiers. Obviously, no matter it is at the meta-frontier or the group frontier, the TFP shows large spatial differences. Moreover, areas with similar efficiencies show a trend of spatial aggregation. Comparing coastal region and inland region, it can be seen that higher TFPs are located in inland region. At meta-frontier, only Liaoning in the coastal region has a higher level. At the group frontier, the situation is slightly more impressive, with Fujian, Jiangsu, and Liaoning in the coastal region at a higher level. Moreover, Liaoning ranks among the top 5 in China under the group frontier. This may be because, on the one hand, Liaoning has always paid attention to scientific and technological investment in aquaculture and used scientific guidance to effectively prevent the development of diseases. On the other hand, Liaoning has a good aquaculture management level. Liaoning has been committed to the establishment and improvement of aquaculture mechanisms, including inputs and aquaculture water testing. At the same time, with the continuous development of the level of technology and management, the scale of the aquaculture industry in Liaoning has also continued to expand. Shaanxi, Guizhou, and Xinjiang are in the top 5 of TFP both at the two frontiers ( Fig. 4 (II), (IV)), and these three provinces are all inland cities. Among them, Shaanxi is in the first place. This is mainly because Shaanxi had a very high TFP in 2012, which was largely due to the strong investment and support of the central government for fishery infrastructure construction in 2012. At the same time, Shaanxi government has also implemented financial discounts to support fishery infrastructure. In addition, the fishery department of Shaanxi organizes fishery science and technology personnel to visit the grassroots level to promote aquaculture technology. It can be seen that technological progress and management level improvement are really critical for the sustainable development of freshwater aquaculture. Shanghai, Zhejiang, Jiangxi, and Beijing are all ranked in the bottom 5 under the two frontiers ( Fig. 4 (II), (IV)). Among them, Shanghai and Zhejiang are both coastal provinces.
As shown in Fig. 5, the EC and TC of Shaanxi, Guizhou, and Xinjiang in the two frontiers are really considerable, especially in Shaanxi and Guizhou. This determines that these provinces have higher TFP. As for the provinces with the lowest TFP, the values of TC in Shanghai, Zhejiang, Jiangxi, and Beijing are not low, all greater than 1. In other words, the technology of freshwater aquaculture in these four provinces is progressive. The lower TFP of Shanghai, Zhejiang, and Beijing is mainly due to the lower EC value. The average EC value of Shanghai, Zhejiang, and Beijing is less than 1. This shows that the management level of fisheries in these provinces is at a declining level. This is mainly because, in recent years, Shanghai, Zhejiang, Beijing, Jiangxi pay more and more attention to the development of electronic information industry and modern service industry, and gradually develop into the main gathering place of China's electronic information industry cluster and business exhibition cluster area, while ignoring the management of fishery. It can be further found that if these provinces with high technical level are willing to further improve their fishery management level, their TFP of freshwater aquaculture will be greatly improved, which will help to promote the sustainable development of freshwater aquaculture.
In addition, from a global perspective, the TC value of each province is greater than 1, which means that the technology is in a state of progress. However, in the single frontier, more than half of the provinces and cities have TC values below the average. In the meta-front and group front, the provinces with TC values below the average are Anhui, Hunan, and Jiangxi in inland region, and 7 provinces in coastal region, including Guangxi, Hainan, and Hebei. This also shows that freshwater aquaculture technology exists a large spatial difference, and there is a large space for improvement of technology. Hence, it is necessary to strengthen the exchange and cooperation of freshwater aquaculture technology between provinces. Especially for provinces with low level of freshwater aquaculture technology, the local government should actively introduce advanced technology and strengthen the promotion of freshwater aquaculture technology.  Temporal and spatial characteristics of TFP in freshwater aquaculture between regions It can be seen from Fig. 6, whether it is in coastal or inland regions, freshwater aquaculture TFP fluctuated greatly during 2004 to 2012. In the coastal region, the TFP was the lowest in 2009, with 0.868 and 0.867 at the meta-front and the group front respectively, representing a decrease of 13.2% and 13.3% from the previous year. TFP was the highest in 2012, with 1.472 for both frontiers, an increase of 47.2% over the previous year. As for the inland region, the lowest TFP was in 2011, and the meta-frontier and group frontier were 0.819 and 0.800 respectively; they are decreased by 18.1% and 20% from the previous year. In the inland area, the lowest TFP was in 2011, and its values were 0.819 and 0.800 under the meta-frontier and group frontier, respectively, which were 18.1% and 20% lower than the previous year. The highest TFP was in 2012, which was 1.768 under the meta-frontier, an increase of 76.8% over the previous year, and 1.777 under the group frontier, an increase of 77.7% over the previous year. From 2012 to 2013, TFP showed a decline both at coastal and inland regions. After 2013, TFPs began to show steady and small fluctuations. It can be seen that after 2013, both coastal and inland regions have begun to enter a relatively stable level in the development of freshwater aquaculture. Moreover, after 2013, TFPs were greater than 1, which means freshwater aquaculture remained in an effective state, except in 2015. This also indicates that the development level of freshwater aquaculture in coastal and inland regions has been steadily improved after 2013. The freshwater aquaculture industry has gradually become competitive in the market, and the industrial structure has been further optimized. However, the impressive breakthrough value does not appear. This is consistent with the analysis of the time characteristics of the overall national TFP in "Temporal and spatial characteristics of TFP in freshwater aquaculture" section.
From 2004 to 2019, TFPs of coastal region and inland region under the meta-frontier were 1.101 and 1.154 respectively (Fig. 7). It can be seen that under the meta-frontier, the freshwater aquaculture efficiency of coastal region is significantly lower than the efficiency of inland region. TFPs of coastal and inland at group frontier were 1.101 and 1.143e respectively. That is to say, the freshwater aquaculture efficiency in inland region is still superior to the efficiency in coastal region. It indicates that the development of freshwater aquaculture in inland region is more advantageous regardless of the regional factors. Combined with Fig. 8, the average values of TC and EC in coastal region are lower than those in inland region. Especially for EC, the average value of EC in coastal region is significantly lower than that in inland region. In addition, the EC values in coastal region are more concentrated, while those in inland areas are more dispersed. It can be seen that there are great differences in the management level of freshwater aquaculture of inland provinces. This means that many inland provinces still have much space for improvement in freshwater aquaculture management. It is obvious that coastal region has relatively developed economies and high levels of science and technology; with the development of society, they have increasingly concentrated on the development of high-tech industries and tertiary industries, thus ignoring the development of agriculture to a certain extent. At the same time, coastal region is rich in seawater resources, and the emphasis on marine fisheries has made a lot of fishery production factors invested in marine fisheries, thus slowing the development of freshwater fisheries. However, many provinces in the inland region still focus on the primary industry. Taking Heilongjiang and Shanxi as examples, the primary industry in Heilongjiang accounts for the highest proportion of the three industries, and it also shows a gradual upward trend. The emphasis on the primary industry has made its agriculture, including the freshwater fishery industry, develop on a larger scale. Therefore, the local freshwater aquaculture TFP is relatively high. As for Shanxi, although it is not a major fishery province, the province attaches great importance to the development of fisheries. In the past few years, Shanxi has been committed to the transformation of fishery production methods so as to improve the level of intensification of the fishery industry. In addition, advanced aquaculture technology has been introduced through the "Three North" technical cooperation group. And at the same time, the local area is also making efforts to promote freshwater aquaculture technology (National Bureau of Statistic of China 2009). With the joint action of many parties, the technical ability of fish farming management in Shanxi has been greatly improved. In summary, the top priority for freshwater aquaculture in coastal region is to invest necessary management resources to increase their freshwater aquaculture management level. Some provinces with lower management levels in inland region should actively seek communication between provinces to coordinate the improvement of freshwater aquaculture management.
Analysis of TGR in regional freshwater aquaculture TGR refers to technology gap rate, which reflects the technology gap between group frontier and meta-frontier. The higher the TGR value, the closer the DMU's technical level is to the potential optimal level.
The average TGR of coastal and inland regions are 0.997 and 0.740 respectively (see Fig. 9 (I)). The results indicate that the technical level of freshwater aquaculture in coastal region has reached 99.7% of the meta-frontier level, while the technical level of freshwater aquaculture in inland region has only reached 74% of the meta-frontier level. This means that the technical level of freshwater aquaculture in coastal region is more in line with the potential optimal technology level, while the technical efficiency in inland region has a large gap with the optimal level, and there is more space for improvement. According to the TGR value of each province, the value of TGRs in the coastal region is concentrated in a really close level, which shows that the freshwater aquaculture technology level of each place in the coastal region has a characteristic of agglomeration. The TGRs of the provinces in the inland region are relatively scattered, which means that the development of freshwater aquaculture technology in the inland region is quite uneven. Therefore, it is very necessary to strengthen the exchange and cooperation in freshwater aquaculture technology between provinces in inland region.
From a dynamic point of view ( Fig. 9 (II)), from 2004 to 2019, TGR in coastal region had been stable at around 1, with no significant fluctuations. It also shows that the level of freshwater aquaculture technology in coastal region is very close to the optimal level of potential technology. On the whole, the TGR in the inland region showed a rising state from 2004 to 2019, with the value from 0.708 to 0.77. During the period from 2008 to 2010, the TGR in the inland region experienced successive declines, which may be affected by the rising labor and resource costs. After 2010, TGR began to rebound and showed a relatively stable trend. In recent years, TGR in Fig. 7 Provincial average TFP of freshwater aquaculture in two regions inland region has shown an upward trend. With the continuous introduction of advanced technologies in inland areas, its TGR is expected to maintain a growing trend.
Combined with the above analysis of freshwater aquaculture TFP in coastal and inland regions, although the overall performance of inland region is better than coastal region in the freshwater aquaculture industry, when it comes to TGR, coastal region has absolute advantages. The main reason is that coastal areas have been the frontiers to take the lead in developing industrial clusters since reform and opening up in China. Then, through in situ expansion, market pull, off-site incubation, and foreign transplantation and other ways, new technologies are continuously introduced and popularized, and development restrictions on the original location are broken. This has led to further advances in technology, so as to drive the development of the local economy. Obviously, there is a high correlation between economic development and technological development. Thus, the development of economy further promotes the progress of science and technology, and the development of economy and science and technology form a complementary effect. For these reasons, the technical efficiency level of freshwater aquaculture in coastal region is relatively high. Coastal region should give full play to their technological advantages, invest necessary elements in freshwater aquaculture, and continuously optimize the fishery industry. As for inland region, inland areas are generally less economically developed than coastal areas. In contrast, the aquaculture technology level is lagging behind, and they are more inclined to traditional aquaculture methods in terms of fish farming. Therefore, in addition to giving full play to their own resource advantages, inland regions should also devote themselves to the improvement of freshwater aquaculture technology, and constantly approach the potential optimal technical level, thereby promoting the sustainable development of the freshwater fishery industry.

Further discussion
In order to further verify the accuracy of the results, this part further optimizes the input indicators. Considering the input effect of intermediate consumption cost (including feed, fertilizer, drugs, and fuel cost), this paper adds the intermediate consumption cost into the original input-output system, and constructs the evaluation index system of freshwater Based on the above analysis, it is found that there is almost no difference in aquaculture efficiency between meta-frontier and group frontier. Due to the article length, this part discusses the situation under the meta-front. As shown in Fig. 10, after adding intermediate consumption, the results are slightly different from the results obtained before, indicating that the intermediate consumption plays a role in the input-output efficiency of aquaculture. But the general trend is unchanged. From 2004 to 2012, TFP in coastal and inland regions fluctuated significantly. After 2013, TFP in coastal and inland regions began to develop steadily around the value of 1, showing a negative development trend. This is consistent with the empirical results of the first stage model. Unlike the first stage modeling results, in the coastal region, the lowest TFP was in 2011 (0.827), followed by 2009 (0.877). The highest TFP was 1.342 in 2012. In the inland region, the highest TFP was in 2012 (1.598). In terms of the average level of each region, the coastal region TFP is adjusted from 1.101 to 1.071 when considering the intermediate consumption, and in inland region, it was adjusted from 1.154 to 1.079. That is, the TFP of the two regions decreased in varying degrees, indicating that further optimization of intermediate consumption input in aquaculture has a positive effect on improving freshwater culture TFP.
From the perspective of various provinces, as shown in Fig.  11, freshwater aquaculture efficiency still presents a trend of spatial agglomeration, and the southeast area is still dominated by low and medium level. The difference is that East China, including Beijing, Hebei, Shandong, Jiangsu, and Fujian, has changed from a medium level to a medium-high level. The TFP level in South China of Henan, Hubei, Hunan, and Guangxi decreased. It shows that East China has great advantages in intermediate consumption and investment of aquaculture. However, in South China, input of intermediate consumption exists spillover effect, which leads to the low TFP.
The main reason is the difference of land resource endowment. In the process of breeding, the input of intermediate consumption cost is largely based on the size of breeding area, which happens to be larger in South China, resulting in input spillover. While in East China, most of the breeding areas are small, and due to the more developed technology, they are more inclined to intensive farming. In terms of intermediate consumption material input, they also adopt an intensive way to make the use of intermediate material input more fully and effectively. For coastal region part (Fig. 11 (II)), it is consistent with the empirical results of the first modeling, showing a spatial pattern of high in the north and low in the south. Fig.  11(III) shows the distribution of freshwater aquaculture TFP in inland regional group; it is obvious that Shaanxi and Guizhou are still in the leading position. In South China, TFP is not as good as that of the first stage model due to intermediate consumption input spillover.
As for decomposition indicators, Fig. 12 shows the relationship between TFP and decomposition indicators in coastal and inland regions. After adding intermediate consumptive substances into the input index system for optimization, it can be found that the results are the same as the empirical results of the first stage model. Obviously, the moving trend of TFP is roughly the same as the trend of TC and EC; once again, it proves that the change of TFP is caused by the joint effect of TC and EC. In addition, in terms of index decomposition efficiency, the technical efficiency of coastal and inland regions has declined, while the management efficiency has little change. Different from the first stage model, the effect of TC on TFP was enhanced, while EC was weakened. From the perspective of time, after 2013, no matter in coastal region or inland region, EC and TC keep fluctuating slightly around the value of 1. In particular, compared with the TC before 2013, TC is quite different after 2013, which means that the technical level of freshwater aquaculture in China has reached a relatively stable development level after 2013. The disadvantage is that instead of achieving an impressive breakthrough value, it is in a more negative state of development. These are consistent with the analysis of the first modeling analysis, and it also illustrates the necessity of raising the level of science and technology and management in aquaculture.

Comparative analysis and discussion
From the perspective of time trend, the TFP of freshwater aquaculture has not changed significantly before and after the optimization of input variable. In the sampling years, the TFP shows a relatively large fluctuation development trend from 2004 to 2012, and a stable but negative fluctuation state after 2013. From the perspective of regional distribution, the addition of intermediate material consumption mainly affects East China in coastal area and South China in inland central area. This is directly related to the rationality of intermediate material consumption in these areas. However, the comparison results of the two models both show that the freshwater aquaculture efficiency in coastal region is lower than that in inland region. From the decomposition index, it is still the common effect of EC and TC that dominates the change of TFP after adding intermediate material consumption, but the effect of TC is further strengthened. The optimized results will be more accurate. Therefore, it can be seen that TC contributes more to the change of TFP than EC.
From the above analysis, it can be found that the overall results of the two stage models are consistent; thus, the results of this paper are true and reliable. However, there are still limitations in this paper. On the one hand, although this paper uses the latest data that can be collected at present, the data still exists a certain lag. Therefore, this study can be further expanded when the data is updated. On the other hand, due to the limited data, this paper does not adjust the model considering climate and other factors, which can be further explored in future research.

Discussion
The empirical results show that the change of TFP of freshwater aquaculture is jointly guided by EC and TC, especially TC. And its breeding efficiency has room to rise in the fluctuation trend. This section takes Hebei Province as an example to further illustrate the applicability of this study. In order to accelerate the optimization and upgrading of freshwater aquaculture and improve aquaculture efficiency, freshwater aquaculture innovation team of Hebei developed, integrated, and promoted a number of green and healthy aquaculture technologies in 2019, and created a number of demonstration sites with high production efficiency, high quality, water conservation, and emission reduction. Specifically, in terms of culture structure adjustment, Hebei Province has developed and integrated 10 efficient culture methods of famous and high-quality varieties such as Penaeus vannamei and coldwater fish. In terms of aquaculture technology, Hebei Province has built 7 demonstration sites for standardized and efficient freshwater aquaculture technology and 8 demonstration sites for pond engineering recycling technology. And the R&D of comprehensive treatment technology of aquaculture tail water covers all aquaculture modes. In terms of breeding of new varieties of aquaculture, a breeding base for new freshwater products are established in Hebei to solve the key problem of low coverage of main varieties of freshwater aquaculture in the province. The development of these aquaculture technologies has not only widened the development space of aquaculture, but also adjusted the local industrial structure. Combined with the empirical results, the technical progress index of freshwater aquaculture in Hebei Province in 2019 Fig. 11 Provincial distribution of Average TFP Fig. 12 Trend of TFP and its decomposition index was 1.126, a large increase over the previous year (0.999), and exceeded the average technical progress index of Hebei Province (1.089). In addition, the TFP index of freshwater aquaculture in the province was 1.126, showing an increase over the previous year (1.103). In this year, Hebei Province has made considerable improvements in the technical efficiency and production efficiency of freshwater aquaculture. This part tries to compare the efficiency of aquaculture in Malaysia. Malaysia has good natural conditions and location advantages of aquaculture, and has a relatively complete aquaculture industry chain and basic conditions, with rich aquaculture development. At present, aquaculture in Malaysia is in the stage of optimization and upgrading, lacking in modern aquaculture such as seedling breeding, aquaculture construction, and aquaculture health, which may hinder the improvement of aquaculture efficiency. Some scholars have evaluated the efficiency of cage culture in Peninsular Malaysia and pond culture in Malaysia with SFA and DEA models (Iliyasu et al. 2016;Iliyasu and Mohamed 2016). The technical efficiency was measured to be 0.79 and 0.86 respectively, which has space for improvement. If they can make further breakthroughs in seedling breeding, healthy breeding, and breeding mode, the breeding technical efficiency and production efficiency will be further improved. This has some similarities with the situation faced by Hebei Province before. The Chinese aquaculture researcher and Malaysia carried out aquaculture technology training and fishery science and technology exchange activities in 2019, and in-depth discussions on breeding techniques, healthy breeding, and industrial development. It can be reflected from the side that measuring the efficiency of freshwater aquaculture in China and exploring the reasons for efficiency changes also have some applicability to other countries, which can provide some help and reference in aquaculture policy and sustainable development of aquaculture.

Conclusions and policy recommendations
This paper constructs a double-hierarchy meta-frontier Malmquist index, based on the DDF-DEA model, to calculate the freshwater aquaculture TFP of 28 provinces in China from 2004 to 2019, and draws the following conclusions through analysis: (1) No matter in the meta-frontier or the group frontier, TFP of freshwater aquaculture presents dynamic fluctuations and spatial differences. From the perspective of time, TFP fluctuated sharply, especially from 2004 to 2013. After 2013, TFP showed slight and stable fluctuations between years. From a spatial point of view, combined with regional heterogeneity, inland region has obvious advantages in freshwater aquaculture efficiency compared with coastal region.
(2) According to the calculation of the decomposition index of TFP, the change of TFP in freshwater aquaculture is driven by the combined effect of EC and TC. The overall performance of decomposition index efficiency is that the technical efficiency decreases and the management efficiency changes little. In terms of regions, the relatively low TFP in coastal region is largely due to the low value of EC. It means that coastal regions are not making efforts to improve freshwater aquaculture management. The overall situation in the inland region is better than the situation in the coastal region, but the spatial differences of EC in the inland region are greater. Therefore, it can be seen that there is still a lot of space for development in freshwater aquaculture management capabilities in both coastal and inland regions. It is an entry point to promote the sustainable development of freshwater aquaculture.
(3) The TGR of freshwater aquaculture in coastal region has always been in a leading position; TGR remains around 1, which is quite close to the potential optimal technology level. The TGR in inland region is generally on the rise, but its value is much lower than the TGR in coastal region, and it has a characteristic of volatile, which is far from the potential optimal level. To a certain extent, it limits the sustainable development of freshwater aquaculture. Based on the above conclusions, this paper proposes the following suggestions to improve the efficiency of freshwater aquaculture and promote the sustainable development of freshwater aquaculture industry.
(1) Strengthen the construction of aquatic science and technology system, and form a long-term mechanism for transforming technological achievements of freshwater aquaculture into actual productivity. Technical level plays a very crucial role in the freshwater aquaculture process. However, no matter, the TC value or the TGR show an imbalance status in space. Many provinces in China have greater space for improvement in freshwater aquaculture technology. In particular, the TGR in inland region is significantly lower than the TGR in coastal region. Therefore, the government should strengthen the R&D of freshwater aquaculture, and implement the research results into the breeding process, thus to increase the conversion rate of aquatic science and technology achievements, and promote the development of freshwater fishery technology industrialization. Moreover, for the area with low freshwater aquaculture technology, it should pay more attention to the improvement of technology, strengthen cooperation with other areas in the freshwater aquaculture industry, and actively introduce advanced technologies to improve the freshwater aquaculture production efficiency and promote its sustainable development.
(2) Improve the management level of freshwater aquaculture.
The management level of freshwater aquaculture in coastal region is generally lower than that of inland region. Hence, on the basis of its technical advantages, coastal region should vigorously cultivate management talents and strengthen the improvement of freshwater aquaculture management capabilities. As for inland region, there are obvious spatial differences in the degree of change in technical efficiency. Therefore, inland region should improve the coordination of management capabilities between provinces according to their own management level, so as to increase the contribution of management capabilities to the freshwater aquaculture efficiency.
(3) Coordinate the differences between regions and balance the spatial layout of the freshwater aquaculture industry.
Since freshwater aquaculture has presented a considerable spatial difference in China, it is necessary to fully consider the factor, such as regional resource endowments, economic development level, and technological level, so as to form an interactive cooperation mechanism between coastal region and coastal region, coastal region and inland region, and inland region and inland region. Obviously, this will ensure that advanced freshwater aquaculture technology and management methods can be effectively promoted and popularized, which will enable each region to play its own comparative advantage. So that the efficiency of freshwater aquaculture in each area can be improved, and a spatial pattern of coordinated development will be presented, which will provide support for the sustainable development of freshwater aquaculture. (4) Optimize the structure of fershwater culture cost input.
Cost input is one of the factors that affect the efficiency of aquaculture, and the correct control of cost is an important means to improve the input-output conversion rate of freshwater aquaculture. The government should guide fishermen to improve the breeding management and adjust the aquaculture structure scientifically, so as to achieve a reasonable input of intermediate consumption cost and realize the effective increase of output value.