Yuanyuan ZHANG，Shim in SUN

1．College of Economics and Management，Shandong Agricultural University，Tai'an 271018，China；2．College of Management Science and Engineering，Shandong University of Finance and Economics，Jinan 250014，China

1 Introduction

China is the world's largest pork producer and consumer，and researching China's pig breeding TFP and regional differences is of great theoretical and practical significance to speeding up the transformation of the mode of pig production，optimizing space layout of pig production and promoting the healthy development of the pig industry．In recent years，scholars have carried out a lot of studies on the pig production efficiency．The studies of Chen Shiboet al．，Tan Ying and Liao Yiet al．demonstrate that overall，the technical efficiency of scale pig breeding is higher than that of free-range breeding；both the technical efficiency and allocative efficiency of large-scale breeding are high and constantly increase；the production efficiency in the eastern regions is higher than in the western regions；technological regress causes TFP of different scale pig breeding to negatively increase［1-3］．Wang Fanget al．calculate TFP of free-range pig breeding households and specialized pig breeding households and its growth rate，and point out that TFP of free-range pig breeding households is higher than that of specialized pig breeding households，but the TFP growth rate of specialized pig breeding households is higher than that of free range pig breeding households［4］．Pan Guoyanet al．make a comprehensive study of the pig production efficiency in the regions where production is connected with marketing［5］．Zhang Yuanyuanet al．point out that except large-scale breeding，free-range pig breeding，small-scale breeding and medium-scale breeding show decreasing economies of scale，and the four breeding scales have redundancy in purchase price of piglets，feed cost and labor cost［6］．In addition，some scholars explore the reasons for differences in pig productivity．Tian Luet al．point out TFP of pig breeding shows an increasing trend due to rising scale efficiency and technological progress［7］．Yan Zhenyu believes that larger scale pig breeding may not mean higher production efficiency，and the optimal scale hinges on the resources，economic and geographical characteristics of different regions［8］．On the basis of existing research，this paper uses five statistical indicators about free-range pig breeding，small-scale pig breeding，medium-scale pig breeding and large-scale pig breeding in main pig producing provinces（profit ratio of cost，main product output value，purchase price of piglets，feed cost and labor cost）fromNational Agricultural Cost-Benefit Data Compilation（2006-2013），and employs Malmquist-DEA model to calculate and compare the TFP of different scale pig breeding in main pig producing provinces and its decomposition indicators in order to clearly understand the differences in pig production efficiency of main pig producing provinces．

2 Indicator selection，data sources and modeling

2.1 Indicator selectionFrom the data inNational Agricultural Cost-Benefit Data Compilation，it is found that the main product output value of pig breeding accounts for more than 99%of total output value；the sum of purchase price of piglets，feed cost and labor cost accounts for about 95%of total costs．Therefore，this paper finally selects profit ratio of cost，main product output value，purchase price of piglets，feed cost and labor cost as five indicators．

2.2 Data sourcesThe data about the main pig producing prov-inces in this paper，involving profit ratio of cost，main product output value，purchase price of piglets，feed cost and labor cost of free-range pig breeding，small-scale pig breeding，medium-scale pig breeding and large-scale pig breeding in various provinces，are all fromNational Agricultural Cost-Benefit Data Compilation（2006-2013）．

2.3 ModelingDEA，developed by Charnes and Cooper，originating in the late 1970s，is a method to evaluate the efficiency of multiple decision units［9］，and Malmquist index，as a method generally used by the academia in recent years，has been widely used in all walks of life and achieved good results．Assuming（xt，yt）and（xt＋1，yt＋1）are the input-output relationship in periodtandt＋1，respectively，and the change of input-output relationship from（xt，yt）to（xt＋1，yt＋1）is just the change in productivity．Technical efficiency is the use efficiency of production technology，and also the distance between production frontier and actual output．The change in the level of technology is the movement of production frontier．The distance function can be used to calculate technical efficiency and technological progress．Malmquist index is defined as：

The Malmquist index in formula（1）is the distance function under constant returns to scale，namely TFP．So if the index is greater than 1，the productivity makes progress；if the index is less than 1，productivity lags behind；if the index is equal to 1，productivity does not change．The productivity index in the above formula can be divided into technical efficiency change and technological change．

The first term in formula（2）shows the efficiency change，namely the contribution of technical efficiency change in periodtandt＋1 to productivity，and the second term shows the changes in technology，namely the contribution of production frontier movement to productivity change．However，the Malmquist index is under the hypothesis of constant returns to scale，so the above formula can not indicate the contribution of economies of scale to productivity．The Malmquist index is further developed into：

The first term in formula（3）shows pure efficiency change，the second term shows scale efficiency change，and the third term shows technological change．The third term in formula（3）is the same as the second term in formula（2）．The first and second terms in formula（3）are from the decomposition of the first term in formula（2）．Compared with the simple cross-sectional data DEA analysis，the Malmquist index analysis separates the factors of technological progress to make results more accurate．From the angle of output，this paper studies the change in Malmquist index，and establishes model with profit ratio of cost and main product output value of different scale pig breeding in various provinces as output indicators，and purchase price of piglets，feed cost and labor cost as input indicators．

3 Estimation results and analysis

3.1 Estimation resultsBy running DEAP2．1 software，we can get TFP of free-range，small-scale，medium-scale and large scale pig breeding in the main pig producing provinces during2005-2012 as well as its decomposition（comprehensive technical efficiency，technological progress change，pure technical efficiency change and scale efficiency change），as shown in Tables1 to 4．

Table 1 TFP of free-range pig breeding and its decomposition

Table 2 TFP of small-scale pig breeding and its decomposition

Table 3 TFP ofmedium-scale pig breeding and its decomposition

Table 4 TFP of large-scale pig breeding and its decomposition

3.2 Longitudinal difference analysis

3.2.1 Comprehensive technical efficiency．As can be seen from Table 1 to Table 4，except Hunan Province，the comprehensive technical efficiency of free-range pig breeding is DEA effective in the rest of the provinces，and both the input and output do not reach optimal state of DEA．The comprehensive technical efficiency is lowest in Jiangsu Province，indicating that the input-output efficiency is lowest；the comprehensive technical efficiency is close in Yunnan，Guangxi，Shandong，Henan and Hebei，and there is＂excess＂input and＂deficiency＂output；the free-range pig breeding in Guangdong，Hubei and Sichuan is not DEA effective，but the comprehensive technical efficiency is high，and there is a certain amount of＂excess＂input and＂deficiency＂output；the free-range pig breeding is only DEA effective in Hunan，and its input and output are in the best condition．Different from free range pig breeding，the comprehensive technical efficiency of small-scale breeding is DEA effective in 8 main pig producing provinces，and there is no＂excess＂input and＂deficiency＂output．The comprehensive technical efficiency is less than 1 in Yunnan and Guangxi，falling within DEA inefficiency，and the comprehensive technical efficiency is lower in Yunnan，indicating that its input-output efficiency is lower，and there is a greater need to improve．The comprehensive technical efficiency of medium-scale breeding is greater than 1 in Sichuan，Hunan，Shandong，Yunnan and Jiangsu，falling within DEA efficiency，while the comprehensive technical efficiency of medium-scale breeding is less than 1 in Henan，Hubei，Guangdong，Hebei and Guangxi，falling within DEA inefficiency，and there is＂excess＂input and＂deficiency＂output，needing to be improved．The comprehensive technical efficiency of large-scale breeding is greater than 1 in Sichuan，Shandong，Hubei，Guangxi，Yunnan and Jiangsu，falling within DEA efficiency，and the input and output are in the best condition，and there is no＂excess＂input and＂deficiency＂output．The comprehensive technical efficiency of large-scale breeding is between 0．99 and 1 in Hunan，Henan，Guangdong and Hebei，and there is a certain amount of＂excess＂input and＂deficiency＂output．

3.2.2 Technical progress change．As shown in Table 1 to Table 4，the mean of technical progress change of free-range pig breeding is1．111 in main pig producing provinces，and the technical progress change value of free-range pig breeding is greater than 1 in various provinces，indicating that the free-range pig breeding achieved technical progress during 2005-2012．The technical progress change value of small-scale breeding in Sichuan，Guangdong and Guangxi is1．038，1．027 and 1．008，respectively，achieving technical progress，while the technical progress change value of the remaining provinces is less than 1，indicating that there is degeneracy of technology for small-scale breeding．The mean of technical progress change value of medium-scale breeding in main pig producing provinces is larger than 1，that is，there is technical progress for medium-scale breeding．In the main pig producing provinces，the technical progress change value of large-scale breeding in Guangdong and Yunnan is0．993 and 0．997，respectively，and there is technical setback，while the technical progress change value of large-scale breeding in the remaining provinces is greater than 1，and there is technical progress．

3.2.3 Pure technical efficiency change．As shown in Table1 to Table 4，the pure technical efficiency change value of free-range pig breeding is greater than 1 in Sichuan，Hunan，Henan and Guangdong，indicating that the technical efficiency of free-range pig breeding in these provinces continues to rise，and technical efficiency decrease does not appear．The pure technical progress efficiency change value of free-range pig breeding is less than 1 in other provinces，that is，there is inefficient technical use．The pure technical efficiency change value of small-scale breeding is less than 1 in Guangdong，Hebei and Yunnan．Except Henan，Hubei，Guangdong and Jiangsu，the pure technical efficiency change value of medium-scale breeding is greater than 1 in other provinces，and the technical use efficiency of medium-scale breeding continues to rise．The pure technical efficiency change value of large-scale breeding is substantially greater than 1 in main pig producing provinces，that is，the technical use efficiency of large scale breeding continues to rise，except Hunan and Guangdong．

3.2.4 Scale efficiency change．As shown in Table1 to Table4，in terms of free-range pig breeding，the scale efficiency change value is 1．009 in Hunan，indicating that its free-range pig breeding scale is increasingly close to optimal state，while the scale efficiency change value is less than 1 in the remaining provinces，indicating that the free-range pig breeding has not reached the optimal scale of operation．The scale efficiency change value of small scale breeding is less than 1 in Henan，Guangxi and Yunnan，while it is greater than 1 in the remaining 7 provinces，and the small-scale breeding is closer to the optimum state．The scale efficiency change value of medium-scale breeding in Sichuan，Hunan，Hubei and Jiangsu is not less than 1，indicating that the medium-scale breeding is increasingly close to the optimal scale while the remaining provinces do not reach the optimal scale of operation．The scale efficiency change value of large-scale breeding in Sichuan，Shandong and Jiangsu is not less than 1，indicating that the large-scale breeding in these three provinces is increasingly close to the optimal scale of operation，while the large-scale breeding in the remaining provinces has not yet reached the optimum scale．

3.2.5 TFP．As shown in Table 1 to Table4，the mean of free range pig breeding TFP in the main pig producing provinces is greater than 1，that is，the TFP of free-range pig breeding is increasing in various provinces．Except Sichuan，Guangdong and Hebei，the TFP change value of small-scale breeding is less than 1 in the remaining provinces，indicating that the technical setback or low scale efficiency makes TFP continue to decrease．In terms of medium-scale breeding，the TFP change value in Henan and Hebei is0．991 and 0．998，less than 1，that is，TFP continues to lower，while TFP is rising in the remaining provinces．In terms of large-scale breeding，the TFP change value is larger than 1 in Guangdong but less than 1 in the remaining provinces，which indicates that the large-scale breeding TFP continues to increase as a whole in the main pig producing provinces．

3.3 Horizontal difference analysis

3.3.1 The provinces with production efficiency advantages in free-range pig breeding．Overall，there are significant differences in the pig production efficiency between different breeding scales in Hunan．The comprehensive technical efficiency of free-range pig breeding，small-scale breeding and medium-scale breeding is greater than 1，and it is DEA effective，while the comprehensive technical efficiency of large-scale breeding is DEA ineffective；except small-scale breeding，the remaining three kinds of breeding scale have technical progress change value of greater than 1，to achieve the technological advances；except large-scale breeding，the remaining three kinds of breeding scale have rising technical efficiency and are increasingly close to the optimal scale of operation．The TFP of small-scale breeding in Hunan continues to fall，while the TFP of the remaining three kinds of breeding scale is rising．

3.3.2 The provinces with production efficiency advantages in small-scale pig breeding．The comprehensive technical efficiency of free-range pig breeding in Sichuan is DEA ineffective，while the comprehensive technical efficiency of small-scale breeding，medium-scale breeding and large-scale breeding is DEA effective；the technical progress change value of four kinds of breeding scale is greater than 1，to achieve technical progress，and the technical use efficiency is increasing；the scale efficiency change value of free-range pig breeding is less than 1，and it has not yet reached the optimal scale，while the scale efficiency of three other breeding modes is getting close to the optimal scale of operation．TFP of four kinds of breeding scale in Sichuan continues to increase．In Guangdong，only the comprehensive technical efficiency of small scale breeding is greater than 1 and is DEA effective，while the comprehensive technical efficiency of the other three breeding scales is not DEA effective；free-range pig breeding achieves technical progress，and the technical use efficiency is continuously improved；small-scale breeding and medium-scale breeding achieve technical progress，but the technical use efficiency continues to lower；large-scale breeding undergoes technical setback and the technical use efficiency continues to lower；in terms of operating scale，only small-scale breeding is getting close to the optimal level．The TFP of free-range pig breeding，small-scale breeding and medium-scale breeding continues to improve，with the exception of large-scale breeding．In Hebei，only the comprehensive technical efficiency of small-scale breeding is greater than 1 and it is DEA effective，while the comprehensive technical efficiency of the other three breeding scales is not DEA effective；the free-range pig breeding achieves technical progress，but the technical use efficiency continues to lower；small-scale breeding is facing technical setback，and technical use efficiency continues to lower；medium scale and large-scale breeding achieves technical progress，and the technical use efficiency continues to increase；only small-scale breeding is getting close to the optimal scale of operation，while the other three breeding modes have not yet reached the optimal scale．Except medium-scale breeding，the TFP of the other three breeding scales continues to increase．

3.3.3 The provinces with production efficiency advantages in medium-scale pig breeding．The comprehensive technical efficiency of free-range pig breeding in Henan is less than 1 and it is DEA ineffective，while the comprehensive technical efficiency of the other three kinds of scale breeding is not DEA effective；the technical progress change value of free-range pig breeding，medium scale breeding and large-scale breeding is greater than 1，to achieve technical progress，and technical use efficiency is increasing；although small-scale breeding is faced with technical setback，the technical use efficiency continues to rise；except the free-range pig breeding，the scale efficiency change value of the three kinds of scale breeding is greater than 1，getting close to the optimal scale of operation．The TFP of free-range pig breeding，medium scale breeding and large-scale breeding continues to improve，with the exception of small-scale breeding．The comprehensive technical efficiency of free-range pig breeding and small-scale breeding in Yunnan is less than 1 and it is DEA ineffective，while the comprehensive technical efficiency of medium-scale and large-scale breeding is DEA effective；free-range pig breeding and medium scale breeding achieve technical progress，while the small-scale and large-scale breeding is facing technical setback；the technical use efficiency of free-range pig breeding and small-scale breeding continues to lower，while the technical use efficiency of medium scale and large-scale breeding continues to improve；four kinds of breeding do not reach the optimal scale．Except small-scale breeding，the TFP of the other three kinds of breeding scale continues to increase．

3.3.4 The provinces with production efficiency advantages in large-scale pig breeding．The comprehensive technical efficiency of free-range pig breeding in Shandong is less than 1 and it is not DEA effective，while the comprehensive technical efficiency of the other three kinds of scale breeding is DEA effective；free-range，medium-scale and large-scale breeding achieves technical progress，while small-scale breeding is facing technical setback；except free-range pig breeding，the technical use efficiency of the other three kinds of breeding scale is rising；the scale efficiency change value of free-range pig breeding and medium-scale breeding is less than 1 and the optimal scale of operation is not reached，while the small-scale and large-scale breeding is increasingly close to the optimal scale of production．The TFP of small-scale breeding continues to lower，while the TFP of the remaining three kinds of breeding scale is on the rise．The comprehensive technical efficiency of small-scale and large-scale breeding in Hubei is greater than 1 and it is DEA effective，while the comprehensive technical efficiency of free-range pig breeding and medium-scale breeding is DEA ineffective；the technical progress change value of small scale breeding is less than 1 and there is technical setback，while the remaining three kinds of breeding have achieved the technical progress；the technical use efficiency of free-range pig breeding and medium-scale breeding continues to lower，while the technical use efficiency of small-scale and large-scale breeding is rising；the scale efficiency change value of free-range pig breeding and large scale breeding is less than 1 and it does not reach the optimal scale，while the small-scale and medium-scale breeding is close to the optimal scale．Except small-scale breeding，the TFP of the other three kinds of breeding continues to rise．Only the comprehensive technical efficiency of large-scale breeding in Guangxi is greater than 1 and it is DEA effective，while the remaining three kinds of breeding are DEA ineffective；four kinds of breeding scale achieve technical progress，and except free-range pig breeding，the technical use efficiency of the other three kinds of breed-ing scale is getting higher；the scale efficiency change value of four kinds of breeding scale is less than 1 and the optimal scale of operation is not reached．Except small-scale breeding，the TFP of the other three kinds of breeding continues to increase．The comprehensive technical efficiency of free-range pig breeding in Jiangsu is less than 1 and it is DEA ineffective，while the comprehensive technical efficiency of the remaining three kinds of breeding scale is more than 1 and it is DEA effective；the free-range，medium-scale and large-scale breeding achieves technical progress，while the small-scale breeding is facing technical setback；the technical use efficiency of free-range and medium-scale breeding continues to improve，while the technical use efficiency of small scale and large-scale breeding continues to lower；except free range pig breeding，the other three kinds of breeding are getting close to the optimal production scale．The TFP of small-scale breeding continues to lower，while the TFP of free-range，medium-scale and large-scale breeding is rising．

4 Conclusions and policy recommendations

4.1 ConclusionsIn this paper，Malmquist-DEA model is adopted to analyze the statistical data；TFP and its decomposition indicators of different pig breeding scale among the top ten pig producing provinces are calculated；both horizontal and longitudinal comparisons are made．Results show that among different pig breeding scales，free-range breeding scale is dominant in Hunan，small breeding scale is dominant in Sichuan，medium breeding scale is dominant in Sichuan and Hunan，and large breeding scale is dominant in Sichuan，Shandong and Jiangsu；among the provinces，pig production efficiency varies with breeding scale，and small-scale pig breeding in Sichuan，Guangdong and Hebei，free range and medium-scale pig breeding in Hunan，medium-scale pig breeding in Henan and Yunnan，large-scale pig breeding in the rest of the provinces，have significant efficiency advantage．

4.2 Policy recommendations（i）Strengthening publicity，education and training to improve the cultural quality and professional knowledge of pig raisers．Through training courses，expert advice and so on，it is necessary to use a variety of channels such as radio，television，Internet and newspaper，to introduce basic knowledge and technology management essentials about breeding for the majority of pig farming households，and vigorously promote the basics and computation methods about pig production efficiency．（ii）Giving play to the role of government departments and accelerating transformation of pig breeding mode．It is necessary to continue to intensify policy support，adjust breeding structure in accordance with local conditions，and focus on the development of scale breeding with production efficiency advantages；strengthen policy guidance，and comprehensively develop multiple breeding modes；improve the scientific and rational layout of pig production，and give play to the production efficiency advantages in various regions，to develop small-scale pig breeding in Sichuan，Guangdong and Hebei，develop medium-scale pig breeding in Hunan and Henan，and vigorously develop large-scale pig breeding in Henan，Hebei，Shandong，Hubei，Guangxi and Jiangsu．（iii）Strengthening information dissemination and update and improve the grass-roots pig industry service system．It is necessary to continue to promote pig breeding network services，timely release technical services，efficiency assessment and production information，and establish effective long-term counseling and positive feedback mechanism for pig farming households；strengthen the close connection between breeding households and scientific research units at all levels to improve the technological content of animal husbandry service．

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