
Research Article


Application of Region Agricultural Circular Economy Measurement Model 

Xiaoyuan Geng
and
Leng Zhijie



ABSTRACT

For the comparison of regional agricultural circular economy
development regularity, this study utilizes national 31 provinces or municipalities
1997~2011 panel data, designs region agricultural circular economy measurement
model, analyzes the dynamic performance of technical efficiency level about
agricultural circular economy. The result shows: The agricultural circular economy
technology efficiency level in most places are lower but it has become a rising
trend year by year; in the eastern, central and western three regional agricultural
circular economy, the difference of technical efficiency is bigger and the volatility
is stronger; eastern and central trends rather similar, present negative growth,
only the west is positive growth. Results show that: Enhancing the technology
efficiency of China’s agriculture
circular economy and reducing regional gap among efficiency is currently the
crux of the problem, the method of this study can guide how to gain good sample
region about agricultural circular economy development.





Received: October 24, 2013;
Accepted: January 07, 2014;
Published: February 08, 2014


INTRODUCTION
Agricultural circular economy is the application and outspread of circular
economic theory in agricultural production in the field, namely, under the comprehensive
constraints. Given the capacity of agricultural resources and the deposit of
ecological environment, from of angle of saving agricultural resources, protecting
ecological environment and improving the economic benefit, using the activities
of agricultural production and organization of agricultural production system
by recycling economics method, forming the material energy recycling closedloop
agricultural production system through the end of the material energy backflow
(Huang, 2004).
The study of technical efficiency began with Koopmans (1951),
Debreu (1951) and Shephard (1953).
Koopmans (1951) gives the definition of technical efficiency
of: A feasible inputoutput vector is called technology effective, if keeping
other outputs (or other inputs), technically it is impossible to add any output
(or reducing any input). According to the above definition: From the angle of
output, technical efficiency refers to economic units under the same input,
it’s the ratio of actual output and ideal output (maximum likelihood output);
from investment perspective, the technical efficiency means under the same output,
it’s the ratio of actual input and ideal input (minimum possibility input).
Namely, it is used to measure under the existing technical level, the ability
of producers getting maximum output (or minimum input costing), shows the extent
of producers actual production close to the frontier, reflects the degree of
existing technology played.
Currently, the technology efficiency of agricultural circular economy is not
explicitly defined, based on the above definition we will define it: In a certain
period, under certain technical equipment and agricultural resources, ecological
environmental inputs, it is the ratio of actual agricultural output and ideal
output (maximum likelihood output) by making full use of agricultural input
resources for economic units (an area, agricultural enterprises or farmers).
Visibly, the technology efficiency of agricultural circular economy reflects
the relation of elements, ecological input and output under certain production
function, reflects the production function effectiveness.
Farrell (1957) first advanced the technical efficiency
measurement methods from the view of input point, simple calculation; the method
of measuring the technical efficiency is widely used (1957). But Farrell’s
method has fault. Main show: (1) The frontier production function only by partial
sample observation decision, not make use of all sample data, (2) The estimation
of frontier production function is severely influenced by the data quality and
(3) Due to the calculated parameters by this method without statistical properties,
it isn’t able to perform statistical tests and statistical inference. In
1966, Le Penn's from the output angle, made a new definition of technology efficiency,
namely technical efficiency are the actual output to achieve the maximum output
percentage in market prices unchanged, investment scale and factor ratio invariable.
This is generally accepted, also applied (Wang et al.,
2009).
About the estimating agricultural production technology efficiency, commonly
used methods are parameters method and nonparametric methods, the parameters
method is mainly stochastic frontier analysis and nonparametric methods is
DEA. Because DEA as a mathematical programming method, without statistical characteristic,
impossible to inspection and the boundary of measure production function is
not affirmation and it’s impossible to separate the influence from random
factors and measurement error. Compared, in stochastic frontier analysis, the
frontier is random, every decision unit does not need to use the same frontier
and distinguish the error term, the more accurately reflect the actual technical
efficiency level and the results can be inspected by hypothesis test (Wang
et al., 2009). Combined with the purpose, we apply stochastic frontier
approach to measure agricultural circular economy technical efficiency.
At present, there are more research by using nonparametric in existing research
(Kang and Liu, 2005; Chen, 2006).
These studies will help us to deepen understanding China agricultural technical
efficiency. And there is relatively rare research by using parameter. Kalirajan
using provincial data analysis agriculture TFP growth and compared them (Kalirajan
et al., 1996); based on the crosssection data of rice farmers in
Jiangsu province Xu compared the technical efficiency and technological progress
between modern agriculture and traditional agricultural and tried to prove "Schultz
hypothesis" (Xu and Jeffrey, 1998), Fan also used this
example to illustrate the agricultural technology progress, technology and allocate
efficiency (Fan and Pardey, 1997), he study of technical
efficiency of agricultural production is relatively less.
Michael selecting agricultural output, land, mechanical power, chemical fertilizer
and labor, five indicators, using China's 30 provinces, city, region’s
19911997 year agricultural production panel data, build stochastic frontier
production model and calculate the Chinese provinces, city, region agricultural
efficiency of production technology, by random effects model estimate the result
shows: the efficiency of agriculture production technology in various regions
in China keep rising, the gap of technical efficiencies between the eastern
and western regions widening; technology efficiency is the main driver of agricultural
production growth in China (Baiding and McAleer, 2005).
Zheng (2009) using stochastic frontier production function
method, the selecting agricultural output, crop planting area, agricultural
labor, chemical fertilizer and agricultural machinery power, per capita GDP,
calculated the 20002007 China agricultural efficiency of production technology
and studied its influencing factors and the analysis shows that China's agricultural
production average technical efficiency is low, obvious differences between
regions, the efficiency of agricultural production technology among 31 provinces,
municipalities and areas basically concentrated in 0.5~0.9, agricultural production
technology used in eastern region is more efficient than in central and western.
It has not found in the literature temporary by using parameters method to measure
agricultural circular economy technology efficiency.
Based on the circular economy theory, we first attempt to use since 1997 agricultural
circular economy provincial panel data, apply stochastic frontier translog production
function, analyze the technical efficiency regional agricultural circular economy
and based on this we try to analyze and explain the regional gap and fluctuation.
Design of region agricultural circular economy measurement model: Stochastic
frontier production function is put forward initially by Aigner
et al. (1977) and Meeusen and van den Broeck (1977)
and soon became a remarkable branch in econometrics. Stochastic frontier production
function not only want to consider the factors leading technology progress but
also consider the forefront of technological progress and productivity of input
factors on the interaction effect and substitution effect between the input
factors. Expresses as follows with the equation:
Y_{i} = f(X_{i}, β)
exp (ε ≡ V_{i}U_{i}) 
(1) 
In Y_{i} = in f(X_{i},
β)+V_{i}U_{I} 
(2) 
Model (2) is the model (1) ‘logarithmic, Y: The actual output; f(•):
Certainty on the production possibilities frontier output, it represents the
best available technology under the conditions of output; X_{i}: Inputs
(including the land, capital, labor and other inputs); β: The unknown parameters;
ε: Synthetic error term, V_{i}: For a sample unit in the production
of factors beyond the control is used to determine measurement error and random
interference effects, such as the statistical error, climate, natural disasters
and V_{i}~(0, σ^{2}_{v}); tU^{i}: sample
cell technical inefficiency of production parts, namely, the sample output and
productionpossibility frontier of the distance, U_{i} obeys truncated
normal distribution, that is U_{i}>0, U_{i}~N(m_{t},
σ^{2}_{u}) (Zhang et al., 2006).
This study studies the sample was a panel data, each element on output with
time and area contribution will vary from, so choose this kind of functional
form. The general form for:
Te_{it} = exp(u_{it}) 
(4) 
Among them, type (4) that the i samples provinces in the period t rate the
level of technology; type (4) and (5) quantitative description of the time factor
is the impact on the u_{it}; in statistical tests, if γ = 0 this
one of the original hypothesis is accepted, then no need to use stochastic frontier
translog production function model to analyze the panel data, OLS method can
be directly transported. The model should be used in parameter estimation maximum
likelihood method; of these, the key step is the γ = 0 using the likelihood
of this hypothesis testing; observation error variance, σ^{2}_{v}
and the variance of technical efficiency, σ^{2}_{u}, hence,
γ ∈(0, 1), the estimated value of the statistical test can reflect
variations in technical efficiency of agriculture whether to have the statistical
significance.
Variables defined and data processing: Sample data used in this study is from
1997 to 2011 panel data in 31 provinces and from the “China
Statistical Yearbook”, “China
Rural Statistical Yearbook”,
“China Agriculture Statistical Yearbook”,
Statistical Bulletin around and the China Agricultural Information Network.
This is the reason why the selected sample data from 1997 and not be traced
back to earlier years, Chongqing since 1997 was independent from Sichuan Province,
became a municipality. If the sample data selected data in earlier years in
order to ensure a consistent diameter, the practice is to refer to other literature
after 1997, data for each year sum to Chongqing in Sichuan Province, which appears
as a region of Sichuan Province. This article does not take this approach, because
taking into account Chongqing becoming municipality before and after accepted
policy support and so there are still some differences, even if the sum of the
data will cause data Sichuan caliber not the same as a certain degree. So this
year is the beginning and end of sample data from 1997 to 2011.
Variable determinations: In determining the variables, based on the
existing literature on the research of agricultural technical efficiency, this
study not only considering the inputoutput factors of agricultural circular
economy elements but also the “3R” of recycle economy involved (Li
et al., 2008), obtains the following variables:
• 
Output variables Y: Using gross index agricultural
output value 
• 
Capital element variable K: The capital essential factor's investment
has selected the recycle fixed assets in production. In dealing with fixed
assets for production, it will be productive rural households and rural
households in the original value of fixed assets obtained by multiplying
the production statistics for the original value of fixed assets, in order
to make the data along the same lines, assuming that the sample interval
of the productive fixed assets were purchased in 1997, so the sample interval
for each year of the original value of fixed assets for production in 1997
is actually worth and then in 1997 as a constant 100 to the price deflated,
this time the data will be met caliber consistency (Li
et al., 2008) 
• 
Intermediate input variables I: The selection responds the resources
decrement input, such as t the mechanical animal operations, seedlings,
fertilizer, plastic, pesticides, diesel fuel costs, as well as the security
situation in response to resources and environmental costs of electricity
and water for irrigation indicators 
• 
Human elements variables in the above L: In the above, variables
are used the magnitude of value that contains price information indicators,
where if only by the number of agricultural employees, likely to bring the
problems caused by different variable dimension, this here too should be
characterized by the magnitude of value indicators but no direct access
to the price of labor. To address this problem, we refer to Tu
and Xiao (2005) approach, from the perspective of labor income, so human
capital input factor is the number of agricultural employees and agricultural
employees in net income to be multiply 
• 
Land elements variable E: The use of land for agricultural activities
is unique, this is the important input variable in the development of agricultural
cycle economy but must be transformed the land as the value variable. Taking
into account the recycling of agricultural land, the cropping situation,
we have chosen a total sown area of agriculture and through the unit cost
of land to be translated into value terms 
• 
Time trend function T: T = l,...,13, corresponding 1997 to 2011,
reflecting the technological change 
Table 1: 
Stochastic frontier translog production function estimates
results 

***,**,*: Seperately 1, 5, 10% of the significant level, significance
levels separately, twotailed test 
In order to ensure the overall comparability of data on the magnitude of value
indices excluding the price factor treatment, using a sample interval of rural
areas and rural consumer price index retail price index of manufactured goods
converted to constant prices of 1997.
Estimation results analysis
Model estimation results interpretation: According to the model (3) and
the above other hypotheses, making use of China 19972011 31 provinciallevel
panel data to estimate the region, the results shown in Table
1:
Results show that:
• 
Technical inefficiency mean μ passed the level of significance
of 1% of the test, indicating that there is technical inefficiency in the
various regions of the agricultural cycle economy 
• 
γ = 0.979, about, after controlling the input factors and other noncontrollable
factors, 97.9% did not meet frontier level of output which is caused by
technical inefficiency. LR test statistic were significant at 1% significant
level, indicating the error term in type (1) has a very significant composite
structure. Therefore, for the sample data using the stochastic frontier
production function technique is very necessary 
• 
η (timevarying technical efficiency) = 0.005, did not pass inspection,
which indicates that the technical efficiency of all regions and time trend
is not obvious 
In the model the coefficient of time t for all items included in the regression
were largely through the significant test, indicating that technological progress
in agriculture and recycling economy exist and the time with each investment
essential factor's cross term's regression coefficient through the examination,
suggesting that technical is nonneutral, which means that technology is not
independent of the factors of production.
The labor force essential factor L result is quite special, a regression coefficient
for negative (two items not through examination). Presents this result the reason
to have the possibility is the investment manpower essential factor makes the
positive contribution by no means to the agricultural circulation economy development,
some areas temporarily have not possibly realized to the development circulation
agriculture importance, therefore still exists does not favor the agricultural
circulation economic development the phenomenon.
Technical efficiency analysis
Technical efficiency of volatility: Figure 1, the gap
was significant and volatile about the technical efficiency of the agricultural
cycle economy. Through Table 2, average efficiency is uneven,
the highest is 0.98, it shows China agricultural recycling economy across regions
there is a big room to improve technical efficiency (compared with 1).
Table 2: 
Provinces, municipalities and autonomous regional technical
efficiency value 

Reason may be that since the 21st century began about agriculture circulation
economy development, the relationship of agriculture circulation economy system
in all aspects is not very well straighten out, the circular economy in a variety
of agricultural resources, technology has not integrated well. There can not
be wellintegrated environmental and economic phenomenon. Although the interval
around the agricultural cycle of economic and technical efficiency is low, the
rise year by year. This is because with the economic development of the agricultural
cycle more and more important, all regions are active and reasonable correction
of their own resources, technical configuration issues and thus more in line
with the premise of the economic development of agricultural cycles.
To investigate the agricultural circular economy technology efficiency is convenient,
the 31 regions divided into three regions: Eastern (Beijing, Tianjin, Hebei,
Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Hainan),
central (Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan) and
western (Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Inner Mongolia,
Guangxi, Ningxia, Qinghai, Xinjiang, Tibet), for convenience, below the paper
“areas” shall mean 31 provinces, “regions” shall mean the
eastern, central and western. To make each region more representatives about
the average technical efficiency, here we measure them by taking the weighted
average. Weights for all areas are the proportions where agricultural output
in its region total agricultural output (Shi et al.,
2008).
Through the Table 3 can be seen, the average technical efficiency
of the eastern, middle and western regions three regions are at three different
levels and there is a clear difference among, the middle owns the highest technical
efficiency, followed by the east and western minimum. Table 2
can be combined, the average technical efficiency is not high for all areas
of the middle region which owning the highest technical efficiency, low level
of technical efficiency in some areas and some even lower than the east and
western regions, such as Shanxi. The western region is not included in the technical
efficiency of all regions are at the lowest level, where the level of technical
efficiency in Sichuan exceeds the average level of the middle region. The reason
why the agriculture is a relatively traditional sector, although its related
technologies continue to progress, compared to similar industrial sector, is
still slower.
Table 5: 
1997~2011 31 Provincial level area technical efficiency coefficient
of variation 

Expressed separately compares the change direction with the
last year 
If the agricultural cycle economy technology in a few areas in the region
is advanced, then other areas will be at the cutting edge below the corresponding
region. Only when the technology of agricultural cycle economy in most regions
contained has improved to some extent, then there is a clear increase in efficiency
only when the technology makes the region as a whole. From Fig.
2 we can see the technological growth rates of efficiency of agricultural
cycle economy in western region are significantly higher than other regions.
Regional difference analysis: And from Table 4, in
regional agricultural circular economy technology efficiency coefficient of
variation changes also can see, the gap of 31 provincial areas of agricultural
circular economy technology efficiency is in constant fluctuations. 1997~2011
regional gap has been enlarging. In order to narrow differences among areas,
to assume the stable development, the state should be give policy support, in
implementing policy should provide the proper guidance and make the resource,
technology in accord with agricultural circular economy development premise
conduct optimum integration.
From the points of view area, as shown in Table 5 shows,
the variety track of eastern and central two regions’ agricultural circular
economy technical efficiency compare similar, 1997~2011 fluctuated declines
in trend but the central region down faster than the eastern region, the eastern
region decline relatively gentle. The change track of western region is opposite
with eastern and central. Western region is 1997~2011 increasing year by year,
rises relatively gentle. From the fluctuation, with range to measure, the western
range is about 0.00028, eastern range is about 0.00039, while in the middle
of the fluctuation is the largest, for 0.00052. Visibly, central region is obviously
higher than the east, west about the fluctuation extent.
CONCLUSION
By constructing a Stochastic frontier translog production function model, 1997~2011,
31 areas agricultural circular economy panel data, we study the technical efficiency
of agricultural circular economy, regional fluctuations and differences, found:
• 
Studying agricultural circular economy, stochastic frontier
translog production function model is a suitable model 
• 
1997~2011, agricultural circular economy technology efficiency low level,
reason might be since the 21st century began about agriculture circular
economy development of agriculture circular economy system in all aspects
of relationship is not very good, straighten, agricultural circular economy
of various resources, technology also failed to integrate well, existing
environmental and economic cannot very good fusion phenomenon. But agriculture
circular economy technology efficiency standards were to increase year by
year trend, this is due to agriculture with the development of circular
economy more and more attention to various areas were actively reasonable
rectification of its own resources, technology configuration, thus more
in line with the agricultural circular economy development of premise 
• 
In the eastern, central and western agricultural circular economy, technical
efficiency level difference is bigger and volatility is stronger. Eastern
and central change trend rather similar and present negative growth, only
to the west is positive growth. To narrow differences between areas to assume
the stable development, the state should be policy support and guidance,
make resources, technology in accord with agricultural circular economy
development premise can conduct optimum integration 
Therefore, the key current issues are improving the technical efficiency of
agricultural cycle economy and narrowing the efficiency gap among regions.
ACKNOWLEDGMENT
This study is supported by National Social Science Fund (08BJY067).

REFERENCES 
1: Baiding, H. and M. McAleer, 2005. Estimation of Chinese agricultural production efficiencies with Panel data. Math. Comput. Simul., 68: 475484. CrossRef  Direct Link 
2: Chen, W.P., 2006. China agricultural productivity growth, technology progress and efficiency changes: from 1990 to 2003. J. Chinese Rural Observation, 1: 1823.
3: Debreu, G., 1951. The coefficient of resource utilization. Econometrica, 19: 273292. Direct Link 
4: Fan, S. and P.G. Pardey, 1997. Research, productivity, and output growth in Chinese agriculture. J. Dev. Econ., 53: 115137. Direct Link 
5: Farrell, M.J., 1957. The measurement of productive efficiency. J. R. Stat. Soc. Ser. A, 120: 253290. Direct Link 
6: Huang, X.J.Z., 2004. Circular Economy: Industrial Mode and Policy System. Nanjing University Press, China, ISBN: 9787305043901.
7: Kalirajan, K.P., M.B. Obwona and S. Zhao, 1996. A decomposition of total factor productivity growth: The case of Chinese agricultural growth before and after reforms. Am. J. Agric. Econ., 78: 331338. Direct Link 
8: Kang, X. and X.M. Liu, 2005. China's grain production of technical efficiencies of analysis. J. Chinas Rural Observation, 4: 25 32.
9: Koopmans, T.C., 1951. An Analysis of Production as an Efficient Combination of Activities. In: Activity Analysis of Production and Allocation, Cowles Commission for Research in Economics, Koopmans, T.C. (Ed.). Jone Wiley, New York.
10: Li, G.C., Z.C. Feng and S.W. Zhan, 2008. Family endowment on their household operation technical efficiency of influence of Hubei province farmer's impact  based on stochastic frontier production function empirical study. Stat. Study, 1: 3542.
11: Shephard, R. W, 1953. Cost and Production Functions. Princeton University Press, Princeton, NJ., USA., Pages: 104.
12: Shi, H., L.J. Meng and H.M. Wang, 2008. China's agricultural productivity, the regional difference and volatility based on stochastic frontier research production function analysis. Econ. Sci., 3: 2033. Direct Link 
13: Tu, Z.G. and G. Xiao, 2005. China's industrial productivity revolution  use stochastic frontier model of production of China's stateowned industrial enterprises total factor productivity growth of decomposition and analysis. J. Political Econ., 3: 4149.
14: Wang, J., X.F. Lei, X.H. Pi and J.J. Qian, 2009. Technical efficiency measurement method review. Coastal Enterprise Sci. Technol., 9: 2831. Direct Link 
15: Xu, X. and S.R. Jeffrey, 1998. Efficiency and technical progress in traditional and modern agriculture: Evidence from rice production in China. Agric. Econo., 18: 157165. CrossRef  Direct Link 
16: Zhang, Z.G., Y. Zhou, C. Qian and D.L. Lai, 2006. Based on our district SFA model of technology innovation efficiency of empirical research. Soft Sci., 2: 125128. Direct Link 
17: Zheng, X.G., 2009. Chinese agricultural technology efficiency and its influence factors. Stat. Decis., 23: 102104. Direct Link 
18: Meeusen, W. and J. van den Broeck, 1977. Efficiency estimation from CobbDouglas production functions with composed error. Int. Econ. Rev., 18: 435444. Direct Link 
19: Aigner, D., C.A.K. Lovell and P. Schmidt, 1977. Formulation and estimation of stochastic frontier production function models. J. Econometrics, 6: 2137. CrossRef  Direct Link 



