2013 International Conference on Management Science & Engineering (20th)
July 17-19, 2013
Harbin, P.R.China
A Spatial Econometric Analysis of County Economic Growth:
A Case Study of 108 Counties in Shandong Province
XIE Hai-jun，WANG Wei
Qingdao Binhai University, P.R.China，266555
Abstract: County is the basic unit of studying
regional economy, and the realization of a coordinating
and harmonious development of county economy would
be much easier if we can clarify and thoroughly
understand the characteristics and key factors of county
economic growth. This thesis first combs the
achievements of spatial economic theories and methods
that gained in recent years in the research of regional
economic growth, describes the characteristics of
economic spatial distribution in the 108 counties in
Shandong province and makes an elaborate analysis of
the spatial relativity of county economy by utilizing
methods like global spatial autocorrelation and local
spatial autocorrelation; and then, based on the fact that
county economy has obvious space correlation, the thesis
makes an spatial econometric analysis of the eleven
factors that affect the county economic growth by
adopting spatial lag model; and at last comes to the
conclusion that the key to the county economic growth
includes industrialization, government investment
leading factor and farmers’ own economic level.
Keywords: county, economic growth, Moran index,
space distribution, spatial autocorrelation, spatial lag
model
1 Introduction
In recent years, as the rapid development of Chinese
economy, the difference of economic growth between
inter-regions and intra-regions is increasingly prominent,
and the problem of regional difference has been a hotspot
that is widely concerned by scholars at home and abroad.
The traditional measurement indexes are Gini coefficient
and Ellison-Glaeser index and so on, but none of these
indexes take mutual effect of economies in adjoining
areas into consideration; spatial autocorrelation is a kind
of spatial statistical method used to describe the
interaction phenomenon in space and this method has
been widely applied to analyze socioeconomic data so as
to explore the spatial pattern and abnormal distribution
of socioeconomic phenomenon[1-3]. Wu Yuming and Xu
Jianhua, et al, analyzed the gathering phenomenon of 31
provincial regional economic growths in China and its
Supported by the Humanities and Social Sciences Research
Program of Shandong Province University of 2009 (J09WH62)
978-1-4799-0474-7/13/$31.00 ©2013 IEEE
influencing factors by utilizing Moran I index and
spatial-temporal model[4]. Lu Feng and Xu Jianhua, et al,
disclosed the spatial autocorrelation between economical
growth level and growth in all provinces and regions
nationally during 1978 and 2001 as well as
comprehended its law of development[5]. Wu Yuming,
Lin Guangping, Long Zhihe and Wu Mei, et al, studied
the convergence problem of provincial regional
economies through adopting spatial econometrics
model[6-7]. Pu Yingxia, Ge Ying and Ma Ronghua, et al,
explored the features and causes of variation trend in
terms of global and local spatial differences in the
regions of Jiangsu province through analyzing the spatial
autocorrelation of regional per capita GDP in Jiangsu
province during 1998 and 2002[8]. The research of spatial
distribution situation of GDP done by Tang Xiaoxu,
Zhang Huaiqing and Liu Rui, et al, disclosed the effect of
regional population and area to the economic growth. All
these analyses that investigated the spatial law of
regional economy are based on the data in different
provinces or in one province nationwide[9]; and there are
many other scholars analyzed the spatial distribution
mode and spatial relevancy relationship of economies in
all provinces and counties by combining the spatial
autocorrelation and the spatial statistical method of
GIS[10-17]. Dai Hezhi and Zhao Xu utilized both single
indicator and multi-index to construct the index of
economy developing level, and further measured the
distribution situation of economic growth level in
Shandong regions[18-19]. Liu Yu, Pan Yuchun and Chen
Yangfen, first of all, constructed an index of
comprehensive developing level, and then utilized ESDA
method to display the distribution situation of county
economy and analyzed the degree of spatial correlation
by adopting Moran I index[20].
These research works analyzed the difference
between different regions or between county regions in
one province from all aspects. However, the research
concerning county economy in Shandong province is not
rich yet, especially in the condition of having spatial
correlation, since it didn’t involve analyzing the
influencing factors of county economic growth. On the
basis of the previous studies, this thesis will study the
spatial distribution features of the economic growth of
the 108 counties in Shandong province by utilizing
spatial statistical method, and make a spatial
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econometrics model analysis of the economic growth
factors. The aim of the thesis is to explain the essence of
county economic growth in Shandong from the aspect of
spatial economy and provide some help for developing a
sustained and steady economy in Shandong regions as
well as narrowing down the developing difference
between regions.
2 Spatial autocorrelation
2.1 Spatial weighted matrix
The purpose of any one element in the spatial
weighted matrix is to define the mutual adjoining
relationship of county space unit so as to place the
relevant attribute data in the geographic space and then
to analyze and compare it more conveniently[21]. Spatial
weighted matrix is a n-element matrix which can be
expressed with Wn×n, and its element is Wij ,which means
the spatial neighborhood relation between region i and
region j, and usually the diagonal element is set as W.
Spatial neighborhood relation is the fundamental
measurement of GIS with adjoining criterion or distance
criterion. According to the adjacent criterion, when
region i and region j adjoins, Wij=1, or else Wij=0;
according to the distance criterion, when the distance
between region i and region j is within the given standard
distance range (d), Wij=1, or else Wij=0.
The matrix shows as following:
w11 w12  w1n
wij =
w21

w22

wm1
wm 2
 w2 n


 wmn
When adopting the adjoining rule，
1 When I and j adjoin
wij = 
0 When I and j disjoint
When adopting the distance rule，
1 When distance between I and j ≤ d
wij = 
0 When the distance between I and j  d
2.2 Global autocorrelation coefficient
I =n/
n
m
∑∑
Wij ×
i =1 j =1
n
m
∑∑
i =1 j =1
( x i − x )( x j − x ) /
n
∑ (x − x)
i
2
(1)
i =1
In (1), Wij is the spatial weighted matrix, Xi is the
per capita GDP, x is the average quantity of per capita
GDP, i=1,2,3, ……, n, j=1,2,3, ……, m, m=n.
2.3 Local spatial autocorrelation
If per capita GDP (x) is regarded as the index of
measuring one county economic growth, then the
computational formula for the local spatial
autocorrelation index Local Moran I index of the
economic growth in central county i is:
m
LMI i = Z i ∑ Wij Z j
In (2), Zi and Zj are respectively the standardized
value of per capita GDP of central county i and the
adjoining county j, which shows the deviation degree
between per capita GDP and mean value in different
counties, i.e. Z i = ( xi − x ) / s, s 2 =
( xi − x ) 2 /(n − 1)
∑
Xi is the per capita GDP of county i, x is the
average value of all county population’s per capita
GDP,Zi and Zj are alike, Wij is the element of spatial
weighted matrix of binary symmetric.
3 Spatial distributions and spatial
autocorrelation analysis of county economy
3.1 Index and data
In the research of the spatial correlation in county
economy, the statistical data of economic attribute, such
as the GDP, per capita GDP, income of fiscal budget, of
every county (city, region), is mainly from Shandong
Statistical Yearbook, Regional Economic Statistical
Yearbook of China, Economic Social Statistical
Yearbook of Chinese Counties (Cities), and the statistic
yearbook officially published by the 17 Prefecture
Statistic Bureau of Shandong. Geographic spatial data,
such as the digital map that divides boundaries of every
city’s administration region, mainly comes from the
1:4,000,000 proportional China County Administration
Boundary Diagram of National Geomantic Center of
China, and of which the building of spatial adjoining
weighted matrix is based on the calculation result of
every cities’ digital map. The sample range includes the
31 county-level cities, 60 counties and 17 municipal
districts in Shandong. (owing to the change of municipal
district data, it is unable to regard every district as an
administrative unit but to combine the municipal districts
and regard them as one administrative unit; this may
affect the reliability of the results, but thanks to the
utilization of the average value in economic index, it
decreased the risk of unreliability; besides, the relation
between Changdao county and its adjoining district is
regarded as an adjoining relation when analyzing since
Chanddao county is an island.)
The selection of time scale is based on the data of
2010 and also refers to partial data of 2005. As for the
data structure, all adopt the ArcView SHP file format,
and the data type includes both basic geographic data
like point, line, face, etc., and the economic attribute data
of every county unit.
3.2 The spatial distribution status of Shandong county
economies
Below, the spatial distribution situation of the
counties’ per capita GDP data is adopted to demonstrate
and reflect the spatial distribution status of Shandong
county economies since per capita GDP can reflect the
regional economic growing level better (Fig.1, Fig.2).
(2)
j =1
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the 108 counties (cities, regions) from Shandong in 2010
as the analyzing target, and adopting the adjacency
relation between Rook and distance to calculate the
Moran index. We can see from the result (Tab.1) that
since the Moran index of the adjacency relation between
the first order rook and the minimum distance is
comparatively big, and through testing, the spatial
weighted matrix will be built with the adjoining relation
between first order rook and the minimum distance in the
analysis of local spatial autocorrelation and spatial
econometric correlation.
Tab.1 Global autocorrelation index and test in 2010
First
Second
Minimum
Double
Program
order
order rook
distance
distance
rook
(cumulative)
Moran
0.4701
0.4378
0.5132
0.3290
Index
Small
0.0000
0.0000
0.0000
0.0000
Probability
Fig.1 Equal-interval spatial distribution
of per capita GDP in 2005
Fig.2 Equal-interval spatial distribution
of per capita GDP in 2010
3.2.1 The county economic growth is extremely
imbalance, and the regional difference is obvious.
Up to the end of 2010, the per capita GDP of the
108 counties (cities, regions) in Shandong is 36589.06
Yuan, and per capital GDP scale of 66 counties (cities,
regions) is under the average level which accounts for
61.11% of the whole province. The lowest per capita
GDP of 7198.95 Yuan is from Heze Municipal District,
while the highest per capita GDP of 116316.28 Yuan is
from Changdao County. The stage head is 109117.33
Yuan which shows the obvious difference of economic
growing level in different counties.
3.2.2 The county economy appears to converges to the
peninsula district
According to the spatial distribution of per capita
GDP in 2005, the Peninsula district (Yantai, Weihai,
Qingdao) and Capital district (Jinan, Zibo) have
comparatively higher per capita GDP, while other places’
are a little lower. Up to 2010, places with higher per
capita GDP gradually converge to the Shandong
Peninsula Region which appears to have the tendency of
piling up in the Blue Economic Zone of peninsula
region.
3.3.2 The spatial-temporal analysis of global spatial
correlation in county economy
Through regarding the per capita GDP of 2005 and
2010 as the analyzing target, respectively adopting the
adjoining relation weighted matrix of first order rook,
second order rook, the minimum distance and double
distance to calculate Moran index. We can see from the
calculating result (Tab.2) that the Moran index value of
county economic spatial autocorrelation in Shandong
province are all greater than 0.3 which means that there
are spatial correlation in higher (lower) regions in terms
of per capita GDP index in the 108 counties (cities,
regions) in Shandong Province. From the perspective of
choosing the two times node of 2005 and 2010, the
Moran index in 2010 are higher than that of 2005; this
demonstrates that as time moves on, the degree of spatial
dependence in Shandong county economies is
strengthening, the economic relationship is much tighter,
and the effect between adjoining counties is deeper.
From the perspective of the Moran index value under the
adjoining weighted matrix of second rook and double
distance, as the expansion of adjoining relation and
adjoining distance, the spatial correlation tends to
weakening which also accords with the first law of
geography[23].
3.3 Spatial correlation analysis of county economy
3.3.1 The selection of spatial weighted matrix
Through utilizing the spatial adjoining weighted
tool given by GeoDa[22], regarding the per capita GDP of
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Tab.2 Global autocorrelation index in different years
Index
First
order
rook
Second
order rook
(cumulative)
Minimum
Distance
Double
Distance
Moran
index in
2005
0.4588
0.3549
0.5111
0.3752
Moran
index in
2010
0.4701
0.4378
0.5132
0.3290
3.3.3 Local spatial autocorrelation analysis of county
economy
We choose the per capita GDP in 2005 and 2010and
analyze the local spatial autocorrelation in two periods;
utilize the GeoDa software to calculate and demonstrate
the scatter diagrams of local spatial autocorrelation
(diagram3, diagram4, diagram5, diagram 6) under the
weighted matrix of first order rook and the minimum
distance. We can see from the scatter diagrams of local
spatial autocorrelation that the economic growth in 2005
mainly gathers in the third quadrant (low-low region)
and then in the first quadrant (high-high region) no
matter for the first order rook adjoining relation or the
minimum distance adjoining relation. By combining with
the map, we can see that these regions are mainly in the
Shandong Peninsula region and the southwest of
Shandong province. And up to 2010, the gathering of
economic growth migrates to the first quadrant
(high-high region), and combining with map, we can
conclude that it migrates from mere Shandong Peninsula
region to the west along the shoreline, i.e. the current
Blue Economic Zone in Shandong; while the low-low
region in the southwest of Shandong province expands
towards east along the provisional boundary. All these
changes form the situation of developing from economic
high-growth region to the inland both in depth and scope.
Fig.5 The scatter diagram of local spatial
autocorrelation in 2005 (minimum distance)
Fig.6 The scatter diagram of local spatial
autocorrelation in 2010 (minimum distance)
4 The spatial econometric analysis of
Shandong county economic growth
Fig.3 The scatter diagram of local spatial
autocorrelation in 2005 (first rook)
Fig.4 The scatter diagram of local spatial
autocorrelation in 2010 (first rook)
4.1 Spatial dependence test
Through adopting the residual Moran index of
expanded spatial regression model[24], as well as two
testing methods of Lagrange Multiplier (LM) and Robust
Lagrange Multiplier that can test spatial lad and spatial
error to verify the spatial effect of economic growth.
According to the Moran index, they are all obviously
greater than zero which means that there are spatial
correlations in county economies. By utilizing the
regression function in the GeoDa software, basing on the
spatial weighted matrix of first order rook and minimum
distance, and according to the result of spatial
dependence test in Tab.3, we comes to the conclusion
that Spatial Lag Model is the most ideal model form,
(LM (lag) is more obvious than LM (error) in statistics)
[25]
.
4.2 Model and variable declaration
4.2.1 Model form
Construct double logarithmic linear spatial lag
model on the basis of the new economic growth theory,
the model form is as following:
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Tab.3 The spatial dependence test of per capita
GDP in Shandong counties
First order rook
Test
MI/DF
Standardized
value
Small probability
P
Moran's I
0.0518
1.5739
0.0155
LM (lag)
1
14.1386
0.0001
R-LM (lag)
1
16.0910
0.0000
LM(error)
1
0.6578
0.4173
R-LM(error)
LM
(SARMA)
1
2.6102
0.1061
2
16.7489
0.0002
Test
Minimum distance
MI/DF
Standardized
value
Small probability
P
Moran's I
0.0274
1.0014
0.0165
LM (lag)
1
7.0248
0.0080
R-LM (lag)
1
8.7360
0.0031
LM(error)
1
0.1668
0.6829
R-LM(error)
LM
(SARMA)
1
1.8779
0.1705
2
8.9028
0.0116
ln AVGDP = β 0 + β 1 ln XCCYRS + β 2 ln CZSR
+ β 3 ln JGDKYE + β 4 ln LSCL + β 5 ln GYZCZ
+ β 6 ln XFPLSE + β 7 ln CK + β 8 ln GDZCTZ
(3)
+ β 9 ln ZXZXRS + β 10 ln NMCSR + D + u
4.2.2 Variable declaration
(1)The performance of county economic growth
Explained variable adopts per capita GDP (Yuan) to
measure the performance difference of county economic
growth, and is expressed with AVGDP.
(2)Labor force
Labor force is measured with employed person
number in rural areas and expressed with XCCYRS. It
mainly measures the effect of rural labor force in the
county economic growth.
(3)Human capital
The thesis adopts the middle-school students
enrollment as the measurement index (the stock of
college student in county is very few), and is expressed
with ZXZXRS.
(4)Savings level
Chooses the loan remaining (ten thousand Yuan) of
every intra-county organization as a substitute scalar of
capital input and is expressed with JGDKYE. It is used
to measure the effect of capital input to county economic
growth.
(5)Fiscal revenue
Fiscal revenue can measure the potential support of
government to the county economic growth, and is
expressed with GYZCZ.
(6)Industrialization
Chooses the total industrial output value (ten
thousand Yuan) that are above a designated scale to
represent the promotion effect of industrialization to the
county economic growth. It is expressed with GYZCZ.
(7)Grain production
County economy, especially the grain production
plays a fundamental role in the sustainable development
of national economy and society in our country. LSCL
represents grain production (ton) and is used to measure
the function and contribution of grain to every county’s
economic growth.
(8)Final consumption
The turnover of consumer goods is used to measure
the influence of consumption to the county economic
growth, and is expressed with XFPLSE.
(9)Fixed-asset investment
The influence of infrastructure construction to the
economy is remarkable. We introduce the fixed-asset
investment (ten thousand Yuan) to measure the influence
of infrastructure construction that built by the
government to the economy. It is expressed with
GDZCTZ.
(10)Export
Shandong is an open and coastal province. In order
to measure the influence of the openness degree to the
county economy, we introduce product value of exports
(ten thousand dollars) to measure the influence of export
to the economy. It is expressed with CK.
(11)Net income of peasants
In the process of county economic growth, the
function of individual’s (peasant household) behavior to
the economic growth cannot be ignored. We introduce
the net income of peasants (Yuan) as one factor that
influences economic growth. It is expressed with
NMCSR.
(12)Area dummy variable
Since the chosen regions have included county, city
and municipal district, and in order to distinguish the
economic growth difference in different administrative
districts, we introduce area dummy variable. We set
county as 1, city and municipal district as 0.
4.3 Analysis of spatial lag model (SLM)
The estimation output of spatial lag model (SLM) is
shown as Tab.4. And we can see that since the analyzing
results made on the basis of both first order rook and
minimum distance spatial weighted are basically the
same, and most variables have passed the significant test.
Different variance Breusch-Pagan test indicates that
model has no different variance anymore; spatial
dependence Likelihood Ratio test indicates that space
possesses the feature of correlation and convergence. The
goodness of fit of the model R2 is above 0.8 and the
global fitting is good.
In the estimation of spatial lad model, CK,
GDZCTZ, and XFPLSE do not pass the significance test
which means that in the county economic growth of
Shandong, export, fix-asset investment and consumption
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do not become the key factors of economic growth.
Tab.4 SLM estimation of the economic
growth factors in Shandong counties
First order rook
Variable
β
Std.E
z-value
P
W_lnAVGDP
0.3017
0.0741
4.0671
0.0000
β0
-0.6042
1.7923
-0.3371
0.7360
lnXCCYRS
-0.1303
0.0542
-2.4033
0.0162
lnCZSR
lnJGDKYE
lnLSCL
0.1925
-0.2410
-0.1249
0.0622
0.0560
0.0344
3.0906
-4.2980
-3.6288
0.0019
0.0000
0.0002
lnGYZCZ
lnXFPLSE
lnCK
0.3767
-0.1711
-0.0402
0.0649
0.1023
0.0271
5.8007
-1.6733
-1.4830
0.0000
0.0942
0.1380
lnGDZCTZ
lnZXZXRS
0.1562
-0.1227
0.0905
0.0524
1.7251
-2.3386
0.0844
0.0193
0.1943
4.7211
0.0760
0.9036
0.8563
DF
VALUE
0.0000
0.3661
lnNMCSR
0.9176
D
0.0686
R2
TEST
Breusch-Pagan
11
Likelihood Ratio
64.1782
0.0000
1
13.027
Minimum distance
Std.E
z-value
0.0003
Variable
β
0.1726
-0.6560
0.0770
1.8791
2.2415
-0.3491
0.0249
0.7269
lnXCCYRS
lnCZSR
lnJGDKYE
-0.1454
0.1633
-0.2477
0.0567
0.0649
0.0586
-2.5611
2.5128
-4.2270
0.0104
0.0119
0.0000
lnLSCL
lnGYZCZ
lnXFPLSE
-0.1353
0.3852
-0.1442
0.0355
0.0680
0.1078
-3.8014
5.6577
-1.3377
0.0001
0.0000
0.1809
lnCK
lnGDZCTZ
lnZXZXRS
lnNMCSR
D
R2
TEST
-0.0323
0.1854
-0.1420
1.0676
0.0785
0.0284
-1.1380
0.0976
1.8999
0.0548
-2.5877
0.1974
5.4058
0.0795
0.9868
0.8427
DF
VALUE
0.2551
0.0574
0.0096
0.0000
0.3237
11
1
64.17821
4.657415
5 Conclusions and suggestion
According to the relevant theoretical hypothesis of
new economic geography and new economic growth, in
the research of county economic growth, the spatial
correlation
between
counties
and
their
mutual-“allied”-type development are of great
importance in promoting the regional economic growth.
The fact that economic growth is affected by its
geographic position indicates that the geographic
spillover effect between counties cannot be ignored to
the economic growth. The thesis makes a beneficial
exploration of Shandong county economic growth which
exactly is based on the spatial heterogeneity. In the
research of economic growth, Shandong region needs to
attach great importance to the input intensity and
orientation of government finance which is very
important to economic growth, and to exert great efforts
on promoting the course of industrialization, and make
full use of industrialization to spur the economic growth
while paying adequate attention to the fundamental status
of agriculture. Adjusting distribution system of the
second salary and making great efforts to enhance the
income level of peasants so as to activate peasants and
rural market has become an important impetus of
economic growth. Without doubt, owing to the limitation
of data, the variables selection and dynamic analysis of
models still leave much space for further explorations.
PROB
W_lnAVGDP
β0
Breusch-Pagan
Likelihood Ratio
boost the county economic growth yet.
In the analysis, there are several important variables
that need to be paid more attention. Spatial lag variable
(W_lnAVGDP), i.e. the promotion function of economic
growth in the adjoining regions is remarkable. This
demonstrates that group development of regional
economy do have advantages. The three indicators of
fiscal revenue (CZSR), industrialization (GYZCZ) and
net income of peasants (NMCSR) all have positive
promotional effect to economic growth; this means that
whether the financial resources and economy of
government enters into the industrialization process or
not, as well as the enhancement of peasantry’s income
are very significant. Besides, area dummy variable
manifests that, in the condition of area, the speed of
economic growth doesn’t rely upon type, county (city,
region), and the economic gap has little relations with
administrative type.
P
PROB
0.0000
0.0309
Although the four variables of XCCYRS, ZXZXRS,
JGDKYEH, and LSCL, etc has passed the significance
test and the employed person number and the human
capital stock do have promotional effect to the economy
according to the economic theory, the estimation
coefficient in the Shandong county economic analysis is
negative. This maybe is caused by two reasons, one is
data error, and the other is that the index data in the vast
county regions of Shandong is on a declining curve
which is opposite to the trend of per capita GDP. This
also, to some degree, shows that these factors do not
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