American Journal of Theoretical and Applied Statistics
Volume 4, Issue 4, July 2015, Pages: 312-316

Spatial Correlation Analysis of 2013 Per capita GDP in the Area of Beijing, Tianjin and Hebei

Renhao Jin, Tao Liu, Fang Yan, Jie Zhu

School of Information, Beijing Wuzi University, Beijing, China

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(Renhao Jin)

To cite this article:

Renhao Jin, Tao Liu, Fang Yan, Jie Zhu. Spatial Correlation Analysis of 2013 Per capita GDP in the Area of Beijing, Tianjin and Hebei. American Journal of Theoretical and Applied Statistics. Vol. 4, No. 4, 2015, pp. 312-316. doi: 10.11648/j.ajtas.20150404.22


Abstract: This paper is based on the Moran's I coefficient and Geary's c coefficient, and with the support of SAS statistical analysis software, using the spatial analysis of Beijing-Tianjin-Hebei’s per capita GDP and Geographical coordinates together. The research results show that the Moran's I coefficient is 0.098, Geary's c coefficient is 0.868, which is showing that there is a positive correlation between Beijing-Tianjin- Hebei region’s city economy. But the degree of correlation is low, which is showing that Beijing-Tianj-Hebei collaborative development is still in the initial stage, and regional economic integration has not fully realized.

Keywords: Regional Economic Integration, Collaborative Development, Spatial Analysis


1. Introduction

There are 28 provinces and 4 municipalities directly under the Central Government in China mainland. Beijing and Tianjin are the two of the four municipalities, and Beijing is also the capital of China. Beijing also is the China capital of politics, economics, and culture, and it offer a lot of opportunities for the People. Beijing has a population of more than 21.15 million, which causes a lot of traffic, pollution and accommodation problems. However, things are a little different in Hebei Provinces, as it is ten times larger than Beijing but its population is only two times more than Beijing. Based on these problems, the central China government is promote a strategy of Regional economic integration on Beijing, Tianjin and Hebei. This paper is to investigate the status of the process of this economic integration.

The 2013 Per capita GDP data of this area and spatial autocorrelation analysis are used to measure the status of economic integration. The GDP is a comprehensive index, which can represent a lot of economic status. Considering the area of Hebei province is relative larger, Per capita GDP is used for analysis. Spatial autocorrelation is the correlation among values of a single variable strictly attributable to their relatively close locational positions. Tobler’s first law of geography encapsulates this situation: ‘‘everything is related to everything else, but near things are more related than distant things.’’ This paper use Moran's I coefficients and Geary's C coefficients to measure the Spatial autocorrelation in the Per capita GDP data for the study area. The definition of these two coefficients are explained below.

Figure 1. The map of Beijing, Tianjin, and Hebei from Google map. The dash area is Hebei Province, and the area included by Hebei and Sea is Beijing and Tianjin, which have same area size.

2. Data Description

The data used in this paper are collected from the website of sohu.com. The county data of Beijing and Tianjin, and city data of Hebei Province are used, which contains per capita GDP and longitude and latitude of the local government site. The whole data are listed in Table 1. As shown in the table, there are 16 counties in Beijing and Tianjin respectively, and 11 cites in Hebei Provinces. The distribution of per capita GDP values are displayed in the boxplot of Figure 2.

Table 1. The 2013 per capita GDP data of Beijing, Tianjin and Hebei with the longitude and latitude data.

Area City/county 2013 per capita GDP (China Yuan) Longitude Latitude
Beijing Xicheng 214888.72 116.372454 39.918191
Dongcheng 172167.22 116.42276 39.934769
Shunyi 135350.97 116.661085 40.136507
Haidian 107130.87 116.309969 39.992281
Chaoyang 102056.76 116.44976 39.92656
Daxing 89256.80 116.348055 39.732472
Shijinshan 56677.02 116.229563 39.911342
Huairou 52460.73 116.638156 40.322312
Fangshan 48514.85 116.149663 39.754185
Fengtai 44576.20 116.292652 39.864803
Miyun 41239.50 116.849711 40.382106
Mengtougou 40990.10 116.10875 39.946234
Pinggu 39928.91 117.12759 40.146966
Tongzhou 37858.22 116.663214 39.91623
Changping 29115.93 116.237897 40.226372
Yanqing 29082.28 115.981706 40.462339
Tianjin Binhai 304240.95 117.71713 39.009822
Heping 202227.43 117.221184 39.123191
Dongli 106618.20 117.320777 39.092262
Xiqing 99185.50 117.015262 39.147496
Beichen 97188.21 117.141985 39.23004
Ninghe 92960.29 117.831069 39.336646
Jinnan 85199.10 117.363487 38.943845
Wuqing 75002.37 117.050707 39.389024
Hexi 70411.77 117.229775 39.115759
Jinghai 66853.93 116.980747 38.953441
Baodi 55797.02 117.316431 39.723239
Nankai 52679.38 117.156626 39.144152
Ji 45804.40 117.414869 40.051473
Hebei 44547.40 117.203344 39.153791
Hedong 33369.21 117.258675 39.135023
Hongqiao 28404.05 117.157216 39.173205
Hebei Tangshan 79365.20 118.186678 39.636637
Shijiazhuang 46828.20 114.521409 38.048234
Langfang 44854.57 116.69041 39.544007
Cangzhou 40571.77 116.845322 38.310336
Qinhuangdao 38681.49 119.608614 39.941588
Chengde 34107.95 117.969493 40.959115
Handan 30827.71 114.545866 36.631195
Zhangjiakou 29974.05 114.892592 40.774341
Hengshui 25090.42 115.676782 37.745031
Baoding 23609.42 115.47105 38.880045
Xingtai 22321.45 114.511441 37.076789

Figure 2. The boxplot of 2013 per capita GDP in Beijing, Tianjin and Hebei.

From the Figure 2, the median per capita GDP of the counties in Tianjin are the highest, and the counterpart of Beijing is in the second place. At the same time, the fluctuations in Tianjin’s GDP data are larger than the remaining two areas. In the Figure 3, spatial distribution of 2013 per capita GDP data of Beijing, Tianjin and Hebei are displayed. Comparing Figure 1 and Figure 3, it can be found that the part with relative larger circles (39<x<40.5 and 116<y<118) are Beijing and Tianjin, and from the spatial distribution the spatial autocorrelations can be seen in the GDP data. The counties around and in Beijing and Tianjin area are tended to large values, while the counties , far away from this area are tended to be small values. To make an accurate inference, Moran's I coefficient and Geary's c coefficient are introduced in the next section.

Figure 3. The spatial distribution of 2013 per capita GDP data of Beijing, Tianjin and Hebei. The size of the circles represents the scale of the per capita GDP values in such counties.

3. Moran's I and Geary's c

The Moran’s I coefficient are defined as

,

and the Geary's c coefficient are calculated as

.

In statistics, Moran's I is a measure of spatial autocorrelation developed by Patrick A.P. Moran. Like autocorrelation, spatial autocorrelation means that adjacent observations of the same phenomenon are correlated. However, autocorrelation is about proximity in time. Spatial autocorrelation is about proximity in (two-dimensional) space. Spatial autocorrelation is more complex than autocorrelation because the correlation is two-dimensional and bi-directional. Negative (positive) values indicate negative (positive) spatial autocorrelation. Values range from −1 (indicating perfect dispersion) to +1 (perfect correlation). A zero values indicates a random spatial pattern. For statistical hypothesis testing, Moran's I values can be transformed to Z-scores in which values greater than 1.96 or smaller than −1.96 indicate spatial autocorrelation that is significant at the 5% level. The Z-scores transformation can be easily written as

.

Geary's C is also a measure of spatial autocorrelation or an attempt to determine if adjacent observations of the same phenomenon are correlated. Geary's C is inversely related to Moran's I, but it is not identical. Moran's I is a measure of global spatial autocorrelation, while Geary's C is more sensitive to local spatial autocorrelation. Geary's C is also known as Geary's contiguity ratio or simply Geary's ratio. The value of Geary's C lies between 0 and 2. 1 means no spatial autocorrelation. Values lower than 1 demonstrate increasing positive spatial autocorrelation, whilst values higher than 1 illustrate increasing negative spatial autocorrelation.

The Moran's I coefficient and Geary's c coefficient are calculated and shown in table 2. It can be seen that the 2013 per capita GDP data in the study area are displayed positive autocorrelation both from Moran's I coefficient and Geary's c coefficient, which means the per capita GDP data in the nearby counties or cities are tended to similar. The p-value of the spatial autocorrelation test are 0.3395 and 0.5725 for Moran's I coefficient and Geary's c coefficients respectively. However, at the same time it is also noticed that only week positive autocorrelation are found in the data, as the Moran's I coefficient are close to 0, and Geary's c coefficient are close to 1.

Table 2. The Moran's I coefficient and Geary's c coefficient are computed from the 2013 per capita GDP in counties or cities in Beijing, Tianjin and Hebei.

Spatial autocorrelation coefficients
Assumption Coefficient Observed Pr > |Z|
Randomization Moran's I 0.098 0.3395
Randomization Geary's C 0.868 0.5725

4. Conclusion

This paper use Moran's I coefficients and Geary's C coefficients to measure the Spatial autocorrelation in the Per capita GDP data for the study area to investigate the status of the process of the region economic integration. Based on the results from Figure 2 and Table 2, it can conclude that only week positive autocorrelation are found in this region, and the Per capita GDP value is high in Beijing and Tianjin area. It can be predicted that the center of region economic integration should be around in Beijing and Tianjin, hopefully it can gradually promote the whole area economics. From the Moran's I coefficient and Geary's c coefficient, it can find that the extent of region economic integration is still low and need more investments to increase the integration extent. Meanwhile, to solve the traffic and population problem in Beijing, the government should make more people and companies move to Hebei area by economic inspiring and better polices.

Acknowledgements

This paper is funded by the project of National Natural Science Fund, Logistics distribution of artificial order picking random process model analysis and research (Project number: 71371033); and funded by intelligent logistics system Beijing Key Laboratory (No.BZ0211); and funded by scientific-research bases---Science & Technology Innovation Platform---Modern logistics information and control technology research (Project number: PXM2015_014214_000001); University Cultivation Fund Project of 2014-Research on Congestion Model and algorithm of picking system in distribution center (0541502703).


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