1. Effect Factors and Evaluation of China’s Per Capita GDP
ZANG Yanning ZHAO Qiang*
School of Mathematical Sciences, Shandong Normal University, P.R.China,
250300
Abstract: According to the National Bureau of Statistics’ data of 2011, China’s GDP has ranked
second of the world by 580.000 million after the United States, but the per capita is only $5,432, the
world 87th, the issue of the low per capita GDP has becoming more and more distinct. The paper centers
on the principal components analysis setting a multivariate linear regression model that focus on the
China’s per capita GDP of recent years. It also analyses the main factors influencing the capita GDP and
gives reasonable suggestions.
Key Words: Principal components analysis, Multivariate linear regression model, Per capita GDP
1 Introduction
With the rapid development in recent years, China’s comprehensive national strength and
international status have improved markedly, and have received extensive attention all over the world.
The per capita GDP, one of the most important indexes to measure both the level and degree of a
country’s development, is the most effective tools to understand and grasp the national macroeconomic
operation not only for China but also in any other countries. Therefore, researches on China’s per capita
GDP are essential to the study of the past achievements as well as the future tend of economic
development.
2 The selection and interpretation of data
2.1The principle of index selection
On the basis of the exiting evaluation system, index selection should be purposeful, practical and
comprehensive specially,
(1) The choice of index must be able to reflect the content of the evaluation, those which have nothing to
do with the evaluation objects should be removed.
(2) The choice of index should be operable, namely meeting the digital measurement.
(3) The selection of index should be covered by contents of the evaluation so as not to appear omissions.
2.2Sources of data
According to the “China Statistical Yearbook 2012” “China Population Statistics Yearbook 2012”
and “China Education Statistical Yearbook 2011”,selecting 8 variables such as investment in fixed
assets, the total import and export volume, total population, state financial education funds and so on.
2.3The selection of the evaluation index
The improvement of per capita GDP is measured by the improvement of national economy and

2. national standard of living. The enchantment of national economy refers to both the growth of the social
investment in fixed assets and the total volume of import and export. The improvement of national
standard of living is based on the increase of total retail sales of consumer goods as well as the
household savings balance at the end of the year. Even the importance of data of populations can not be
missed.These three aspects are absolutely important for the improvement of per capita GDP, so we
select 8 factors included those three factors as variables.
( ) The index of national economy: 1X social investment infixed assets (100 million yuan), 2X total
volume of import and export (million dollar), 5X the tertiary industry population (million)
（ ）The index of people’s standard of living: 3X total retail sales of consumer goods(100 million
yuan), 6X outstanding amount of saving deposit(year-end) (100 million yuan)
( ) The index of population: 4X the total population(year-end) (million people), 7X the city
population (million people)
( ) Investment in education 8X , education investment has a necessary influence on both the strength
and the economics of an country which can not be negative, so the education should be input for a single
variable.
2.4The explanation of variables
( ) Social investment in fixed assets ( 1X ): social investment in fixed assets is also known as the total
social fixed assets investment, which is the main means of social reproduction of fixed assets.
( ) Total volume of import and export ( 2X ): the total volume of import and export refers to the total
amount of the actual China’s gradual import and transit cargo As one of the most important factors
which influencing the economic development of a country, the total volume of import and export plays
an important role in promoting the growth of GDP.
( ) Total retail sales of consumer goods ( 3X ): As the most effective factor reflecting the level of
people’s cultural life during a certain period of time, the total retail sales of consumer goods can fully
represent the scale of social purchasing power.
( ) The total population (year-end)( 4X ): GDP = per capita output(the total of GDP )/total population,
so that the total number of population at the end of the year as an crucial base is essential.
( ) The tertiary industry population ( 5X ): Because of the close relationship between the development
of the tertiary industry and the national economy, the increasing population of the tertiary industry
promotes the acceleration of its development.
( ) Outstanding amount of saving deposit (year-end)( 6X ): Outstanding amount of saving balance
(year-end) reflects the demand tendency of residents of our savings.
( ) City population ( 7X ): City population refers to the population which has a close relationship with
the city development. The growth of the urban population accelerates the rapid development of the
whole city and the city economic.
( ) Investment in education ( 8X ): With the rapid development of science and technology, stronger by
the technology, powerful by talents are gradually in high demand, the input of a country’s education
determines the output of high technical talents.

3. 2.5Deficiencies
( ) Because of the limitation the data, the main factors influencing the per capita GDP can only be
explored from the national level rather than be examined in detail from each area and every working
group. As a result, there may be come limited range or population differences.
( ) Because of the limitation of statistical data of per capita GDP, we do not consider the recessive
population productivity, the real per capita GDP should be slightly lower than the statistical data.
3 Empirical Analysis
3.1The linear stepwise regression model to test variables
Take above 8 variables into the SAS REG auto regressive model, obtained the following data
Table 1 Stepwise Regression Test
Analysis of Variance DF sum of squares mean square F value Pr.>f R-square
Model 6 1380266939 230044490 6858．91 <.0001 0.9998
Error 10 335395 33540
corrected total 16 1380602334
Table 2 Stepwise Regression Test
Parameter estimates parameter estimate Pr>|t| condition index
intercept -58881 <.0001 <.0001
1X 0.07740 <.0001 3.40435
2X 0.04902 <.0001 5.66811
3X -0.00475 0.0033 15.72659
4X 0.69537 <.0001 19.35145
5X -1.30560 <.0001 119.21378
8X 0.00001057 0.0189 939.57733
By observing the data from graph 1 , it is easy to find a general model fitted the data very well
（F=6858.91，p<.0001, 2
R =0.9998）. During the stepwise regression test in graph 2, only six variables
absorbed into the model, and 6X (outstanding amount of saving deposit), 7X (the city population)did
not enter the model, therefore we will eliminate the two variables as the insignificant variable. By
observing the graph 2,
1X (P<.0001), 2X (P<.0001), 3X (P=0.0033), 4X (P<.0001), 5X (P.0001), 8X (P=0.0189) their partial
regression coefficient is not significantly different with zero, and the third condition listed index was
939.5773, far higher than 10. According to the above two clues, we can draw the conclusion that the
data should exist between the correlation. So we use principal component analysis for data processing.
3.2Using principal component analysis to find out the principal component variables
Table 3 Principal Component Analysis
Eigenvalues of the correlation matrix eigenvalue difference proportion cumulative

4. 1 5.00208393 4.20115251 0.8337 0.8337
2 0.80093142 0.069663640 0.1335 0.9672
3 0.10429502 0.04394718 0.0184 0.9846
4 0.06034783 0.03127456 0.0101 0.9946
5 0.02907328 0.02580476 0.0048 0.9995
6 0.00326852 0.0005 1.0000
Table 4 Principal Component Analysis
Eigenvectors 1Z 2Z 3Z 4Z 5Z 6Z
1X 0.434912 0.088945 -.0432303 -.574775 0.526924 0.89656
2X 0.439783 -.040749 0.202459 -.444260 -.714762 0.235985
3X 0.261762 0.898193 0.292811 0.182297 0.074159 -.016136
4X 0.416509 -.354184 0.440184 0.339040 0.359723 0.512800
5X 0.434251 -.241167 0.272925 0.024305 0.072295 -.820341
8X 0.432284 -.008392 -.646634 0.568767 -.267092 0.009478
Observe in graph 3, the first to the accumulated contribution ratio of the third principal components
are 83.37%、96.72%、98.46%, thus we could select the first and the second principal components, we
can draw it according to the graph 4:
1 1 2 3 4 5 80.434912 0.439783 0.261762 0.416509 0.434251 0.432284Z X X X X X X= + + + + +
2 1 2 3 4 5 80.088945 0.40749 0.898193 0.354184 0.241167 0.008392Z X X X X X X= − + − − −
3.3The first two principal components regression model for regression testing
Table 5 On 1Z , 2Z Stepwise Regression Test
Analysis of Variance DF sum of squares mean square F value Pr.>f R-square
Model 2 1345849671 672924836 271.09 <.0001 0.9748
Error 14 34752662 2482333
corrected total 16 1380602334
Table 6 On 1Z , 2Z Stepwise Regression Test
Parameter estimates Parameter estimate Pr>|t| Pr>|t|
Intercept 14435 <.0001 0
1Z 4099.92378 <.0001 0.98714
2Z 204.99378 0.6485 0.01975
The observed results of hypothesis testing is general model (graph 5)found that the model fits the data
（F=271.09，P<.0001, 2
R =0.9748）, according to the graph 6 there is no significant differences of 1Z （P<.0001）
and there are significant differences of 2Z (P=0.6485),linear regression equations can be obtained in the main
component of Y is, 114435 4099.92378Y Z= +
We will express principal component 1Z into the regression model, and obtained a linear regression model by

5. the dependent variable Y and the standard argument 1X , 2X , 3X , 4X , 5X , 8X ,
1 2 3 4 5 814435 1783.10605 1803.07678 1073.02469 1707.65515 1780.39600 1772.33145Y X X X X X X= + + + + + +
Finally, we will be standard variables into the original variables, get the primitive variables model of the dependent
variable Y,
1 2 3 4 5 860238.98 0.01959 0.02537 0.0178 0.40653 0.55183 0.00042Y X X X X X X= − + + + + + +
Through the observation of the model, it is easy for us to find the correlation coefficients of 8X is not in the
same level as other variables. As 8X is a special variable which must be introduced to other national policy factor,
and we will explore in great depth in the following passages.
3.4Analysis of influence of variables on the dependent variable
Viewing the obtained model, we conclude the correlation coefficients of per GDP and six variables,
the correlation coefficients are 0.01959、0.02537、0.0178、0.40653、0.55183、0.000042. Obviously 5X
(the tertiary industry population) has the greatest impact, 4X (the total population(year-end)) followed,
and 1X (social investment fixed assets), 2X (total volume of import and export), 3X (total retail sales
of consumer goods), influence of these three factors on the variable of per capita GDP is consistent. The
variable 8X (investment in education) has feeble influence on per capita GDP.
We will analyze these three factors in details in following passages,
( ) The tertiary industry population 5X , as the main industry to promote the development of the
national economy, has a far-reaching effect on the contribution of GDP.A correlation coefficient of
0.40653 also reveals its powerful driving force for promoting China’s per capita GDP. “Classification of
National Economic Industries”, classified the tertiary industry into 47 categories which is the largest
industrial classification of three main industries. Not only it provides the society with not more
employment opportunities, but also provides the development of the national economy with abundant
labor productivity. Since the reform and opening up, the development of the tertiary industry has
attracted government’s great attention, along with the adjustment and optimization of industrial results
are constantly growing. After entered the twenty- first century, the tertiary industry does benefit the first
and second industry ,and showed its advantages gradually. The lift of population in tertiary industry
certainly provides rich resources for the development of per capita GDP.
( ) The total population (year-end) 4X plays a crucial role in the development of per capita GDP.As a
country with the largest population in the world, high growth of population in China have certain
constraints on the improvement of per capita GDP. On the other hand, the increasing of total population
will provide more labor for the society, which means the society would gain more productivity.
( ) Investment in fixed assets is the volume of activities constructing and purchasing the fixed assets in
money form. In the model, effects of social investment in fixed assets of the average GDP is 0.01959,
including private investment, foreign investment regional group investment and state-owned
investment, supplement each other between the four, which seems to have the investment and
state-owned investment occupied high proportion. Privatization is conductive to the development of
enterprises, do better to improve the ability of competition and development, so that it can make a
contribution to the progress of the national economy.

6. ( ) Since 1990’s, as an important source of national economy, import and export began to show its
leading position in China’s economic stage. The component has been beyond the primary products at
first in the total import and export industrial manufactured goods, but a variety of industrial
manufactured goods export in China, the defects as low technical content, weak deep processing and
added value, which still restricts China’s foreign economic and trade development.
( ) Total retail sales of social consumer goods is a response to our people’s living standards, its
improvement is also a behalf of quality of life of the Chinese people’s lift, which obviously reflects by
the Chinese people’s consumption capacity. According to the Chinese tradition thrift, many people still
prefer saving ways to hedge, and we need to change it by improve the people’s consumption
consciousness, enhancing their purchasing power and stimulating domestic demand, which is advocated
by the government for raising national economic.
( ) The correlation coefficient of education investment is 0.00042, this result do not seem consistent
with common sense. Firstly, considering the situation of our country, education investments could
restrict each other with the GDP. According to the policy of our government, it made an announcement
in 1995 that a year of education investment budget must be based on last year’s GDP, and it can not be
lower than 0.04. According to the circumstances, the actual figures never up to 0.025, so it is difficult
for the correlation coefficient of 8X in the same level with others. Secondly, in this paper we are
discussing about the per capita GDP of China, because of the large population base, the impact on the
per capita GDP is negligible though we can’t ignore it. Chinese government has already promoted the
budgets for the economic backward area, which could make contributions to local GDP. Considering the
actual situation, it will take years to equalize the distribution of resources throughout the country in few
years. When comes to the per capita GDP which has a crucial relationship with population and
geographical position, it is difficult for us to get an accurate and equalization digital of it.
4 Improvement and suggestion
( ) The population of the tertiary industry is one of the main factors when considering the per capita
GDP, we suggest the government should have further and deepen attention on it. Measures like provide
favorable welfare for high-quality personnel and technical personnel, in order to attract more talents and
technology into the tertiary industry chain, so as to bring abundant resources and labors, even drive the
tertiary industry and national economic development.
( ) In the social investment in fixed assets, it is in rush time for our government to strengthen the power
to control the scale of investment in fixed assets, and prevent unreasonable excessive growth of it, in
order to promote the rational development of fixed assets. For instance, we can increase the fixed
investment in backward area, driving the development of regional economy, and promoting the
extension of the national economic, even have an effective function on easing the regional disparity
between the rich and the poor.
( ) On the aspect of import and export trade, there is an urgent demand in constructing a new structure
of import and export trade, by the way of accelerating technological progress in export industries,

7. aiming to improve the position of exports in the international market. By improving the investment cost
to gain a favorable development space for the domestic part of the market in order to protect our
national enterprises, while encouraging national enterprises to the world, enlarge the export volume by
expanding the overseas’ market.
( ) Increase the investment education, such as the extension of compulsory education, the creation of
more high-quality talents for the society, the establishment of a more scientific and enough research
fund, even the supplement of advanced research conditions for talents in a certain field. By these
measures, talented people can make contribution to the future development of China’s economy.
5 Conclusion
Along with the economic strength and the enhancement of comprehensive national strength,
China’s GDP showed a rising trend in 2010 to $ 5.88 trillion, ranking second in the world. As a result of
a large amount of population, per capita GDP placed 87 in the world far from other countries. As an
important indicator of a nation’s living standard, it is imminent for China to improve the per capita GDP.
The gap between rich and poor, regional detachment even other factors seriously affect China’s per
capita GDP. Therefore, by increasing social capita investment, encouraging national enterprises to
foreign development and using strategies of rejuvenating the country through science and education. In
order to promote the balanced development in economics of our country, further more benefiting the per
capita GDP so as to improve the living standards of residents, in this way could truly constructing a
harmonious society even a harmonious China.
References
[1]Gao Huixuan，Applied multivariate statistical analysis，2005：01
[2] National Bureau of Statistics，《2012 China statistical yearbook 》[M].Beijing：Chinese Statistics
Press，2012
[3] National Bureau of Statistics，《2012 China Demographic Yearbook》[M]. Beijing：Chinese Statistics
Press，2012
[4] National Bureau of Statistics，《2011 Chinese education statistical yearbook》[M]. Beijing：Chinese
Statistics Press，2010
Author in brief:
Zhao Qiang, Corresponding author, Associate Professor, mainly engaged in Bayesian networks, causal
inference, graphical models and statistical computing. E-mail: zhaoqstat@126.com.
Acknowledgement:
This research was supported by NSFC(11001155) and A Project of Shandong Province Higher
Educational Science and Technology Program(J11LA08).