Download Research on Affecting Savings Deposits of Urban and Rural Residents

Research on Affecting Savings Deposits of Urban and Rural Residents
Based on Factor Analysis
ZHANG Jilin, CAI Jing
Department of Mathematic and Physics, Fujian University of Technology, Fuzhou, P.R.C., 350108
[email protected]
Abstract: An effective and simple parameter estimating method—Factor Analysis method, for savings
deposits of urban and rural residents model is proposed in this paper. As is known to all of us, there are
many factors influencing savings deposits. The essential purpose of factor analysis is to describe, if
possible, the covariance relationships among many variables in terms of a few underlying, but
unobservable, random quantities called factors. This essay uses the method receiving two unrelated
common factors which contain the whole information of five original elements. Therefore, we get the
principal component deposit model. Through test, the new model could be proved to be accurate.
Moreover the principal component deposit model has fairly good analysis result. In the end, this new
model is applied to Chinese resident deposit forecasting based on the statistic data. From the comparison
between new forecasting data and the statistic data, we could conclude that the main factor deposit
model is a quite effective and simple method for forecasting Resident Deposit.
Keywords: Factor analysis, Resident deposit, Principal component deposit model, Relation
1. Introduction
Currently, there have been many people doing the research about defining variable factors of savings
deposits of urban and rural residents. Deaton (1991) and Carroll (1992, 1997) presented the buffering
Savings deposits and so on. Obviously, economic growth,income,interest rate, age structure of
population, inflation, wealth, savings from abroad, the social security system, spending habits and other
factors all will affect the savings deposits of urban and rural residents.
The key of create deposits model is factor selection. However, there exist too many factors to be
considered, at the same time, we can not decide which ones play important parts in this model. Suppose
m
the number of factors is n and the real number this model need is m, we will get C n kinds of
combination. In the end, we should find out the best one. Frankly, it needs great computational costs. A
principle component analysis is concerned with explaining the variance-covariance structure of a set of
variables through a few linear combinations of these variables. Its general objectives are data reduction
and interpretation. Although k components are required to reproduce the total system variability, often
much of this variability can be accounted for by a small number m of the principle components. If so,
there is almost as much as information in the m components as there is in the original k components.
The m principle components can then replace the initial k variables, and the original data set, consisting
of n measurements on k variables, is reduced to a data set consisting of n measurements on m principal
components. An analysis of principal components often reveals relationships that were not previously
suspected and thereby allows interpretations that would not ordinarily results.
Therefore, in this paper, we uses the principal component analysis method to carry on the factor analysis
on possible factors influencing savings deposits of urban and rural residents.

2. Factor Combination
After summarizing the related research work, we hold that savings deposits model at least need 3
different kinds of factors: a business activities indicator interest rate and composition of population. In
this situation, this essay put GDP, exchange rate of RMB to US dollar, worker average wage, household
，
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consumption and the population as the original 5 components, basing on the relevant statistical data of
Statistics Yearbook during 1978-2007 of China, to do the factor analysis.
2.1 Linear correlation of the original components
In this paper, we use KMO (Kaiser-Meyer-Olkin) test and Bartlett examination (as shown in the table1).
KMO statistic value is 0.704, greater than 0.6. According to standard of statistician Kaiser, the principle
components are fit for factor analysis. Bartlett test value is 225.269; asymp.sig is 0.000, less than the
remarkable level 0.05, so the principle components are fit for factor analysis.
GDP
GDP 
exchange rate 
average wage 

household consumption 
population 
exchange rate
wage consumption population
1.000
0.578
0.996
0.993
0.578
0.996
1.000
0.527
0.527
1.000
0.650
0.983
0.993
0.894
0.650
0.827
0.983
0.827
1.000
0.930
Table 1 KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy.
Bartlett's Test of Sphericity
Approx. Chi-Square
---------
df
Sig.
0.894

0.827
0.827

0.930
1.000
704
225 269
10
000
2.2 Principal components
2.2.1 The number of principal components
A useful visual aid to determining an appropriate number of principal components is a scree plot.
Figure1 shows a scree plot, for a situation with five principal components. An elbow occurs in the
figure1 at about i=3. That is, the eigenvalues after the second factor are all relatively small and about the
same size. In this case, it appears, without any other evidence, that two sample principal components
effectively summarize the total sample variance.
2.2.2 Summarizing sample variation
In table2, the first principal component explains 86.69% of the total sample variance. The first two
principal components, collectively, explain 99.102
of the total sample variance. Consequently,
sample variation is summarized very well by two principal components and a reduction in the data from
12 observations on 5 observations to 12 observations on 2 principal components is reasonable.
2.2.3 Factor rotation
The rationale is very much akin to sharpening the focus of a microscope in order to see the detail more
clearly. According to the scree plot, this paper makes two principal components to describe the whole
information influencing savings deposits of urban and rural residents. Their eigenvalue are 8.744
1.348 0.729 and 0.126. These four components explain a proportion 99.522
of the total population
variance. Especially, the first principal component explains a proportion 79.49% of the total population
variance.
After factor rotation, the eigenvalue are 3.246 and 1.709, explaining a proportion 64.914 and 34.188
of the total population variance, making a total of 99.102
information of five original
components. Therefore, that two sample principal components effectively summarize the total sample
variance.
％
、
、
％
％
％
805
％
Compo
nent
Initial Eigenvalues
Total
1
2
3
4
5
Figure 1
Table 2
Extraction Sums
Loadings
4
621
039
005
001
% of
Variance
8
12.412
7.78
102
0.18
of
Squared
Rotation Sums of Squared
Loadings
Cumulat
Total
% of
Cumul
Total
% of
Cumul
86
99.102
99.880
99.982
100.000
4
621
8
12.412
86
99.102
3
1.709
6
34.188
6
99.102
2.3 Renamed the principal components through Component Matrix(a) and Rotated Component
Matrix(a)
It can be seen from Table 4 that, before factor rotation, except for exchange rate, GDP, average wage,
household consumption and the population these 4 original components, which represent a country’s
economic situation, contribute lots to the first principal component. Their values are all above 0.95. On
the other hand, GDP, average wage and household consumption have reverse correlation with the
second principal component. And, exchange rate and the population are correlated positively with the
second principal component. This includes the value of exchange rate is as far as 0.654, others are all
less than 0.3. Obviously, two original principal components contain some same information, which is no
good for us to find out the different meanings of different principal factor. Therefore, the factors must be
rotated.
Base on variance maximization, we rotate the Component Matrix. After rotation, each principal
component has a relatively clear economic implications, according to table 4 and figure 2. The first
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rotated principal component mainly reflects GDP, average wage, household consumption and the
population, which represent a country’s economic situation. The second rotated principal component
mainly reflects variation about exchange rate. Basically, each original indicator variables has been
attributed to one rotated principal component. Can be said that the effect of rotation is still good.
It can be seen that savings deposits of urban and rural residents is not only mainly related to the level of
country's overall economy, but also relevant to exchange rate of RMB to US dollar. Statistical analysis
indicated that two rotated principal components are N (0, 1) random variables and completely irrelevant.
So, they are very suitable as factors in savings deposits model.
Table 3 Component Matrix (a)
Component
1
970
752
954
988
971
GDP
exchange rate
average wage
household consumption
population
2
-237
654
-296
-145
168
C omponent Plot in Rotated Space
汇率
1.0
人口总数
C omponent 2
0.5
消费水平
GDP
职工平均工资
0.0
-0.5
-1.0
-1.0
-0.5
0.0
0.5
Component 1
Figure 2
GDP
Table 4
Rotated Component Matrix(a)
Component
1
2
944
326
807
1.0
exchange rate
average wage
household consumption
population
278
962
909
726
957
268
413
667
3. Construction and Inspection of Savings Deposits Model
3.1Construction of savings deposits model
By the analysis, we define country's overall economy situation and exchange rate as two new principal
components. And through factor scores, we achieve the values of two common factors, using the
original 5 components statistical data of Statistics Yearbook during 1978-2007 of China.
Given the two principal components as y1 and y2, and zxi as standardized observation.
The factor scores is
：
f1 = 0.944 zx1 + 0.278 zx2 + 0.962 zx3 + 0.909 zx4 + 0.726 zx5
（）
f 2 = 0.326 zx1 + 0.957 zx2 + 0.268 zx3 + 0.413zx4 + 0.667 zx5
1
Then, do stepwise linear regression analysis between the two principal components and the dependent
variable savings deposits of urban and rural residents.
The composite factor score is
：
y = 0.958 f1 + 0.275 f 2
：
Based on the above foundation, construct the principal component deposit mode
y =0.958f1 +0.275f2
（2）
=0.958(0.944zx1 +0.278zx2 +0.962zx3 +0.909zx4 +0.726zx5)+0.275(0.326zx1 +0.957zx2 +0.268zx3 +0.413zx4 +0.667zx5)
=0.994zx1 +0.534zx2 +0.995zx3 +0.984zx4 +0.879zx5
（）
3
In (3), we can find that in one hand, the sensitivity of savings deposits of urban and rural residents y to
the five factors, GDP, exchange rate, average wage, household consumption and the population, are
positive. On the other hand, the weighting of different factors is different. Comparing other four factors,
the exchange rate smallest relatives to the weight of the principal component deposit mode, that is, the
adjustment of the exchange rate change will not largely impact on the savings deposits of urban and
rural residents
3.2 Inspection of savings deposits model
Model
1
Model
1
R
.996(a)
Regression
Residual
Total
Table 5
R Square
.993
Model Summary (b)
Adjusted R Square
.992
Std. Error of the
Estimate
4903.88294
Table 6 ANOVA (b)
Sum of Squares
df
Mean Square
51444447616.331
2
25722223808.166
384769086.471
16
24048067.904
51829216702
18
808
Durbin-Watson
1.423
F
1069.617
Sig.
.000(a)
From Table 5 and Table 6 we can see that the regression equation fit better, and there is a significant
linear relationship. The last one DW = 1.423 in table 5 shows residual has no correlation properties
Unstandardized
Coefficients
Table 7 Coefficients (a)
Standardized
Coefficients
Collinearity Statistics
Modle
Sig
t
1(Constant)
REGRfactorscoe1
for analysis 1
REGRfactorsce 2
for analysis
B
Std. Error
64068.868
1125.028
51381.063
1155.856
14765.204
1155.856
Beta
Tolerance
VIF
56.949
0
.958
44.453
0
1.000
1.000
.958
12.774
0
1.000
1.000
From table 7, we get the fitting regression equation:
y = 0.958 f1 + 0.275 f 2
y represents savings deposits and f1 , f 2 , represent two principal components. Each independent
variable and dependent variable has a significant linear relationship. The last two columns we can see
from the table show variables without collinearity.
According foregoing analysis, we can believe the principal component deposit model gained by factor
analysis is accurate.
4. Conclusion
In this paper, we introduce the factor analysis to integrate and simplify five components GDP, exchange
rate of RMB to US dollar, worker average wage, household consumption and the population, and extract
2 common factors with a clear significance of economy, respectively, reflecting the role of the country's
overall economic level and exchange rate. Relevant statistical analysis shows that these 2 common
factors are very effective. This essay constructs and inspects the principal component deposit model
using two rotated principal components. Inspection shows that this essay constructs the principal
component deposit model through screening for factor based on factor analysis has a good analysis of
results.
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