重庆市城乡居民储蓄存款的计量模型分析_经济学毕业论文
发布时间：2015-04-17
来源：人大经济论坛
重庆市城乡居民储蓄存款的计量模型分析_经济学毕业论文
重庆市城乡居民储蓄存款的计量模型分析
选题及选题的目的和意义
我们小组选定的分析对象是重庆市城乡居民储蓄存款，研究的目的在于通过对多个影响因素的分析，最终得出影响重庆市居民储蓄存款的主要因素是什么，它们分别对储蓄存款是如何影响的，以及影响的程度是怎样的，从而对我国制定宏观经济政策起一定的指导作用。
计量模型分析
理论陈述
我们把重庆市储蓄存款年末余额作为模型的应变量，把可能影响到其变化的8个因素：储蓄存款年增长率、人均储蓄存款余额、城镇居民人均可支配收入、农村人均纯收入、国内生产总值（GDP）、GDP边际储蓄倾向、消费物价比上年上涨率（通货膨胀率）、实际利率分别作为X1、X2、X3、X4、X5、X6、X7、X8。我们取得1986年到2000年的数据（其中利率为1990年到2000年）见表1。
表1
OBSYX1X2X3X4X5X6X7X8
198625.2935.6179987.45358.86169.80.364.2NA
198732.64290.0055871113.61385.82189.680.349.8NA
198836.1810.841791281.77457.54239.110.0722.7NA
198948.8835.10.0055871452.66510.09277.270.3317.1 NA
199067.3137.71791695.78586.73298.410.871.46.64
199188.18310.0055871894.46628.89339.810.570.56
1992111.6826.71792200.8677.46417.870.311.2-4.64
1993158.7442.10.0055872785748.08549.790.3618.7-7.72
1994214.22351793645.971018.24751.210.2829.7-18.72
1995304.5124.20.0055874391.51270.411009.470.3519.4-8.42
1996503.3565.31795042.241479.051179.091.179.7-2.23
1997581.315.50.0055875322.61692.3613500.463.32.37
1998724.5424.61795466.881810.171429.261.81-3.67.38
1999909.125.529595895.971835.541479.713.7-0.72.95
20001085.319.435226275.981892.441589.341.6-3.25.45
模型设定
我们初步设模型为Y=C+α1X1+α2X2+α3X3+α4X4+α5X5+α6X6+α7X7+α8X8，对该模型进行回归，结果见表2。
表2
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:26
Sample(adjusted): 1990 2000
Included observations: 11 after adjusting endpoints
VariableCoefficientStd. Errort-StatisticProb.
X15.4694721.8381572.9755190.0968
X20.1583590.0328444.8215120.0404
X3-0.9315070.331858-2.8069440.1069
X40.1977660.4620520.4280170.7103
X53.5684531.0898733.2741930.0820
X6-44.6936320.48663-2.1816000.1609
X70.95667910.398000.0920060.9351
X8-8.2702899.452063-0.8749720.4739
C340.0799183.53621.8529310.2051
R-squared0.999032 Mean dependent var431.6573
Adjusted R-squared0.995160 S.D. dependent var354.9019
S.E. of regression24.68950 Akaike info criterion9.182249
Sum squared resid1219.143 Schwarz criterion9.507799
Log likelihood-41.50237 F-statistic258.0367
Durbin-Watson stat3.244507 Prob(F-statistic)0.003866
分析表2，发现X3、X6、X7、X8的符号与先验符号相反，不符合经济意义。所有解释变量的T值均不显著，但可决系数很高，说明某几个解释变量间存在严重的多重共线性。故应做Y对8个解释变量的分别回归。结果见表3到表10（其中X8的样本为1990年到2000年）
表3
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:33
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X1-4.9646317.430933-0.6681030.5158
C477.5158244.74911.9510420.0729
R-squared0.033196 Mean dependent var326.0813
Adjusted R-squared-0.041174 S.D. dependent var350.4721
S.E. of regression357.6144 Akaike info criterion14.72035
Sum squared resid1662545. Schwarz criterion14.81476
Log likelihood-108.4027 F-statistic0.446362
Durbin-Watson stat0.197003 Prob(F-statistic)0.515755
表4
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:36
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X20.2466960.0540574.5635980.0005
C198.884264.544403.0813550.0088
R-squared0.615685 Mean dependent var326.0813
Adjusted R-squared0.586122 S.D. dependent var350.4721
S.E. of regression225.4703 Akaike info criterion13.79782
Sum squared resid660879.3 Schwarz criterion13.89223
Log likelihood-101.4836 F-statistic20.82642
Durbin-Watson stat0.515496 Prob(F-statistic)0.000532
表5
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:36
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X30.1700540.0173679.7916500.0000
C-234.560365.81286-3.5640500.0035
R-squared0.880599 Mean dependent var326.0813
Adjusted R-squared0.871414 S.D. dependent var350.4721
S.E. of regression125.6755 Akaike info criterion12.62885
Sum squared resid205326.2 Schwarz criterion12.72326
Log likelihood-92.71637 F-statistic95.87641
Durbin-Watson stat0.304992 Prob(F-statistic)0.000000
表6
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:40
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X40.5745520.05109711.244260.0000
C-261.941559.64064-4.3919960.0007
R-squared0.906765 Mean dependent var326.0813
Adjusted R-squared0.899594 S.D. dependent var350.4721
S.E. of regression111.0540 Akaike info criterion12.38148
Sum squared resid160328.8 Schwarz criterion12.47588
Log likelihood-90.86107 F-statistic126.4333
Durbin-Watson stat0.491931 Prob(F-statistic)0.000000
表7
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:41
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X50.6286280.05425211.587190.0000
C-146.220349.39553-2.9601930.0111
R-squared0.911723 Mean dependent var326.0813
Adjusted R-squared0.904932 S.D. dependent var350.4721
S.E. of regression108.0614 Akaike info criterion12.32684
Sum squared resid151804.6 Schwarz criterion12.42125
Log likelihood-90.45132 F-statistic134.2629
Durbin-Watson stat0.435621 Prob(F-statistic)0.000000
表8
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:41
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X6287.792465.048424.4242790.0007
C86.2543780.360481.0733430.3026
R-squared0.600912 Mean dependent var326.0813
Adjusted R-squared0.570213 S.D. dependent var350.4721
S.E. of regression229.7631 Akaike info criterion13.83554
Sum squared resid686284.0 Schwarz criterion13.92995
Log likelihood-101.7666 F-statistic19.57424
Durbin-Watson stat1.375241 Prob(F-statistic)0.000686
表9
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:42
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X7-20.337137.917007-2.5687910.0233
C524.9785108.83304.8237080.0003
R-squared0.336690 Mean dependent var326.0813
Adjusted R-squared0.285666 S.D. dependent var350.4721
S.E. of regression296.2129 Akaike info criterion14.34360
Sum squared resid1140647. Schwarz criterion14.43801
Log likelihood-105.5770 F-statistic6.598685
Durbin-Watson stat0.373405 Prob(F-statistic)0.023347
表10
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:42
Sample(adjusted): 1990 2000
Included observations: 11 after adjusting endpoints
VariableCoefficientStd. Errort-StatisticProb.
X821.4848113.126231.6367840.1361
C463.6501100.92744.5938970.0013
R-squared0.229390 Mean dependent var431.6573
Adjusted R-squared0.143767 S.D. dependent var354.9019
S.E. of regression328.4009 Akaike info criterion14.58931
Sum squared resid970624.5 Schwarz criterion14.66166
Log likelihood-78.24122 F-statistic2.679062
Durbin-Watson stat0.263408 Prob(F-statistic)0.136103
分析以上结果，X1、X2的符号与先验符号不相符，故剔除。X8的T值不显著，X7的T值虽然显著，但可决系数太低，都予以剔除。比较X3、X4、X5、X6的的回归结果，发现X5最佳。故以X5作为第一个解释变量引入模型，逐个加入X3到X8进行回归。回归结果见表11到表15。
表11
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:49
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X3-0.2473170.148290-1.6677960.1212
X51.5231130.5387352.8272010.0153
C-2.90026897.62408-0.0297090.9768
R-squared0.928334 Mean dependent var326.0813
Adjusted R-squared0.916390 S.D. dependent var350.4721
S.E. of regression101.3404 Akaike info criterion12.25170
Sum squared resid123238.5 Schwarz criterion12.39331
Log likelihood-88.88777 F-statistic77.72205
Durbin-Watson stat0.828045 Prob(F-statistic)0.000000
表12
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:51
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X4-0.1373610.851677-0.1612830.8746
X50.7782320.9292990.8374400.4187
C-118.0392182.1215-0.6481340.5291
R-squared0.911913 Mean dependent var326.0813
Adjusted R-squared0.897232 S.D. dependent var350.4721
S.E. of regression112.3522 Akaike info criterion12.45801
Sum squared resid151476.2 Schwarz criterion12.59962
Log likelihood-90.43508 F-statistic62.11483
Durbin-Watson stat0.429695 Prob(F-statistic)0.000000
表13
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 21:51
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X50.5227380.0620578.4235370.0000
X688.1814934.994622.5198590.0269
C-140.147641.64600-3.3652110.0056
R-squared0.942270 Mean dependent var326.0813
Adjusted R-squared0.932648 S.D. dependent var350.4721
S.E. of regression90.95532 Akaike info criterion12.03547
Sum squared resid99274.44 Schwarz criterion12.17708
Log likelihood-87.26603 F-statistic97.93186
Durbin-Watson stat1.063634 Prob(F-statistic)0.000000
表14
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 22:32
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
X50.5719570.05127911.153760.0000
X7-6.7721602.729948-2.4806920.0289
C-37.4107260.59009-0.6174400.5485
R-squared0.941647 Mean dependent var326.0813
Adjusted R-squared0.931922 S.D. dependent var350.4721
S.E. of regression91.44465 Akaike info criterion12.04620
Sum squared resid100345.5 Schwarz criterion12.18781
Log likelihood-87.34651 F-statistic96.82253
Durbin-Watson stat0.831580 Prob(F-statistic)0.000000
表15
Dependent Variable: Y
Method: Least Squares
Date: 12/11/03 Time: 22:34
Sample(adjusted): 1990 2000
Included observations: 11 after adjusting endpoints
VariableCoefficientStd. Errort-StatisticProb.
X50.6390920.0746628.5597960.0000
X88.1617834.6371521.7600850.1164
C-160.070880.23437-1.9950400.0811
R-squared0.924143 Mean dependent var431.6573
Adjusted R-squared0.905179 S.D. dependent var354.9019
S.E. of regression109.2849 Akaike info criterion12.45279
Sum squared resid95545.53 Schwarz criterion12.56131
Log likelihood-65.49037 F-statistic48.73104
Durbin-Watson stat0.834345 Prob(F-statistic)0.000033
分析以上结果，X3与X5、X4与X5存在共线性，其系数矩阵见表16、表17。
表16
X3 X5
1.000000 0.995531
0.995531 1.000000
表17
X4 X5
1.000000 0.998156
0.998156 1.000000
再看X5与X6，X5与X7，X5与X8，发现X6，X7，X8的T值都不显著，应剔除，所以模型中只含有解释变量X5，所以模型重新设定为Y=C+αX5
参数估计
Y对X5的回归结果见表7，估计参数为Y=-146.2203+0.628628X5
模型的各种检验
共线性检验
由于方程只含有一个解释变量，所以不存在共线性问题。
自相关检验
查德宾——沃林D统计量表，N=15，K′=1，得到DL=1.077，DU=1.361，4-DU=2.639，4-DL=2.923，DW=0.435621，即DWDL，所以存在正自相关。利用对数线形回归修正正自相关，得到表18。
表18
Dependent Variable: LY
Method: Least Squares
Date: 12/11/03 Time: 22:39
Sample: 1986 2000
Included observations: 15
VariableCoefficientStd. Errort-StatisticProb.
LX51.5749850.05302729.701570.0000
C-4.8712500.338780-14.378810.0000
R-squared0.985478 Mean dependent var5.115019
Adjusted R-squared0.984361 S.D. dependent var1.287252
S.E. of regression0.160980 Akaike info criterion-0.691509
Sum squared resid0.336889 Schwarz criterion-0.597102
Log likelihood7.186316 F-statistic882.1831
Durbin-Watson stat0.926220 Prob(F-statistic)0.000000
同时考虑Cochrane-Orcutt迭代法，得到结果见表19。
表19
Dependent Variable: LY
Method: Least Squares
Date: 12/11/03 Time: 22:42
Sample(adjusted): 1987 2000
Included observations: 14 after adjusting endpoints
Convergence achieved after 12 iterations
VariableCoefficientStd. Errort-StatisticProb.
C-4.8455430.844517-5.7376480.0001
LX51.5741110.12740812.354910.0000
AR(1)0.5535390.2988141.8524530.0910
R-squared0.986887 Mean dependent var5.249634
Adjusted R-squared0.984502 S.D. dependent var1.221374
S.E. of regression0.152048 Akaike info criterion-0.741831
Sum squared resid0.254305 Schwarz criterion-0.604890
Log likelihood8.192819 F-statistic413.9197
Durbin-Watson stat1.552650 Prob(F-statistic)0.000000
Inverted AR Roots .55
DW值为1.552650，不存在自相关。所以模型修正为
LOGY=-4.845543+1.574111LOGX5
异方差检验
由于为小样本，故不能使用White检验，应使用ARCH检验，选择滞后1期。结果见表20。
表20
ARCH Test:
F-statistic0.026194 Probability0.874121
Obs*R-squared0.030493 Probability0.861376
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 12/11/03 Time: 22:46
Sample(adjusted): 1987 2000
Included observations: 14 after adjusting endpoints
VariableCoefficientStd. Errort-StatisticProb.
C0.0230670.0095622.4124060.0328
RESID^2(-1)0.0502180.3102840.1618450.8741
R-squared0.002178 Mean dependent var0.024048
Adjusted R-squared-0.080974 S.D. dependent var0.026604
S.E. of regression0.027660 Akaike info criterion-4.206073
Sum squared resid0.009181 Schwarz criterion-4.114779
Log likelihood31.44251 F-statistic0.026194
Durbin-Watson stat1.855136 Prob(F-statistic)0.874121
Obs*R-squared值的T值为0.861376，大于显著性水平0.05，所以不存在异方差。
综上检验，重庆市城乡居民储蓄存款的计量模型为
LOGY=-4.845543+1.574111LOGX5
三、结论及评价
重庆市居民储蓄存款的增加主要原因是国内生产总值的提高。出于统计口径的一致性，储蓄存款年末余额用的是名义货币，所以国内生产总值不必换算成实际GDP，两者直接相比即可。
众所周之,实际利率是影响居民储蓄存款行为的一个重要因素,但我们所得到的数据表明居民储蓄增长与实际利率的关系不大,这也是很多经济学家认为中国目前陷入流动性陷阱的主要依据.
理论上,通货膨胀应与居民储蓄存款成负相关关系,但我们所得到的数据表明两者的关系是不确定的,因为要受到通货膨胀的预期,汇率变动的方向,汇率制度以及消费品存量的多少等因素的影响。
关于GDP边际储蓄倾向，一般认为两者成正相关，但就我国的实际情况而言，相关关系并不显著，即GDP边际储蓄倾向对居民储蓄存款的影响不明确
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