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
OBS Y X1 X2 X3 X4 X5 X6 X7 X8
1986 25.29 35.6 179 987.45 358.86 169.8 0.36 4.2  NA
1987 32.64 29 0.005587 1113.61 385.82 189.68 0.34 9.8  NA 
1988 36.18 10.84 179 1281.77 457.54 239.11 0.07 22.7  NA
1989 48.88 35.1 0.005587 1452.66 510.09 277.27 0.33 17.1     NA
1990 67.31 37.7 179 1695.78 586.73 298.41 0.87 1.4 6.64
1991 88.18 31 0.005587 1894.46 628.89 339.81 0.5 7 0.56
1992 111.68 26.7 179 2200.8 677.46 417.87 0.3 11.2 -4.64
1993 158.74 42.1 0.005587 2785 748.08 549.79 0.36 18.7 -7.72
1994 214.22 35 179 3645.97 1018.24 751.21 0.28 29.7 -18.72
1995 304.51 24.2 0.005587 4391.5 1270.41 1009.47 0.35 19.4 -8.42
1996 503.35 65.3 179 5042.24 1479.05 1179.09 1.17 9.7 -2.23
1997 581.3 15.5 0.005587 5322.6 1692.36 1350 0.46 3.3 2.37
1998 724.54 24.6 179 5466.88 1810.17 1429.26 1.81 -3.6 7.38
1999 909.1 25.5 2959 5895.97 1835.54 1479.71 3.7 -0.7 2.95
2000 1085.3 19.4 3522 6275.98 1892.44 1589.34 1.6 -3.2 5.45

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
Variable Coefficient Std. Error t-Statistic Prob. 
X1 5.469472 1.838157 2.975519 0.0968
X2 0.158359 0.032844 4.821512 0.0404
X3 -0.931507 0.331858 -2.806944 0.1069
X4 0.197766 0.462052 0.428017 0.7103
X5 3.568453 1.089873 3.274193 0.0820
X6 -44.69363 20.48663 -2.181600 0.1609
X7 0.956679 10.39800 0.092006 0.9351
X8 -8.270289 9.452063 -0.874972 0.4739
C 340.0799 183.5362 1.852931 0.2051
R-squared 0.999032     Mean dependent var 431.6573
Adjusted R-squared 0.995160     S.D. dependent var 354.9019
S.E. of regression 24.68950     Akaike info criterion 9.182249
Sum squared resid 1219.143     Schwarz criterion 9.507799
Log likelihood -41.50237     F-statistic 258.0367
Durbin-Watson stat 3.244507     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
Variable Coefficient Std. Error t-Statistic Prob. 
X1 -4.964631 7.430933 -0.668103 0.5158
C 477.5158 244.7491 1.951042 0.0729
R-squared 0.033196     Mean dependent var 326.0813
Adjusted R-squared -0.041174     S.D. dependent var 350.4721
S.E. of regression 357.6144     Akaike info criterion 14.72035
Sum squared resid 1662545.     Schwarz criterion 14.81476
Log likelihood -108.4027     F-statistic 0.446362
Durbin-Watson stat 0.197003     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
Variable Coefficient Std. Error t-Statistic Prob. 
X2 0.246696 0.054057 4.563598 0.0005
C 198.8842 64.54440 3.081355 0.0088
R-squared 0.615685     Mean dependent var 326.0813
Adjusted R-squared 0.586122     S.D. dependent var 350.4721
S.E. of regression 225.4703     Akaike info criterion 13.79782
Sum squared resid 660879.3     Schwarz criterion 13.89223
Log likelihood -101.4836     F-statistic 20.82642
Durbin-Watson stat 0.515496     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
Variable Coefficient Std. Error t-Statistic Prob. 
X3 0.170054 0.017367 9.791650 0.0000
C -234.5603 65.81286 -3.564050 0.0035
R-squared 0.880599     Mean dependent var 326.0813
Adjusted R-squared 0.871414     S.D. dependent var 350.4721
S.E. of regression 125.6755     Akaike info criterion 12.62885
Sum squared resid 205326.2     Schwarz criterion 12.72326
Log likelihood -92.71637     F-statistic 95.87641
Durbin-Watson stat 0.304992     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
Variable Coefficient Std. Error t-Statistic Prob. 
X4 0.574552 0.051097 11.24426 0.0000
C -261.9415 59.64064 -4.391996 0.0007
R-squared 0.906765     Mean dependent var 326.0813
Adjusted R-squared 0.899594     S.D. dependent var 350.4721
S.E. of regression 111.0540     Akaike info criterion 12.38148
Sum squared resid 160328.8     Schwarz criterion 12.47588
Log likelihood -90.86107     F-statistic 126.4333
Durbin-Watson stat 0.491931     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
Variable Coefficient Std. Error t-Statistic Prob. 
X5 0.628628 0.054252 11.58719 0.0000
C -146.2203 49.39553 -2.960193 0.0111
R-squared 0.911723     Mean dependent var 326.0813
Adjusted R-squared 0.904932     S.D. dependent var 350.4721
S.E. of regression 108.0614     Akaike info criterion 12.32684
Sum squared resid 151804.6     Schwarz criterion 12.42125
Log likelihood -90.45132     F-statistic 134.2629
Durbin-Watson stat 0.435621     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
Variable Coefficient Std. Error t-Statistic Prob. 
X6 287.7924 65.04842 4.424279 0.0007
C 86.25437 80.36048 1.073343 0.3026
R-squared 0.600912     Mean dependent var 326.0813
Adjusted R-squared 0.570213     S.D. dependent var 350.4721
S.E. of regression 229.7631     Akaike info criterion 13.83554
Sum squared resid 686284.0     Schwarz criterion 13.92995
Log likelihood -101.7666     F-statistic 19.57424
Durbin-Watson stat 1.375241     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
Variable Coefficient Std. Error t-Statistic Prob. 
X7 -20.33713 7.917007 -2.568791 0.0233
C 524.9785 108.8330 4.823708 0.0003
R-squared 0.336690     Mean dependent var 326.0813
Adjusted R-squared 0.285666     S.D. dependent var 350.4721
S.E. of regression 296.2129     Akaike info criterion 14.34360
Sum squared resid 1140647.     Schwarz criterion 14.43801
Log likelihood -105.5770     F-statistic 6.598685
Durbin-Watson stat 0.373405     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
Variable Coefficient Std. Error t-Statistic Prob. 
X8 21.48481 13.12623 1.636784 0.1361
C 463.6501 100.9274 4.593897 0.0013
R-squared 0.229390     Mean dependent var 431.6573
Adjusted R-squared 0.143767     S.D. dependent var 354.9019
S.E. of regression 328.4009     Akaike info criterion 14.58931
Sum squared resid 970624.5     Schwarz criterion 14.66166
Log likelihood -78.24122     F-statistic 2.679062
Durbin-Watson stat 0.263408     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
Variable Coefficient Std. Error t-Statistic Prob. 
X3 -0.247317 0.148290 -1.667796 0.1212
X5 1.523113 0.538735 2.827201 0.0153
C -2.900268 97.62408 -0.029709 0.9768
R-squared 0.928334     Mean dependent var 326.0813
Adjusted R-squared 0.916390     S.D. dependent var 350.4721
S.E. of regression 101.3404     Akaike info criterion 12.25170
Sum squared resid 123238.5     Schwarz criterion 12.39331
Log likelihood -88.88777     F-statistic 77.72205
Durbin-Watson stat 0.828045     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
Variable Coefficient Std. Error t-Statistic Prob. 
X4 -0.137361 0.851677 -0.161283 0.8746
X5 0.778232 0.929299 0.837440 0.4187
C -118.0392 182.1215 -0.648134 0.5291
R-squared 0.911913     Mean dependent var 326.0813
Adjusted R-squared 0.897232     S.D. dependent var 350.4721
S.E. of regression 112.3522     Akaike info criterion 12.45801
Sum squared resid 151476.2     Schwarz criterion 12.59962
Log likelihood -90.43508     F-statistic 62.11483
Durbin-Watson stat 0.429695     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
Variable Coefficient Std. Error t-Statistic Prob. 
X5 0.522738 0.062057 8.423537 0.0000
X6 88.18149 34.99462 2.519859 0.0269
C -140.1476 41.64600 -3.365211 0.0056
R-squared 0.942270     Mean dependent var 326.0813
Adjusted R-squared 0.932648     S.D. dependent var 350.4721
S.E. of regression 90.95532     Akaike info criterion 12.03547
Sum squared resid 99274.44     Schwarz criterion 12.17708
Log likelihood -87.26603     F-statistic 97.93186
Durbin-Watson stat 1.063634     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
Variable Coefficient Std. Error t-Statistic Prob. 
X5 0.571957 0.051279 11.15376 0.0000
X7 -6.772160 2.729948 -2.480692 0.0289
C -37.41072 60.59009 -0.617440 0.5485
R-squared 0.941647     Mean dependent var 326.0813
Adjusted R-squared 0.931922     S.D. dependent var 350.4721
S.E. of regression 91.44465     Akaike info criterion 12.04620
Sum squared resid 100345.5     Schwarz criterion 12.18781
Log likelihood -87.34651     F-statistic 96.82253
Durbin-Watson stat 0.831580     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
Variable Coefficient Std. Error t-Statistic Prob. 
X5 0.639092 0.074662 8.559796 0.0000
X8 8.161783 4.637152 1.760085 0.1164
C -160.0708 80.23437 -1.995040 0.0811
R-squared 0.924143     Mean dependent var 431.6573
Adjusted R-squared 0.905179     S.D. dependent var 354.9019
S.E. of regression 109.2849     Akaike info criterion 12.45279
Sum squared resid 95545.53     Schwarz criterion 12.56131
Log likelihood -65.49037     F-statistic 48.73104
Durbin-Watson stat 0.834345     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DW<DL，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
Variable Coefficient Std. Error t-Statistic Prob. 
LX5 1.574985 0.053027 29.70157 0.0000
C -4.871250 0.338780 -14.37881 0.0000
R-squared 0.985478     Mean dependent var 5.115019
Adjusted R-squared 0.984361     S.D. dependent var 1.287252
S.E. of regression 0.160980     Akaike info criterion -0.691509
Sum squared resid 0.336889     Schwarz criterion -0.597102
Log likelihood 7.186316     F-statistic 882.1831
Durbin-Watson stat 0.926220     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
Variable Coefficient Std. Error t-Statistic Prob. 
C -4.845543 0.844517 -5.737648 0.0001
LX5 1.574111 0.127408 12.35491 0.0000
AR(1) 0.553539 0.298814 1.852453 0.0910
R-squared 0.986887     Mean dependent var 5.249634
Adjusted R-squared 0.984502     S.D. dependent var 1.221374
S.E. of regression 0.152048     Akaike info criterion -0.741831
Sum squared resid 0.254305     Schwarz criterion -0.604890
Log likelihood 8.192819     F-statistic 413.9197
Durbin-Watson stat 1.552650     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-statistic 0.026194     Probability 0.874121
Obs*R-squared 0.030493     Probability 0.861376
    
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
Variable Coefficient Std. Error t-Statistic Prob. 
C 0.023067 0.009562 2.412406 0.0328
RESID^2(-1) 0.050218 0.310284 0.161845 0.8741
R-squared 0.002178     Mean dependent var 0.024048
Adjusted R-squared -0.080974     S.D. dependent var 0.026604
S.E. of regression 0.027660     Akaike info criterion -4.206073
Sum squared resid 0.009181     Schwarz criterion -4.114779
Log likelihood 31.44251     F-statistic 0.026194
Durbin-Watson stat 1.855136     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