利率及收入对货币供应量的影响
内容摘要：本文以宏观货币需求理论为基础,引入存款利率和央行再贷款利率两个解释变量,利用计量经济学的方法,分析货币供应量与这两者的关系.从中国的实际情况出发,利用年度数据着重分析利率对货币需求的影响,从而将经济理论和中国现实情况结合进行分析.
关键字：货币供应量 利率
一．理论模型的设定
由于我们正在摸索阶段，所以先把模型设定为线性模型：
模型设定如下：
Y=β0+β1X1+β2X2+ui，
Y—货币供应量
X1—央行再贷款利率（一年期）
X2—存款基准利率（一年期）
ui--随机扰动项
β0、β1、β2 --参数
二、 数据来源及搜集处理方法
1 、货币供应量Y数据的搜集：
M用广义货币供应量M2代替，因为货币的供给主要是由中央银行来进行，而货币的需求则取决于流动性偏好，尤其是投机动机。由于流动性偏好是一种心理活动，难以操纵和控制，货币需求也就难以预测和控制，需要变动的是货币供应量。这种替代具有一定的合理性.
M= M2= M1+M0.
M0=现金流通量，
M1= M0+银行活期存款，
M2= M1+储蓄存款+定期存款。
广义货币的供给量可以从中国人民银行网站中查得，但是由于统计项目的调整，只能直接得到广义货币供给量1999-2004年的数据。
2、利率数据的搜集
在目前中国的利率体系下存在这多种利率,按借贷主体可以分为:银行利率,非银行金融机构利率,有价证券的利率和市场利率.从数据的代表性和可获得性两方面考虑,选用了中央银行的一年期再贷款利率.
央行的再贷款利率是中国人民银行向金融机构进行信用放贷时所使用的利率.从1984年起,再贷款利率成为中国中央银行的基准利率之一,起着宏观调控的作用.有关资料表明，1984-1993年，中央银行基础货币投放主要渠道是再贷款，95％以上的基础货币是通过再贷款投放出去的。由于该时段较长，占样本长度的一半，因此，用再贷款利率数据是合理的，且考虑到数据的可获得性，于是统一使用再贷款利率数据。对于利率有变动的年度，按天数进行加权平均。
数据来源：中国人民银行网站
这样,模型所需变量的数据都搜集齐了.下面就利用Eviews进行模拟.
Dependent Variable: Y
Method: Least Squares
Date: 06/08/05 Time: 00:35
Sample: 1999 2004
Included observations: 6
Variable Coefficient Std. Error t-Statistic Prob.
C 230280.8 560854.2 0.410589 0.7089
X1 -62576.68 123000.7 -0.508750 0.6460
X2 71406.33 326460.8 0.218729 0.8409
R-squared 0.084133 Mean dependent var 161517.0
Adjusted R-squared -0.526446 S.D. dependent var 50685.59
S.E. of regression 62621.75 Akaike info criterion 25.23447
Sum squared resid 1.18E+10 Schwarz criterion 25.13035
Log likelihood -72.70340 F-statistic 0.137792
Durbin-Watson stat 0.611858 Prob(F-statistic) 0.876494
从表中数据来看，拟合优度明显偏低，而且从d-w检验来看，存在明显的自相关，但是我们还是做了一下white检验和ARCH检验，虽然并没有什么实际意义，但是我们想找出问题出在哪里，检验结果如下：
ARCH Test:
F-statistic 3.695173 Probability 0.345231
Obs*R-squared 3.523262 Probability 0.171765
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/08/05 Time: 00:35
Sample(adjusted): 2001 2004
Included observations: 4 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 7.93E+09 2.36E+09 3.354496 0.1844
RESID^2(-1) -1.720323 2.068470 -0.831689 0.5583
RESID^2(-2) -4.940001 2.028766 -2.434979 0.2481
R-squared 0.880815 Mean dependent var 2.38E+09
Adjusted R-squared 0.642446 S.D. dependent var 3.74E+09
S.E. of regression 2.24E+09 Akaike info criterion 46.00886
Sum squared resid 5.01E+18 Schwarz criterion 45.54858
Log likelihood -89.01772 F-statistic 3.695173
Durbin-Watson stat 1.900689 Prob(F-statistic) 0.345231
White Heteroskedasticity Test:
F-statistic 197.7849 Probability 0.005035
Obs*R-squared 5.979844 Probability 0.112595
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/08/05 Time: 00:36
Sample: 1999 2004
Included observations: 6
Variable Coefficient Std. Error t-Statistic Prob.
C 1.41E+12 7.22E+10 19.48685 0.0026
X1 -8.09E+11 4.13E+10 -19.57591 0.0026
X1^2 1.15E+11 5.85E+09 19.73195 0.0026
X2 8.15E+08 1.43E+09 0.570725 0.6258
R-squared 0.996641 Mean dependent var 1.96E+09
Adjusted R-squared 0.991602 S.D. dependent var 2.97E+09
S.E. of regression 2.73E+08 Akaike info criterion 41.91907
Sum squared resid 1.49E+17 Schwarz criterion 41.78024
Log likelihood -121.7572 F-statistic 197.7849
Durbin-Watson stat 3.191815 Prob(F-statistic) 0.005035
从检验结果来看，各项数据都显示出模型设定的不合理，所以决定将模型进行修改：
在设立模型时将利率作为决定货币需求总量的解释变量.由于三个变量之间数量级存在差异,若直接回归会存在一些潜在问题,为了回避这一 问题,本文在设定模型时采用了双对数模型,此外,双对数模型中,各解释变量的参数即为弹性,具有良好的经济解释意义.
故模型修改如下：
logY=c++
Y—货币供应量
X1—央行再贷款利率（一年期）
X2—存款基准利率（一年期）
ui--随机扰动项
β0、β1、β2 --参数
注: 利率采用百分比,一方面可以避免对数取负,另一方面,可以用数学推导证明这种代入并不影响参数的意义, β2则表示利率对货币供应量的弹性.
Dependent Variable: LOG(Y)
Method: Least Squares
Date: 06/08/05 Time: 09:47
Sample: 1999 2004
Included observations: 6
Variable Coefficient Std. Error t-Statistic Prob.
C 13.36639 2.779027 4.809737 0.0171
LOG(X1) -1.604095 2.534671 -0.632861 0.5718
LOG(X2) 0.814678 4.038057 0.201750 0.8530
R-squared 0.133972 Mean dependent var 11.95281
Adjusted R-squared -0.443379 S.D. dependent var 0.305031
S.E. of regression 0.366466 Akaike info criterion 1.137033
Sum squared resid 0.402893 Schwarz criterion 1.032912
Log likelihood -0.411098 F-statistic 0.232046
Durbin-Watson stat 0.641835 Prob(F-statistic) 0.805931
F-statistic 3.343312 Probability 0.360688
Obs*R-squared 3.479615 Probability 0.175554
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/08/05 Time: 09:48
Sample(adjusted): 2001 2004
Included observations: 4 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 0.274674 0.085232 3.222653 0.1915
RESID^2(-1) -2.425082 2.099849 -1.154884 0.4543
RESID^2(-2) -4.634939 2.019299 -2.295321 0.2616
R-squared 0.869904 Mean dependent var 0.082210
Adjusted R-squared 0.609712 S.D. dependent var 0.129219
S.E. of regression 0.080727 Akaike info criterion -2.081780
Sum squared resid 0.006517 Schwarz criterion -2.542059
Log likelihood 7.163559 F-statistic 3.343312
Durbin-Watson stat 1.797040 Prob(F-statistic) 0.360688
White Heteroskedasticity Test:
F-statistic 105.8244 Probability 0.009376
Obs*R-squared 5.962438 Probability 0.113452
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/08/05 Time: 09:49
Sample: 1999 2004
Included observations: 6
Variable Coefficient Std. Error t-Statistic Prob.
C 84.51720 5.869432 14.39955 0.0048
LOG(X1) -135.7081 9.387113 -14.45685 0.0048
(LOG(X1))^2 54.25838 3.731943 14.53891 0.0047
LOG(X2) 0.049806 0.142556 0.349375 0.7602
R-squared 0.993740 Mean dependent var 0.067149
Adjusted R-squared 0.984349 S.D. dependent var 0.103003
S.E. of regression 0.012886 Akaike info criterion -5.630639
Sum squared resid 0.000332 Schwarz criterion -5.769466
Log likelihood 20.89192 F-statistic 105.8244
Durbin-Watson stat 3.193308 Prob(F-statistic) 0.009376
从表中结果看出，拟合优度还是偏小，所以我们觉得可能是数据收集和选题上出了问题，所以，我们借鉴了一下学长们文章里的数据，将模型数据修改了一下，得出以下结果：
线性模型：
Dependent Variable: Y
Method: Least Squares
Date: 06/08/05 Time: 10:50
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
C 188624.9 28029.32 6.729556 0.0000
X1 243594.9 801019.2 0.304106 0.7663
X2 -1948879. 759125.2 -2.567269 0.0247
R-squared 0.691036 Mean dependent var 96219.35
Adjusted R-squared 0.639542 S.D. dependent var 67534.31
S.E. of regression 40546.36 Akaike info criterion 24.23514
Sum squared resid 1.97E+10 Schwarz criterion 24.37675
Log likelihood -178.7635 F-statistic 13.41973
Durbin-Watson stat 0.533591 Prob(F-statistic) 0.000870
ARCH Test:
F-statistic 1.034925 Probability 0.390383
Obs*R-squared 2.229361 Probability 0.328020
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/08/05 Time: 10:51
Sample(adjusted): 1992 2004
Included observations: 13 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 8.58E+08 1.14E+09 0.751750 0.4695
RESID^2(-1) 0.796613 0.668656 1.191364 0.2610
RESID^2(-2) -0.326112 0.811268 -0.401977 0.6962
R-squared 0.171489 Mean dependent var 1.34E+09
Adjusted R-squared 0.005787 S.D. dependent var 1.89E+09
S.E. of regression 1.88E+09 Akaike info criterion 45.74792
Sum squared resid 3.54E+19 Schwarz criterion 45.87829
Log likelihood -294.3615 F-statistic 1.034925
Durbin-Watson stat 1.436975 Prob(F-statistic) 0.390383
White Heteroskedasticity Test:
F-statistic 0.703472 Probability 0.607292
Obs*R-squared 3.293952 Probability 0.509891
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/08/05 Time: 10:52
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
C 3.68E+09 4.86E+09 0.756392 0.4669
X1 9.40E+09 2.59E+11 0.036241 0.9718
X1^2 -1.84E+11 1.49E+12 -0.123637 0.9041
X2 -8.97E+10 1.96E+11 -0.457063 0.6574
X2^2 7.49E+11 1.28E+12 0.586501 0.5705
R-squared 0.219597 Mean dependent var 1.32E+09
Adjusted R-squared -0.092565 S.D. dependent var 1.76E+09
S.E. of regression 1.84E+09 Akaike info criterion 45.76069
Sum squared resid 3.37E+19 Schwarz criterion 45.99671
Log likelihood -338.2052 F-statistic 0.703472
Durbin-Watson stat 1.040008 Prob(F-statistic) 0.607292
双对数模型：
Dependent Variable: LOG(Y)
Method: Least Squares
Date: 06/08/05 Time: 10:52
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
C 9.104053 0.751291 12.11787 0.0000
LOG(X1) 1.724152 0.759135 2.271206 0.0423
LOG(X2) -2.231608 0.550211 -4.055914 0.0016
R-squared 0.767403 Mean dependent var 11.18738
Adjusted R-squared 0.728637 S.D. dependent var 0.851629
S.E. of regression 0.443635 Akaike info criterion 1.389227
Sum squared resid 2.361743 Schwarz criterion 1.530837
Log likelihood -7.419202 F-statistic 19.79570
Durbin-Watson stat 0.780945 Prob(F-statistic) 0.000158
ARCH Test:
F-statistic 1.371904 Probability 0.297512
Obs*R-squared 2.798968 Probability 0.246724
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/08/05 Time: 10:53
Sample(adjusted): 1992 2004
Included observations: 13 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 0.173028 0.051951 3.330601 0.0076
RESID^2(-1) -0.108394 0.268104 -0.404300 0.6945
RESID^2(-2) -0.300785 0.193299 -1.556062 0.1507
R-squared 0.215305 Mean dependent var 0.116330
Adjusted R-squared 0.058366 S.D. dependent var 0.118729
S.E. of regression 0.115212 Akaike info criterion -1.284912
Sum squared resid 0.132738 Schwarz criterion -1.154539
Log likelihood 11.35193 F-statistic 1.371904
Durbin-Watson stat 2.418769 Prob(F-statistic) 0.297512
White Heteroskedasticity Test:
F-statistic 0.587970 Probability 0.678925
Obs*R-squared 2.856099 Probability 0.582188
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/08/05 Time: 10:54
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
C 1.265529 3.019411 0.419131 0.6840
LOG(X1) -1.153200 2.574276 -0.447971 0.6637
(LOG(X1))^2 -0.181204 0.493874 -0.366904 0.7213
LOG(X2) 1.771056 1.904494 0.929936 0.3743
(LOG(X2))^2 0.260797 0.332239 0.784969 0.4507
R-squared 0.190407 Mean dependent var 0.157450
Adjusted R-squared -0.133431 S.D. dependent var 0.166267
S.E. of regression 0.177013 Akaike info criterion -0.363991
Sum squared resid 0.313334 Schwarz criterion -0.127974
Log likelihood 7.729932 F-statistic 0.587970
Durbin-Watson stat 1.432611 Prob(F-statistic) 0.678925
从利率与货币需求的散点图可以看出，利率和货币需求明显成反方向变动关系。
Estimation Command:
=====================
LS LOG(Y) C LOG(X1) LOG(X2)
Estimation Equation:
=====================
LOG(Y) = C(1) + C(2)*LOG(X1) + C(3)*LOG(X2)
Substituted Coefficients:
=====================
LOG(Y) = 9.104053025 + 1.724151652*LOG(X1) - 2.231607684*LOG(X2)
现在的拟合优度明显比前两次高得多了，现在我们终于找到了问题的关键所在，原来我们一直把利率写成了*.**的格式，而不是0.****的格式，所以造成了数据上的严重错误，但是从WHITE检验和ARCH检验的拟合优度来看，又比较低，而用最小二乘法做出来的数据来看，D-W值为0.780945，其结果表明存在自相关，而WHITE检验和ARCH检验的犯错误的概率都比较大，所以还需要对模型进行进一步修正，但是log（x1）和log（x2）都为负值，在EVIEWS上无法进行进一步修正（我只知道用ar（x）这种方法，试过了，不行……）。所以我们猜断这个问题的关键可能出在选择解释变量时两个利率本来就存在一定的联系，基本上都是同时浮动的，所以我们可能是一开始选题就出了问题，我们阅读了学长的一篇文章，上面选择的解释变量是收入和央行再贷款利率，可能这样选择解释变量更为科学一点，避免了两个利率之间的自相关，但是由于篇幅有限，而且学长们已经做了这个课题了，所以我们希望下次能够吸取教训，争取下次做得更好！
三、经济现象浅析
从以上对年度数据和季度数据的分析。我们认为，虽然再贷款利率是央行根据货币市场需求进行调整的，但是由于中国货币市场的市场化程度较低，其作用性仍然很低。随着，金融体制的改革，再贷款利率的市场代表性提高。
注：由于金融理论知识的欠缺，因此不能作出很好的经济解释。本^论文的着重点并非在结论，而在于利用计量经济学这种定量的分析方法，解决现实中的问题。
补充：
由于模型设定有误，我们重新设定了模型，把x2设为收入，既GDP，模型重新设定如下：
Y=
Y--货币需求总量
X2--收入
X1--利率（%）
ui--随机扰动项
β0、β1、β2 --参数
数据平稳性检验：
ADF Test Statistic -2.090711 1% Critical Value* -4.3260
5% Critical Value -3.2195
10% Critical Value -2.7557
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(X1)
Method: Least Squares
Date: 07/01/05 Time: 12:54
Sample(adjusted): 1992 2001
Included observations: 10 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
X1(-1) -0.380698 0.182090 -2.090711 0.0749
D(X1(-1)) 0.919158 0.293195 3.134968 0.0165
C 0.032264 0.016274 1.982530 0.0879
R-squared 0.586641 Mean dependent var -0.003640
Adjusted R-squared 0.468538 S.D. dependent var 0.016227
S.E. of regression 0.011829 Akaike info criterion -5.793128
Sum squared resid 0.000980 Schwarz criterion -5.702353
Log likelihood 31.96564 F-statistic 4.967214
Durbin-Watson stat 1.727237 Prob(F-statistic) 0.045409
ADF Test Statistic -1.774646 1% Critical Value* -4.4613
5% Critical Value -3.2695
10% Critical Value -2.7822
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(X2)
Method: Least Squares
Date: 07/01/05 Time: 12:44
Sample(adjusted): 1993 2001
Included observations: 9 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
X2(-1) -0.052738 0.029717 -1.774646 0.1361
D(X2(-1)) 0.833179 0.273405 3.047422 0.0285
D(X2(-2)) -0.505207 0.238098 -2.121839 0.0873
C 8260.113 2639.968 3.128868 0.0260
R-squared 0.811418 Mean dependent var 7699.467
Adjusted R-squared 0.698269 S.D. dependent var 2998.985
S.E. of regression 1647.343 Akaike info criterion 17.95282
Sum squared resid 13568700 Schwarz criterion 18.04047
Log likelihood -76.78768 F-statistic 7.171234
Durbin-Watson stat 2.594088 Prob(F-statistic) 0.029258
ADF Test Statistic -7.584454 1% Critical Value* -4.3260
5% Critical Value -3.2195
10% Critical Value -2.7557
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y)
Method: Least Squares
Date: 07/01/05 Time: 12:58
Sample(adjusted): 1992 2001
Included observations: 10 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
从表中看出，只y是平稳的，x1、x2都有可能是非平稳序列。
回归如下：
Dependent Variable: Y
Method: Least Squares
Date: 07/01/05 Time: 12:27
Sample: 1990 2001
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C 4884.729 8538.390 0.572090 0.5813
X1 -195491.6 71636.27 -2.728948 0.0233
X2 1.381533 0.071401 19.34894 0.0000
R-squared 0.983602 Mean dependent var 69465.50
Adjusted R-squared 0.979958 S.D. dependent var 41050.42
S.E. of regression 5811.429 Akaike info criterion 20.38536
Sum squared resid 3.04E+08 Schwarz criterion 20.50659
Log likelihood -119.3122 F-statistic 269.9303
Durbin-Watson stat 1.124471 Prob(F-statistic) 0.000000
ARCH Test:
F-statistic 16.63761 Probability 0.002189
Obs*R-squared 8.261959 Probability 0.016067
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 07/01/05 Time: 12:34
Sample(adjusted): 1992 2001
Included observations: 10 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 5963322. 10085707 0.591265 0.5729
RESID^2(-1) -0.626371 0.441135 -1.419908 0.1986
RESID^2(-2) 2.508035 0.436696 5.743201 0.0007
R-squared 0.826196 Mean dependent var 29821600
Adjusted R-squared 0.776538 S.D. dependent var 50360420
S.E. of regression 23806285 Akaike info criterion 37.05212
Sum squared resid 3.97E+15 Schwarz criterion 37.14290
Log likelihood -182.2606 F-statistic 16.63761
Durbin-Watson stat 2.200372 Prob(F-statistic) 0.002189
White Heteroskedasticity Test:
F-statistic 2.999141 Probability 0.097505
Obs*R-squared 7.578148 Probability 0.108312
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 07/01/05 Time: 12:35
Sample: 1990 2001
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C 1.23E+08 1.87E+08 0.656433 0.5325
X1 -1.11E+09 4.64E+09 -0.240222 0.8170
X1^2 8.20E+09 2.89E+10 0.284316 0.7844
X2 -4697.178 3699.568 -1.269656 0.2448
X2^2 0.050797 0.036053 1.408943 0.2017
R-squared 0.631512 Mean dependent var 25329530
Adjusted R-squared 0.420948 S.D. dependent var 46753534
S.E. of regression 35577322 Akaike info criterion 37.90665
Sum squared resid 8.86E+15 Schwarz criterion 38.10870
Log likelihood -222.4399 F-statistic 2.999141
Durbin-Watson stat 2.585745 Prob(F-statistic) 0.097505
我们决定按照以前的方法，再试一试双对数模型，模型设定如下：
lnY=β0+β1lnX1+β2lnX2+ui，
Y--货币需求总量
X2--收入
X1--利率（%）
ui--随机扰动项
β0、β1、β2 --参数
回归结果如下：
Dependent Variable: LOG(Y)
Method: Least Squares
Date: 07/01/05 Time: 13:06
Sample: 1990 2001
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C -2.912563 0.363818 -8.005561 0.0000
LOG(X1) -0.104478 0.052415 -1.993287 0.0774
LOG(X2) 1.252898 0.036680 34.15767 0.0000
R-squared 0.993932 Mean dependent var 10.93112
Adjusted R-squared 0.992584 S.D. dependent var 0.748034
S.E. of regression 0.064419 Akaike info criterion -2.434484
Sum squared resid 0.037349 Schwarz criterion -2.313257
Log likelihood 17.60690 F-statistic 737.1016
Durbin-Watson stat 1.000566 Prob(F-statistic) 0.000000
ARCH Test:
F-statistic 2.619451 Probability 0.141496
Obs*R-squared 4.280533 Probability 0.117623
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 07/01/05 Time: 13:07
Sample(adjusted): 1992 2001
Included observations: 10 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 0.002133 0.002072 1.029565 0.3375
RESID^2(-1) -0.657373 0.634981 -1.035265 0.3350
RESID^2(-2) 1.433592 0.635484 2.255904 0.0587
R-squared 0.428053 Mean dependent var 0.003698
Adjusted R-squared 0.264640 S.D. dependent var 0.005199
S.E. of regression 0.004458 Akaike info criterion -7.744744
Sum squared resid 0.000139 Schwarz criterion -7.653968
Log likelihood 41.72372 F-statistic 2.619451
Durbin-Watson stat 2.362453 Prob(F-statistic) 0.141496
从以上结果看Probability的值,拒绝H0犯错误概率较大,同时残差序列的系数的t值并不显著,应该接受残差序列系数为零的原假设，即为模型不存在异方差. 另一方面,从White检验看,也不存在异方差.
White Heteroskedasticity Test:
F-statistic 1.573377 Probability 0.281511
Obs*R-squared 5.681125 Probability 0.224261
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 07/01/05 Time: 13:07
Sample: 1990 2001
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C 0.438517 0.928484 0.472294 0.6511
LOG(X1) -0.004873 0.083923 -0.058066 0.9553
(LOG(X1))^2 -0.000283 0.015544 -0.018211 0.9860
LOG(X2) -0.087720 0.174478 -0.502757 0.6306
(LOG(X2))^2 0.004285 0.008235 0.520299 0.6189
R-squared 0.473427 Mean dependent var 0.003112
Adjusted R-squared 0.172528 S.D. dependent var 0.004898
S.E. of regression 0.004455 Akaike info criterion -7.695083
Sum squared resid 0.000139 Schwarz criterion -7.493039
Log likelihood 51.17050 F-statistic 1.573377
Durbin-Watson stat 2.429343 Prob(F-statistic) 0.281511
C LOG(X1) LOG(X2)
C 0.132363 -0.001369 -0.012518
LOG(X1) -0.001369 0.002747 0.000788
LOG(X2) -0.012518 0.000788 0.001345
从以上结果可以看出,两者的相关系数较小,即不存在多重共线性.
自相关检验
模拟结果显示DW值为1.000566,而通过查表得到dL的值为0.812,du的值为1.579.DW的值正好落在无决定区域,因此需要对自相关进行修正.利用Cochrane-Orcutt 法对自相关性进行修正,得到以下结果.
Dependent Variable: LOG(Y)
Method: Least Squares
Date: 07/01/05 Time: 13:28
Sample(adjusted): 1991 2001
Included observations: 11 after adjusting endpoints
Convergence achieved after 39 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C 0.697884 8.821613 0.079111 0.9392
LOG(X1) -0.096270 0.237552 -0.405259 0.6974
LOG(X2) 0.938376 0.686270 1.367356 0.2138
AR(1) 0.801861 0.315456 2.541913 0.0386
R-squared 0.993641 Mean dependent var 11.04894
Adjusted R-squared 0.990916 S.D. dependent var 0.657491
S.E. of regression 0.062664 Akaike info criterion -2.426757
Sum squared resid 0.027488 Schwarz criterion -2.282068
Log likelihood 17.34717 F-statistic 364.6239
Durbin-Watson stat 0.715180 Prob(F-statistic) 0.000000
Inverted AR Roots .8
