计量经济学模型分析方法.docx
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计量经济学模型分析方法
计量经济学上机模型分析方法总结
一、随机误差项的异方差问题的检验与修正
模型一:
DependentVariable:
LOG(Y)
Method:
LeastSquares
Date:
07/29/12Time:
09:
03
Sample:
131
Includedobservations:
31
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
1.602528
0.860978
1.861288
0.0732
LOG(X1)
0.325416
0.103769
3.135955
0.0040
LOG(X2)
0.507078
0.048599
10.43385
0.0000
R-squared
0.796506
Meandependentvar
7.448704
AdjustedR-squared
0.781971
S.D.dependentvar
0.364648
S.E.ofregression
0.170267
Akaikeinfocriterion
-0.611128
Sumsquaredresid
0.811747
Schwarzcriterion
-0.472355
Loglikelihood
12.47249
F-statistic
54.79806
Durbin-Watsonstat
1.964720
Prob(F-statistic)
0.000000
(一)异方差的检验
1、GQ检验法
模型二:
DependentVariable:
LOG(Y)
Method:
LeastSquares
Date:
07/29/12Time:
09:
19
Sample:
112
Includedobservations:
12
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
3.744626
1.191113
3.143804
0.0119
LOG(X1)
0.344369
0.082999
4.149077
0.0025
LOG(X2)
0.168904
0.118844
1.421228
0.1890
R-squared
0.669065
Meandependentvar
7.239161
AdjustedR-squared
0.595524
S.D.dependentvar
0.133581
S.E.ofregression
0.084955
Akaikeinfocriterion
-1.881064
Sumsquaredresid
0.064957
Schwarzcriterion
-1.759837
Loglikelihood
14.28638
F-statistic
9.097834
Durbin-Watsonstat
1.810822
Prob(F-statistic)
0.006900
模型三:
DependentVariable:
LOG(Y)
Method:
LeastSquares
Date:
07/29/12Time:
09:
20
Sample:
2031
Includedobservations:
12
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-0.353381
1.607461
-0.219838
0.8309
LOG(X1)
0.210898
0.158220
1.332942
0.2153
LOG(X2)
0.856522
0.108601
7.886856
0.0000
R-squared
0.878402
Meandependentvar
7.769851
AdjustedR-squared
0.851381
S.D.dependentvar
0.390363
S.E.ofregression
0.150490
Akaikeinfocriterion
-0.737527
Sumsquaredresid
0.203824
Schwarzcriterion
-0.616301
Loglikelihood
7.425163
F-statistic
32.50732
Durbin-Watsonstat
2.123203
Prob(F-statistic)
0.000076
进行模型二和模型三两次回归,目的仅是得到出去中间7个样本点以后前后各12个样本点的残差平方和RSS1和RSS2,然后用较大的RSS除以较小的RSS即可求出F统计量值进行显著性检验。
2、怀特检验法(White)
模型一的怀特残差检验结果:
WhiteHeteroskedasticityTest:
F-statistic
4.920995
Probability
0.004339
Obs*R-squared
13.35705
Probability
0.009657
TestEquation:
DependentVariable:
RESID^2
Method:
LeastSquares
Date:
05/29/13Time:
09:
04
Sample:
131
Includedobservations:
31
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
3.982137
2.882851
1.381319
0.1789
LOG(X1)
-0.579289
0.916069
-0.632364
0.5327
(LOG(X1))^2
0.041839
0.066866
0.625710
0.5370
LOG(X2)
-0.563656
0.203228
-2.773514
0.0101
(LOG(X2))^2
0.040280
0.013879
2.902173
0.0075
R-squared
0.430873
Meandependentvar
0.026185
AdjustedR-squared
0.343315
S.D.dependentvar
0.038823
S.E.ofregression
0.031460
Akaikeinfocriterion
-3.933482
Sumsquaredresid
0.025734
Schwarzcriterion
-3.702194
Loglikelihood
65.96898
F-statistic
4.920995
Durbin-Watsonstat
1.526222
Prob(F-statistic)
0.004339
一方面,根据上面的Obs*R2=31*0.430873=13.35705>χ2(4),说明存在显著的异方差问题;另一方面,根据下面的辅助回归模型可以看出LOG(X2)与(LOG(X2))^2均通过了t检验,说明异方差的形式可以用LOG(X2)与(LOG(X2))^2的线性组合表示,权变量可以简单确定为1/LOG(X2)。
(二)加权最小二乘法(WLS)修正
1、方法原理:
具体参见教材。
2、回归结果分析
模型四:
DependentVariable:
LOG(Y)
Method:
LeastSquares
Date:
07/29/12Time:
09:
06
Sample:
131
Includedobservations:
31
Weightingseries:
1/LOG(X2)
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
1.478085
0.817610
1.807811
0.0814
LOG(X1)
0.377915
0.096925
3.899044
0.0006
LOG(X2)
0.473471
0.048398
9.782864
0.0000
WeightedStatistics
R-squared
0.872646
Meandependentvar
7.423264
AdjustedR-squared
0.863550
S.D.dependentvar
0.436598
S.E.ofregression
0.161276
Akaikeinfocriterion
-0.719639
Sumsquaredresid
0.728274
Schwarzcriterion
-0.580866
Loglikelihood
14.15440
F-statistic
49.27256
Durbin-Watsonstat
2.036239
Prob(F-statistic)
0.000000
UnweightedStatistics
R-squared
0.789709
Meandependentvar
7.448704
AdjustedR-squared
0.774688
S.D.dependentvar
0.364648
S.E.ofregression
0.173088
Sumsquaredresid
0.838862
Durbin-Watsonstat
2.028211
加权修正以后的模型四怀特检验结果如下:
WhiteHeteroskedasticityTest:
F-statistic
6.555091
Probability
0.000870
Obs*R-squared
15.56541
Probability
0.003661
可以看出并没有消除异方差性,加权修正无效。
下面采用1/abs(e)权变量进行WLS回归,结果如下:
模型五:
DependentVariable:
LOG(Y)
Method:
LeastSquares
Date:
07/29/12Time:
09:
10
Sample:
131
Includedobservations:
31
Weightingseries:
1/ABS(E)
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
1.227929
0.297268
4.130708
0.0003
LOG(X1)
0.375748
0.056830
6.611734
0.0000
LOG(X2)
0.510120
0.017781
28.68847
0.0000
WeightedStatistics
R-squared
0.999990
Meandependentvar
7.558578
AdjustedR-squared
0.999989
S.D.dependentvar
12.31758
S.E.ofregression
0.041062
Akaikeinfocriterion
-3.455703
Sumsquaredresid
0.047210
Schwarzcriterion
-3.316930
Loglikelihood
56.56339
F-statistic
1960.131
Durbin-Watsonstat
2.487309
Prob(F-statistic)
0.000000
UnweightedStatistics
R-squared
0.794514
Meandependentvar
7.448704
AdjustedR-squared
0.779836
S.D.dependentvar
0.364648
S.E.ofregression
0.171099
Sumsquaredresid
0.819694
Durbin-Watsonstat
2.007122
对加权以后的模型五进行怀特检验如下:
WhiteHeteroskedasticityTest:
F-statistic
0.199645
Probability
0.936266
Obs*R-squared
0.923778
Probability
0.921125
可以看出,模型已经不再存在异方差问题,模型五可以作为修正以后的最终模型。
二、随机误差项序列相关性问题的检验与修正
模型一:
DependentVariable:
Y
Method:
LeastSquares
Date:
07/29/12Time:
09:
48
Sample:
19912011
Includedobservations:
21
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
178.9755
55.06421
3.250305
0.0042
X
0.020002
0.001134
17.64157
0.0000
R-squared
0.942463
Meandependentvar
922.9095
AdjustedR-squared
0.939435
S.D.dependentvar
659.3491
S.E.ofregression
162.2653
Akaikeinfocriterion
13.10673
Sumsquaredresid
500270.3
Schwarzcriterion
13.20621
Loglikelihood
-135.6207
F-statistic
311.2248
Durbin-Watsonstat
0.658849
Prob(F-statistic)
0.000000
初始回归模型一经济意义合理,统计指标较为理想,但DW值偏低,模型可能存在序列相关性。
(一)序列相关性的检验方法
1、自回归模型检验法
DependentVariable:
E
Method:
LeastSquares
Date:
07/29/12Time:
09:
49
Sample(adjusted):
19922011
Includedobservations:
20afteradjustments
Variable
Coefficient
Std.Error
t-Statistic
Prob.
E(-1)
0.717080
0.201852
3.552497
0.0021
R-squared
0.398929
Meandependentvar
2.801737
AdjustedR-squared
0.398929
S.D.dependentvar
161.7297
S.E.ofregression
125.3870
Akaikeinfocriterion
12.54939
Sumsquaredresid
298716.2
Schwarzcriterion
12.59918
Loglikelihood
-124.4939
Durbin-Watsonstat
1.080741
说明模型一的随机误差项至少存在一阶正序列相关性,结合该自回归模型的DW值为1.08,怀疑存在更高阶的序列相关,继续引入e(-2)如下:
DependentVariable:
E
Method:
LeastSquares
Date:
07/29/12Time:
09:
49
Sample(adjusted):
19932011
Includedobservations:
19afteradjustments
Variable
Coefficient
Std.Error
t-Statistic
Prob.
E(-1)
1.094974
0.178768
6.125108
0.0000
E(-2)
-0.815010
0.199977
-4.075513
0.0008
R-squared
0.692885
Meandependentvar
7.790341
AdjustedR-squared
0.674819
S.D.dependentvar
164.5730
S.E.ofregression
93.84710
Akaikeinfocriterion
12.02051
Sumsquaredresid
149723.7
Schwarzcriterion
12.11993
Loglikelihood
-112.1949
Durbin-Watsonstat
1.945979
由于e(-2)的t检验显著,说明模型一的随机误差项确实存在二阶正序列相关性,结合该二阶自回归模型的DW值为1.95,基本确定不存在更高阶的序列相关。
Breusch-GodfreySerialCorrelationLMTest:
F-statistic
0.888958
Probability
0.431668
Obs*R-squared
1.998924
Probability
0.368077
可以看出二阶自回归模型的随机误差项不存在序列相关性,论证了原模型仅存在二阶序列相关。
2、DW检验法
0DLDU3、LM检验法
原理:
一方面,根据上面的假设检验结果判断是否存在序列相关性,即根据(n-p)*R2统计量值与卡方检验临界值χ2(P)进行比较,其中n为原模型样本容量,P为选择的滞后阶数,R2为下面辅助回归模型的可决系数。
若(n-p)*R2﹥χ2(P),则拒绝不序列相关的原假设,说明模型存在显著的序列相关性;另一方面,结合下面的辅助回归模型中残差滞后变量是否通过t检验及DW值判断序列相关的具体阶数,方法与上面的自回归模型检验法相同。
选择滞后一阶检验:
Breusch-GodfreySerialCorrelationLMTest:
F-statistic
13.15036
Probability
0.001931
Obs*R-squared
8.865308
Probability
0.002906
TestEquation:
DependentVariable:
RESID
Method:
LeastSquares
Date: