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空间联立方程--广义空间三阶段最小二乘法估计
空间联立方程--广义空间三阶段最小二乘法估计
对于空间联立方程除了可以使用这样的一个命令,spregcs,还可以使用广义空间三阶段最小二乘法估计命令gs3sls与gs3slsxt,其中gs3sls适用于横截面空间数据,gs3slsxt适用于面板空间数据。
另外由于这是一个外部命令,因此需要进行下载安装,查看外部命令的下载、安装与使用以及ADO/PLUS文件夹分享
1、截面空间数据---广义空间三阶段最小二乘法估计命令gs3sls
语法格式为:
gs3sls depvar indepvars [weight] , wmfile(weight_file) var2(varlist) eq(1, 2)
[ ols 2sls 3sls sure mvreg lmspac lmhet lmnorm diag tests stand inv inv2
aux(varlist) mfx(lin, log) order(#) coll zero tolog noconstant
predict(new_var) resid(new_var) level(#) vce(vcetype) ]
选项含义为:
depvar表示被解释变量
indepvars表示解释变量
order(1, 2, 3, 4)表示选择的滞后阶数,最大四阶的阶数。
var2中,y2为方程中第二个方程的被解释变量,x3,x4为解释变量
model表示选择估计的方法为GS3SLS或GS3 SLSAR(广义空间自回归)
eq(1,2)对方程(#)的检验,默认为1。
predict(new_variable)预测值变量
resid(new_variable)残差值变量计算
iter (#) 最大迭代;默认是100,如果iter(#)达到(100),这意味着还没有达到收敛,所以最大迭代次数可以超过100次。
Vce (vcetype) ,方法包括ols, robust, cluster, bootstrap, jackknife, hc2, hc3
level(#)置信区间水平;默认是水平(95)
注意事项:
1:您可以使用:spweight, spweightcs, spweightxt来创建空间权重矩阵。
2:记住,你的空间权重矩阵必须是: 1-截面2-方阵3-对称矩阵
3:您可以对gs3sls使用对话框
2、命令汇总为:
clear all
sysuse gs3sls.dta, clear
* Y1 = Y2 X1 X2
* Y2 = Y1 X3 X4
* (1) Generalized Spatial 3SLS - AR(1) (GS3SLS)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(1) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(lin) test aux(x5)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(log) test tolog
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* (2) Generalized Spatial 3SLS - AR(2) (GS3SLS)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(2) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(lin) test aux(x5)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(2) mfx(log) test tolog
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* (3) Generalized Spatial 3SLS - AR(3) (GS3SLS)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(3) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(lin) test aux(x5)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(3) mfx(log) test tolog
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* (4) Generalized Spatial 3SLS - AR(4) (GS3SLS)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(4) mfx(lin) test
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(lin) test aux(x5)
gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(4) mfx(log) test tolog
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
操作结果为:
clear all
. cd C:\Users\admin\Desktop
C:\Users\admin\Desktop
. gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(1) order(1) mfx(lin) test
==============================================================================
*** Binary (0/1) Weight Matrix: 49x49 (Non Normalized)
==============================================================================
==============================================================================
* Generalized Spatial Three Stage Least Squares (GS3SLS)
==============================================================================
y1 = w1y_y1 + w1y_y2 + y2 + x1 + x2
------------------------------------------------------------------------------
y2 = w1y_y2 + w1y_y1 + y1 + x3 + x4
------------------------------------------------------------------------------
Three-stage least-squares regression
------------------------------------------------------------------------------
Equation Obs Params RMSE "R-squared" F P>F
------------------------------------------------------------------------------
y1 49 5 9.657283 0.7016 26.20 0.0000
y2 49 5 7.414835 0.8091 52.39 0.0000
------------------------------------------------------------------------------
------------------------------------------------------------------------------
| Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
y1 |
w1y_y1 | .1382035 .1740695 0.79 0.429 -.2078352 .4842423
w1y_y2 | -.1088995 .1664627 -0.65 0.515 -.4398164 .2220174
y2 | .8254616 .1429166 5.78 0.000 .5413529 1.10957
x1 | -.0593876 .0751261 -0.79 0.431 -.2087333 .0899582
x2 | -.230459 .3059294 -0.75 0.453 -.8386265 .3777085
_cons | 5.357097 10.72446 0.50 0.619 -15.96243 26.67662
-------------+----------------------------------------------------------------
y2 |
w1y_y2 | .0538141 .1144285 0.47 0.639 -.1736622 .2812905
w1y_y1 | -.0685151 .1202225 -0.57 0.570 -.3075095 .1704794
y1 | .5043856 .204935 2.46 0.016 .0969882 .9117829
x3 | .0517263 .0898243 0.58 0.566 -.1268385 .230291
x4 | .3148184 .0914127 3.44 0.001 .133096 .4965409
_cons | 2.931701 3.871633 0.76 0.451 -4.764852 10.62825
------------------------------------------------------------------------------
Endogenous variables: y1 y2 w1y_y1 w1y_y2
Exogenous variables: x1 x2 x3 x4 w1x_x1 w1x_x2 w1x_x3 w1x_x4 w2x_x1 w2x_x2
w2x_x3 w2x_x4
EQ1: R2= 0.7016 - R2 Adj.= 0.6669 F-Test = 19.748 P-Value> F(5, 42)
LLF = -177.446 AIC = 366.891 SC = 378.242 Root MSE = 9.6573
EQ2: R2= 0.8091 - R2 Adj.= 0.7868 F-Test = 35.591 P-Value> F(5, 42)
LLF = -164.498 AIC = 340.997 SC = 352.348 Root MSE = 7.4148
Yij = LHS Y(i) in Eq.(j)
------------------------------------------------------------------------------
- Overall System R2 - Adjusted R2 - F Test - Chi2 Test
+----------------------------------------------------------------------------+
| Name | R2 | Adj_R2 | F | P-Value | Chi2 | P-Value |
|----------+----------+----------+----------+----------+----------+----------|
| Berndt | 0.9525 | 0.9469 | 176.3281 | 0.0000 | 149.2685 | 0.0000 |
| McElroy | 0.9652 | 0.9611 | 243.8002 | 0.0000 | 164.4958 | 0.0000 |
| Judge | 0.7531 | 0.7244 | 26.8438 | 0.0000 | 68.5424 | 0.0000 |
+----------------------------------------------------------------------------+
Number of Parameters = 12
Number of Equations = 2
Degrees of Freedom F-Test = (10, 88)
Degrees of Freedom Chi2-Test = 10
Log Determinant of Sigma = -6.9131
Log Likelihood Function = -308.4281
------------------------------------------------------------------------------
y1 = w1y_y1 + w1y_y2 + y2 + x1 + x2
------------------------------------------------------------------------------
Sample Size = 49
Wald Test = 130.9922 | P-Value > Chi2(5) = 0.0000
F-Test = 26.1984 | P-Value > F(5 , 43) = 0.0000
(Buse 1973) R2 = 0.7016 | Raw Moments R2 = 0.9457
(Buse 1973) R2 Adj = 0.6669 | Raw Moments R2 Adj = 0.9394
Root MSE (Sigma) = 9.6573 | Log Likelihood Function = -177.4457
------------------------------------------------------------------------------
- R2h= 0.7124 R2h Adj= 0.6790 F-Test = 21.30 P-Value > F(5 , 43) 0.0000
- R2v= 0.8989 R2v Adj= 0.8871 F-Test = 76.43 P-Value > F(5 , 43) 0.0000
------------------------------------------------------------------------------
y1 | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
y1 |
w1y_y1 | .1382035 .1740695 0.79 0.432 -.2128411 .4892482
w1y_y2 | -.1088995 .1664627 -0.65 0.516 -.4446036 .2268046
y2 | .8254616 .1429166 5.78 0.000 .5372429 1.11368
x1 | -.0593876 .0751261 -0.79 0.434 -.2108938 .0921187
x2 | -.230459 .3059294 -0.75 0.455 -.8474244 .3865064
_cons | 5.357097 10.72446 0.50 0.620 -16.27084 26.98503
------------------------------------------------------------------------------
Rho Value = 0.1382 F Test = 0.630 P-Value > F(1, 43) 0.4316
------------------------------------------------------------------------------
==============================================================================
* Model Selection Diagnostic Criteria
==============================================================================
- Log Likelihood Function LLF = -177.4457
---------------------------------------------------------------------------
- Akaike Information Criterion (1974) AIC = 104.5539
- Akaike Information Criterion (1973) Log AIC = 4.6497
---------------------------------------------------------------------------
- Schwarz Criterion (1978) SC = 131.8090
- Schwarz Criterion (1978) Log SC = 4.8814
---------------------------------------------------------------------------
- Amemiya Prediction Criterion (1969) FPE = 104.6831
- Hannan-Quinn Criterion (1979) HQ = 114.1588
- Rice Criterion (1984) Rice = 108.3869
- Shibata Criterion (1981) Shibata = 101.8864
- Craven-Wahba Generalized Cross Validation (1979) GCV = 106.2766
------------------------------------------------------------------------------
==============================================================================
*** Spatial Aautocorrelation Tests
==============================================================================
Ho: Error has No Spatial AutoCorrelation
Ha: Error has Spatial AutoCorrelation
- GLOBAL Moran MI = -0.1656 P-Value > Z(-1.700) 0.0891
- GLOBAL Geary GC = 1.1315 P-Value > Z(1.037) 0.2996
- GLOBAL Getis-Ords GO = 0.7975 P-Value > Z(1.700) 0.0891
------------------------------------------------------------------------------
- Moran MI Error Test = 0.0204 P-Value > Z(0.485) 0.9837
------------------------------------------------------------------------------
- LM Error (Burridge) = 2.4912 P-Value > Chi2(1) 0.1145
- LM Error (Robust) = 5.2022 P-Value > Chi2(1) 0.0226
------------------------------------------------------------------------------
Ho: Spatial Lagged Dependent Variable has No Spatial AutoCorrelation
Ha: Spatial Lagged Dependent Variable has Spatial AutoCorrelation
- LM Lag (Anselin) = 0.9855 P-Value > Chi2(1) 0.3208
- LM Lag (Robust) = 3.6965 P-Value > Chi2(1) 0.0545
------------------------------------------------------------------------------
Ho: No General Spatial AutoCorrelation
Ha: General Spatial AutoCorrelation
- LM SAC (LMErr+LMLag_R) = 6.1877 P-Value > Chi2(2) 0.0453
- LM SAC (LMLag+LMErr_R) = 6.1877 P-Value > Chi2(2) 0.0453
------------------------------------------------------------------------------
==============================================================================
* Heteroscedasticity Tests
==============================================================================
Ho: Homoscedasticity - Ha: Heteroscedasticity
------------------------------------------------------------------------------
- Hall-Pagan LM Test: E2 = Yh = 0.2800 P-Value > Chi2(1) 0.5967
- Hall-Pagan LM Test: E2 = Yh2 = 0.2935 P-Value > Chi2(1) 0.5880
- Hall-Pagan LM Test: E2 = LYh2 = 0.2923 P-Value > Chi2(1) 0.5887
------------------------------------------------------------------------------
- Harvey LM Test: LogE2 = X = 5.3239 P-Value > Chi2(2) 0.0698
- Wald LM Test: LogE2 = X = 13.1361 P-Value > Chi2(1) 0.0003
- Glejser LM Test: |E| = X = 5.6783 P-Value > Chi2(2) 0.0585
------------------------------------------------------------------------------
- Machado-Santos-Silva Test: Ev=Yh Yh2 = 0.1658 P-Value > Chi2(2) 0.9204
- Machado-Santos-Silva Test: Ev=X = 4.7179 P-Value > Chi2(5) 0.4513
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X = 6.4325 P-Value > Chi2(5) 0.2664
- White Test -B-P-G (SSR): E2 = X = 8.1169 P-Value > Chi2(5) 0.1499
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X X2 = 20.6287 P-Value > Chi2(10) 0.0238
- White Test -B-P-G (SSR): E2 = X X2 = 26.0304 P-Value > Chi2(10) 0.0037
------------------------------------------------------------------------------
- White Test -Koenker(R2): E2 = X X2 XX= 31.9934 P-Value > Chi2(20) 0.0434
- White Test -B-P-G (SSR): E2 = X X2 XX= 40.3709 P-Value > Chi2(20) 0.0045
------------------------------------------------------------------------------
- Cook-Weisberg LM Test E2/Sig2 = Yh = 0.3534 P-Value > Chi2(1) 0.5522
- Cook-Weisberg LM Test E2/Sig2 = X = 8.1169 P-Value > Chi2(5) 0.1499
------------------------------------------------------------------------------
*** Single Variable Tests (E2/Sig2):
- Cook-Weisberg LM Test: w1y_y1 = 0.5190 P-Value > Chi2(1) 0.4713
- Cook-Weisberg LM Test: w1y_y2 = 0.6825 P-Value > Chi2(1) 0.4087
- Cook-Weisberg LM Test: y2 = 0.6179 P-Value > Chi2(1) 0.4318
- Cook-Weisberg LM Test: x1 = 0.8495 P-Value > Chi2(1) 0.3567
- Cook-Weisberg LM Test: x2 = 1.2808 P-Value > Chi2(1) 0.2577
------------------------------------------------------------------------------
*** Single Variable Tests:
- King LM Test: w1y_y1 = 0.5607 P-Value > Chi2(1) 0.4540
- King LM Test: w1y_y2 = 1.0068 P-Value > Chi2(1) 0.3157
- King LM Test: y2 = 0.3213 P-Value > Chi2(1) 0.5709
- King LM Test: x1 = 1.1330 P-Value > Chi2(1) 0.2871
- King LM Test: x2 = 1.8200 P-Value > Chi2(1) 0.1773
==============================================================================
* Non Normality Tests
==============================================================================
Ho: Normality - Ha: Non Normality
------------------------------------------------------------------------------
*** Non Normality Tests:
- Jarque-Bera LM Test = 3.4424 P-Value > Chi2(2) 0.1788
- White IM Test = 8.5563 P-Value > Chi2(2) 0.0139
- Doornik-Hansen LM Test = 3.3724 P-Value > Chi2(2) 0.1852
- Geary LM Test = -1.8746 P-Value > Chi2(2) 0.3917
- Anderson-Darling Z Test = 0.7111 P > Z( 1.530) 0.9370
- D'Agostino-Pearson LM Test = 4.5575 P-Value > Chi2(2) 0.1024
------------------------------------------------------------------------------
*** Skewness Tests:
- Srivastava LM Skewness Test = 2.8825 P-Value > Chi2(1) 0.0895
- Small LM Skewness Test = 3.2377 P-Value > Chi2(1) 0.0720
- Skewness Z Test = 1.7994 P-Value > Chi2(1) 0.0720
------------------------------------------------------------------------------
*** Kurtosis Tests:
- Srivastava Z Kurtosis Test = 0.7483 P-Value > Z(0,1) 0.4543
- Small LM Kurtosis Test = 1.3198 P-Value > Chi2(1) 0.2506
- Kurtosis Z Test = 1.1488 P-Value > Chi2(1) 0.2506
------------------------------------------------------------------------------
Skewness Coefficient = 0.5941 - Standard Deviation = 0.3398
Kurtosis Coefficient = 3.5237 - Standard Deviation = 0.6681
------------------------------------------------------------------------------
Runs Test: (19) Runs - (25) Positives - (24) Negatives
Standard Deviation Runs Sig(k) = 3.4619 , Mean Runs E(k) = 25.4898
95% Conf. Interval [E(k)+/- 1.96* Sig(k)] = (18.7045 , 32.2751 )
------------------------------------------------------------------------------
* Marginal Effect - Elasticity: Linear *
+---------------------------------------------------------------------------+
| Variable | Marginal_Effect(B) | Elasticity(Es) | Mean |
|------------+--------------------+--------------------+--------------------|
|y1 | | | |
| w1y_y1 | 0.1382 | 0.6704 | 170.4034 |
| w1y_y2 | -0.1089 | -0.5748 | 185.4260 |
| y2 | 0.8255 | 0.9112 | 38.7779 |
| x1 | -0.0594 | -0.0650 | 38.4362 |
| x2 | -0.2305 | -0.0943 | 14.3749 |
+---------------------------------------------------------------------------+
Mean of Dependent Variable = 35.1288
.
第二个方程的估计结果为:
. gs3sls y1 x1 x2 , var2(y2 x3 x4) wmfile(SPWcs) eq(2) order(1) mfx(lin) test
==============================================================================
*** Binary (0/1) Weight Matrix: 49x49 (Non Normalized)
==============================================================================
==============================================================================
* Generalized Spatial Three Stage Least Squares (GS3SLS)
==============================================================================
y1 = w1y_y1 + w1y_y2 + y2 + x1 + x2
------------------------------------------------------------------------------
y2 = w1y_y2 + w1y_y1 + y1 + x3 + x4
------------------------------------------------------------------------------
Three-stage least-squares regression
------------------------------------------------------------------------------
Equation Obs Params RMSE "R-squared" F P>F
------------------------------------------------------------------------------
y1 49 5 9.657283 0.7016 26.20 0.0000
y2 49 5 7.414835 0.8091 52.39 0.0000
------------------------------------------------------------------------------
------------------------------------------------------------------------------
| Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
y1 |
w1y_y1 | .1382035 .1740695 0.79 0.429 -.2078352 .4842423
w1y_y2 | -.1088995 .1664627 -0.65 0.515 -.4398164 .2220174
y2 | .8254616 .1429166 5.78 0.000 .5413529 1.10957
x1 | -.0593876 .0751261 -0.79 0.431 -.2087333 .0899582
x2 | -.230459 .3059294 -0.75 0.453 -.8386265 .3777085
_cons | 5.357097 10.72446 0.50 0.619 -15.96243 26.67662
-------------+----------------------------------------------------------------
y2 |
w1y_y2 | .0538141 .1144285 0.47 0.639 -.1736622 .2812905
w1y_y1 | -.0685151 .1202225 -0.57 0.570 -.3075095 .1704794
y1 | .5043856 .204935 2.46 0.016 .0969882 .9117829
x3 | .0517263 .0898243 0.58 0.566 -.1268385 .230291
x4 | .3148184 .0914127 3.44 0.001 .133096 .4965409
_cons | 2.931701 3.871633 0.76 0.451 -4.764852 10.62825
------------------------------------------------------------------------------
Endogenous variables: y1 y2 w1y_y1 w1y_y2
Exogenous variables: x1 x2 x3 x4 w1x_x1 w1x_x2 w1x_x3 w1x_x4 w2x_x1 w2x_x2
w2x_x3 w2x_x4
EQ1: R2= 0.7016 - R2 Adj.= 0.6669 F-Test = 19.748 P-Value> F(5, 42)
LLF = -177.446 AIC = 366.891 SC = 378.242 Root MSE = 9.6573
EQ2: R2= 0.8091 - R2 Adj.= 0.7868 F-Test = 35.591 P-Value> F(5, 42)
LLF = -164.498 AIC = 340.997 SC = 352.348 Root MSE = 7.4148
Yij = LHS Y(i) in Eq.(j)
------------------------------------------------------------------------------
- Overall System R2 - Adjusted R2 - F Test - Chi2 Test
+----------------------------------------------------------------------------+
| Name | R2 | Adj_R2 | F | P-Value | Chi2 | P-Value |
|----------+----------+----------+----------+----------+----------+----------|
| Berndt | 0.9525 | 0.9469 | 176.3281 | 0.0000 | 149.2685 | 0.0000 |
| McElroy | 0.9652 | 0.9611 | 243.8002 | 0.0000 | 164.4958 | 0.0000 |
| Judge | 0.7531 | 0.7244 | 26.8438 | 0.0000 | 68.5424 | 0.0000 |
+----------------------------------------------------------------------------+
Number of Parameters = 12
Number of Equations = 2
Degrees of Freedom F-Test = (10, 88)
Degrees of Freedom Chi2-Test = 10
Log Determinant of Sigma = -6.9131
Log Likelihood Function = -308.4281
------------------------------------------------------------------------------
y2 = w1y_y2 + w1y_y1 + y1 + x3 + x4
------------------------------------------------------------------------------
Sample Size = 49
Wald Test = 261.9502 | P-Value > Chi2(5) = 0.0000
F-Test = 52.3900 | P-Value > F(5 , 43) = 0.0000
(Buse 1973) R2 = 0.8091 | Raw Moments R2 = 0.9725
(Buse 1973) R2 Adj = 0.7868 | Raw Moments R2 Adj = 0.9693
Root MSE (Sigma) = 7.4148 | Log Likelihood Function = -164.4984
------------------------------------------------------------------------------
- R2h= 0.9241 R2h Adj= 0.9153 F-Test = 104.68 P-Value > F(5 , 43) 0.0000
- R2v= 0.8268 R2v Adj= 0.8067 F-Test = 41.06 P-Value > F(5 , 43) 0.0000
------------------------------------------------------------------------------
y1 | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
y2 |
w1y_y2 | .0538141 .1144285 0.47 0.641 -.176953 .2845812
w1y_y1 | -.0685151 .1202225 -0.57 0.572 -.3109669 .1739368
y1 | .5043856 .204935 2.46 0.018 .0910947 .9176764
x3 | .0517263 .0898243 0.58 0.568 -.1294216 .2328742
x4 | .3148184 .0914127 3.44 0.001 .1304671 .4991698
_cons | 2.931701 3.871633 0.76 0.453 -4.876192 10.73959
------------------------------------------------------------------------------
Rho Value = -0.0685 F Test = 0.325 P-Value > F(1, 43) 0.5717
------------------------------------------------------------------------------
==============================================================================
* Model Selection Diagnostic Criteria
==============================================================================
- Log Likelihood Function LLF = -164.4984
---------------------------------------------------------------------------
- Akaike Information Criterion (1974) AIC = 61.6358
- Akaike Information Criterion (1973) Log AIC = 4.1212
---------------------------------------------------------------------------
- Schwarz Criterion (1978) SC = 77.7031
- Schwarz Criterion (1978) Log SC = 4.3529
---------------------------------------------------------------------------
- Amemiya Prediction Criterion (1969) FPE = 61.7120
- Hannan-Quinn Criterion (1979) HQ = 67.2981
- Rice Criterion (1984) Rice = 63.8954
- Shibata Criterion (1981) Shibata = 60.0633
- Craven-Wahba Generalized Cross Validation (1979) GCV = 62.6514
------------------------------------------------------------------------------
==============================================================================
*** Spatial Aautocorrelation Tests
==============================================================================
Ho: Error has No Spatial AutoCorrelation
Ha: Error has Spatial AutoCorrelation
- GLOBAL Moran MI = 0.1457 P-Value > Z( 1.953) 0.0509
- GLOBAL Geary GC = 0.7969 P-Value > Z(-1.634) 0.1022
- GLOBAL Getis-Ords GO = -0.7019 P-Value > Z(-37.568) 0.0000
------------------------------------------------------------------------------
- Moran MI Error Test = 0.1895 P-Value > Z(2.466) 0.8497
------------------------------------------------------------------------------
- LM Error (Burridge) = 0.6624 P-Value > Chi2(1) 0.4157
- LM Error (Robust) = 1.9332 P-Value > Chi2(1) 0.1644
------------------------------------------------------------------------------
Ho: Spatial Lagged Dependent Variable has No Spatial AutoCorrelation
Ha: Spatial Lagged Dependent Variable has Spatial AutoCorrelation
- LM Lag (Anselin) = 0.1384 P-Value > Chi2(1) 0.7099
- LM Lag (Robust) = 1.4092 P-Value > Chi2(1) 0.2352
------------------------------------------------------------------------------
Ho: No General Spatial AutoCorrelation
Ha: General Spatial AutoCorrelation
- LM SAC (LMErr+LMLag_R) = 2.0716 P-Value > Chi2(2) 0.3549
- LM SAC (LMLag+LMErr_R) = 2.0716 P-Value > Chi2(2) 0.3549
------------------------------------------------------------------------------
==============================================================================
* Heteroscedasticity Tests
==============================================================================
Ho: Homoscedasticity - Ha: Heteroscedasticity
------------------------------------------------------------------------------
- Hall-Pagan LM Test: E2 = Yh = 0.1648 P-Value > Chi2(1) 0.6848
- Hall-Pagan LM Test: E2 = Yh2 = 0.2276 P-Value > Chi2(1) 0.6333
- Hall-Pagan LM Test: E2 = LYh2 = 0.0328 P-Value > Chi2(1) 0.8563
------------------------------------------------------------------------------
- Harvey LM Test: LogE2 = X = 3.0796 P-Value > Chi2(2) 0.2144
- Wald LM Test: LogE2 = X = 7.5985 P-Value > Chi2(1) 0.0058
- Glejser LM Test: |E| = X = 4.3512 P-Value > Chi2(2) 0.1135
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- Machado-Santos-Silva Test: Ev=Yh Yh2 = 0.8900 P-Value > Chi2(2) 0.6408
- Machado-Santos-Silva Test: Ev=X = 12.6151 P-Value > Chi2(5) 0.0273
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- White Test -Koenker(R2): E2 = X = 11.3622 P-Value > Chi2(5) 0.0447
- White Test -B-P-G (SSR): E2 = X = 2.6579 P-Value > Chi2(5) 0.7526
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- White Test -Koenker(R2): E2 = X X2 = 22.4138 P-Value > Chi2(10) 0.0131
- White Test -B-P-G (SSR): E2 = X X2 = 5.2431 P-Value > Chi2(10) 0.8744
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- White Test -Koenker(R2): E2 = X X2 XX= 49.0000 P-Value > Chi2(20) 0.0003
- White Test -B-P-G (SSR): E2 = X X2 XX= 11.4621 P-Value > Chi2(20) 0.9333
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- Cook-Weisberg LM Test E2/Sig2 = Yh = 0.0385 P-Value > Chi2(1) 0.8444
- Cook-Weisberg LM Test E2/Sig2 = X = 2.6579 P-Value > Chi2(5) 0.7526
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*** Single Variable Tests (E2/Sig2):
- Cook-Weisberg LM Test: w1y_y2 = 0.1023 P-Value > Chi2(1) 0.7491
- Cook-Weisberg LM Test: w1y_y1 = 0.0745 P-Value > Chi2(1) 0.7849
- Cook-Weisberg LM Test: y1 = 0.3018 P-Value > Chi2(1) 0.5828
- Cook-Weisberg LM Test: x3 = 0.0267 P-Value > Chi2(1) 0.8702
- Cook-Weisberg LM Test: x4 = 0.0704 P-Value > Chi2(1) 0.7908
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*** Single Variable Tests:
- King LM Test: w1y_y2 = 0.1563 P-Value > Chi2(1) 0.6926
- King LM Test: w1y_y1 = 0.2200 P-Value > Chi2(1) 0.6390
- King LM Test: y1 = 1.8234 P-Value > Chi2(1) 0.1769
- King LM Test: x3 = 0.0000 P-Value > Chi2(1) 0.9975
- King LM Test: x4 = 0.2134 P-Value > Chi2(1) 0.6441
==============================================================================
* Non Normality Tests
==============================================================================
Ho: Normality - Ha: Non Normality
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*** Non Normality Tests:
- Jarque-Bera LM Test = 3.1586 P-Value > Chi2(2) 0.2061
- White IM Test = 13.6980 P-Value > Chi2(2) 0.0011
- Doornik-Hansen LM Test = 3.2753 P-Value > Chi2(2) 0.1944
- Geary LM Test = -0.3633 P-Value > Chi2(2) 0.8339
- Anderson-Darling Z Test = 0.6935 P > Z( 1.478) 0.9303
- D'Agostino-Pearson LM Test = 4.1301 P-Value > Chi2(2) 0.1268
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*** Skewness Tests:
- Srivastava LM Skewness Test = 2.9192 P-Value > Chi2(1) 0.0875
- Small LM Skewness Test = 3.2751 P-Value > Chi2(1) 0.0703
- Skewness Z Test = 1.8097 P-Value > Chi2(1) 0.0703
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*** Kurtosis Tests:
- Srivastava Z Kurtosis Test = 0.4893 P-Value > Z(0,1) 0.6246
- Small LM Kurtosis Test = 0.8550 P-Value > Chi2(1) 0.3551
- Kurtosis Z Test = 0.9247 P-Value > Chi2(1) 0.3551
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Skewness Coefficient = 0.5979 - Standard Deviation = 0.3398
Kurtosis Coefficient = 3.3424 - Standard Deviation = 0.6681
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Runs Test: (24) Runs - (22) Positives - (27) Negatives
Standard Deviation Runs Sig(k) = 3.4265 , Mean Runs E(k) = 25.2449
95% Conf. Interval [E(k)+/- 1.96* Sig(k)] = (18.5289 , 31.9609 )
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* Marginal Effect - Elasticity: Linear *
+---------------------------------------------------------------------------+
| Variable | Marginal_Effect(B) | Elasticity(Es) | Mean |
|------------+--------------------+--------------------+--------------------|
|y2 | | | |
| w1y_y2 | 0.0538 | 0.2841 | 185.4260 |
| w1y_y1 | -0.0685 | -0.3324 | 170.4034 |
| y1 | 0.5044 | 0.5044 | 35.1288 |
| x3 | 0.0517 | 0.0735 | 49.9263 |
| x4 | 0.3148 | 0.4908 | 54.7676 |
+---------------------------------------------------------------------------+
Mean of Dependent Variable = 35.1288