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
------------------------------------------------------------------------------
- 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
------------------------------------------------------------------------------
- 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
------------------------------------------------------------------------------
- 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
------------------------------------------------------------------------------
- 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
------------------------------------------------------------------------------
- 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
------------------------------------------------------------------------------
*** 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
------------------------------------------------------------------------------
*** 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
------------------------------------------------------------------------------
*** 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
------------------------------------------------------------------------------
*** 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
------------------------------------------------------------------------------
*** 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
------------------------------------------------------------------------------
    Skewness Coefficient =  0.5979     - Standard Deviation =  0.3398
    Kurtosis Coefficient =  3.3424     - Standard Deviation =  0.6681
------------------------------------------------------------------------------
    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 )
------------------------------------------------------------------------------

* 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