天鹰—2021
天鹰（中南财大——博士研究生）
E-mail: [[email protected]]
前文主要讲解了常用的空间权重矩阵的具体操作，明白了空间权重矩阵在整个空间计量模型中的重要作用，当然，除了上述常见的几种空间矩阵外，我们在文献中也会看到研究者为了更加契合各经济体之间经济空间联系，所构建的更加复杂的权重矩阵，在知道基本原理以后，就可以根据实际需要去构建自己需要的矩阵啦。
- 接下来，本文主要对空间计量的后续一系列操作进行简单的讲解，以期为大家做好流程梳理，使大家能够明白每一步在整个空间计量中所起到的作用。流程图可参考下图，也可根据推荐的视频进行学习。
推荐视频
流程图
1.计算莫兰指数画莫兰图
- 该步骤主要是通过莫兰指数以及图像进行判断各变量是否存在空间相关性，我们在选用一个模型之前，首先应该判断我们研究的问题是否具有空间相关关系，每一个变量（特别是核心解释变量和被解释变量）是否具有空间相关性，常用的判断方法就是计算莫兰指数和画莫兰散点图。
（本文以作者研究中所用的一部分数据进行演示，权重矩阵以0-1矩阵为例。） - 首先调入0-1矩阵
cap log c
clear all
use w0110.dta,clear
keep s*
save "weight1.dta",replace
spatwmat using weight1,name(W) standardize / / 矩阵标准化
- 调入研究的数据
use 3.25panel.dta, clear
keep if year==2003
- 此处需要特别注意的是，stata在计算莫兰指数以及画莫兰散点图时，只能一年一年的进行，为此，需要连续操作多次。
spatgsa indh ,weights(W) moran
spatgsa indh ind32 indr indr2 ai1 ,weights(W) moran
/ / moran值只能一年一年测算，因此需要重复每一年的命令
- 结果显示如下：
Name: W
Type: Imported (binary)
Row-standardized: Yes
--------------------------------------------------------------
Moran's I
--------------------------------------------------------------
Variables | I E(I) sd(I) z p-value*
--------------------+-----------------------------------------
indh | 0.156 -0.034 0.057 3.335 0.000
ind32 | -0.015 -0.034 0.053 0.372 0.355
indr | 0.101 -0.034 0.055 2.469 0.007
indr2 | 0.158 -0.034 0.058 3.347 0.000
ai1 | 0.128 -0.034 0.057 2.872 0.002
--------------------------------------------------------------
spatlsa indh ,weights(W) moran graph(moran) symbol(n) / /计算LISA并画出莫兰散点图(只能一次画一个变量)
indh莫兰散点图1
- 此时个体是以数字进行表示，如果个体加上对应的标签，命令需进行如下修改
spatlsa indh ,weights(W) moran graph(moran) symbol(id) id(name) / /莫兰散点图可以标注出地名
-
结果呈现：
indh莫兰散点图2
以上是针对莫兰指数以及莫兰散点图操作的讲解，具体分析，可参考文献（张万里等（2020）产业智能化对产业结构升级的空间溢出效应——劳动力结构和收入分配不平等的调节作用）
2.模型检验
2.1 LM检验
- 本检验的目的就是判断各变量是否具有空间分布属性，模型是否有必要用空间计量模型，该检验是与混合OLS对比。
reg indh lnai1 lnhum lnurb lnpgdp lnopen lnstr lnfdi
spatdiag, weights(w2b)
- 结果呈现：
Source | SS df MS Number of obs = 480
-------------+---------------------------------- F(7, 472) = 319.57
Model | 167.343496 7 23.9062138 Prob > F = 0.0000
Residual | 35.3088068 472 .074806794 R-squared = 0.8258
-------------+---------------------------------- Adj R-squared = 0.8232
Total | 202.652303 479 .423073702 Root MSE = .27351
------------------------------------------------------------------------------
indh | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnai1 | .0782969 .0207407 3.78 0.000 .0375413 .1190524
lnhum | 1.548572 .2224006 6.96 0.000 1.111554 1.985589
lnurb | -.349849 .1468257 -2.38 0.018 -.638362 -.0613361
lnpgdp | .7436782 .040243 18.48 0.000 .6646006 .8227558
lnopen | -.0631071 .0183946 -3.43 0.001 -.0992524 -.0269617
lnstr | -.0562492 .0206882 -2.72 0.007 -.0969017 -.0155968
lnfdi | -.0562877 .0153621 -3.66 0.000 -.0864742 -.0261012
_cons | -9.563391 .6191849 -15.45 0.000 -10.78009 -8.346691
------------------------------------------------------------------------------
. spatdiag, weights(w2b)
Diagnostic tests for spatial dependence in OLS regression
Fitted model
------------------------------------------------------------
indh = lnai1 + lnhum + lnurb + lnpgdp + lnopen + lnstr + lnfdi
------------------------------------------------------------
Weights matrix
------------------------------------------------------------
Name: w2b
Type: Distance-based (inverse distance)
Distance band: c1.c2 < d <= c3.c4
Row-standardized: No
------------------------------------------------------------
Diagnostics
------------------------------------------------------------
Test | Statistic df p-value
-------------------------------+----------------------------
Spatial error: |
Moran's I | 1.743 1 0.081
Lagrange multiplier | 240.883 1 0.000
Robust Lagrange multiplier | 226.944 1 0.000
|
Spatial lag: |
Lagrange multiplier | 14.632 1 0.000
Robust Lagrange multiplier | 0.693 1 0.405
------------------------------------------------------------
- 此时需要通过Spatial error和Spatial lag进行判断，其原假设分别是误差项不存在空间相关性，滞后项不存在空间相关性，通过对应的p值，可以看出是拒绝原假设的，说明误差项和滞后项均存在空间相关性的。
2.2 Hausman检验
- 该检验的目的是为了判断模型是采用固定效应还是随机效应，注意：此时的命令与非空间计量的操作不一样。
xsmle indh lnai1 lnhum lnurb lnpgdp lnopen lnstr lnfdi,model(sdm) ///
wmat(w2b) hausman nolog
- 结果呈现：
Warning: All regressors will be spatially lagged
estimating fixed-effects model to perform Hausman test
SDM with random-effects Number of obs = 480
Group variable: id Number of groups = 30
Time variable: year Panel length = 16
R-sq: within = 0.8950
between = 0.0004
overall = 0.5128
Log-likelihood = 114.2447
------------------------------------------------------------------------------
indh | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Main |
lnai1 | .0141394 .0172924 0.82 0.414 -.019753 .0480318
lnhum | .5715857 .3544807 1.61 0.107 -.1231838 1.266355
lnurb | -2.304039 .1963603 -11.73 0.000 -2.688898 -1.91918
lnpgdp | 1.036132 .0713559 14.52 0.000 .8962768 1.175987
lnopen | -.0362019 .0305358 -1.19 0.236 -.096051 .0236473
lnstr | -.0095572 .0612648 -0.16 0.876 -.1296339 .1105196
lnfdi | .0069282 .0163646 0.42 0.672 -.0251458 .0390021
_cons | -12.0415 1.064581 -11.31 0.000 -14.12804 -9.954956
-------------+----------------------------------------------------------------
Wx |
lnai1 | .0101005 .0303298 0.33 0.739 -.0493448 .0695457
lnhum | .3715369 .5259231 0.71 0.480 -.6592534 1.402327
lnurb | .7866186 .3070776 2.56 0.010 .1847576 1.38848
lnpgdp | -.6691565 .0863862 -7.75 0.000 -.8384704 -.4998426
lnopen | -.0427657 .0811575 -0.53 0.598 -.2018316 .1163001
lnstr | .8479178 .1382939 6.13 0.000 .5768666 1.118969
lnfdi | .197277 .0740422 2.66 0.008 .052157 .3423969
-------------+----------------------------------------------------------------
Spatial |
rho | .4981421 .0610269 8.16 0.000 .3785316 .6177525
-------------+----------------------------------------------------------------
Variance |
lgt_theta | -2.231347 .2005747 -11.12 0.000 -2.624466 -1.838228
sigma2_e | .0265422 .0018263 14.53 0.000 .0229628 .0301216
------------------------------------------------------------------------------
Ho: difference in coeffs not systematic chi2(15) = 25.20 Prob>=chi2 = 0.0474
------------------------------------------------------------------------------
- 由最终系数判断，拒绝原假设，也即个体系数之间是存在显著的差异的，最终选择固定效应模型进行后续操作。
3. LR+Wald检验
这两个检验是在通过LM检验已经确定变量之间存在空间相关性，可以利用空间计量模型进行后续操作的基础上，去进一步判断空间计量模型具体采用哪个。其思想均是假设模型是空间杜宾模型（SDM），看看能否进一步退化为空间误差模型（SEM）或者空间自相关模型（SAR），如果能够退化，那么采用更具针对性的退化后的模型，若不能退化，那么就采用包容性更强的SDM模型。
3.1 LR检验
xsmle indh lnai1 lnhum lnpgdp lnopen lnstr lnfdi ,wmat(w2b) model(sdm) ///
fe type(ind) nsim(500) nolog effects //effects（偏微分分解）
est store sdm_a
xsmle indh lnai1 lnhum lnurb lnpgdp lnopen lnstr lnfdi ,wmat(w2b) model(sar) ///
fe type(ind) nsim(500) nolog effects //effects（偏微分分解）
est store sar_a
xsmle indh lnai1 lnhum lnurb lnpgdp lnopen lnstr lnfdi ,emat(w2b) model(sem) ///
fe type(ind) nsim(500) nolog effects //effects（偏微分分解）
est store sem_a
lrtest sdm_a sar_a / /比较sdm与sar模型
lrtest sdm_a sem_a / /比较sdm与sem模型
- 结果显示：
lrtest sdm_a sar_a //比较sdm与sar模型
Likelihood-ratio test LR chi2(5) = -90.40
(Assumption: sar_a nested in sdm_a) Prob > chi2 = 1.0000
lrtest sdm_a sem_a //比较sdm与sem模型
Likelihood-ratio test LR chi2(5) = -134.85
(Assumption: sem_a nested in sdm_a) Prob > chi2 = 1.0000
说明：LR的原假设是sdm模型能够退化成sar模型和sem模型，本文的检测结果由P值可知，是接受原假设的，也即应该采用退化后的结果。
（本数据仅仅为了演示，具体情况要具体分析）
3.2 Wald检验
注意：为方便后续演示，Wald检验被解释变量替换成indr
xsmle indr lnai1 lnhum lnurb lnpgdp lnopen lnstr lnfdi ,wmat(w2b) model(sdm) ///
fe type(both) nsim(500) nolog effects / /effects（偏微分分解）
test[Wx]lnai1=[Wx]lnhum=[Wx]lnurb=[Wx]lnpgdp=[Wx]lnopen=[Wx]lnstr=[Wx]lnfdi=0 //比较sdm与sar模型
- 结果显示1：
( 1) [Wx]lnai1 - [Wx]lnhum = 0
( 2) [Wx]lnai1 - [Wx]lnurb = 0
( 3) [Wx]lnai1 - [Wx]lnpgdp = 0
( 4) [Wx]lnai1 - [Wx]lnopen = 0
( 5) [Wx]lnai1 - [Wx]lnstr = 0
( 6) [Wx]lnai1 - [Wx]lnfdi = 0
( 7) [Wx]lnai1 = 0
chi2( 7) = 105.36
Prob > chi2 = 0.0000 / /此时可以发现拒绝原假设
**[Wx]后面跟变量表示该变量的空间滞后项，[Wx]lnai1表示lnai1的空间滞后项
testnl([Wx]lnai1=-[Spatial]rho*[Main]lnai1) ([Wx]lnhum=-[Spatial]rho*[Main]lnhum) ///
([Wx]lnurb=-[Spatial]rho*[Main]lnurb) ([Wx]lnpgdp=-[Spatial]rho*[Main]lnpgdp) ///
([Wx]lnopen=-[Spatial]rho*[Main]lnopen) ([Wx]lnstr=-[Spatial]rho*[Main]lnstr) ///
([Wx]lnfdi=-[Spatial]rho*[Main]lnfdi) / /比较sdm与sem模型
- 结果显示2
(1) [Wx]lnai1 = -[Spatial]rho*[Main]lnai1
(2) [Wx]lnhum = -[Spatial]rho*[Main]lnhum
(3) [Wx]lnurb = -[Spatial]rho*[Main]lnurb
(4) [Wx]lnpgdp = -[Spatial]rho*[Main]lnpgdp
(5) [Wx]lnopen = -[Spatial]rho*[Main]lnopen
(6) [Wx]lnstr = -[Spatial]rho*[Main]lnstr
(7) [Wx]lnfdi = -[Spatial]rho*[Main]lnfdi
chi2(7) = 119.50
Prob > chi2 = 0.0000 / /此时拒绝原假设
- 此时，我们可以发现，Wald检验结果比较一致，也即SDM不能退化成SEM或者SAR，因此，最终模型选择SDM模型进行后续模型的回归。
4. SDM模型回归
通过上述各种检验，最终确定模型选择空间计量模型进行回归，对于固定效应模型，空间计量中也存在对应三种形式：时间固定、个体固定、个体时间双固定，在命令中通过对应选项进行设定。
4.1 时间固定
. xsmle indh lnai1 lnurb lnpgdp lnopen lnstr lnfdi ,wmat(w2b) model(sdm) ///
fe type(time) nsim(500) nolog
Warning: All regressors will be spatially lagged
convergence not achieved
SDM with time fixed-effects Number of obs = 480
Group variable: id Number of groups = 30
Time variable: year Panel length = 16
R-sq: within = 0.8218
between = 0.1327
overall = 0.4361
Mean of fixed-effects = -8.6828
Log-likelihood = -27.3910
------------------------------------------------------------------------------
indh | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Main |
lnai1 | .0647171 .0234792 2.76 0.006 .0186986 .1107355
lnurb | -.0078166 .1606611 -0.05 0.961 -.3227067 .3070734
lnpgdp | .9957974 .0801324 12.43 0.000 .8387408 1.152854
lnopen | -.1451156 .0249105 -5.83 0.000 -.1939393 -.0962919
lnstr | -.0361917 .0228758 -1.58 0.114 -.0810275 .008644
lnfdi | -.0114885 .0176561 -0.65 0.515 -.0460937 .0231168
-------------+----------------------------------------------------------------
Wx |
lnai1 | .1966633 .0903494 2.18 0.030 .0195817 .3737448
lnurb | -.8798602 .2550649 -3.45 0.001 -1.379778 -.3799423
lnpgdp | -.1560619 .076158 -2.05 0.040 -.3053287 -.006795
lnopen | -.1927672 .0980735 -1.97 0.049 -.3849876 -.0005467
lnstr | .3537218 .092058 3.84 0.000 .1732913 .5341522
lnfdi | .3702656 .0781735 4.74 0.000 .2170484 .5234828
-------------+----------------------------------------------------------------
Spatial |
rho | .2594026 . . . . .
-------------+----------------------------------------------------------------
Variance |
sigma2_e | .0647799 .0041508 15.61 0.000 .0566444 .0729154
------------------------------------------------------------------------------
. estat ic / /AIC BIC test
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 480 . -27.39105 13 80.7821 135.0413
-----------------------------------------------------------------------------
Note: N=Obs used in calculating BIC; see [R] BIC note.
. est store M_1
4.2 个体固定
. xsmle indh lnai1 lnurb lnpgdp lnopen lnstr lnfdi ,wmat(w2b) model(sdm) ///
fe type(ind) nsim(500) nolog
Warning: All regressors will be spatially lagged
SDM with spatial fixed-effects Number of obs = 480
Group variable: id Number of groups = 30
Time variable: year Panel length = 16
R-sq: within = 0.8956
between = 0.0772
overall = 0.0875
Mean of fixed-effects = -6.6100
Log-likelihood = 206.7967
------------------------------------------------------------------------------
indh | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Main |
lnai1 | .0032059 .0163587 0.20 0.845 -.0288566 .0352684
lnurb | -2.575745 .1834151 -14.04 0.000 -2.935232 -2.216258
lnpgdp | 1.038779 .068828 15.09 0.000 .9038787 1.173679
lnopen | -.0688752 .0291643 -2.36 0.018 -.1260361 -.0117143
lnstr | .1202283 .0601734 2.00 0.046 .0022906 .238166
lnfdi | .0178616 .0156416 1.14 0.253 -.0127954 .0485185
-------------+----------------------------------------------------------------
Wx |
lnai1 | .0088397 .0277297 0.32 0.750 -.0455096 .0631889
lnurb | 2.015259 .4894426 4.12 0.000 1.055969 2.974548
lnpgdp | -.7986693 .1039317 -7.68 0.000 -1.002372 -.594967
lnopen | -.0706365 .0795821 -0.89 0.375 -.2266145 .0853415
lnstr | .493464 .1816466 2.72 0.007 .1374433 .8494848
lnfdi | .2208083 .0723264 3.05 0.002 .0790511 .3625656
-------------+----------------------------------------------------------------
Spatial |
rho | .6025657 .0638191 9.44 0.000 .4774827 .7276488
-------------+----------------------------------------------------------------
Variance |
sigma2_e | .0238286 .0015567 15.31 0.000 .0207775 .0268797
------------------------------------------------------------------------------
. estat ic / /AIC BIC test
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 480 . 206.7967 14 -385.5934 -327.1604
-----------------------------------------------------------------------------
Note: N=Obs used in calculating BIC; see [R] BIC note.
. est store M_2
4.3 个体时间双固定
. xsmle indh lnai1 lnurb lnpgdp lnopen lnstr lnfdi ,wmat(w2b) model(sdm) ///
fe type(both) nsim(500) nolog effects
Warning: All regressors will be spatially lagged
convergence not achieved
Computing marginal effects standard errors using MC simulation...
SDM with spatial and time fixed-effects Number of obs = 480
Group variable: id Number of groups = 30
Time variable: year Panel length = 16
R-sq: within = 0.8446
between = 0.0229
overall = 0.0433
Mean of fixed-effects = -4.1053
Log-likelihood = 231.7637
------------------------------------------------------------------------------
indh | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Main |
lnai1 | .0195483 .0166901 1.17 0.241 -.0131637 .0522603
lnurb | -2.64566 .181635 -14.57 0.000 -3.001658 -2.289662
lnpgdp | .8247339 .0816866 10.10 0.000 .6646311 .9848366
lnopen | -.0730921 .0308264 -2.37 0.018 -.1335106 -.0126735
lnstr | .0152735 .0644112 0.24 0.813 -.1109702 .1415171
lnfdi | .0371711 .0160669 2.31 0.021 .0056804 .0686617
-------------+----------------------------------------------------------------
Wx |
lnai1 | .123214 .0634018 1.94 0.052 -.0010513 .2474793
lnurb | 2.293344 .5723017 4.01 0.000 1.171653 3.415034
lnpgdp | -.5517104 .1647168 -3.35 0.001 -.8745493 -.2288715
lnopen | -.2323947 .151855 -1.53 0.126 -.5300251 .0652356
lnstr | .4248028 .2585176 1.64 0.100 -.0818825 .9314881
lnfdi | .3483528 .0834773 4.17 0.000 .1847404 .5119653
-------------+----------------------------------------------------------------
Spatial |
rho | .3 .1503035 2.00 0.046 .0054105 .5945895
-------------+----------------------------------------------------------------
Variance |
sigma2_e | .0225831 .001499 15.07 0.000 .0196452 .025521
-------------+----------------------------------------------------------------
LR_Direct |
lnai1 | .0237485 .0174309 1.36 0.173 -.0104154 .0579125
lnurb | -2.613857 .176801 -14.78 0.000 -2.960381 -2.267333
lnpgdp | .8259336 .0798606 10.34 0.000 .6694097 .9824574
lnopen | -.078957 .0315847 -2.50 0.012 -.1408619 -.0170521
lnstr | .0260854 .0646428 0.40 0.687 -.1006121 .1527829
lnfdi | .0478904 .0173831 2.75 0.006 .0138202 .0819607
-------------+----------------------------------------------------------------
LR_Indirect |
lnai1 | .1790068 .0958373 1.87 0.062 -.0088309 .3668445
lnurb | 2.043289 .7305513 2.80 0.005 .611435 3.475143
lnpgdp | -.4040708 .2032038 -1.99 0.047 -.8023428 -.0057987
lnopen | -.331528 .2026713 -1.64 0.102 -.7287564 .0657005
lnstr | .5663275 .3772711 1.50 0.133 -.1731102 1.305765
lnfdi | .5024553 .1476957 3.40 0.001 .2129772 .7919335
-------------+----------------------------------------------------------------
LR_Total |
lnai1 | .2027553 .1014327 2.00 0.046 .0039508 .4015598
lnurb | -.570568 .7393432 -0.77 0.440 -2.019654 .8785182
lnpgdp | .4218628 .2312038 1.82 0.068 -.0312883 .8750139
lnopen | -.410485 .2166001 -1.90 0.058 -.8350134 .0140435
lnstr | .5924129 .4040514 1.47 0.143 -.1995133 1.384339
lnfdi | .5503457 .1560449 3.53 0.000 .2445034 .8561881
------------------------------------------------------------------------------
. estat ic / /AIC BIC test
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 480 . 231.7637 14 -435.5273 -377.0943
-----------------------------------------------------------------------------
Note: N=Obs used in calculating BIC; see [R] BIC note.
. est store M_3
- 三个模型结果汇总：
local m "M_1 M_2 M_3"
esttab `m', mtitle(`m') nogap s(r2 ll aic bic N) ///
star(* 0.1 ** 0.05 *** 0.01) b(%6.3f)
------------------------------------------------------------
(1) (2) (3)
M_1 M_2 M_3
------------------------------------------------------------
Main
lnai1 0.065*** 0.003 0.020
(2.76) (0.20) (1.17)
lnurb -0.008 -2.576*** -2.646***
(-0.05) (-14.04) (-14.57)
lnpgdp 0.996*** 1.039*** 0.825***
(12.43) (15.09) (10.10)
lnopen -0.145*** -0.069** -0.073**
(-5.83) (-2.36) (-2.37)
lnstr -0.036 0.120** 0.015
(-1.58) (2.00) (0.24)
lnfdi -0.011 0.018 0.037**
(-0.65) (1.14) (2.31)
------------------------------------------------------------
Wx
lnai1 0.197** 0.009 0.123*
(2.18) (0.32) (1.94)
lnurb -0.880*** 2.015*** 2.293***
(-3.45) (4.12) (4.01)
lnpgdp -0.156** -0.799*** -0.552***
(-2.05) (-7.68) (-3.35)
lnopen -0.193** -0.071 -0.232
(-1.97) (-0.89) (-1.53)
lnstr 0.354*** 0.493*** 0.425
(3.84) (2.72) (1.64)
lnfdi 0.370*** 0.221*** 0.348***
(4.74) (3.05) (4.17)
------------------------------------------------------------
Spatial
rho 0.259 0.603*** 0.300**
(.) (9.44) (2.00)
------------------------------------------------------------
Variance
sigma2_e 0.065*** 0.024*** 0.023***
(15.61) (15.31) (15.07)
------------------------------------------------------------
r2 0.436 0.088 0.043
ll -27.391 206.797 231.764
aic 80.782 -385.593 -435.527
bic 135.041 -327.160 -377.094
N 480.000 480.000 480.000
------------------------------------------------------------
t statistics in parentheses
* p<0.1, ** p<0.05, *** p<0.01
- 注意：具体结果的解读，请参考相关文献，此处不再赘述。
5. 进一步延伸——动态空间计量模型
spregdhp indh lnai1 lnhum lnurb lnpgdp lnopen lnstr lnfdi,nc(30) /// model(sdm) wmfile(weight1.dta) mfx(lin) fe test
- 具体结果呈现：
*** Spatial Weight Matrix Has (1) Location with No Neighbors
==============================================================================
*** Binary (0/1) Weight Matrix: 480x480 - NC=30 NT=16 (Non Normalized)
==============================================================================
==============================================================================
* Spatial Durbin Han-Philips Linear Dynamic Panel Data Regression
==============================================================================
indh = lnai1 + lnhum + lnurb + lnpgdp + lnopen + lnstr + lnfdi + w1x_lnai1 + w1x_lnhum + w1x_lnurb +
w1x_lnpgdp + w1x_lnopen + w1x_lnstr + w1x_lnfdi
------------------------------------------------------------------------------
Sample Size = 450 | Cross Sections Number = 30
Wald Test = 1424.2048 | P-Value > Chi2(15) = 0.0000
F-Test = 94.9470 | P-Value > F(15 , 435) = 0.0000
(Buse 1973) R2 = 0.7660 | Raw Moments R2 = 0.7990
(Buse 1973) R2 Adj = 0.7585 | Raw Moments R2 Adj = 0.7925
Root MSE (Sigma) = 17.3047 | Log Likelihood Function = -418.0409
------------------------------------------------------------------------------
- R2h= 0.7180 R2h Adj= 0.7089 F-Test = 73.67 P-Value > F(15 , 435)0.0000
------------------------------------------------------------------------------
indh | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
indh |
L1. | 1.464642 .1391751 10.52 0.000 1.191864 1.73742
|
lnai1 | -.0021971 .0116581 -0.19 0.851 -.0250466 .0206523
lnhum | .1956269 .2028405 0.96 0.335 -.2019332 .5931869
lnurb | -1.344261 .2254866 -5.96 0.000 -1.786207 -.9023154
lnpgdp | .7709002 .0570397 13.52 0.000 .6591043 .882696
lnopen | -.0811523 .0277325 -2.93 0.003 -.135507 -.0267976
lnstr | .0774429 .0416614 1.86 0.063 -.0042119 .1590978
lnfdi | -.0362189 .0146448 -2.47 0.013 -.0649221 -.0075157
w1x_lnai1 | -.0028346 .0011974 -2.37 0.018 -.0051816 -.0004877
w1x_lnhum | .0135636 .0201096 0.67 0.500 -.0258505 .0529778
w1x_lnurb | .0433338 .0591794 0.73 0.464 -.0726556 .1593233
w1x_lnpgdp | -.0082215 .0103883 -0.79 0.429 -.0285822 .0121393
w1x_lnopen | .002222 .003673 0.60 0.545 -.004977 .0094209
w1x_lnstr | .0199601 .0103436 1.93 0.054 -.0003129 .0402332
w1x_lnfdi | -.0066894 .0049708 -1.35 0.178 -.0164319 .0030531
_cons | 4.894664 1.179578 4.15 0.000 2.582734 7.206594
------------------------------------------------------------------------------
==============================================================================
* Panel Model Selection Diagnostic Criteria
==============================================================================
- Log Likelihood Function LLF = -418.0409
---------------------------------------------------------------------------
- Akaike Information Criterion (1974) AIC = 0.4084
- Akaike Information Criterion (1973) Log AIC = -0.8955
---------------------------------------------------------------------------
- Schwarz Criterion (1978) SC = 0.4858
- Schwarz Criterion (1978) Log SC = -0.7220
---------------------------------------------------------------------------
- Amemiya Prediction Criterion (1969) FPE = 0.4047
- Hannan-Quinn Criterion (1979) HQ = 0.4373
- Rice Criterion (1984) Rice = 0.4100
- Shibata Criterion (1981) Shibata = 0.4070
- Craven-Wahba Generalized Cross Validation (1979) GCV = 0.4092
------------------------------------------------------------------------------
==============================================================================
*** Spatial Panel Aautocorrelation Tests
==============================================================================
Ho: Error has No Spatial AutoCorrelation
Ha: Error has Spatial AutoCorrelation
- GLOBAL Moran MI = 0.9548 P-Value > Z(53.714) 0.0000
- GLOBAL Geary GC = 0.0725 P-Value > Z(-35.873) 0.0000
- GLOBAL Getis-Ords GO = -12.8576 P-Value > Z(-53.714) 0.0000
------------------------------------------------------------------------------
- Moran MI Error Test = 5.0236 P-Value > Z(282.089) 0.0000
------------------------------------------------------------------------------
- LM Error (Burridge) =2581.0442 P-Value > Chi2(1) 0.0000
- LM Error (Robust) = 1.84e+04 P-Value > Chi2(1) 0.0000
------------------------------------------------------------------------------
Ho: Spatial Lagged Dependent Variable has No Spatial AutoCorrelation
Ha: Spatial Lagged Dependent Variable has Spatial AutoCorrelation
- LM Lag (Anselin) =1101.7864 P-Value > Chi2(1) 0.0000
- LM Lag (Robust) = 1.69e+04 P-Value > Chi2(1) 0.0000
------------------------------------------------------------------------------
Ho: No General Spatial AutoCorrelation
Ha: General Spatial AutoCorrelation
- LM SAC (LMErr+LMLag_R) = 1.95e+04 P-Value > Chi2(2) 0.0000
- LM SAC (LMLag+LMErr_R) = 1.95e+04 P-Value > Chi2(2) 0.0000
------------------------------------------------------------------------------
==============================================================================
*** Panel Heteroscedasticity Tests
==============================================================================
Ho: Panel Homoscedasticity - Ha: Panel Heteroscedasticity
- Engle LM ARCH Test AR(1): E2 = E2_1 = 227.9877 P-Value > Chi2(1) 0.0000
------------------------------------------------------------------------------
- Hall-Pagan LM Test: E2 = Yh = 1.0343 P-Value > Chi2(1) 0.3091
- Hall-Pagan LM Test: E2 = Yh2 = 2.2574 P-Value > Chi2(1) 0.1330
- Hall-Pagan LM Test: E2 = LYh2 = 0.2879 P-Value > Chi2(1) 0.5916
------------------------------------------------------------------------------
- Harvey LM Test: LogE2 = X = 148.8733 P-Value > Chi2(2) 0.0000
- Wald Test: LogE2 = X = 367.3299 P-Value > Chi2(1) 0.0000
- Glejser LM Test: |E| = X = 164.3446 P-Value > Chi2(2) 0.0000
- Breusch-Godfrey Test: E = E_1 X = 285.9815 P-Value > Chi2(1) 0.0000
------------------------------------------------------------------------------
- White Test - Koenker(R2): E2 = X = 231.0490 P-Value > Chi2(14) 0.0000
- White Test - B-P-G (SSR): E2 = X = 103.4140 P-Value > Chi2(14) 0.0000
------------------------------------------------------------------------------
- White Test - Koenker(R2): E2 = X X2 = 279.4980 P-Value > Chi2(28) 0.0000
- White Test - B-P-G (SSR): E2 = X X2 = 125.0990 P-Value > Chi2(28) 0.0000
------------------------------------------------------------------------------
- White Test - Koenker(R2): E2 = X X2 XX= 377.1644 P-Value > Chi2(119)0.0000
- White Test - B-P-G (SSR): E2 = X X2 XX= 168.8130 P-Value > Chi2(119)0.0018
------------------------------------------------------------------------------
- Cook-Weisberg LM Test: E2/S2n = Yh = 0.4629 P-Value > Chi2(1) 0.4962
- Cook-Weisberg LM Test: E2/S2n = X = 103.4140 P-Value > Chi2(14) 0.0000
------------------------------------------------------------------------------
*** Single Variable Tests (E2/Sig2):
- Cook-Weisberg LM Test: lnai1 = 17.3032 P-Value > Chi2(1) 0.0000
- Cook-Weisberg LM Test: lnhum = 1.0716 P-Value > Chi2(1) 0.3006
- Cook-Weisberg LM Test: lnurb = 3.0495 P-Value > Chi2(1) 0.0808
- Cook-Weisberg LM Test: lnpgdp = 0.6924 P-Value > Chi2(1) 0.4054
- Cook-Weisberg LM Test: lnopen = 0.5348 P-Value > Chi2(1) 0.4646
- Cook-Weisberg LM Test: lnstr = 1.8047 P-Value > Chi2(1) 0.1791
- Cook-Weisberg LM Test: lnfdi = 1.4470 P-Value > Chi2(1) 0.2290
- Cook-Weisberg LM Test: w1x_lnai1 = 0.0080 P-Value > Chi2(1) 0.9287
- Cook-Weisberg LM Test: w1x_lnhum = 0.7712 P-Value > Chi2(1) 0.3799
- Cook-Weisberg LM Test: w1x_lnurb = 2.6665 P-Value > Chi2(1) 0.1025
- Cook-Weisberg LM Test: w1x_lnpgdp = 0.3460 P-Value > Chi2(1) 0.5564
- Cook-Weisberg LM Test: w1x_lnopen = 0.3767 P-Value > Chi2(1) 0.5394
- Cook-Weisberg LM Test: w1x_lnstr = 1.0104 P-Value > Chi2(1) 0.3148
- Cook-Weisberg LM Test: w1x_lnfdi = 1.3242 P-Value > Chi2(1) 0.2498
------------------------------------------------------------------------------
*** Single Variable Tests:
- King LM Test: lnai1 = 17.1618 P-Value > Chi2(1) 0.0000
- King LM Test: lnhum = 0.6876 P-Value > Chi2(1) 0.4070
- King LM Test: lnurb = 3.4760 P-Value > Chi2(1) 0.0623
- King LM Test: lnpgdp = 0.0600 P-Value > Chi2(1) 0.8065
- King LM Test: lnopen = 0.5522 P-Value > Chi2(1) 0.4574
- King LM Test: lnstr = 1.2860 P-Value > Chi2(1) 0.2568
- King LM Test: lnfdi = 1.9319 P-Value > Chi2(1) 0.1646
- King LM Test: w1x_lnai1 = 0.7515 P-Value > Chi2(1) 0.3860
- King LM Test: w1x_lnhum = 0.2341 P-Value > Chi2(1) 0.6285
- King LM Test: w1x_lnurb = 1.8259 P-Value > Chi2(1) 0.1766
- King LM Test: w1x_lnpgdp = 0.0118 P-Value > Chi2(1) 0.9137
- King LM Test: w1x_lnopen = 0.0828 P-Value > Chi2(1) 0.7736
- King LM Test: w1x_lnstr = 0.3801 P-Value > Chi2(1) 0.5375
- King LM Test: w1x_lnfdi = 0.9717 P-Value > Chi2(1) 0.3243
------------------------------------------------------------------------------
==============================================================================
* Panel Non Normality Tests
==============================================================================
Ho: Normality - Ha: Non Normality
------------------------------------------------------------------------------
*** Non Normality Tests:
- Jarque-Bera LM Test = 24.0873 P-Value > Chi2(2) 0.0000
- White IM Test = 64.5926 P-Value > Chi2(2) 0.0000
- Doornik-Hansen LM Test = 41.2587 P-Value > Chi2(2) 0.0000
- Geary LM Test = -15.4752 P-Value > Chi2(2) 0.0004
- Anderson-Darling Z Test = 6.3697 P > Z( 7.675) 1.0000
- D'Agostino-Pearson LM Test = 154.7377 P-Value > Chi2(2) 0.0000
------------------------------------------------------------------------------
*** Skewness Tests:
- Srivastava LM Skewness Test = 1.2001 P-Value > Chi2(1) 0.2733
- Small LM Skewness Test = 1.2296 P-Value > Chi2(1) 0.2675
- Skewness Z Test = 1.1089 P-Value > Chi2(1) 0.2675
------------------------------------------------------------------------------
*** Kurtosis Tests:
- Srivastava Z Kurtosis Test = -4.7841 P-Value > Z(0,1) 0.0000
- Small LM Kurtosis Test = 153.5081 P-Value > Chi2(1) 0.0000
- Kurtosis Z Test = -12.3898 P-Value > Chi2(1) 0.0000
------------------------------------------------------------------------------
Skewness Coefficient = 0.1265 - Standard Deviation = 0.1151
Kurtosis Coefficient = 1.8952 - Standard Deviation = 0.2297
------------------------------------------------------------------------------
Runs Test: (62) Runs - (219) Positives - (231) Negatives
Standard Deviation Runs Sig(k) = 10.5872 , Mean Runs E(k) = 225.8400
95% Conf. Interval [E(k)+/- 1.96* Sig(k)] = (205.0890 , 246.5910 )
------------------------------------------------------------------------------
* Marginal Effect - Elasticity (Model= sdm): Linear *
+---------------------------------------------------------------------------+
| Variable | Marginal_Effect(B) | Elasticity(Es) | Mean |
|------------+--------------------+--------------------+--------------------|
| L.indh | 1.4646 | 1.4595 | 1.1544 |
| lnai1 | -0.0022 | 0.0095 | -5.0094 |
| lnhum | 0.1956 | 0.3640 | 2.1555 |
| lnurb | -1.3443 | 0.7928 | -0.6832 |
| lnpgdp | 0.7709 | 6.8374 | 10.2747 |
| lnopen | -0.0812 | 0.1180 | -1.6839 |
| lnstr | 0.0774 | 0.5248 | 7.8498 |
| lnfdi | -0.0362 | 0.1285 | -4.1089 |
| w1x_lnai1 | -0.0028 | 0.1678 | -68.5763 |
| w1x_lnhum | 0.0136 | 0.3409 | 29.1117 |
| w1x_lnurb | 0.0433 | -0.3401 | -9.0909 |
| w1x_lnpgdp | -0.0082 | -0.9849 | 138.7821 |
| w1x_lnopen | 0.0022 | -0.0427 | -22.2636 |
| w1x_lnstr | 0.0200 | 1.8222 | 105.7570 |
| w1x_lnfdi | -0.0067 | 0.3079 | -53.3221 |
+---------------------------------------------------------------------------+
Mean of Dependent Variable = 1.1584
- 具体解释，请参考:刘成坤（2019）人口老龄化对产业结构升级的溢出效应研究——基于空间动态杜宾模型；李婧等（2010）中国区域创新生产的空间计量分析——基于静态与动态空间面板模型的实证研究.