面板空间计量模型(Stata)_空间面板计量模型

面板空间计量模型(Stata)

文章目录

• 面板空间计量模型(Stata)
• • @[toc]
  • 1 面板空间自回归模型
  • 2 面板空间误差模型
  • 3 面板空间自相关模型
  • 4 面板空间杜宾模型
  • 5 动态面板空间计量模型

1 面板空间自回归模型

空间自回归(空间滞后)模型形式：
$$y_{it}=\rho \sum _{j=1}^N{w}_{ij}{y}_{jt}+{\mathbf{x}}_{it}^{\prime }\mathbf{\beta }+{\mu }_i+{\epsilon }_{it},i=1,2,\cdots ,N,t=1,2,\cdots ,T$$
其中$y$是因变量，$x$是自变量，$w$是空间权重矩阵元素，$\rho$是空间自回归系数，$\mu$是个体固定效应，$\epsilon$是随机扰动项，$i$是截面个体，$t$

时间。可以用Stata中xsmle命令进行估计。数据集是线上数据，由于是国外网站，下载特别慢，出现卡顿建议关掉重试，多试几次就可以了。下载后建议保存。

*use http://www.econometrics.it/stata/data/xsmle/product.dta, clear
*spmat use usaww using http://www.econometrics.it/stata/data/xsmle/usaww.spmat
use product.dta, clear
xtdescribe
des
spmat use usaww using usaww.spmat
gen lngsp = log(gsp)
gen lnpcap = log(pcap)
gen lnpc = log(pc)
gen lnemp = log(emp)
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结果如下：

Contains data from product.dta
 Observations:           816                  
    Variables:            10                  13 Nov 2021 18:07
--------------------------------------------------------------------------------------
Variable      Storage   Display    Value
    name         type    format    label      Variable label
--------------------------------------------------------------------------------------
state           long    %14.0g     pid        
year            int     %8.0g                 
pcap            float   %9.0g                 
hwy             float   %9.0g                 
water           float   %9.0g                 
util            float   %9.0g                 
pc              float   %9.0g                 
gsp             long    %12.0g                
emp             float   %9.0g                 
unemp           float   %9.0g                 
--------------------------------------------------------------------------------------
Sorted by: state  year
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使用如下命令进行SAR估计

*SAR+FE
xsmle lngsp lnpcap lnpc lnemp unemp, wmat(usaww) model(sar) fe hausman nolog effects
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结果如下,其中fe表示固定效应，可以换成re随机效应，hausman用以检验fe和re。effects表示显示空间直接、间接和总效应

SAR with spatial fixed-effects                       Number of obs =       816

Group variable: state                             Number of groups =        48
Time variable: year                                   Panel length =        17

R-sq:    within  = 0.9433
         between = 0.9557
         overall = 0.9547

Mean of fixed-effects =  1.7573

Log-likelihood =  1900.8344
------------------------------------------------------------------------------
       lngsp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Main         |
      lnpcap |  -.0465815   .0254001    -1.83   0.067    -.0963647    .0032017
        lnpc |   .1874323   .0233795     8.02   0.000     .1416094    .2332553
       lnemp |   .6250903    .028505    21.93   0.000     .5692215     .680959
       unemp |  -.0044816   .0008666    -5.17   0.000      -.00618   -.0027832
-------------+----------------------------------------------------------------
Spatial      |
         rho |   .2746886   .0210851    13.03   0.000     .2333625    .3160147
-------------+----------------------------------------------------------------
Variance     |
    sigma2_e |   .0011114   .0000551    20.16   0.000     .0010033    .0012194
-------------+----------------------------------------------------------------
LR_Direct    |
      lnpcap |  -.0465542   .0265982    -1.75   0.080    -.0986858    .0055774
        lnpc |   .1900105   .0229369     8.28   0.000      .145055     .234966
       lnemp |   .6398299    .027523    23.25   0.000     .5858859    .6937739
       unemp |  -.0045656   .0008838    -5.17   0.000    -.0062978   -.0028334
-------------+----------------------------------------------------------------
LR_Indirect  |
      lnpcap |  -.0163173   .0095843    -1.70   0.089    -.0351022    .0024677
        lnpc |   .0663106   .0085757     7.73   0.000     .0495026    .0831186
       lnemp |   .2237421   .0196861    11.37   0.000      .185158    .2623262
       unemp |  -.0015995   .0003466    -4.61   0.000    -.0022789   -.0009201
-------------+----------------------------------------------------------------
LR_Total     |
      lnpcap |  -.0628714   .0360627    -1.74   0.081    -.1335531    .0078102
        lnpc |   .2563211   .0297273     8.62   0.000     .1980567    .3145856
       lnemp |    .863572   .0356999    24.19   0.000     .7936015    .9335425
       unemp |   -.006165   .0012052    -5.12   0.000    -.0085272   -.0038029
------------------------------------------------------------------------------
Ho: difference in coeffs not systematic chi2(5) =  3.22    Prob>=chi2 = 0.6659
------------------------------------------------------------------------------

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2 面板空间误差模型

空间误差模型形式为
y i t = x i t β + μ i + μ i t μ i t = λ ∑ j = 1 N w i j μ j t + ε i t

$$\begin{aligned} &y_{i t}=\boldsymbol{x}_{i t} \boldsymbol{\beta}+\mu_{i}+\mu_{i t} \\ &\mu_{i t}=\lambda \sum_{j=1}^{N} w_{i j} \mu_{j t}+\varepsilon_{i t} \end{aligned}$$ ​yit​=xit​β+μi​+μit​μit​=λj=1∑N​wij​μjt​+εit​​
下面是估计命令，

xsmle lngsp lnpcap lnpc lnemp unemp, emat(usaww) model(sem) fe hausman nolog
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估计结果

R-sq:    within  = 0.9401
         between = 0.9907
         overall = 0.9896

Mean of fixed-effects =  2.8470

Log-likelihood =  1900.8344
------------------------------------------------------------------------------
       lngsp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Main         |
      lnpcap |   .0051441   .0250122     0.21   0.837    -.0438789    .0541671
        lnpc |   .2053021   .0237393     8.65   0.000      .158774    .2518303
       lnemp |   .7822543   .0278151    28.12   0.000     .7277378    .8367708
       unemp |  -.0022317   .0010861    -2.05   0.040    -.0043603    -.000103
-------------+----------------------------------------------------------------
Spatial      |
      lambda |   .5574017   .0329539    16.91   0.000     .4928132    .6219902
-------------+----------------------------------------------------------------
Variance     |
    sigma2_e |   .0009765   .0000498    19.60   0.000     .0008789    .0010741
------------------------------------------------------------------------------
Ho: difference in coeffs not systematic chi2(5) = 10.99    Prob>=chi2 = 0.0516

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3 面板空间自相关模型

面板空间自相关模型(SAC)形式
$$\begin{gathered} y_{it}=\rho W{y}_{it}+\beta X_{it}+v_{it} \\ {v}_{it}=\lambda E{v}_{it}+u_{it} \end{gathered}$$
估计命令为

xsmle lngsp lnpcap lnpc lnemp unemp, wmat(usaww) emat(usaww) model(sac)  fe  nolog
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其中wmat(usaww)是因变量对应空间权重矩阵， emat(usaww)是扰动项对应的空间权重矩阵。估计结果

SAC with spatial fixed-effects                       Number of obs =       816

Group variable: state                             Number of groups =        48
Time variable: year                                   Panel length =        17

R-sq:    within  = 0.9423
         between = 0.9854
         overall = 0.9844

Mean of fixed-effects =  2.4143

Log-likelihood =  1900.8344
------------------------------------------------------------------------------
       lngsp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Main         |
      lnpcap |  -.0103492    .025797    -0.40   0.688    -.0609104    .0402119
        lnpc |   .1905778   .0241401     7.89   0.000     .1432642    .2378915
       lnemp |   .7552378   .0301064    25.09   0.000     .6962302    .8142453
       unemp |  -.0030613   .0010688    -2.86   0.004    -.0051561   -.0009665
-------------+----------------------------------------------------------------
Spatial      |
         rho |   .0885753   .0298792     2.96   0.003     .0300131    .1471375
      lambda |    .455313   .0502814     9.06   0.000     .3567632    .5538628
-------------+----------------------------------------------------------------
Variance     |
    sigma2_e |   .0010589    .000051    20.77   0.000      .000959    .0011588
------------------------------------------------------------------------------

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4 面板空间杜宾模型

SDM模型形式为
$$\mathbf{y}=\mathbf{\alpha }+\rho \mathbf{W}\mathbf{y}+\mathbf{X}\mathbf{\beta }+\mathbf{W}\overline{\mathbf{X}}\mathbf{\gamma }+\mathbf{\epsilon }$$
根据时间、空间和时空固定的不同，又可以对命令进行调整。下面三条命令都是固定效应，还可以尝试用随机效应，尽管不常用。估计命令

* 空间固定
xsmle lngsp lnpcap lnpc lnemp,  wmat(usaww) model(sdm) type(ind) fe  nolog
* 时间固定
xsmle lngsp lnpcap lnpc lnemp,  wmat(usaww) model(sdm) type(time) fe  nolog
* 时空固定
xsmle lngsp lnpcap lnpc lnemp,  wmat(usaww) model(sdm) type(both) fe  nolog
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下面只显示最后一条的估计结果

SDM with spatial and time fixed-effects              Number of obs =       816

Group variable: state                             Number of groups =        48
Time variable: year                                   Panel length =        17

R-sq:    within  = 0.9429
         between = 0.9886
         overall = 0.9875

Mean of fixed-effects =  2.4199

Log-likelihood =  1900.8344
------------------------------------------------------------------------------
       lngsp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Main         |
      lnpcap |  -.0279948   .0244525    -1.14   0.252    -.0759209    .0199313
        lnpc |   .1606445   .0256644     6.26   0.000     .1103432    .2109457
       lnemp |   .7718209   .0266684    28.94   0.000     .7195518      .82409
-------------+----------------------------------------------------------------
Wx           |
      lnpcap |  -.1163453   .0420475    -2.77   0.006    -.1987568   -.0339337
        lnpc |   .0139823   .0461253     0.30   0.762    -.0764216    .1043862
       lnemp |  -.2501777   .0513908    -4.87   0.000    -.3509018   -.1494536
-------------+----------------------------------------------------------------
Spatial      |
         rho |   .3809206   .0394352     9.66   0.000     .3036291    .4582121
-------------+----------------------------------------------------------------
Variance     |
    sigma2_e |   .0009275   .0000466    19.90   0.000     .0008362    .0010189
------------------------------------------------------------------------------

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5 动态面板空间计量模型

广义的空间面板模型形式非常复杂
Y t = δ W Y t + τ Y t − 1 + η W Y t − 1 + β 1 X t + β 2 W X t + β 3 X t − 1 + β 4 W X t − 1 + Z t θ + v t v t = γ ν t − 1 + ρ W ν t − 1 + μ + λ t ℓ N + ε t , μ = κ W μ + ξ

$$\begin{aligned} &\boldsymbol{Y}_{t}=\delta \boldsymbol{W} \boldsymbol{Y}_{t}+\tau \boldsymbol{Y}_{t-1}+\eta \boldsymbol{W} \boldsymbol{Y}_{t-1}+\boldsymbol{\beta}_{1} \boldsymbol{X}_{t}+\boldsymbol{\beta}_{2} \boldsymbol{W} \boldsymbol{X}_{t}+\boldsymbol{\beta}_{3} \boldsymbol{X}_{t-1}+\boldsymbol{\beta}_{4} \boldsymbol{W} \boldsymbol{X}_{t-1}+\boldsymbol{Z}_{t} \boldsymbol{\theta}+\boldsymbol{v}_{t} \\ &\boldsymbol{v}_{t}=\gamma \boldsymbol{\nu}_{t-1}+\rho \boldsymbol{W} \boldsymbol{\nu}_{t-1}+\boldsymbol{\mu}+\lambda_{t} \boldsymbol{\ell}_{N}+\boldsymbol{\varepsilon}_{t}, \quad \boldsymbol{\mu}=\kappa \boldsymbol{W} \boldsymbol{\mu}+\xi \end{aligned}$$ ​Yt​=δWYt​+τYt−1​+ηWYt−1​+β1​Xt​+β2​WXt​+β3​Xt−1​+β4​WXt−1​+Zt​θ+vt​vt​=γνt−1​+ρWνt−1​+μ+λt​ℓN​+εt​,μ=κWμ+ξ​
其中动态的滞后性体现在时间上、空间上或时空上。既体现在因变量上又体现在自变量上，最后还体现在扰动项的时空上。根据不同参数的取值，又可以转化为以上的不同模型。下面给出不含扰动项动态性和空间滞后性的特例。命令如下：

*DSPM
* dlag(1)时间滞后
xsmle lngsp lnpcap lnpc lnemp unemp, wmat(usaww) model(sdm) fe dlag(1) nolog r
* dlag(2)空间滞后
xsmle lngsp lnpcap lnpc lnemp unemp, wmat(usaww) model(sdm) fe dlag(2) nolog r
* dlag(3)时空滞后
xsmle lngsp lnpcap lnpc lnemp unemp, wmat(usaww) model(sdm) fe dlag(3) nolog r

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下面仅汇报第三条结果

Dynamic SDM with spatial fixed-effects               Number of obs =       768

Group variable: state                             Number of groups =        48
Time variable: year                                   Panel length =        16

R-sq:    within  = 0.9662
         between = 0.9985
         overall = 0.9979

Mean of fixed-effects =  0.4269

Log-likelihood =  1930.9498
------------------------------------------------------------------------------
       lngsp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Main         |
       lngsp |
         L1. |    .889765   .0221781    40.12   0.000     .8462968    .9332332
             |
      Wlngsp |
         L1. |   -.770734   .0321557   -23.97   0.000     -.833758   -.7077099
             |
      lnpcap |  -.0518792   .0159358    -3.26   0.001    -.0831128   -.0206455
        lnpc |  -.0666301   .0160119    -4.16   0.000    -.0980127   -.0352474
       lnemp |    .168119   .0242772     6.92   0.000     .1205366    .2157014
       unemp |  -.0065448   .0007519    -8.70   0.000    -.0080184   -.0050712
-------------+----------------------------------------------------------------
Wx           |
      lnpcap |   .0210242    .028116     0.75   0.455    -.0340822    .0761305
        lnpc |   .1397731    .024275     5.76   0.000     .0921949    .1873512
       lnemp |  -.0539297    .038193    -1.41   0.158    -.1287865    .0209271
       unemp |   .0040633    .000989     4.11   0.000      .002125    .0060017
-------------+----------------------------------------------------------------
Spatial      |
         rho |   .7213969    .023442    30.77   0.000     .6754513    .7673424
-------------+----------------------------------------------------------------
Variance     |
    sigma2_e |    .000332   .0000167    19.93   0.000     .0002993    .0003646
------------------------------------------------------------------------------

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更多option使用help(xsmle)。还有一些空间计量模型使用Matlab更方便，这里不再介绍。

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