面板数据协整检验(Stata)
当时间序列数据存在非平稳性时，直接将经济变量进行回归可能产生伪回归问题。针对非平稳数据计量建模，首先要判定这些变量是否存在同阶单整，如果满足同阶单整，才有必要对这些变量进行协整检验。当所涉及的变量存在协整时，由这些变量构建的回归模型才有意义，这也是区别于真实回归和虚假回归的标志。协整检验的前提是原始变量是非平稳的，或者变量具有单位根过程。因此在实际操作时，先对原始变量进行单位根检验，当所有变量都是非平稳，且同阶差分平稳时（或者同阶单整），才有必要采取协整检验。在Stata软件中，提供了Kao、pedroni和 westerlund三种检验方式，不同方式有其不同的适用条件，具体如下：
kao检验只能用于同质面板，命令选择项包括
- lags(#)ADF检验滞后阶数#，见下文
- kernel()协方差矩阵核估计方法，见下文
- demean个体去均值
Pedroni检验适用于异质面板，命令选择项包括
- ar(panelspecific|same) ADF检验中AR系数异质(默认)否
- lags(#)ADF检验滞后阶数#
- kernel()协方差矩阵核估计方法
- demean个体去均值
- trend 趋势效应
- noconstant 无个体效应
westerlund检验适用于异质面板，命令选择项包括
- trend 趋势效应
- demean个体去均值
- somepanles 一定比例的面板数据存在协整(默认)
- allpanels 全部变量存在协整
其中ADF的检验形式包括：
- # 表示滞后阶数，缺失默认为1
- aic # 以aic准则确定最大滞后阶数 #
- bic # 以bic准则确定最大滞后阶数 #
- hqic # 以hqic准则确定最大滞后阶数 #
协方差核估计选择项包括：barlett newest 、barlett # 、parzen newest、parzen #、quadraticspectral newst、quadraticspectral #。上述三种检验的原假设为H0:变量间不存在协整关系；Kao、pedroni检验备择假设H1:全部变量之间存在协整关系。westerlund检验的备择假设存在两种形式，包括H1-a:全部变量存在协整关系；H1-b:存在一定比例的变量具有协整关系。文章来源：https://www.toymoban.com/news/detail-448800.html
代码(Stata)操作如下:文章来源地址https://www.toymoban.com/news/detail-448800.html
* help xtcointtest
**# 1 数据准备
webuse xtcoint //调用网页数据
summarize rddomestic- productivity //描述统计
**# 2 单位根检验
xtunitroot ht productivity
/*
xtunitroot ht productivity
Harris-Tzavalis unit-root test for productivity
-----------------------------------------------
H0: Panels contain unit roots Number of panels = 100
Ha: Panels are stationary Number of periods = 150
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Not included
------------------------------------------------------------------------------
Statistic z p-value
------------------------------------------------------------------------------
rho 0.9822 0.9741 0.8350
------------------------------------------------------------------------------
*/
xtunitroot ht rddomestic
/*
Harris-Tzavalis unit-root test for rddomestic
---------------------------------------------
H0: Panels contain unit roots Number of panels = 100
Ha: Panels are stationary Number of periods = 150
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Not included
------------------------------------------------------------------------------
Statistic z p-value
------------------------------------------------------------------------------
rho 0.9999 9.3783 1.0000
------------------------------------------------------------------------------
*/
xtunitroot ht rdforeign
/*
Harris-Tzavalis unit-root test for rdforeign
--------------------------------------------
H0: Panels contain unit roots Number of panels = 100
Ha: Panels are stationary Number of periods = 150
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Not included
------------------------------------------------------------------------------
Statistic z p-value
------------------------------------------------------------------------------
rho 0.9990 8.9594 1.0000
------------------------------------------------------------------------------
*/
*以上结果表明productivity、rddomestic和rdforeign非平稳，接下来考虑一阶差分，再进行单位根检验
xtunitroot ht d.productivity,demean
/*
Harris-Tzavalis unit-root test for D.productivity
-------------------------------------------------
H0: Panels contain unit roots Number of panels = 100
Ha: Panels are stationary Number of periods = 149
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Not included Cross-sectional means removed
------------------------------------------------------------------------------
Statistic z p-value
------------------------------------------------------------------------------
rho -0.3755 -6.4e+02 0.0000
------------------------------------------------------------------------------
*/
xtunitroot ht d.rddomestic,demean
/*
xtunitroot ht d.rddomestic,demean
Harris-Tzavalis unit-root test for D.rddomestic
-----------------------------------------------
H0: Panels contain unit roots Number of panels = 100
Ha: Panels are stationary Number of periods = 149
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Not included Cross-sectional means removed
------------------------------------------------------------------------------
Statistic z p-value
------------------------------------------------------------------------------
rho -0.0039 -4.6e+02 0.0000
------------------------------------------------------------------------------
*/
xtunitroot ht d.rdforeign,demean
/*
Harris-Tzavalis unit-root test for D.rdforeign
----------------------------------------------
H0: Panels contain unit roots Number of panels = 100
Ha: Panels are stationary Number of periods = 149
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Not included Cross-sectional means removed
------------------------------------------------------------------------------
Statistic z p-value
------------------------------------------------------------------------------
rho -0.0029 -4.6e+02 0.0000
------------------------------------------------------------------------------
*/
* 以上结果表明，所有变量满足一阶单整I(1)，下面考虑协整
**# 3 协整检验
xtcointtest kao productivity rddomestic rdforeign //Kao检验
/*
Kao test for cointegration
--------------------------
H0: No cointegration Number of panels = 100
Ha: All panels are cointegrated Number of periods = 148
Cointegrating vector: Same
Panel means: Included Kernel: Bartlett
Time trend: Not included Lags: 3.60 (Newey–West)
AR parameter: Same Augmented lags: 1
------------------------------------------------------------------------------
Statistic p-value
------------------------------------------------------------------------------
Modified Dickey–Fuller t -23.6733 0.0000
Dickey–Fuller t -15.1293 0.0000
Augmented Dickey–Fuller t -3.6909 0.0001
Unadjusted modified Dickey–Fuller t -46.7561 0.0000
Unadjusted Dickey–Fuller t -20.2521 0.0000
------------------------------------------------------------------------------
*共有5个统计量，最后两个没有校正，主要看ADF检验
*/
xtcointtest pedroni productivity rddomestic rdforeign //pedroni检验
/*
Pedroni test for cointegration
------------------------------
H0: No cointegration Number of panels = 100
Ha: All panels are cointegrated Number of periods = 149
Cointegrating vector: Panel specific
Panel means: Included Kernel: Bartlett
Time trend: Not included Lags: 4.00 (Newey–West)
AR parameter: Panel specific Augmented lags: 1
------------------------------------------------------------------------------
Statistic p-value
------------------------------------------------------------------------------
Modified Phillips–Perron t -26.1145 0.0000
Phillips–Perron t -21.2436 0.0000
Augmented Dickey–Fuller t -25.3701 0.0000
------------------------------------------------------------------------------
三个统计量都具有参考价值
*/
xtcointtest westerlund productivity rddomestic rdforeign // westerlund检验，默认部分比例存在协整
/*
Westerlund test for cointegration
---------------------------------
H0: No cointegration Number of panels = 100
Ha: Some panels are cointegrated Number of periods = 150
Cointegrating vector: Panel specific
Panel means: Included
Time trend: Not included
AR parameter: Panel specific
------------------------------------------------------------------------------
Statistic p-value
------------------------------------------------------------------------------
Variance ratio -8.0237 0.0000
------------------------------------------------------------------------------
*/
* 下面考虑将H1:全部变量存在协整 作为备择假设
xtcointtest westerlund productivity rddomestic rdforeign, allpanels
/*
Westerlund test for cointegration
---------------------------------
H0: No cointegration Number of panels = 100
Ha: All panels are cointegrated Number of periods = 150
Cointegrating vector: Panel specific
Panel means: Included
Time trend: Not included
AR parameter: Same
------------------------------------------------------------------------------
Statistic p-value
------------------------------------------------------------------------------
Variance ratio -5.9709 0.0000
------------------------------------------------------------------------------
*/
** 以上结果表明，变量productivity rddomestic rdforeign存在协整，可以考虑非平稳建模，如面板向量误差修正模型等。
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