目录
以面板数据mus08psidextract.dta为例：
1.导入数据集
stata自带数据集：Stata打开自带的数据合集_9997PZ的博客-CSDN博客_stata数据
外部导入：
. use "F:\个人嘿嘿嘿\北师大BNU\研一上-课业资料\商务与经济统计\作业1\mus08psidextract.dta",clear 2.面板数据有关信息
2.1设定面板数据的个体变量和时间变量
. xtset id t //id：个体变量 t：时间变量 顺序不可以变
Panel variable: id (strongly balanced)
Time variable: t, 1 to 7
Delta: 1 unit
2.2显示面板数据的结构：
. xtdes
2.3显示数据集中变量的统计特征：
. xtsum
. xtsum lwage ed exp exp2 wks id t
Variable | Mean Std. dev. Min Max | Observations
-----------------+--------------------------------------------+----------------
lwage overall | 6.676346 .4615122 4.60517 8.537 | N = 4165
between | .3942387 5.3364 7.813596 | n = 595
within | .2404023 4.781808 8.621092 | T = 7
| |
ed overall | 12.84538 2.787995 4 17 | N = 4165
between | 2.790006 4 17 | n = 595
within | 0 12.84538 12.84538 | T = 7
| |
exp overall | 19.85378 10.96637 1 51 | N = 4165
between | 10.79018 4 48 | n = 595
within | 2.00024 16.85378 22.85378 | T = 7
| |
exp2 overall | 514.405 496.9962 1 2601 | N = 4165
between | 489.0495 20 2308 | n = 595
within | 90.44581 231.405 807.405 | T = 7
| |
wks overall | 46.81152 5.129098 5 52 | N = 4165
between | 3.284016 31.57143 51.57143 | n = 595
within | 3.941881 12.2401 63.66867 | T = 7
| |
id overall | 298 171.7821 1 595 | N = 4165
between | 171.906 1 595 | n = 595
within | 0 298 298 | T = 7
| |
t overall | 4 2.00024 1 7 | N = 4165
between | 0 4 4 | n = 595
within | 2.00024 1 7 | T = 7
.
std.dev:基于样本估算标准偏差，反映数值相对于平均值的离散程度；
可以看出id的组内离散程度为0（同一个体内，个体无变化），t的组间离散程度为0（同一时间，每一个个体之间时间无差别）；ed可以看作，是可以观测到的个体异质性；
3.混合回归
. reg y x1 x2 x3…,vce(cluster id)
其中vce(cluster id)【聚类标准误】可替换为：robust / r【稳健标准误】 or 什么都不加【普通标准误】，下面各种模型回归同理。
注：_cons为默认加入的常数项，如果要求不含常数项则使用：reg y x1 x2 x3…,nocons
reg lwage exp exp2 wks ed,vce(cluster id) //使用聚类稳健标准误
Linear regression Number of obs = 4,165
F(4, 594) = 72.58
Prob > F = 0.0000
R-squared = 0.2836
Root MSE = .39082
(Std. err. adjusted for 595 clusters in id)
------------------------------------------------------------------------------
| Robust
lwage | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
exp | .044675 .0054385 8.21 0.000 .0339941 .055356
exp2 | -.0007156 .0001285 -5.57 0.000 -.0009679 -.0004633
wks | .005827 .0019284 3.02 0.003 .0020396 .0096144
ed | .0760407 .0052122 14.59 0.000 .0658042 .0862772
_cons | 4.907961 .1399887 35.06 0.000 4.633028 5.182894
------------------------------------------------------------------------------
4.随机效应模型
4.1随机效应模型or混合回归模型的选择：LM检验
LM检验 检验是否存在个体效应 从而确定使用
（使用FGLS法会提供一个theta值，从而完成LM检验）
4.2随机效应模型：两种估计方法
A.FGLS法：广义离差模型
. xtreg y x1 x2…, re r theta
. xtreg lwage exp exp2 wks ed, re r theta
Random-effects GLS regression Number of obs = 4,165
Group variable: id Number of groups = 595
R-squared: Obs per group:
Within = 0.6340 min = 7
Between = 0.1716 avg = 7.0
Overall = 0.1830 max = 7
Wald chi2(4) = 1598.50
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
theta = .82280511
(Std. err. adjusted for 595 clusters in id)
------------------------------------------------------------------------------
| Robust
lwage | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
exp | .0888609 .0039992 22.22 0.000 .0810227 .0966992
exp2 | -.0007726 .0000896 -8.62 0.000 -.0009481 -.000597
wks | .0009658 .0009259 1.04 0.297 -.000849 .0027806
ed | .1117099 .0083954 13.31 0.000 .0952552 .1281647
_cons | 3.829366 .1333931 28.71 0.000 3.567921 4.090812
-------------+----------------------------------------------------------------
sigma_u | .31951859
sigma_e | .15220316
rho | .81505521 (fraction of variance due to u_i)
------------------------------------------------------------------------------
可以看到theta=0.8228，LM检验中：强烈拒绝“不存在个体随机效应”的原假设，个体效应存在，在混合回归和随机效应模型当中应该选择随机效应模型；
rho=0.8151 进一步证明ui部分在方程中起到重要的作用，是不可以被忽略的；
B.MLE法：极大似然估计
. xtreg y x1 x2 x3…,mle
4.3双向随机效应模型（LSDV法估计）
. xtreg y x1 x2 x3…i.year,re
5.固定效应模型
5.1固定效应模型or混合回归之间的选择：
H0：all ui=0
普通标准误的估计时会给出一个F检验结果：F=53.12 p=0.000 则拒绝原假设，即应当使用固定效应模型
5.2固定效应模型估计方法
A.组内法：FE
. xtreg y x1 x2…, fe
缺点：无法估计出可观测的个体异质性的系数
，所以下表中ed 为omitted状态
注意：xtreg下r（robust）等价于聚类稳健标准误
. xtreg lwage exp exp2 wks ed, fe //普通标准误
note: ed omitted because of collinearity.
Fixed-effects (within) regression Number of obs = 4,165
Group variable: id Number of groups = 595
R-squared: Obs per group:
Within = 0.6566 min = 7
Between = 0.0276 avg = 7.0
Overall = 0.0476 max = 7
F(3,3567) = 2273.74
corr(u_i, Xb) = -0.9107 Prob > F = 0.0000
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
exp | .1137879 .0024689 46.09 0.000 .1089473 .1186284
exp2 | -.0004244 .0000546 -7.77 0.000 -.0005315 -.0003173
wks | .0008359 .0005997 1.39 0.163 -.0003399 .0020116
ed | 0 (omitted)
_cons | 4.596396 .0389061 118.14 0.000 4.520116 4.672677
-------------+----------------------------------------------------------------
sigma_u | 1.0362039
sigma_e | .15220316
rho | .97888036 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(594, 3567) = 53.12 Prob > F = 0.0000
. xtreg lwage exp exp2 wks ed, fe vce(cluster id) //聚类稳健标准误
note: ed omitted because of collinearity.
Fixed-effects (within) regression Number of obs = 4,165
Group variable: id Number of groups = 595
R-squared: Obs per group:
Within = 0.6566 min = 7
Between = 0.0276 avg = 7.0
Overall = 0.0476 max = 7
F(3,594) = 1059.72
corr(u_i, Xb) = -0.9107 Prob > F = 0.0000
(Std. err. adjusted for 595 clusters in id)
------------------------------------------------------------------------------
| Robust
lwage | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
exp | .1137879 .0040289 28.24 0.000 .1058753 .1217004
exp2 | -.0004244 .0000822 -5.16 0.000 -.0005858 -.0002629
wks | .0008359 .0008697 0.96 0.337 -.0008721 .0025439
ed | 0 (omitted)
_cons | 4.596396 .0600887 76.49 0.000 4.478384 4.714408
-------------+----------------------------------------------------------------
sigma_u | 1.0362039
sigma_e | .15220316
rho | .97888036 (fraction of variance due to u_i)
------------------------------------------------------------------------------
B.LSDV法
. reg y x1 x2 x3…i.id,vce(cluster id)
i.id：表示根据变量id而产生的虚拟变量，生成n个虚拟变量（or 有截距项时生成n-1个）
优点：可以求出可观测的个体异质性的系数
C.一阶差分法FD
无专门命令，可以使用一些其他方法来附带进行（？待补充）
5.3.双向固定效应模型LSDV法
法一：. xtreg y x1 x2…i.year, fe r
法二：. reg lwage exp exp2 wks ed i.id i.year, robust
若数据未变形：（如把1976-1982转为1-7）
. tab year,gen(year)
若数据已经为标准形式，则直接使用
. xtreg lwage exp exp2 wks ed i.t, fe r
note: ed omitted because of collinearity.
note: 7.t omitted because of collinearity.
Fixed-effects (within) regression Number of obs = 4,165
Group variable: id Number of groups = 595
R-squared: Obs per group:
Within = 0.6599 min = 7
Between = 0.0275 avg = 7.0
Overall = 0.0480 max = 7
F(8,594) = 412.33
corr(u_i, Xb) = -0.9089 Prob > F = 0.0000
(Std. err. adjusted for 595 clusters in id)
------------------------------------------------------------------------------
| Robust
lwage | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
exp | .1119927 .0041184 27.19 0.000 .1039043 .1200812
exp2 | -.0004051 .0000834 -4.86 0.000 -.0005688 -.0002413
wks | .00068 .0008812 0.77 0.441 -.0010506 .0024105
ed | 0 (omitted)
|
t |
2 | -.0083984 .0049321 -1.70 0.089 -.0180849 .0012881
3 | .0259652 .0084359 3.08 0.002 .0093974 .0425329
4 | .0289134 .0078093 3.70 0.000 .0135762 .0442506
5 | .0239406 .0065275 3.67 0.000 .0111208 .0367604
6 | .0069955 .0064617 1.08 0.279 -.0056949 .019686
7 | 0 (omitted)
|
_cons | 4.618339 .0599451 77.04 0.000 4.500609 4.736069
-------------+----------------------------------------------------------------
sigma_u | 1.0268811
sigma_e | .15159041
rho | .97867247 (fraction of variance due to u_i)
------------------------------------------------------------------------------
6.豪斯曼检验：固定效应模型or随机效应模型
6.1传统Hausman检验
前提条件：ui与eit都为iid
. xtreg lwage exp exp2 wks ed, fe
. estimates store FE
. xtreg lwage exp exp2 wks ed, re theta
. estimates store RE
. hausman FE RE,constant sigmamore
注：必须使用普通标准误，不可以使用稳健标准误
H0：ui与xi和zi不相关
若原假设成立，则认为ui与xi和eit无相关性，应当使用随机效应模型；
. hausman FE RE,constant sigmamore
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| FE RE Difference Std. err.
-------------+----------------------------------------------------------------
exp | .1137879 .0888609 .0249269 .0012778
exp2 | -.0004244 -.0007726 .0003482 .0000285
wks | .0008359 .0009658 -.0001299 .0001108
_cons | 4.596396 3.829366 .7670299 .
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.
Test of H0: Difference in coefficients not systematic
chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 1374.55
Prob > chi2 = 0.0000
(V_b-V_B is not positive definite)
.
由结果来看p值为0.0000则强烈拒绝原假设，应当选择固定个体效应模型；
再对时间效应进行检验（？应当比较时间固定模型还是直接比较双向固定模型
6.2非传统Hausman检验
前提：ui与eit都不再是iid情况下
即当聚类稳健标准误与普通标准误相差较大时，显然不再满去传统Hausman检验的前提，此时要使用另一种方法：
H0：=0
. ssc install xtoverid
. xtreg y x1 x2 …,re r //先运行聚类稳健标准误的RE
. xtoverid
. xtoverid //非传统豪斯曼检验
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(id)
Sargan-Hansen statistic 1792.412 Chi-sq(3) P-value = 0.0000