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* >>>>>>>>>>>>>>>>>>>>>>>>>>>>
*
* 直击面板数据模型
*
* >>>>>>>>>>>>>>>>>>>>>>>>>>>>
*------------- Outline ---------------
- 简介：面板数据结构、优势和挑战
- 什么是「固定效应」？辛普森悖论
- 一维和二维固定效应模型
- 估计方法对比分析：POLS，DVLS，Within-FE
- 聚类标准误：一维聚类和多维聚类
- 实证分析中的主要陷阱
- 动态面板和面板门限模型简介
*--------------------------------------
*-注意：执行后续命令之前，请先执行如下命令
global path "D:\Lec\Lian_Panel" //定义课程目录,可以酌情修改
global D "$path\data" //范例数据
global R "$path\refs" //参考文献
global Out "$path\out" //结果：图形和表格
cd "$D"
set scheme s2color
*-----------
*- 参考资料
shellout "$R\连玉君(2011)_Panel_Data.pdf" //连玉君讲义
* Stata: 面板数据模型-一文读懂
view browse "https://www.jianshu.com/p/e103270ce674"
* [reghdfe：多维面板固定效应估计]
view browse "https://www.jianshu.com/p/e0c02607e82b"
* [Frisch-Waugh定理与部分回归图：图示多元线性回归的系数]
view browse "https://blog.csdn.net/arlionn/article/details/96779492"
*-Good Review of various FE models
*-McCaffrey, D.F., Lockwood, J., Mihaly, K., Sass, T.R., 2012.
* A review of Stata commands for fixed-effects estimation in
* normal linear models. Stata Journal 12(3): 406-432
shellout "$R\SJ12-3-ReviewFE.pdf" //一维面板,二维面板,标准误
*-多维固定效应模型
*-Rios-Avila, F., 2015.
* Feasible fitting of linear models with N fixed effects.
* Stata Journal 15(3): 881-898.
shellout "$R\Rios_2015_SJ_15-3_FE.pdf"
help regxfe //Fit a linear high-order fixed-effects model
*---------
*-应用
*-Fixed Effect Model, FE
*-Flannery, M. J., K. P. Rangan, 2006,
* Partial adjustment toward target capital structures,
* Journal of Financial Economics, 79 (3): 469-506.
shellout "$R\Flannery_2006_FE.pdf"
* 叶德珠,连玉君,黄有光,李东辉.
* "消费文化、认知偏差与消费行为偏差".
* 经济研究, 2012(2): 80-92.
shellout "$R\连玉君_2012_消费文化.pdf"
*-SE of Panel data models
*-Petersen, M. A., 2009,
* Estimating standard errors in finance panel data sets: Comparing approaches,
* Review of Financial Studies, 22 (1): 435-480.
shellout "$R\Petersen-2009.pdf"
*-Stata 实现 codes:
view browse "http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/se_programming.htm"
*--------------------
*-1. 面板数据的结构 (兼具截面资料和时间序列资料的特征)
use "nlswork.dta", clear // 大 N 小 T
replace year = 1900+year
keep if year>1980
browse idcode year ln_wage wks_work collgrad race
list idcode year ln_wage wks_work collgrad race in 1/40, sepby(idcode)
/*
+----------------------------------------------------------------+
| idcode year ln_wage hours ttl_exp collgrad race |
|----------------------------------------------------------------|
| 1 83 2.420261 49 5.294872 0 black |
| 1 85 2.614172 42 7.160256 0 black |
| 1 87 2.536374 45 8.98718 0 black |
| 1 88 2.462927 48 10.33333 0 black |
|----------------------------------------------------------------|
| 2 82 1.808289 38 7.666667 0 black |
| 2 83 1.863417 38 8.583333 0 black |
| 2 85 1.789367 38 10.17949 0 black |
| 2 87 1.84653 40 12.17949 0 black |
| 2 88 1.856449 40 13.62179 0 black |
|----------------------------------------------------------------|
| 3 82 1.603419 40 11.75 0 black |
| 3 83 1.614229 40 12.61539 0 black |
| 3 85 1.730799 40 14.61539 0 black |
| 3 87 1.525765 40 16.34615 0 black |
| 3 88 1.612777 40 17.73077 0 black |
| ... ... |
+----------------------------------------------------------------+
*/
xtset id year //告诉 Stata: 我的数据是面板数据
* panel variable: idcode (unbalanced)
* time variable: year, 68 to 88, but with gaps
* delta: 1 unit
xtdes // 数据特征描述
/*
idcode: 1, 2, ..., 5159 n = 4711
year: 68, 69, ..., 88 T = 15
Delta(year) = 1 unit
Span(year) = 21 periods
(idcode*year uniquely identifies each observation)
Distribution of T_i: min 5% 25% 50% 75% 95% max
1 1 3 5 9 13 15
Freq. Percent Cum. | Pattern
---------------------------+-----------------------
136 2.89 2.89 | 1....................
114 2.42 5.31 | ....................1
89 1.89 7.20 | .................1.11
87 1.85 9.04 | ...................11
86 1.83 10.87 | 111111.1.11.1.11.1.11
61 1.29 12.16 | ..............11.1.11
56 1.19 13.35 | 11...................
54 1.15 14.50 | ...............1.1.11
54 1.15 15.64 | .......1.11.1.11.1.11
3974 84.36 100.00 | (other patterns)
---------------------------+-----------------------
4711 100.00 | XXXXXX.X.XX.X.XX.X.XX
*/
use "invest2.dta", clear // 小 N 大 T
browse
xtset id t
xtdes
*--------------------------
*-2.1 静态面板数据模型简介
*--------------------------
* ==本节目录==
*-2.1.1 简介
*-2.1.2 固定效应模型
*-2.1.2.1 FE模型的基本原理
*-2.1.2.2 stata的估计方法解析
*-2.1.2.3 解读 xtreg,fe 的估计结果
*-R^2
*-个体效应是否显著？
*-如何得到调整后的 adj-R2 ？?
*-拟合值和残差
*-2.1.3 随机效应模型
*-2.1.3.1 RE 与 FE 的异同
*-2.1.3.2 解读 xtreg,re 的估计结果
*---------------------------
*-2.1.1 面试中的辛普森悖论：个体效应是什么？
*-问题描述
use "FE_mark.dta", clear //do FE_mark_DGP.do 数据生成过程
list, sep(6) //面试成绩
+-------------------+
| group id mark |
|-------------------|
1. | A组 1 75 |
2. | A组 2 73 |
3. | A组 3 85 |
4. | A组 4 81 |
5. | A组 5 79 |
6. | A组 6 87 |
|-------------------|
7. | B组 1 85 |
8. | B组 2 83 |
9. | B组 3 95 |
10. | B组 4 92 |
11. | B组 5 88 |
12. | B组 6 97 |
+-------------------+
gsort -mark //排名情况
list, sep(6)
+-------------------+
| group id mark |
|-------------------|
1. | B组 6 97 |
2. | B组 3 95 |
3. | B组 4 92 |
4. | B组 5 88 |
5. | A组 6 87 |
6. | B组 1 85 |
|-------------------|
7. | A组 3 85 |
8. | B组 2 83 |
9. | A组 4 81 |
10. | A组 5 79 |
11. | A组 1 75 |
12. | A组 2 73 |
+-------------------+
tabstat mark, by(group) s(mean sd min max) f(%4.2f)
group | mean sd min max
-------+----------------------------------------
A组 | 80.00 5.48 73.00 87.00
B组 | 90.00 5.59 83.00 97.00
-------+----------------------------------------
Total | 85.00 7.42 73.00 97.00
------------------------------------------------
do "XT_FE_fig1.do" //图示
*-讨论:
*------------------------------------------------------
*
*-面试成绩 = 面试官的偏好 + 个人实际能力 + 运气
* ------------ ------------ ----
*
* Y[it] = a[i] + X[it] + e[it] (1)
*
* i = 1,2 表示面试组别
*
* t = 1,2,...6 表示面试者序号
*
*------------------------------------------------------
*-Question: 如何去除 a[i] ?
*
* Y[i]_m = a[i] + X[i]_m + e[i]_m (2)
*
* (1)-(2)
*
* Y[it]-Y[i]_m = + X[it]-X[i]_m + e[it]-e[i]_m (3)
*-处理方法: 组内去心, 组内差分
*-面试成绩初步调整后图示
do "XT_FE_fig2.do"
*-调整后的最终面试成绩
do "XT_FE_fig3.do"
gsort -mark_FE //最终排名情况
list group id mark_FE, sep(6)
*-最终调整方案：
*
* -------------------------------------------
* 最终成绩 = 原始成绩 - 组内均值 + 样本均值
* -------------------------------------------
*-Comments:
*
* (1)应用面板数据模型的一个主要目的就是控制不可观测的个体效应
* 即本例中的：面试评委偏好
*
* (2)公司研究中，个体效应包括：公司文化, CEO 特征等；
*
* (3)个人消费行为研究中，个体效应包括：个人习惯, 能力, 消费理念等；
*
* (4)上述处理方法就是大名鼎鼎的「组内估计量 Within Estimator」
*--------------------
*-2.1.2 固定效应模型 (Fixed Effect Model)
*-2.1.2.1 基本思想
* 实质上就是在传统的线性回归模型中加入 N-1 个虚拟变量，
* 使得每个截面都有自己的截距项，
* 截距项的不同反映了个体的某些不随时间改变的特征
*
* 例如： lny = a_i + b1*lnK + b2*lnL + e_it
* 考虑中国28个省份的C-D生产函数
*
* Q: a_i 代表什么意思？包含了哪些因素？
* OLS 估计的偏误
* 一份模拟数据
use "FE_simudata.dta", clear
twoway (scatter y x) (lfit y x)
reg y x
*---------------------------------------begin--------------------
#delimit
twoway (scatter y x if id==1, mcolor(green*0.5) msymbol(T))
(scatter y x if id==2, mc(blue*0.5) ms(O))
(scatter y x if id==3, mc(red*0.5) ms(d))
(lfit y x, lcolor(black))
(lfit y x if id==1, lc(green))
(lfit y x if id==2, lc(blue))
(lfit y x if id==3, lc(red)),
legend(off) ;
#delimit cr
*---------------------------------------over---------------------
*-回归分析
tab id, gen(dum)
reg y x // Pooled OLS
est store OLS
reg y x dum2 dum3 // FE: OLS with Dummy varibles
est store OLS_dum2
reg y x dum1-dum3, nocons // FE: OLS with Dummy varibles, no constant
est store OLS_dum3
xtset id t //声明面板数据的结构, 这一步必须做，注意变量的先后顺序
xtdes //这一步可以忽略
xtreg y x, fe // FE: (withi-group estimator)
est store FE
local m "OLS OLS_dum2 OLS_dum3 FE"
esttab `m', mtitle(`m') r2(%4.2f) b(%3.1f) not nogap ///
star(* 0.1 ** 0.05 *** 0.01) compress
/*
------------------------------------------------------
(1) (2) (3) (4)
OLS OLS_dum2 OLS_dum3 FE
------------------------------------------------------
x -0.2* 0.4*** 0.4*** 0.4***
dum2 6*** 9***
dum3 15*** 18***
dum1 3***
_cons 10*** 3*** 10***
------------------------------------------------------
N 60 60 60 60
R-sq 0.05 0.96 0.99 0.72
------------------------------------------------------
* p<0.1, ** p<0.05, *** p<0.01
* Note: dum* 的估计系数进行了四舍五入调整
*/
* 真实的数据生成过程
doedit "FE_simudata_00.do"
*-Note:
* [1]Pooled OLS 主要反映了截面差异;
* [2]对于 x 的系数而言，OLS+dummies 与 FE 结果无异;
* [3]如果关注 R2, 则 OLS_dum2 对应的 R2 是最完整的 R2;
* 而 FE 的 R2 仅仅反映了 x 对 y 的解释力度, 没有考虑个体效应的贡献,
* 本质上是 "squared partial-correlation" (self-reading)
*-2.1.2.2 FE: Stata的估计方法解析
* 目的：如果截面的个数非常多，那么采用虚拟变量的方式运算量过大
* 因此，要寻求合理的方式去除掉个体效应
* 因为，我们关注的是 x 的系数，而非每个截面的截距项
* 处理方法：
shellout "$R\XT_FE_RE.pptx"
* y_it = a + u_i + x_it*b + e_it (1)
*
* ym_i = a + u_i + xm_i*b + em_i (2) 组内平均
*
* ym = a + um + xm*b + em (3) 样本平均
* um = (u1+u2+...+uN)/N
* (1)-(2), 可得：
* (y_it - ym_i) = (x_it - xm_i)*b + (e_it - em_i) (4) //组内去心
* (4)+(3), 可得：
* (y_it-ym_i+ym) = (a+um) + (x_it-xm_i+xm)*b + (e_it-em_i+em)
* 可重新表示为：
*
* Y_it = a_0 + X_it*b + E_it
*
* 对该模型执行 OLS 估计，即可得到 b 的无偏估计量
use "FE_simudata.dta", clear
xtreg y x, fe
est store xtreg
egen y_meanw = mean(y), by(id) /*公司内部平均*/
egen y_mean = mean(y) /*样本平均*/
egen x_meanw = mean(x), by(id)
egen x_mean = mean(x)
gen dy = y - y_meanw + y_mean
gen dx = x - x_meanw + x_mean
reg dy dx
est store OLS_demean
esttab xtreg OLS_demean, r2 b(%6.3f)nogap ///
star(* 0.1 ** 0.05 *** 0.01) compress
/*
------------------------------------
(1) (2)
y dy
------------------------------------
x 0.380***
(12.10)
dx 0.380***
(12.31)
_cons 9.633*** 9.633***
(66.97) (68.16)
------------------------------------
N 60 60
R-sq 0.723 0.723
------------------------------------
t statistics in parentheses, * p<0.1, ** p<0.05, *** p<0.01
*/
*-2.1.2.3 解读 xtreg,fe 的估计结果
. use "invest2.dta", clear
. xtset id t
. browse
. xtreg market invest stock, fe
/*
--------------------------Output----------------------------------
Fixed-effects (within) regression Number of obs = 100
Group variable: id Number of groups = 5
R-sq: Obs per group:
within = 0.4168 min = 20
between = 0.6960 avg = 20.0
overall = 0.6324 max = 20
F(2,93) = 33.23
corr(u_i, Xb) = 0.5256 Prob > F = 0.0000
------------------------------------------------------------------
market | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------
invest | 3.053 0.458 6.67 0.000 2.144 3.962
stock | -0.676 0.222 -3.05 0.003 -1.116 -0.236
_cons | 1372.613 76.964 17.83 0.000 1219.776 1525.449
---------+--------------------------------------------------------
sigma_u |1023.5914
sigma_e | 370.9569
rho |.88390837 (fraction of variance due to u_i)
------------------------------------------------------------------
F test that all u_i=0: F(4, 93) = 97.68 Prob > F = 0.0000
*/
*-- R^2
*-model
* y_it = a_0 + x_it*b_o + e_it (1) pooled OLS
* y_it = a_0 + u_i + x_it*b_w + e_it (2) within estimator
* ym_i = a_0 + u_i + xm_i*b_b + em_i (3) between estimator
*-- R^2
* -> R-sq: within 模型(2)对应的 R2，x 的解释力, 个体效应的贡献未包含进来
* -> R-sq: between corr{xm_i*b_w,ym_i}^2
* -> R-sq: overall corr{x_it*b_w,y_it}^2
*
*-Note:
* T
* ym_i 表示 y_it 的组内均值, 即 ym_i = (1/T)SUM(y_it)
* t=1
*-- F(2,93) = 33.23 检验除常数项外其他解释变量的联合显著性
* 93 = 100-2-5
*-- corr(u_i, Xb) = 0.5256
*-- sigma_u, sigma_e, rho
* rho = sigma_u^2 / (sigma_u^2 + sigma_e^2)
* 个体效应的波动占总波动的比重
dis e(sigma_u)^2 / (e(sigma_u)^2 + e(sigma_e)^2)
dis 1023.5914^2 / (1023.5914^2 + 370.9569^2)
*-- 个体效应是否显著？（假设检验）
* F(4, 93) = 97.68 H0: a1 = a2 = a3 = a4 = 0
* Prob > F = 0.0000 表明，固定效应高度显著
*-- 如何得到调整后的 R2,即 adj-R2 ？
*-Stata 13 以后的版本会直接计算 R2_adj
use "invest2.dta", clear
reg market invest stock i.id
est store LSDV
xtreg market invest stock , fe
est store FE
*-对比呈现
. local m "LSDV FE"
. esttab `m', mtitle(`m') s(r2 r2_w r2_a) nogap
/*
--------------------------------------------
(1) (2)
LSDV FE
--------------------------------------------
invest 3.053*** 3.053***
(6.67) (6.67)
stock -0.676** -0.676**
(-3.05) (-3.05)
1.id 0
(.)
2.id -2404.0***
(-12.40)
3.id -1016.6***
(-4.59)
4.id -2318.4***
(-11.30)
5.id -1979.4***
(-15.50)
_cons 2916.3*** 1372.6***
(14.99) (17.83)
--------------------------------------------
r2 0.936 0.417
r2_w 0.417
r2_a 0.932 0.379
--------------------------------------------
*/
*-- 拟合值和残差
* y_it = u_i + x_it*b + e_it
* predict newvar, [option]
/*
xb xb, fitted values; the default
stdp calculate standard error of the fitted values
ue u_i + e_it, the combined residual
xbu xb + u_i, prediction including effect
u u_i, the fixed- or random-error component
e e_it, the overall error component */
xtreg market invest stock, fe
predict y_hat, xbu //真正意义的拟合值，y_hat = u_i + x_it*b
predict a , u //得到每家公司的截距项
predict res , e //真正意义的随机干扰项,用这个来估计过度投资
predict cres, ue
gen ares = a + res
. list ares cres in 1/5
/*
+-----------------------+
| ares cres |
|-----------------------|
1. | 738.23406 738.23406 |
2. | 2128.6036 2128.6036 |
3. | 2867.1548 2867.1548 |
4. | 774.38981 774.38981 |
5. | 2068.3128 2068.3128 |
+-----------------------+
*/
*-Notes：
* [1] 不要用 predict yhat 来计算拟合值
* [2] 不能用 predict e, res 来计算残差
*-------------------------------
*-2.1.3 FE 与其他估计方法的关系
*-2.1.3.1 视角不同：横看成岭侧成峰
*-POLS, FE 之间的关系
/* Case I */ do "FE_OLS_Negative.do"
/* Case II */ do "FE_OLS_Positive.do"
/* Case III */ do "FE_OLS_Zero.do"
/* Case IV */ do "FE_OLS_Nodiff.do"
*-FE 能控制个体效应，却无法估计出个体效应;
*-POLS+Dummies 可以实现与 FE 相同的效果，且能估计出个体效应;
*-2.1.3.2 R2 不同: 组内去心，到底去掉了什么?
help xtdata
help center
help xtcenter
*-2.1.3.3 POLS, FE, BE 之间的关系
use "FE_simudata.dta", clear
egen yi_mean = mean(y), by(id) //公司内部平均
egen y_mean = mean(y) //样本平均
egen xi_mean = mean(x), by(id)
egen x_mean = mean(x)
gen dy = y - yi_mean + y_mean
gen dx = x - xi_mean + x_mean
*--------------------------------------------------begin-------
#delimit
twoway (scatter y x if id==1, mcolor(green*0.6) msymbol(T) msize(*0.6))
(scatter y x if id==2, mc(black*0.6) ms(O) msize(*0.6))
(scatter y x if id==3, mc(red*0.8) ms(d) msize(*0.6))
(scatter yi xi, msize(*2.5) mc(blue) ms(O))
(lfit y x, lcolor(red) lw(*1.3))
(lfit yi xi, lcolor(blue) lw(*1.3) lp(dash))
(lfit y x if id==1, lc(black*0.6) lw(*1.2))
(lfit y x if id==2, lc(black*0.6) lw(*1.2))
(lfit y x if id==3, lc(black*0.6) lw(*1.2)),
ylabel(0(5)20,angle(0))
legend(off)
text( 7.4 10.3 "POLS")
text(17.5 3.5 "FE(Within)")
text(12.4 -1.9 "Between")
;
#delimit cr
*--------------------------------------------------over--------
*--------------------
*-2.1.4 随机效应模型
*--------
*-2.1.4.1 RE 与 FE 的异同
*-RE的模型设定：
* y_it = x_it*b + (a_i + u_it)
* = x_it*b + v_it
* 基本思想：将随机干扰项分成两种
* 一种是不随时间改变的，即个体效应 a_i
* 另一种是随时间改变的，即通常意义上的干扰项 u_it
shellout "$R\XT_FE_RE.pptx"
* 估计方法：FGLS
* Var(v_it) = sigma_a^2 + sigma_u^2
* Cov(v_it,v_is) = sigma_a^2
* Cov(v_it,v_js) = 0
* 利用Pooled OLS，Within Estimator, Between Estimator
* 可以估计出sigma_a^2和sigma_u^2,进而采用GLS或FGLS
* Re估计量是Fe估计量和Be估计量的加权平均
* yr_it = y_it - theta*ym_i
* xr_it = x_it - theta*xm_i
* theta = 1 - sigma_u / sqrt[(T*sigma_a^2 + sigma_u^2)]
*--------
*-2.1.4.2 解读 xtreg,re 的估计结果
use "invest2.dta", clear
xtreg market invest stock, re
/*
Random-effects GLS regression Number of obs = 100
Group variable: id Number of groups = 5
R-sq: Obs per group:
within = 0.4163 min = 20
between = 0.7054 avg = 20.0
overall = 0.6380 max = 20
Wald chi2(2) = 95.98
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
-------------------------------------------------------------------
market | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------+---------------------------------------------------------
invest | 3.847 0.483 7.96 0.000 2.899 4.795
stock | -0.798 0.257 -3.11 0.002 -1.301 -0.295
_cons | 1212.764 154.621 7.84 0.000 909.712 1515.815
---------+---------------------------------------------------------
sigma_u | 223.80826
sigma_e | 370.9569
rho | .26686395 (fraction of variance due to u_i)
-------------------------------------------------------------------
*/
*-- R2
* -> R-sq: within corr{(x_it-xm_i)*b_r, y_it-ym_i}^2
* -> R-sq: between corr{xm_i*b_r,ym_i}^2
* -> R-sq: overall corr{x_it*b_r,y_it}^2
* 上述R2都不是真正意义上的R2，因为Re模型采用的是GLS估计。
*-- rho = sigma_u^2 / (sigma_u^2 + sigma_e^2)
dis e(sigma_u)^2 / (e(sigma_u)^2 + e(sigma_e)^2)
*-- corr(u_i, X) = 0 (assumed)
* 这是随机效应模型的一个最重要，也限制该模型应用的一个重要假设
* 然而，采用固定效应模型，我们可以粗略估计出corr(u_i, X)
xtreg market invest stock, fe
*-- Wald chi2(2) = 95.98 Prob> chi2 = 0.0000
*------------------------------------
*-2.2 时间效应、模型的筛选和常见问题
*------------------------------------
* ==本节目录==
*-2.2.1 时间效应
*-2.2.1.1 时间虚拟变量的设定
*-2.2.1.2 检验时间效应是否显著
*-2.2.2 模型的筛选
*-2.2.2.1 固定效应模型还是Pooled OLS？
*-2.2.2.2 随机效应模型还是Pooled OLS？
*-2.2.2.3 固定效应模型还是随机效应模型？Hausman检验
*-2.2.3 一些常见问题
*-2.2.3.1 为何xtset命令总是报告错误信息？
*-2.2.3.2 为何有些变量会被drop掉？
*-2.2.3.3 unbalance —> balance
*-2.2.3.4 得到连续的公司编号
*----------------------------------
*-2.2.1 时间效应: 双向固定效应模型 (很常用)
*-2.2.1.1 时间虚拟变量的设定
* 单向固定效应模型
* y_it = u_i + x_it*b + e_it
* 双向固定效应模型
* y_it = u_i + f_t + x_it*b + e_it
* 固定效应模型中的时间效应 (Two-way FE)
use "xtcs.dta", clear
xtreg tl size ndts tang tobin npr i.year, fe
dis _b[1999.year] //估计系数的引用方法
/*
-----------------------------------------------
tl | Coef. Std. Err. t P>|t|
--------+--------------------------------------
size | 0.134 0.006 22.93 0.000
ndts | -0.093 0.031 -2.99 0.003
tang | 0.086 0.015 5.71 0.000
tobin | -0.013 0.004 -3.04 0.002
npr | -0.158 0.015 -10.84 0.000
year
1999 | -0.014 0.005 -2.62 0.009
2000 | -0.019 0.006 -3.23 0.001
2001 | -0.023 0.006 -3.78 0.000
2002 | -0.026 0.006 -4.12 0.000
2003 | -0.022 0.007 -3.34 0.001
2004 | -0.020 0.007 -2.80 0.005
_cons | -2.359 0.124 -18.97 0.000
--------+--------------------------------------
*/
* 随机效应模型中的时间效应
xtreg tl size ndts tang tobin npr i.year, re
*-2.2.1.2 检验时间效应是否显著
xtreg tl size ndts tang tobin npr , fe
est store fe
xtreg tl size ndts tang tobin npr i.year, fe
est store fe_dumt
esttab fe fe_dumt, nogap s(N r2 ll)
lrtest fe fe_dumt // LR test, LR = -2*(LL1-LL2)
* Likelihood-ratio test LR chi2(6) = 23.23
* (Assumption: fe nested in fe_dumt) Prob > chi2 = 0.0007
dis -2*(3838.1-3849.7) //手动计算
*-----------------
*-2.2.2 模型的筛选
shellout "$R\XT_FE_RE.pptx"
* Stata: 面板数据模型-一文读懂
view browse "https://www.jianshu.com/p/e103270ce674"
*-2.2.2.1 固定效应模型还是Pooled OLS？(不重要)
* Wald 检验
*
* FE: y_it = a + u_i + x_it*b + e_it (1)
*
* H0: u_i=0 (u1 = u2 = ... = uN = 0)
use "invest2.dta", clear
xtreg market invest stock, fe
*-F test that all u_i=0: F(4, 93) = 97.68 Prob > F = 0.0000
*-2.2.2.2 随机效应模型还是Pooled OLS？(不重要)
* RE: y_it = a + x_it*b + u_i + e_it (1) u~N(0, Var(u))
*
* H0: Var(u) = 0
xtreg market invest stock, re mle //LR test
* LR test of sigma_u=0: chibar2(01) = 135.69 Prob >= chibar2 = 0.000
*-2.2.2.3 固定效应模型还是随机效应模型？Hausman检验 (也不重要)
shellout "$R\XT3_Hausman.pptx"
*- FE v.s. RE
*--------------------------------------
* FE
* --解释变量--
* ------------
* y_it = a0 + x_it*b + u_i + e_it
* -----------
* --干扰项---
* RE
*--------------------------------------
* 假设条件的区别:
* FE: corr(x,u)=0
* RE: corr(x,u)=0 | corr(x,a_i)=0
* 基本思想：
* 如果 Corr(u_i,x_it) = 0, FE 和 RE 都是无偏的，但 RE 更有效
* 如果 Corr(u_i,x_it)!= 0, FE 仍然无偏，但 RE 却是有偏的
* 基本步骤
use "xtcs.dta", clear
xtreg tl size ndts tang tobin npr, fe
est store fe
xtreg tl size ndts tang tobin npr, re
est store re
hausman fe re
/*
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
------+-----------------------------------------------------------
size | .1197523 .0952139 .0245384 .0018098
ndts | -.1312198 -.2086307 .0774109 .0109313
tang | .087448 .0788076 .0086405 .0028921
tobin | -.0178802 -.021615 .0037348 .
npr | -.1472081 -.1983802 .0511721 .001267
------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 166.58
Prob>chi2 = 0.0000
(V_b-V_B is not positive definite)
*/
* Hausman 检验值为负怎么办？
* 通常是因为RE模型的基本假设 Corr(x,u_i)=0 无法得到满足
use "invest2.dta", clear
xtreg market invest stock, fe
est store m_fe
xtreg market invest stock, re
est store m_re
hausman m_fe m_re
/*
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| m_fe m_re Difference S.E.
--------+-----------------------------------------------------------
invest | 3.05273 3.847014 -.794284 .
stock | -.6763434 -.7981618 .1218184 .
--------------------------------------------------------------------
Test: Ho: difference in coefficients not systematic
chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -47.57 chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test
*/
* 检验过程中两个模型的方差-协方差矩阵都采用Fe模型的
hausman m_fe m_re, sigmaless
/*
chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 63.63
Prob>chi2 = 0.0000
*/
* 两个模型的方差-协方差矩阵都采用Re模型的
hausman m_fe m_re, sigmamore
/*
chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 38.91
Prob>chi2 = 0.0000
*/
* 如果 Hausman 检验拒绝 RE 模型，怎么办？
* (1) FE
* (2) IV 估计
*- xtoverid 命令
* 基本思想：过度识别检验(over-identification restrictions)
* FE: corr(x,u)=0
* RE: corr(x,u)=0 | corr(x,a_i)=0
xtreg market invest stock, re
xtoverid // Cameron and Trivedi (2009, pp.261),
// Wooldridge (2002, pp. 290-91)
/*
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re
Sargan-Hansen statistic 63.633 Chi-sq(2) P-value = 0.0000
*/
*-Bootstrap Hausman Test
help rhausman // See Camerion and Trivedi (2005, pp. 717)
help hausmanxt // Given by Lian Yujun
use "invest2.dta", clear
xtreg market invest stock, fe
est store m_fe
xtreg market invest stock, re
est store m_re
rhausman m_fe m_re, reps(200) cluster
/*
Cluster-Robust Hausman Test
(based on 200 bootstrap repetitions)
b1: obtained from xtreg market invest stock, fe
b2: obtained from xtreg market invest stock, re
Test: Ho: difference in coefficients not systematic
chi2(2) = (b1-b2)' * [V_bootstrapped(b1-b2)]^(-1) * (b1-b2)
= 0.44
Prob>chi2 = 0.8007
*/
*-小结：
*
* 传统的 Hausman 检验不适用于 Panel data，因为它没有考虑异方差和序列相关
*
* 应该使用 -xtoverid- 或 -rhausman-
*
* 参见： -- CM2015 -- pp.16, 倒数第三段最后一句
*-Cameron, C. A., D. L. Miller, 2015,
* A practitioner’s guide to cluster-robust inference,
* Journal of Human Resources, 50 (2): 317-372.
shellout "$R\Cameron_2015_ClusterSE_JHR.pdf" //cluster SE 使用手册
*-相关论文和推文
*-连玉君, 王闻达, 叶汝财.
* Hausman 检验统计量有效性的Monte Carlo模拟分析[J].
* 数理统计与管理, 2014, 33(5):830-841.
shellout "$R\连玉君_2014_Hausman检验.pdf"
*-Stata连享会推文： Stata: 面板数据模型-一文读懂
view browse "https://www.jianshu.com/p/e103270ce674"
*-2.2.2.4 如何控制年度和行业效应
*-Gormley, T. A., D. A. Matsa, 2014,
* Common errors: How to (and not to) control for unobserved heterogeneity,
* Review of Financial Studies, 27 (2): 617-661.
shellout "$R\Gormley_2014_RFS_FE.pdf"
*---------------------
*-2.2.4 一些常见问题
*-2.2.4.1 为何xtset命令总是报告错误信息？
use invest3.dta, clear
xtset id t // 错误
xtdes
duplicates drop id t, force
xtset id t
*-2.2.4.2 为何有些变量会被drop掉？
use "nlswork.dta", clear
xtset idcode year
label define race 1 "white" 2 "black" 3 "other"
label value race race
xtreg ln_wage hours tenure ttl_exp, fe // 正常执行
*-加入种族虚拟变量
xtreg ln_wage hours tenure ttl_exp i.race, fe
/*
-----------------------------------------------
ln_wage | Coef. Std. Err. t P>|t|
---------+-------------------------------------
hours | -0.000 0.000 -1.03 0.305
tenure | 0.012 0.001 13.77 0.000
ttl_exp | 0.025 0.001 35.64 0.000
|
race |
black | 0.000 (omitted)
other | 0.000 (omitted)
|
_cons | 1.494 0.009 161.20 0.000
---------+-------------------------------------
*/
* 为何会被 dropped ?
* 固定效应模型的设定：y_it = u_i + x_it*b + e_it (1)
* 由于个体效应 u_i 不随时间改变，
* 因此若 x_it 包含了任何不随时间改变的变量，
* 都会与 u_i 构成多重共线性，Stata会自动删除之。
* 使用 FE 时，所有不随时间变化的变量都会被 drop (性别,出生地,星座等)
*
* 简言之，FE 可以控制个体效应，但无法估计其系数
*-----------------------------
*-如何估计不随时间变化的因素？
*-----------------------------
*- a_i 其实是个黑盒子，里面包含了所有不随时间变化的因素
* 我们只需要把这个黑盒子里的东西拆出来放回模型即可
* 把那些不随时间变化，以及随时间变化很慢的因素都放回 POLS 即可
use "nlswork.dta", clear
global dummies "i.occ_code south collgrad union not_smsa"
reg ln_wage hours tenure ttl_exp i.race $dummies
/*
--------------------------------------------------
ln_wage | Coef. Std. Err. t P>|t|
----------+---------------------------------------
hours | -0.001 0.000 -2.74 0.006
tenure | 0.017 0.001 20.98 0.000
ttl_exp | 0.019 0.001 25.62 0.000
|
race |
black | -0.066 0.006 -10.55 0.000
other | 0.008 0.025 0.31 0.759
|
occ_code |
2 | -0.036 0.013 -2.85 0.004
| ... ...
13 | -0.267 0.013 -20.65 0.000
|
south | -0.091 0.006 -15.97 0.000
collgrad | 0.244 0.008 29.10 0.000
union | 0.162 0.007 24.88 0.000
not_smsa | -0.170 0.006 -28.54 0.000
_cons | 1.823 0.014 130.52 0.000
--------------------------------------------------
*/
* ----------------------------------
* ------------几点评论--------------
* ----------------------------------
* (1) 多数实证研究都采用固定效应模型或双向固定效应模型
* (2) 随机效应模型有两个突出的优点：
* 一是比较有效；
* 二是可以分析不随时间改变的变量的影响，如性别、种族、教育程度等
*--------------------------------
*-2.3 异方差、序列相关和截面相关
*--------------------------------
* ==本节目录==
*-2.3.1 简介
*-2.3.3 估计方法
*-2.3.2.1 异方差-序列相关稳健型估计
*-2.3.2.2 采用 Bootstrap 标准误
*-2.3.2.3 一个综合的处理方法：xtscc 命令
*-2.3.2.4 二维聚类标准误
*-2.3.2.5 截面相关和共同因素问题
*-------------
*-2.3.1 简介
* y_it = x_it*b + u_i + e_it
* 由于面板数据同时兼顾了截面数据和时间序列的特征，
* 所以异方差和序列相关必然会存在于面板数据中；
* 同时，由于面板数据中每个截面（公司、个人、国家、地区）
* 之间还可能存在内在的联系，
* 所以，截面相关性也是一个需要考虑的问题。
* 此前的分析依赖三个假设条件：
* （1） Var[e_it] = sigma^2 同方差假设
* (2) Corr[e_it, e_it-s] = 0 序列无关假设
* (3) Corr[e_it, e_jt] = 0 截面不相关假设
* 当这三个假设无法得到满足时，
* 便分别出现 异方差、序列相关和截面相关问题；
* 我们一方面要采用各种方法来检验这些假设是否得到了满足；
* 另一方面，也要在这些假设无法满足时寻求合理的估计方法。
*-----------------
*-2.3.2 估计方法
*-2.3.2.1 异方差-序列相关稳健型估计 (多数文献都用这个)
use "xtcs.dta", clear
xtreg tl size ndts tang tobin npr, fe robust
est store fe_rb
*-等价于(在公司层面上的聚类调整标准误)
xtreg tl size ndts tang tobin npr, fe cluster(code)
*-含义：
* (1) 组内(公司内部)各年度的干扰项可以彼此相关；
* (2) 组间(不同公司之间)的干扰项彼此不相关(同期不相关，跨期也不相关)
* (3) 组间存在异方差 (A 公司干扰项的方差不同于 B 公司)
* Q: cluster(industry), cluster(year), cluster(province) 分别是什么含义？
*-2.3.2.2 采用Bootstrap标准误
*-优点：统计推断并不依赖具体的分布假设
xtreg tl size ndts tang tobin npr, fe vce(bootstrap, reps(500))
est store fe_bs500
*-原理：
* y_it = u_i + x_it*b + v_it (1)
*
* 估计完毕后，将得到b和u_i的估计值，设为 b0 和 u0_i,则
*
* ybs_it = u0_i + x_it*b0 + vbs_it (2) Bootstrap样本
*
* 估计(2)，得到 b_bs1, b_bs2,......b_bs300
* 计算这300个系数的标准差，便可以得到系数 b 的标准误
*-结果对比
xtreg tl size ndts tang tobin npr, fe
est store fe
local s "using $Out\Table01.csv"
local m "fe fe_rb fe_bs500"
esttab `m' `s', mtitle(`m') b(%6.3f) t(%4.2f) nogap ///
replace star(* 0.1 ** 0.05 *** 0.01)
/*
--------------------------------------------------
(1) (2) (3)
fe fe_rb fe_bs500
--------------------------------------------------
size 0.120*** 0.120*** 0.120***
(28.24) (17.48) (17.38)
ndts -0.131*** -0.131*** -0.131***
(-4.60) (-2.76) (-2.71)
tang 0.087*** 0.087*** 0.087***
(5.80) (3.79) (3.63)
tobin -0.018*** -0.018*** -0.018***
(-4.73) (-3.31) (-3.19)
npr -0.147*** -0.147*** -0.147***
(-10.30) (-7.37) (-7.42)
_cons -2.074*** -2.074*** -2.074***
(-22.37) (-14.18) (-14.02)
--------------------------------------------------
N 3066 3066 3066
--------------------------------------------------
t statistics in parentheses
* p<0.1, ** p<0.05, *** p<0.01
*/
*-2.3.2.3 一个综合的处理方法：xtscc 命令
* 详见 Stata Journal，2007(3): 281-312.
* Daniel Hoechle, 2007,
* Robust Standard Errors for Panel Regressions
* with Cross-Sectional Dependence,
* Stata Journal, 7(3): 281–312.
shellout "$R\Daniel_2007_xtscc.pdf"
* 当异方差、序列相关以及截面相关性质未知时
* xtscc相当于White/Newey估计扩展到Panel的情形
* Driscoll and Kraay (1998)
use "xtcs.dta", clear
xtscc tl size ndts tang tobin npr, fe
est store fe_scc
xtscc tl size ndts tang tobin npr, fe lag(1)
est store fe_scc_lag1
xtreg tl size ndts tang tobin npr, fe
* 结果对比
xtreg tl size ndts tang tobin npr, fe
est store fe
local s "using $Out\Table_xtscc.csv"
local m "fe fe_scc fe_scc_lag1"
esttab `m' `s', b(%6.3f) t(%4.2f) nogap ///
mtitle(`m') r2 sca(N r2_w r2_a) replace
*-2.3.2.4 二维聚类标准误
* -- Petersen2009 -- cluter2.ado
*-Petersen, M. A., 2009,
* Estimating standard errors in finance panel data sets:
* Comparing approaches,
* Review of Financial Studies, 22 (1): 435-480.
shellout "$R\Petersen-2009.pdf" //Petersen2009, 面板 SE
* Stata commnd for 2way clutered S.E.: cluster2
* -- CM2015 --
*-Cameron, C. A., D. L. Miller, 2015,
* A practitioner’s guide to cluster-robust inference,
* Journal of Human Resources, 50 (2): 317-372.
shellout "$R\Cameron_2015_ClusterSE_JHR.pdf" //cluster SE 使用手册
* -- CGM2011 -- cgmreg.ado | vce2way.ado
*-Cameron, A. C., J. B. Gelbach, D. L. Miller, 2011,
* Robust inference with multiway clustering,
* Journal of Business & Economic Statistics, 29 (2): 238-249.
shellout "$R\Cameron_2011_ClusterSE.pdf" //多维
shellout "$R\Cameron_2011_ClusterSE_PPT.pdf" // Robust SE PPT
help cgmreg
help vce2way
* -- IM2010 -- clustse.ado | clustbs.ado
*-Ibragimov, Rustam and Ulrich K. Muller. 2010.
* t-Statistic Based Correlation and Heterogeneity Robust Inference.
* Journal of Business and Economic Statistics 28(4):453-468.
shellout "$R\Ibragimov_2010_clustse.pdf"
help clustse // 基于 Bootstrap 的聚类标准误
* -- IM2010 -- clustbs.ado
*-Cameron, A., J. Gelbach and D. Miller. 2008.
* Bootstrap-based improvements for inference with clustered errors.
* Review of Economics and Statistics 90(3): 414-427.
shellout "$R\Cameron_2008_RES_bsClusterSE.pdf" // 基于 Bootstrap 的 SE
help clustbs
* --Thompson2011--
*-Thompson, S. B. (2011).
* Simple formulas for standard errors that cluster by both firm and time.
* Journal of Financial Economics 99(1): 1-10.
shellout "$R\Thompson-2011.pdf"
* -Abadie 2017--
* Alberto Abadie, Susan Athey, Guido W. Imbens, Jeffrey Wooldridge (2017).
* When Should You Adjust Standard Errors for Clustering?, working paper
shellout "$R\Abadie_2017_adjust_SE.pdf"
*----------
*-应用范例：
*-数据和模型基本设定
use "nlswork.dta", clear
xtset id year
gen age2 = age*age
global x "age age2 ttl_exp tenure hours i.year"
*-一维 clustered S.E. 公司层面聚类
*-FE (within Estimator)
xtreg ln_wage $x, fe vce(cluster id) //写法1 }
xtreg ln_wage $x, fe robust //写法2 } --> 三种写法等价
xtreg ln_wage $x, fe cluster(id) //写法3 }
*-LSDV (Least Square Dummy Variable estimator)
areg ln_wage $x, absorb(id) cluster(id) //系数估计值相同，但计算 SE 时的自由度调整不同
est store SE_id
*-一维 clustered S.E. 年度层面聚类 (很少用)
* xtreg ln_wage $x, fe cluster(year) //错误命令
areg ln_wage $x, absorb(id) cluster(year)
est store SE_year
*-二维 clustered S.E. 公司-年度层面聚类 (比较常用)
help vce2way // CGM2011, 支持 Panel data, xtreg 等命令
*-正确命令
vce2way areg ln_wage $x, absorb(id) cluster(id year)
est store SE_id_year
/********* 二维聚类标准误错误陷阱 ！！！错误命令 I
vce2way xtreg ln_wage $x, fe cluster(id year)
*/
*-Note: A4_regress.do, Section 4.2.3 中介绍的
* cluster2 和 cgmreg 都不支持 xtreg
*-特别注意：这是错误的二维聚类标准误
egen IDYEAR = group(id year)
areg ln_wage $x, absorb(id) cluster(IDYEAR) // [EM1]
est store SE2way_Wrong
areg ln_wage $x, absorb(id) robust // [EM2] robust <==> cluster()
est store SE_white
*-上述两条命令(EM1, EM2)本质上等价于如下命令 EM3
gen obsid = _n
areg ln_wage $x, absorb(id) cluster(obsid) // [EM3]
*-对比
local m "SE_id SE_year SE_id_year SE2way_Wrong SE_white"
esttab `m', mtitle(`m') nogap b(%4.3f) t(%4.2f) brackets ///
star(* 0.1 ** 0.05 *** 0.01) s(N r2) compress ///
drop(68.year)
/*
---------------------------------------------------------------------------
(1) (2) (3) (4) (5)
SE_id SE_year SE_id_year SE2way_Wrong SE_white
---------------------------------------------------------------------------
age 0.078*** 0.078*** 0.078*** 0.078*** 0.078***
[5.29] [7.70] [5.89] [6.49] [6.49]
age2 -0.001*** -0.001*** -0.001*** -0.001*** -0.001***
[-10.08] [-11.67] [-8.66] [-15.92] [-15.92]
ttl_exp 0.034*** 0.034*** 0.034*** 0.034*** 0.034***
[12.84] [12.48] [10.04] [19.14] [19.14]
tenure 0.011*** 0.011*** 0.011*** 0.011*** 0.011***
[6.68] [7.71] [5.78] [9.94] [9.94]
hours -0.000 -0.000 -0.000 -0.000 -0.000
[-0.83] [-0.64] [-0.56] [-1.10] [-1.10]
Year dumm ... ...
_cons 0.329 0.329* 0.329 0.329 0.329
[1.23] [1.85] [1.43] [1.47] [1.47]
---------------------------------------------------------------------------
N 2.8e+04 2.8e+04 2.8e+04 2.8e+04 2.8e+04
r2 0.688 0.688 0.688 0.688 0.688
---------------------------------------------------------------------------
Note: t statistics in brackets, * p<0.1, ** p<0.05, *** p<0.01
*/
*-二维聚类标准误的计算方法
shellout "$R\Thompson-2011.pdf" // PP.2
* 方差-协方差矩阵计算公式为：
* V(2way) = V(Firm) + V(Year) - V(White)
scalar Var2way = (0.0148)^2 + (0.0101)^2 - (0.0120)^2
scalar se2way = sqrt(Var2way)
dis "se2way = " %6.4f se2way
*-Comments:
*
* 1. 考虑异方差后的 SE 通常会比同方差(Homo)下的 SE 大一些; 但并不绝对如此;
* 2. 聚类调整后的 SE 要比 Homo SE 大, 如本例中 SE[_cons]
* 3. 本例中，二维聚类 SE 约为 Homo SE 的两倍
* 4. 在截面数据或面板数据中，通常都要使用聚类 SE
* 5. cluster(industry) 同时考虑了行业层面的异方差,
* 以及行业内部不同公司之间的相关性;
* 6. Q: cluster(firm) 是什么含义？
*-2.3.2.5 截面相关和共同因素问题
help xtcce // Common Correlated Effects Estimation for
// Static Panels with Cross-Sectional Dependence.
*--------------
*-其他相关命令
*-统计分析和绘图
help panell //display panel length for a given set of variables
help paverage //calculate p-period-average series in a panel dataset
help mkdensity //graph kernel densities of several variables
help xtgraph //
*-假设检验
help xthrtest //Born&Breitung(2016)纠偏高阶稳健性序列相关检验
*-面板滚动回归
help rolloing2 //rolling window and recursive estimation
help rolloing3 //compute predicted values for rolling regressions
help rollreg //perform rolling regression estimation
help rollstat //rolling-window statistics for time series or panel data
help asrol //Gen rolling-window statistics in TS or panel data
*-高维固定效应模型
help areg //自动消除一维固定效应
help gpreg //消除二维固定效应
help regwls //estimate Weighted Least Squares with factor variables
help fese //Standard errors for fixed effects
help reg2hdfe //Two High Dimensional Fixed Effects
help twfe //Two-way fixed effects or match effects
help a2reg //Models with two fixed effects
help reg3hdfe //Three high dimensional fixed effects
help hdfe // xtdata命令的升级版,
// Partial-out variables with fixed-effects
*-变系数模型
help xtmg //panel time series models with heterogeneous slopes
help xtnptimevar //Non-parametric time-varying coefficients panel data
//models with fixed effects
help xtfixedcoeftvcu //Panel Data Models with Coefficients that Vary over Time and Firm
*-共同因子模型
help xtcce //the Common Correlated Effects estimator
*-面板分位数回归
help qregpd //Quantile Regression for Panel Data
*-聚类分组FE
help xtregcluster //partially heterogeneous linear panel data with fixed effects
*-假设检验
help resetxt //Panel Data REgression Specification Error Tests
use "resetxt.dta", clear
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