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作者: 谢雁翔 (南开大学)
邮箱: xyxmask1995@163.com
编者按: 本文主要参考「Sebastian Kripfganz」 的如下内容,特此致谢!
Source: Kripfganz S . XTDPDGMM: Stata module to perform generalized method of moments estimation of linear dynamic panel data models[J]. Statistical Software Components, 2019. -Link-
Kripfganz S . Generalized method of moments estimation of linear dynamic panel-data models[C]. London Stata Conference 2019. Stata Users Group, 2019. -Link-
目录
[[TOC]]
1. 简介
对于动态面板数据模型 (Dynamic Panel Data, DPD),直接用最小二乘法估计是有偏的,为解决这一问题,Arellano 和 Bond (1991)、 Arellano 和 Bover (1995)、以及 Blundell 和 Bond (1998) 等提出了「一阶差分 GMM (FD-GMM)」和「系统 GMM (SYS-GMM)」估计法。
相应地,Stata 也提供了 xtabond
、xtdpdsys
、以及 xtabond2
等早期估计 GMM 的命令。Kripfganz (2019) 在此基础上,编写了 xtdpdgmm
命令,该命令解决了 xtabond2
等命令的一些缺陷,并使估计更加灵活。特别的,该命令整合了 Ahn 和 Schmidt (1995) 非线性矩条件、更好解决了高度自相关问题、以及提供了 Hansen 等 (1996) 的迭代 GMM 估计。
本文的主要目的是介绍动态面板数据模型的两种估计方法,以及 xtdpdgmm
命令的应用。
2. 估计方法
2.1 差分 GMM
考虑以下动态面板模型:
通过一阶差分消去个体效应 ,可得:
然而,由于 与 相关, 使得 与 相关。也因此, 为内生变量,我们需要为其找到适当的工具变量才能得到一致估计。
为此,Anderson 和 Hsiao (1981) 认为由于 与 相关,若 不存在自相关,则 与 不相关,故 是 的有效工具变量。根据这一思想,更高阶的滞后变量 也是有效工具变量,但是 Anderson 和 Hsiao (1981) 估计并未加以利用,所以估计并非最有效。
Arellano 和 Bond (1991) 使用所有可能的滞后变量作为工具变量 (工具变量个数可能多于内生变量) 进行估计,这一方法又被称为「差分 GMM」。值得注意的是,在使用差分 GMM 时,扰动项 不存在自相关,即 。
差分 GMM 注意事项:
-
如果 非严格外生,即虽然 与当期 不相关,但与 相关,则 与 相关,使得 为内生变量。此时,可以使用 作为 的工具变量。
-
如果 很大,则会有很多工具变量,进而容易产生弱工具变量问题。同时,也会弱化 Hansen 统计量,甚至出现 值等于 1 的不可信结果。解决方法一是在使用
xtabond
命令时,限制最多使用 阶滞后变量作为工具变量。方法二是使用折叠的 Ⅳ 式工具变量,而不使用展开的 GMM 式工具变量。 -
不随时间变化的变量 被消掉了,故差分 GMM 无法估计 的系数。
-
如果序列 具有很强的持续性,即一阶自回归系数接近于 1,则 与 的相关性可能很弱,进而导致弱工具变量问题。
2.2 水平 GMM
为克服上述差分 GMM 将不随时间变化的变量 消掉、以及序列 具有很强的持续性等问题,Arellano 和 Bover(1995) 重新回到了差分之前的水平方程,并使用 作为 的工具变量。但前提是需假设 不存在自相关,以及 与个体效应 不相关。上述过程也被称为「水平 GMM」。
2.3 系统 GMM
Blundell 和 Bond (1998) 将差分 GMM 与水平 GMM 联合进行 GMM 估计,即「系统 GMM」。与差分 GMM 相比,系统 GMM 的优点是,可以提高估计的效率,并且可以估计不随时间变化的变量 的系数。其缺点是,必须假定 与 无关。
Note:本部分内容摘自「陈强. 高级计量经济学及 Stata 应用[M]. 高等教育出版社, 2014. -Link-」,详见 289-291 页,特此感谢!
3. xtdpdgmm 命令介绍
3.1 xtdpdgmm 命令语法
xtdpdgmm
命令的安装:
ssc install xtdpdgmm, replace
xtdpdgmm
命令的语法:
xtdpdgmm depvar [indepvars] [if] [in] [, options]
其中,option
具体选项如下:
iv(iv_spec)
:指定标准式工具变量,并可指定任意多次;gmmiv(gmmiv_spec)
:指定 GMM 式工具变量,并可指定任意多次;nl (nl_spec)
:添加由误差协方差结构得出的非线性矩条件;collapse
:折叠式工具变量为标准式工具变量;model(model_spec)
:设置工具变量的默认形式及标准误;norescale
:不重新缩放转换后的矩条件;wmatrix(wmat_spec)
:指定用于获得一阶 GMM 估计或两步 GMM 估计的初始估计的加权矩阵;onestep|twostep
:确定一步估计或两步估计;igmm
:使用迭代 GMM 估计;teffects
:模型增加时间效应;overid
:计算简化模型的过度识别统计信息;noconstant
:无常数项;vce(vce_spec)
:设置聚类标准误的估计方式进行稳健标准误估计;auxiliary
:显示所有系数作为辅助参数;level(#)
:设置置信区间,默认为水平为 95%;small
:进行自由度调整并报告小样本统计数据;coeflegend
:显示图例而不是统计信息;noheader
:不显示输出表头;notable
:不显示输出系数表;nofootnote
:不显示系数表下脚注;display_options
:控制列和列的格式,行间距,行宽,需要省略的变量以及基础空白单元格、因子变量的标记;noanalytic
:不使用解析封闭解。from(init_spec)
:确定系数的初始值;nodots
:在迭代 GMM 估计中的每个步骤中显示迭代日志,而不是点;igmm_options
:控制迭代的 GMM 过程;minimize_options
:控制最小化过程。
3.2 xtdpdgmm 命令实操
以 abdata.dta 数据集为例,该数据集是 140 个国家 1976 年到 1984 年的各种宏观指标的面板数据。id 代表每个国家的标号,year 代表年份,其他变量包括就业率 emp、平均工资 wage、投资占 GDP 的百分比 cap 等。
*数据下载地址:https://gitee.com/arlionn/data/blob/master/data01/abdata.dta
*use abdata.dta, clear
webuse abdata, clear //调用网络数据
describe //数据结构
sum //描述性统计
xtset id year //声明面板数据
一阶差分 GMM 估计:
. xtdpdgmm L(0/1).n w k, ///
model(diff) ///
gmm(n, lag(2 .)) ///
gmm(w, lag(1 .)) ///
gmm(k, lag(. .)) nocons
note: standard errors may not be valid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = .01960406
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions: linear = 126 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 126 max = 8
-----------------------------------------------------------------
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----+-----------------------------------------------------------
n |
L1. | .4144164 .0341502 12.14 0.000 .3474833 .4813495
|
w | -.8292293 .0588914 -14.08 0.000 -.9446543 -.7138042
k | .3929936 .0223829 17.56 0.000 .3491239 .4368634
-----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
1978:L2.n 1979:L2.n 1980:L2.n 1981:L2.n 1982:L2.n 1983:L2.n 1984:L2.n
1979:L3.n 1980:L3.n 1981:L3.n 1982:L3.n 1983:L3.n 1984:L3.n 1980:L4.n
1981:L4.n 1982:L4.n 1983:L4.n 1984:L4.n 1981:L5.n 1982:L5.n 1983:L5.n
1984:L5.n 1982:L6.n 1983:L6.n 1984:L6.n 1983:L7.n 1984:L7.n 1984:L8.n
2, model(diff):
1978:L1.w 1979:L1.w 1980:L1.w 1981:L1.w 1982:L1.w 1983:L1.w 1984:L1.w
1978:L2.w 1979:L2.w 1980:L2.w 1981:L2.w 1982:L2.w 1983:L2.w 1984:L2.w
1979:L3.w 1980:L3.w 1981:L3.w 1982:L3.w 1983:L3.w 1984:L3.w 1980:L4.w
1981:L4.w 1982:L4.w 1983:L4.w 1984:L4.w 1981:L5.w 1982:L5.w 1983:L5.w
1984:L5.w 1982:L6.w 1983:L6.w 1984:L6.w 1983:L7.w 1984:L7.w 1984:L8.w
3, model(diff):
1978:F6.k 1978:F5.k 1979:F5.k 1978:F4.k 1979:F4.k 1980:F4.k 1978:F3.k
1979:F3.k 1980:F3.k 1981:F3.k 1978:F2.k 1979:F2.k 1980:F2.k 1981:F2.k
1982:F2.k 1978:F1.k 1979:F1.k 1980:F1.k 1981:F1.k 1982:F1.k 1983:F1.k
1978:k 1979:k 1980:k 1981:k 1982:k 1983:k 1984:k 1978:L1.k 1979:L1.k
1980:L1.k 1981:L1.k 1982:L1.k 1983:L1.k 1984:L1.k 1978:L2.k 1979:L2.k
1980:L2.k 1981:L2.k 1982:L2.k 1983:L2.k 1984:L2.k 1979:L3.k 1980:L3.k
1981:L3.k 1982:L3.k 1983:L3.k 1984:L3.k 1980:L4.k 1981:L4.k 1982:L4.k
1983:L4.k 1984:L4.k 1981:L5.k 1982:L5.k 1983:L5.k 1984:L5.k 1982:L6.k
1983:L6.k 1984:L6.k 1983:L7.k 1984:L7.k 1984:L8.k
差分 GMM 两步估计:
. xtdpdgmm L(0/1).n w k, model(diff) ///
gmm(n, lag(2 .)) ///
gmm(w, lag(1 .)) ///
gmm(k, lag(. .)) ///
nocons two vce(r) nofootnote
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = .01960406
Step 2 f(b) = .90967907
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 126 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 126 max = 8
(Std. Err. adjusted for 140 clusters in id)
----------------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----+----------------------------------------------------------------
n |
L1. | .4126102 .0740255 5.57 0.000 .2675228 .5576976
|
w | -.8271943 .0944749 -8.76 0.000 -1.012362 -.6420268
k | .3931545 .0484993 8.11 0.000 .2980975 .4882114
----------------------------------------------------------------------
*序列相关检验
. estat serial
Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1:
z = -3.8127 Prob > |z| = 0.0001
H0: no autocorrelation of order 2:
z = -0.8686 Prob > |z| = 0.3851
*过度识别检验
. estat overid
Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid
2-step moment functions, 2-step weighting matrix
chi2(123) = 127.3551
Prob > chi2 = 0.3757
2-step moment functions, 3-step weighting matrix
chi2(123) = 127.6358
Prob > chi2 = 0.3691
差分 GMM 与系统 GMM 对比:
*差分 GMM
. xtdpdgmm L(0/1).n w k, model(diff) collapse ///
gmm(n, lag(2 4)) ///
gmm(w, lag(1 3)) ///
gmm(k, lag(0 2)) nocons two vce(r)
. estat serial, ar(1/3)
. estat overid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = .0006272
Step 2 f(b) = .08562737
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 9 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 9 max = 8
(Std. Err. adjusted for 140 clusters in id)
--------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----+--------------------------------------------------------
n |
L1. | .3564619 .1074848 3.32 0.001 .1457956 .5671281
|
w |-1.432958 .2141048 -6.69 0.000 -1.852595 -1.01332
k | .2860594 .0541221 5.29 0.000 .1799821 .3921367
--------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
L2.n L3.n L4.n
2, model(diff):
L1.w L2.w L3.w
3, model(diff):
k L1.k L2.k
Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1:
z = -2.6865 Prob > |z| = 0.0072
H0: no autocorrelation of order 2:
z = -0.9414 Prob > |z| = 0.3465
H0: no autocorrelation of order 3:
z = -0.3256 Prob > |z| = 0.7447
Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid
2-step moment functions, 2-step weighting matrix
chi2(6) = 11.9878
Prob > chi2 = 0.0622
2-step moment functions, 3-step weighting matrix
chi2(6) = 12.8283
Prob > chi2 = 0.0458
*-系统 GMM
. xtdpdgmm L(0/1).n w k, model(diff) collapse ///
gmm(n, lag(2 4)) ///
gmm(w k, lag(1 3)) ///
gmm(n, lag(1 1) diff model(level)) ///
gmm(w k, lag(0 0) diff model(level)) two vce(r)
. estat serial, ar(1/3)
. estat overid
*---------
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = .00285146
Step 2 f(b) = .11568719
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 13 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 13 max = 8
(Std. Err. adjusted for 140 clusters in id)
---------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------+--------------------------------------------------------
n |
L1. | .5117523 .1208484 4.23 0.000 .2748937 .7486109
|
w |-1.323125 .2383451 -5.55 0.000 -1.790273 -.855977
k | .1931365 .0941343 2.05 0.040 .0086367 .3776363
_cons | 4.698425 .7943584 5.91 0.000 3.141511 6.255339
---------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
L2.n L3.n L4.n
2, model(diff):
L1.w L2.w L3.w L1.k L2.k L3.k
3, model(level):
L1.D.n
4, model(level):
D.w D.k
5, model(level):
_cons
. estat serial, ar(1/3)
Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1: z = -3.3341 Prob > |z| = 0.0009
H0: no autocorrelation of order 2: z = -1.2436 Prob > |z| = 0.2136
H0: no autocorrelation of order 3: z = -0.1939 Prob > |z| = 0.8462
. estat overid
Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid
2-step moment functions, 2-step weighting matrix
chi2(9) = 16.1962
Prob > chi2 = 0.0629
2-step moment functions, 3-step weighting matrix
chi2(9) = 13.8077
Prob > chi2 = 0.1293
3.3 各估计方式呈现
具有严格外生变量的 Anderson-Hsiao IV 估计:
xtdpdgmm L(0/1).n w k, iv(L2.n w k, d) m(d) nocons
xtdpdgmm L(0/1).n w k, iv(L2.n) iv(w k, d) m(d) nocons
note: standard errors may not be valid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = 1.000e-32
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 3 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 3 max = 8
---------------------------------------------------------------
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----+----------------------------------------------------------
n |
L1. | .1512874 .1313926 1.15 0.250 -.1062374 .4088122
|
w | -.5149142 .0512699 -10.04 0.000 -.6154013 -.4144271
k | .4141651 .0468689 8.84 0.000 .3223038 .5060264
---------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
D.L2.n D.w D.k
note: standard errors may not be valid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = 3.096e-32
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 3 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 3 max = 8
----------------------------------------------------------------
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----+-----------------------------------------------------------
n |
L1. | 1.093635 .1414757 7.73 0.000 .816348 1.370922
|
w | -.5565656 .0762891 -7.30 0.000 -.7060895 -.4070417
k | .1353903 .0560407 2.42 0.016 .0255525 .2452282
----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
L2.n
2, model(diff):
D.w D.k
具有严格外生变量和工具变量约束的 Arellano-Bond 一步 GMM 估计:
xtdpdgmm L(0/1).n w k, gmm(L.n, l(1 4) c) iv(w k, d) m(d) nocons
note: standard errors may not be valid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = .00130087
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 6 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 6 max = 8
----------------------------------------------------------------
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----+----------------------------------------------------------
n |
L1. | .8602906 .0979689 8.78 0.000 .6682752 1.052306
|
w | -.5922287 .065327 -9.07 0.000 -.7202672 -.4641902
k | .2072601 .0434627 4.77 0.000 .1220748 .2924454
----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
L1.L.n L2.L.n L3.L.n L4.L.n
2, model(diff):
D.w D.k
具有前定变量和工具变量约束的 Arellano-Bover 两步 GMM 估计:
. xtdpdgmm L(0/1).n w k, ///
gmm(L.n w k, l(0 3) c) m(fod) two vce(r)
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = .00317868
Step 2 f(b) = .11805918
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 13 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 13 max = 8
(Std. Err. adjusted for 140 clusters in id)
-----------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------+----------------------------------------------------------
n |
L1. | .4582898 .1314203 3.49 0.000 .2007107 .7158688
|
w | -1.607401 .3437998 -4.68 0.000 -2.281237 -.9335663
k | .0878702 .1647289 0.53 0.594 -.2349925 .4107329
_cons | 5.644924 1.001522 5.64 0.000 3.681976 7.607871
-----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(fodev):
L.n L1.L.n L2.L.n L3.L.n w L1.w L2.w L3.w k L1.k L2.k L3.k
2, model(level):
_cons
具有前定变量和工具变量约束的 Ahn-Schmidt 两步 GMM 估计:
. xtdpdgmm L(0/1).n w k, ///
gmm(L.n w k, l(1 4) c) m(d) nl(noser) two vce(r)
Generalized method of moments estimation
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 13 Obs per group: min = 6
nonlinear = 6 avg = 6.364286
total = 19 max = 8
(Std. Err. adjusted for 140 clusters in id)
----------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------+---------------------------------------------------------
n |
L1. | .4304133 .1198004 3.59 0.000 .1956088 .6652178
|
w | -1.41989 .2825341 -5.03 0.000 -1.973647 -.8661332
k | .1917874 .1248583 1.54 0.125 -.0529303 .4365051
_cons | 5.112359 .8521958 6.00 0.000 3.442086 6.782632
----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
L1.L.n L2.L.n L3.L.n L4.L.n L1.w L2.w L3.w L4.w L1.k L2.k L3.k L4.k
2, model(level):
_cons
. xtdpdgmm L(0/1).n w k, ///
gmm(L.n w k, l(1 4) c) m(d) nl(iid) two vce(r)
Generalized method of moments estimation
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 19 Obs per group: min = 6
nonlinear = 7 avg = 6.364286
total = 26 max = 8
(Std. Err. adjusted for 140 clusters in id)
-----------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------+---------------------------------------------------------
n |
L1. | .3162345 .1040268 3.04 0.002 .1123458 .5201233
|
w | -1.225117 .2050917 -5.97 0.000 -1.62709 -.8231451
k | .3370022 .1265224 2.66 0.008 .0890228 .5849816
_cons | 4.729435 .6060333 7.80 0.000 3.541632 5.917239
-----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(iid):
1978:L.n 1979:L.n 1980:L.n 1981:L.n 1982:L.n 1983:L.n
2, model(diff):
L1.L.n L2.L.n L3.L.n L4.L.n L1.w L2.w L3.w L4.w L1.k L2.k L3.k L4.k
3, model(level):
_cons
具有前定变量和工具变量约束的 Blundell-Bond 两步 GMM 估计:
. xtdpdgmm L(0/1).n w k, ///
gmm(L.n w k, l(1 4) c m(d)) iv(L.n w k, d) two vce(r)
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions:
linear = 16 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 16 max = 8
(Std. Err. adjusted for 140 clusters in id)
-------------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------+-----------------------------------------------------------
n |
L1. | .4695086 .1167909 4.02 0.000 .2406028 .6984145
|
w | -1.287266 .2672931 -4.82 0.000 -1.811151 -.7633817
k | .2172426 .0913599 2.38 0.017 .0381805 .3963046
_cons | 4.633068 .8721846 5.31 0.000 2.923618 6.342518
-------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
L1.L.n L2.L.n L3.L.n L4.L.n L1.w L2.w L3.w L4.w L1.k L2.k L3.k L4.k
2, model(level):
D.L.n D.w D.k
3, model(level):
_cons
具有前定变量的 Hayakawa-Qi-Breitung IV 估计量:
. xtdpdgmm L(0/1).n w k, iv(L.n w k, bod) m(fod) nocons
note: standard errors may not be valid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = 1.737e-33
Group variable: id Number of obs = 891
Time variable: year Number of groups = 140
Moment conditions: linear = 3 Obs per group: min = 6
nonlinear = 0 avg = 6.364286
total = 3 max = 8
----------------------------------------------------------------
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----+----------------------------------------------------------
n |
L1. | .4698431 .1508717 3.11 0.002 .1741401 .7655461
|
w | -.682973 .3756931 -1.82 0.069 -1.419318 .0533719
k | -.1261108 .339384 -0.37 0.710 -.7912913 .5390696
-----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(fodev):
B.L.n B.w B.k
复制静态 (加权) 固定效应估计:
xtdpdgmm n w k, iv(w k) m(md)
by id: egen weight = count(e(sample))
replace weight = sqrt(weight/(weight-1))
xtreg n w k [aw=weight], fe
note: standard errors may not be valid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = 2.557e-25
Group variable: id Number of obs = 1031
Time variable: year Number of groups = 140
Moment conditions: linear = 3 Obs per group: min = 7
nonlinear = 0 avg = 7.364286
total = 3 max = 9
-----------------------------------------------------------------
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------+---------------------------------------------------------
w | -.3666355 .0522024 -7.02 0.000 -.4689504 -.2643207
k | .6407201 .0200955 31.88 0.000 .6013336 .6801065
_cons | 2.491261 .1627504 15.31 0.000 2.172276 2.810246
-----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(mdev):
w k
2, model(level):
_cons
(1,031 real changes made)
Fixed-effects (within) regression Number of obs = 1,031
Group variable: id Number of groups = 140
R-sq: Obs per group:
within = 0.5707 min = 7
between = 0.8466 avg = 7.4
overall = 0.8341 max = 9
F(2,889) = 590.79
corr(u_i, Xb) = 0.4345 Prob > F = 0.0000
------------------------------------------------------------------------
n | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------+---------------------------------------------------------------
w | -.3666355 .0522948 -7.01 0.000 -.4692711 -.2639999
k | .6407201 .0201368 31.82 0.000 .6011988 .6802413
_cons | 2.492481 .163067 15.29 0.000 2.17244 2.812523
--------+---------------------------------------------------------------
sigma_u | .58858668
sigma_e | .13719403
rho | .94846853 (fraction of variance due to u_i)
------------------------------------------------------------------------
F test that all u_i=0: F(139, 889) = 110.65 Prob > F = 0.0000
复制静态 (未加权) 固定效应估计:
xtdpdgmm n w k, iv(w k) m(md) nores
xtreg n w k, fe
note: standard errors may not be valid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = 4.270e-25
Group variable: id Number of obs = 1031
Time variable: year Number of groups = 140
Moment conditions: linear = 3 Obs per group: min = 7
nonlinear = 0 avg = 7.364286
total = 3 max = 9
----------------------------------------------------------------
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------+--------------------------------------------------------
w | -.367774 .0522015 -7.05 0.000 -.470087 -.2654611
k | .6403675 .020095 31.87 0.000 .6009819 .679753
_cons | 2.494684 .1627475 15.33 0.000 2.175704 2.813663
----------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(mdev):
w k
2, model(level):
_cons
Fixed-effects (within) regression Number of obs = 1,031
Group variable: id Number of groups = 140
R-sq: Obs per group:
within = 0.5704 min = 7
between = 0.8466 avg = 7.4
overall = 0.8341 max = 9
F(2,889) = 590.13
corr(u_i, Xb) = 0.4352 Prob > F = 0.0000
-----------------------------------------------------------------------
n | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+-------------------------------------------------------------
w | -.367774 .0523227 -7.03 0.000 -.4704645 -.2650835
k | .6403675 .0201417 31.79 0.000 .6008366 .6798984
_cons | 2.494684 .1631256 15.29 0.000 2.174527 2.81484
---------+-------------------------------------------------------------
sigma_u | .58883268
sigma_e | .1372825
rho | .94844636 (fraction of variance due to u_i)
--------------------------------------------------------------------------
F test that all u_i=0: F(139, 889) = 110.72 Prob > F = 0.0000
4. 参考文献
- Ahn, S. C., and P. Schmidt. 1995. Efficient estimation of models for dynamic panel data. Journal of Econometrics 68: 5-27. -Link-
- Anderson, T. W., and C. Hsiao. 1981. Estimation of dynamic models with error components. Journal of the American Statistical Association 76: 598-606. -Link-
- Arellano, M., and S. R. Bond. 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58: 277-297. -Link-
- Arellano, M., and O. Bover. 1995. Another look at the instrumental variable estimation of error-components models. Journal of Econometrics 68: 29-51. -Link-
- Blundell, R., and S. R. Bond. 1998. Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87: 115-143. -Link-
- Hansen, L. P., J. Heaton, and A. Yaron. 1996. Finite-sample properties of some alternative GMM estimators. Journal of Business & Economic Statistics 14: 262-280. -Link-
- Hayakawa, K., M. Qi, and J. Breitung. 2019. Double filter instrumental variable estimation of panel data models with weakly exogenous variables. Econometric Reviews 38: 1055-1088. -Link-
- Kiviet, J. F. 2020. Microeconometric dynamic panel data methods: Model specification and selection issues. Econometrics and Statistics 13: 16-45. -Link-
- Kripfganz, S., and C. Schwarz. 2019. Estimation of linear dynamic panel data models with time-invariant regressors. Journal of Applied Econometrics 34: 526-546. -Link-
- Roodman, D. 2009. A note on the theme of too many instruments. Oxford Bulletin of Economics and Statistics 71: 135-158. -Link-
- Windmeijer, F. 2005. A finite sample correction for the variance of linear efficient two-step GMM estimators. Journal of Econometrics 126: 25-51. -Link-
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