Fixed-Effects Model with clustered errors and year-dummy vs. Two-Way Clustered Model

[Marian Dudeck]

Hello,
I'm currently writing my thesis about board composition and ESG-Performance of german firms.
I have data of 121 firms from 2016-2020. Until now i made two regressions, but i don't know which of them is the most valid.
I have a question regarding the solution of the time effect problem.
The literature says that you can either take two-way clustered standard errors, or introduce a year-dummy in a One-Way clustered-error to counteract this.
But when I run both Regressions, i get very different results. Could you tell me, where my mistake is and which one of them is more valid? Thanks in Advance!

Fixed-Effects Model with clustered errors:
xtreg ESG_Score MB SB WomenMB WomenSB Employee_SB Independant_BM VG logTotalDebt CSR_Committee logTotalRevenue RoAt0 RoAt1 RoAt2 i.Year, fe vce(cluster Comp_id)

results:

ESG_Score	Coef.		St.Err.	t-value		p-value	[95% Conf		Interval]		Sig
Anzahl_Vorstand	.121		.423	0.29		.776	-.716		.958
Anzahl_AR	-.093		.424	-0.22		.826	-.933		.747
Frauenquote_Vorstand	-7.12		3.171	-2.25		.027	-13.4		-.841		**
Frauenquote_AR	2.711		5.293	0.51		.609	-7.768		13.19
Arbeitnehmerquote	15.113		9.316	1.62		.107	-3.332		33.558
Independant_BM	10.858		4.3	2.53		.013	2.344		19.371		**
VG	-.734		.437	-1.68		.096	-1.6		.132		*
logTotalDebt	.281		.27	1.04		.3	-.253		.815
CSR_Committee	4.545		1.75	2.60		.011	1.08		8.011		**
logTotalRevenue	9.035		3.996	2.26		.026	1.122		16.947		**
RoAt0	-48.152		9.313	-5.17		0	-66.59		-29.714		***
RoAt1	-7.406		8.917	-0.83		.408	-25.061		10.249
RoAt2	.423		5.879	0.07		.943	-11.217		12.063
2016b	0		.	.		.	.		.
2017	1.804		.792	2.28		.025	.235		3.373		**
2018	4.174		1.041	4.01		0	2.114		6.235		***
2019	6.653		1.263	5.27		0	4.153		9.153		***
2020	10.72		1.535	6.98		0	7.68		13.759		***
Constant	-46.95		37.265	-1.26		.21	-120.732		26.833
Mean dependent var		60.698			SD dependent var			19.464
R-squared		0.516			Number of obs			485
F-test		.			Prob > F			.
Akaike crit. (AIC)		2845.765			Bayesian crit. (BIC)			2912.711
*** p<.01, ** p<.05, * p<.1

Two-Way Clustered Model:
reghdfe ESG_Score MB SB WomenMB WomenSB Employee_SB Independant_BM VG logTotalDebt CSR_Committee logTotalRevenue RoAt0 RoAt1 RoAt2 i.Year, absorb(temp) cluster(Comp_id Year)
results:

			Robust
ESG_Score	Coefficient	std. err		t	P>t	[95%		conf.interval]
Anzahl_Vorstand	0.477	0.712		0.670	0.539	-1.499		2.454
Anzahl_AR	0.091	0.479		0.190	0.858	-1.239		1.422
Frauenquote_Vorstand	0.231	6.036		0.040	0.971	-16.529		16.990
Frauenquote_AR	30.134	9.720		3.100	0.036	3.148		57.121
Arbeitnehmerquote	3.491	8.731		0.400	0.710	-20.752		27.733
Independant_BM	13.207	3.333		3.960	0.017	3.952		22.462
VG	-0.557	0.846		-0.660	0.546	-2.906		1.792
logTotalDebt	-0.091	0.990		-0.090	0.931	-2.838		2.657
CSR_Committee	12.691	2.589		4.900	0.008	5.501		19.880
logTotalRevenue	9.682	3.193		3.030	0.039	0.818		18.547
RoAt0	-3.572	13.226		-0.270	0.800	-40.294		33.151
RoAt1	-10.629	11.630		-0.910	0.412	-42.918		21.661
RoAt2	-3.376	6.363		-0.530	0.624	-21.042		14.291
Jahr
2017	-0.865	0.448		-1.930	0.126	-2.110		0.379
2018	-1.146	0.442		-2.590	0.060	-2.372		0.080
2019	0.591	0.671		0.880	0.428	-1.272		2.454
2020	2.597	0.905		2.870	0.046	0.084		5.110
_cons	-61.650	23.250		-2.650	0.057	-126.203		2.903

[Carlo Lazzaro]

Marian:
welcome to this forum.
In your -reghdfe- code you -absorb()- -timevar- only and clustered standard errors differently..
If coded correctly, both models shoudl give back the same results (exception made for the _cons):

use "https://www.stata-press.com/data/r17/nlswork.dta"
. xtreg ln_wage c.age##c.age i.year, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1162                                         min =          1
     Between = 0.1078                                         avg =        6.1
     Overall = 0.0932                                         max =         15

                                                F(16,4709)        =      79.11
corr(u_i, Xb) = 0.0613                          Prob > F          =     0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0728746    .013687     5.32   0.000     .0460416    .0997075
             |
 c.age#c.age |  -.0010113   .0001076    -9.40   0.000    -.0012224   -.0008003
             |
        year |
         69  |   .0647054   .0155249     4.17   0.000     .0342693    .0951415
         70  |   .0284423   .0264639     1.07   0.283    -.0234395     .080324
         71  |   .0579959   .0384111     1.51   0.131    -.0173078    .1332996
         72  |   .0510671   .0502675     1.02   0.310    -.0474808     .149615
         73  |   .0424104   .0624924     0.68   0.497    -.0801038    .1649247
         75  |   .0151376    .086228     0.18   0.861    -.1539096    .1841848
         77  |   .0340933   .1106841     0.31   0.758    -.1828994     .251086
         78  |   .0537334   .1232232     0.44   0.663    -.1878417    .2953084
         80  |   .0369475   .1473725     0.25   0.802    -.2519716    .3258667
         82  |   .0391687   .1715621     0.23   0.819    -.2971733    .3755108
         83  |    .058766   .1836086     0.32   0.749    -.3011928    .4187249
         85  |   .1042758   .2080199     0.50   0.616    -.3035406    .5120922
         87  |   .1242272   .2327328     0.53   0.594    -.3320379    .5804922
         88  |   .1904977   .2486083     0.77   0.444    -.2968909    .6778863
             |
       _cons |   .3937532   .2469015     1.59   0.111    -.0902893    .8777957
-------------+----------------------------------------------------------------
     sigma_u |  .40275174
     sigma_e |  .30127563
         rho |  .64120306   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.
. reghdfe ln_wage c.age##c.age i.year, absorb(idcode ) vce(cluster idcode)
(dropped 551 singleton observations)
(MWFE estimator converged in 1 iterations)

HDFE Linear regression                            Number of obs   =     27,959
Absorbing 1 HDFE group                            F(  16,   4158) =      79.11
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.6593
                                                  Adj R-squared   =     0.5995
                                                  Within R-sq.    =     0.1162
Number of clusters (idcode)  =      4,159         Root MSE        =     0.3013

                             (Std. err. adjusted for 4,159 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0728746   .0136873     5.32   0.000     .0460402    .0997089
             |
 c.age#c.age |  -.0010113   .0001076    -9.39   0.000    -.0012224   -.0008003
             |
        year |
         69  |   .0647054   .0155252     4.17   0.000     .0342677    .0951432
         70  |   .0284423   .0264645     1.07   0.283    -.0234422    .0803268
         71  |   .0579959   .0384118     1.51   0.131    -.0173118    .1333037
         72  |   .0510671   .0502685     1.02   0.310    -.0474861    .1496203
         73  |   .0424104   .0624936     0.68   0.497    -.0801104    .1649313
         75  |   .0151376   .0862297     0.18   0.861    -.1539187    .1841939
         77  |   .0340933   .1106863     0.31   0.758    -.1829111    .2510976
         78  |   .0537334   .1232256     0.44   0.663    -.1878546    .2953214
         80  |   .0369475   .1473754     0.25   0.802    -.2519871    .3258822
         82  |   .0391687   .1715655     0.23   0.819    -.2971914    .3755288
         83  |    .058766   .1836122     0.32   0.749    -.3012121    .4187442
         85  |   .1042758    .208024     0.50   0.616    -.3035625     .512114
         87  |   .1242272   .2327373     0.53   0.594    -.3320624    .5805167
         88  |   .1904977   .2486132     0.77   0.444    -.2969171    .6779125
             |
       _cons |   .3956251   .2469216     1.60   0.109    -.0884733    .8797234
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
      idcode |      4159        4159           0    *|
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

As an aside, please (and as per FAQ) do not post screenshots, as they are impossible to elaborate on, but use CODE delimiters instead. Thanks.

[Marian Dudeck]

Hey Carlo,

thanks a lot for your help! Very appreciate it.

Kind regards,
Marian