Dear Statalist Community
First, I wanted to thank you for all the helpful posts on this forum! I also wanted to note that this is my first question on this forum, so I apologize if my question is not entirely phrased the way questions should be phrased in this forum. I will gladly provide additional information if necessary.
I am currently working on my bachelor's thesis examining the effect of corporate sustainability (measured by ESG ratings) on implied growth rates in residual income using an international data set. Depending on which variables I include in my model, I have about 25,000 to 30,000 firm-year observations for about 40-70 different countries. I consider the following dependent variable, independent variable of interest, and firm-level and country-level control variables:
Dependent variable: winsor_g: Implied growth rate in residual income of a firm
Independent variable of interest: ESG: A firm's Environmental, social and governance rating
Firm-Level controls: SIZE (log of total assets) Age (years since date of incorporation) TDTA (total debt to total assets ratio) RDS (research and development expenses as a percentage of sales) CR (current ratio) CAPEXTA (capital expenditures as a percentage of total assets)
Country-Level controls: HDI (Human Development Index) GDPPCgrowth (annual GDP per capita growth) KOFGI (KOF Index of Globalisation)
Further: FY: financial year (year variable) ISINID (ID to uniquely identify each firm) Industry_ID (ID generated to uniquely identify each industry) Country_ID (ID generated to uniquely identify each country) ISO_Head (Country_ID is generated based on ISO_Head, also ISO_Head uniquely identifies each country but is a string)
First, I want to investigate the relationship between corporate sustainability and growth across the entire international data set using the abovementioned control variables. Second, I will examine the influence of a country's level of development and cultural dimension scores on this relationship using interaction terms. (Since cultural dimension scores are time-invariant, I cannot use a fixed effects model for the last regression analysis.)
Despite long research, I am still unsure whether to use a firm-fixed effects, random-effects (GLS / ML), or a multilevel (mixed-effects ML regression with random intercepts) model for my regressions. As an example, here is my code and results for some of my regressions, including a Hausman test:
As you can see, the random effects (GLS/ML) and the multilevel model provide highly significant coefficients for ESG. In contrast, the ESG coefficient in the fixed effects model is highly insignificant. However, the Hausman test seems to favor firm fixed effects.
I do not understand why results differ that much depending on the model used! Does this mean that I should not use the random effects (GLS/ML) or multilevel model? Or is it more likely that the fixed effects model is inappropriate in this case? For example, I thought that the ESG variable within a company might not change enough over time, and, therefore, the firm-fixed effects model might not be appropriate.
So I would like to know the following:
1) Do I have fundamentally wrong intuitions or fundamentally wrong code?
2) How should I determine which of these models is most appropriate, and how can I justify my decision?
3) Does my research question, sample size, or a similar factor already make one model theoretically preferable?
4) Are there any other reasons (that I could test) why the models mentioned are or are not suitable?
5) As a previous paper uses a multilevel regression with random intercept modeling (and year and industry fixed effects) when analyzing the effect of time-invariant variables (like cultural values) on the described relationship, I planned on applying this multilevel model on all my regressions (with the idea of having one consistent approach for all hypotheses/regressions) but am now unsure if that is a good approach.
Thank you very much for your help! Please contact me anytime if this description is too unclear or contains too little information to answer my question!
Kind regards
Fabian Büchi
First, I wanted to thank you for all the helpful posts on this forum! I also wanted to note that this is my first question on this forum, so I apologize if my question is not entirely phrased the way questions should be phrased in this forum. I will gladly provide additional information if necessary.
I am currently working on my bachelor's thesis examining the effect of corporate sustainability (measured by ESG ratings) on implied growth rates in residual income using an international data set. Depending on which variables I include in my model, I have about 25,000 to 30,000 firm-year observations for about 40-70 different countries. I consider the following dependent variable, independent variable of interest, and firm-level and country-level control variables:
Dependent variable: winsor_g: Implied growth rate in residual income of a firm
Independent variable of interest: ESG: A firm's Environmental, social and governance rating
Firm-Level controls: SIZE (log of total assets) Age (years since date of incorporation) TDTA (total debt to total assets ratio) RDS (research and development expenses as a percentage of sales) CR (current ratio) CAPEXTA (capital expenditures as a percentage of total assets)
Country-Level controls: HDI (Human Development Index) GDPPCgrowth (annual GDP per capita growth) KOFGI (KOF Index of Globalisation)
Further: FY: financial year (year variable) ISINID (ID to uniquely identify each firm) Industry_ID (ID generated to uniquely identify each industry) Country_ID (ID generated to uniquely identify each country) ISO_Head (Country_ID is generated based on ISO_Head, also ISO_Head uniquely identifies each country but is a string)
First, I want to investigate the relationship between corporate sustainability and growth across the entire international data set using the abovementioned control variables. Second, I will examine the influence of a country's level of development and cultural dimension scores on this relationship using interaction terms. (Since cultural dimension scores are time-invariant, I cannot use a fixed effects model for the last regression analysis.)
Despite long research, I am still unsure whether to use a firm-fixed effects, random-effects (GLS / ML), or a multilevel (mixed-effects ML regression with random intercepts) model for my regressions. As an example, here is my code and results for some of my regressions, including a Hausman test:
Code:
. *Firm-fixed effects model with year fixed effects
. xtreg winsor_g ESG SIZE Age TDTA RDS CR CAPEXTA HDI GDPPCgrowth KOFGI i.FY, fe
Fixed-effects (within) regression Number of obs = 22,590
Group variable: ISINID Number of groups = 5,230
R-squared: Obs per group:
Within = 0.0732 min = 1
Between = 0.0001 avg = 4.3
Overall = 0.0001 max = 9
F(18, 17342) = 76.14
corr(u_i, Xb) = -0.9992 Prob > F = 0.0000
------------------------------------------------------------------------------
winsor_g | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
ESG | -2.39e-06 .0000738 -0.03 0.974 -.000147 .0001423
SIZE | -.0109689 .0022439 -4.89 0.000 -.0153673 -.0065706
Age | .0692884 .0525641 1.32 0.187 -.0337425 .1723194
TDTA | .0103895 .0066061 1.57 0.116 -.0025592 .0233382
RDS | .0000673 .0000965 0.70 0.486 -.0001218 .0002564
CR | .0009998 .0005906 1.69 0.090 -.0001578 .0021575
CAPEXTA | -.0738388 .0198721 -3.72 0.000 -.1127902 -.0348874
HDI | -.0879332 .1241895 -0.71 0.479 -.3313572 .1554907
GDPPCgrowth | .1709007 .0323506 5.28 0.000 .1074903 .2343111
KOFGI | .0048154 .0010288 4.68 0.000 .0027988 .0068319
|
FY |
2014 | -.0654977 .0525822 -1.25 0.213 -.1685642 .0375687
2015 | -.129166 .1050985 -1.23 0.219 -.3351696 .0768376
2016 | -.200469 .1576681 -1.27 0.204 -.5095144 .1085764
2017 | -.2714317 .2102363 -1.29 0.197 -.683516 .1406526
2018 | -.3578895 .2627735 -1.36 0.173 -.8729521 .1571731
2019 | -.4294352 .315333 -1.36 0.173 -1.04752 .1886493
2020 | -.5104639 .3678705 -1.39 0.165 -1.231527 .2105994
2021 | -.5940772 .4204572 -1.41 0.158 -1.418216 .2300612
|
_cons | -2.125849 1.564802 -1.36 0.174 -5.193018 .9413208
-------------+----------------------------------------------------------------
sigma_u | 1.9262269
sigma_e | .06860304
rho | .99873316 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(5229, 17342) = 5.58 Prob > F = 0.0000
. est store fixed
.
. *Random effects model (GLS) with year, industy fixed, and country effects
. xtreg winsor_g ESG SIZE Age TDTA RDS CR CAPEXTA HDI GDPPCgrowth KOFGI i.FY i.Industry_ID i.Country_ID, re
Random-effects GLS regression Number of obs = 22,590
Group variable: ISINID Number of groups = 5,230
R-squared: Obs per group:
Within = 0.0720 min = 1
Between = 0.1766 avg = 4.3
Overall = 0.1303 max = 9
Wald chi2(106) = 2417.79
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
winsor_g | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ESG | .0001875 .0000551 3.40 0.001 .0000795 .0002956
SIZE | -.0100899 .0009226 -10.94 0.000 -.0118982 -.0082817
Age | .0000215 .0000503 0.43 0.669 -.000077 .00012
TDTA | -.0041148 .0048524 -0.85 0.396 -.0136253 .0053957
RDS | .0000451 .0000927 0.49 0.627 -.0001366 .0002269
CR | .0011442 .0004564 2.51 0.012 .0002497 .0020387
CAPEXTA | -.0509159 .0139248 -3.66 0.000 -.0782081 -.0236238
HDI | .1542254 .1174259 1.31 0.189 -.0759252 .384376
GDPPCgrowth | .1552501 .0315294 4.92 0.000 .0934537 .2170466
KOFGI | .0044576 .0009985 4.46 0.000 .0025005 .0064147
|
FY |
2014 | .0035742 .0025988 1.38 0.169 -.0015192 .0086677
2015 | .0082835 .0026534 3.12 0.002 .003083 .013484
2016 | .0056978 .0027884 2.04 0.041 .0002326 .0111629
2017 | .0016247 .0028959 0.56 0.575 -.0040511 .0073005
2018 | -.0152687 .0030754 -4.96 0.000 -.0212964 -.0092411
2019 | -.0186997 .0032168 -5.81 0.000 -.0250045 -.0123949
2020 | -.0290688 .00331 -8.78 0.000 -.0355562 -.0225814
2021 | -.0430519 .0031477 -13.68 0.000 -.0492212 -.0368826
|
Industry_ID |
2 | .0705784 .0165067 4.28 0.000 .0382259 .1029309
3 | .0715423 .103057 0.69 0.488 -.1304458 .2735303
4 | .0224903 .0084473 2.66 0.008 .0059339 .0390467
5 | -.0055045 .008085 -0.68 0.496 -.0213508 .0103417
6 | .0032171 .0114894 0.28 0.779 -.0193017 .0257359
7 | .0555432 .0075052 7.40 0.000 .0408333 .0702531
8 | .0242278 .0078252 3.10 0.002 .0088907 .0395649
9 | .0410719 .0083211 4.94 0.000 .0247629 .0573809
10 | .005025 .009255 0.54 0.587 -.0131145 .0231645
11 | .0087483 .0082823 1.06 0.291 -.0074846 .0249813
12 | .0547788 .007995 6.85 0.000 .0391089 .0704487
13 | .0364164 .008306 4.38 0.000 .020137 .0526959
14 | .0361012 .007815 4.62 0.000 .0207841 .0514182
15 | .0409449 .0120586 3.40 0.001 .0173104 .0645793
16 | .0472682 .0109451 4.32 0.000 .0258162 .0687202
17 | .0205356 .0161921 1.27 0.205 -.0112004 .0522716
18 | .0391114 .0107476 3.64 0.000 .0180465 .0601763
19 | .0464077 .0238153 1.95 0.051 -.0002695 .0930848
21 | -.0164367 .0435808 -0.38 0.706 -.1018534 .0689801
22 | .0526119 .0082974 6.34 0.000 .0363493 .0688745
23 | .0472637 .00826 5.72 0.000 .0310745 .063453
24 | .0575979 .0078828 7.31 0.000 .0421479 .0730479
25 | .0690128 .0076398 9.03 0.000 .0540391 .0839864
26 | .0855683 .0236824 3.61 0.000 .0391517 .1319848
27 | .0234566 .0102391 2.29 0.022 .0033884 .0435248
28 | -.0108079 .0082585 -1.31 0.191 -.0269942 .0053784
29 | .0111107 .0082712 1.34 0.179 -.0051006 .0273219
30 | .0317402 .0200032 1.59 0.113 -.0074653 .0709458
|
Country_ID |
2 | -.095123 .0506553 -1.88 0.060 -.1944057 .0041596
3 | -.0433158 .0334877 -1.29 0.196 -.1089504 .0223188
4 | .0164448 .0270144 0.61 0.543 -.0365026 .0693921
5 | -.0208296 .0329929 -0.63 0.528 -.0854945 .0438354
8 | .0885379 .0332319 2.66 0.008 .0234045 .1536713
9 | .0178278 .0277745 0.64 0.521 -.0366092 .0722649
10 | .0074934 .0309045 0.24 0.808 -.0530782 .0680651
11 | .0188273 .0349724 0.54 0.590 -.0497174 .087372
12 | .1356242 .0319199 4.25 0.000 .0730623 .1981861
13 | .080306 .0491991 1.63 0.103 -.0161224 .1767344
14 | -.1238982 .0584689 -2.12 0.034 -.2384951 -.0093013
15 | -.0082434 .0870052 -0.09 0.925 -.1787705 .1622837
16 | .0002765 .0294804 0.01 0.993 -.0575041 .0580571
17 | -.002065 .0318577 -0.06 0.948 -.064505 .060375
18 | .0333645 .0446763 0.75 0.455 -.0541995 .1209285
19 | .0401376 .0313582 1.28 0.201 -.0213233 .1015985
20 | -.0006863 .0301337 -0.02 0.982 -.0597472 .0583746
22 | -.0037935 .029151 -0.13 0.896 -.0609284 .0533415
23 | -.0154542 .0292095 -0.53 0.597 -.0727038 .0417954
26 | -.0409215 .0372417 -1.10 0.272 -.1139138 .0320708
27 | .053396 .0295183 1.81 0.070 -.0044588 .1112508
28 | -.0905328 .0606798 -1.49 0.136 -.209463 .0283973
29 | .148424 .0377517 3.93 0.000 .074432 .222416
30 | -.0089671 .0310546 -0.29 0.773 -.069833 .0518989
31 | .0787124 .0356722 2.21 0.027 .0087962 .1486287
33 | .1776875 .0417197 4.26 0.000 .0959185 .2594566
34 | .1204773 .0732883 1.64 0.100 -.0231651 .2641197
35 | .0263402 .0342847 0.77 0.442 -.0408566 .0935371
37 | .0565313 .0263539 2.15 0.032 .0048786 .108184
39 | .1532678 .0978257 1.57 0.117 -.038467 .3450026
40 | .0251009 .0275116 0.91 0.362 -.0288209 .0790226
41 | .0638164 .0507098 1.26 0.208 -.035573 .1632058
44 | -.3251124 .1082911 -3.00 0.003 -.5373591 -.1128657
45 | .0205338 .0326722 0.63 0.530 -.0435025 .0845701
46 | .160649 .0591855 2.71 0.007 .0446476 .2766505
49 | -.0094294 .0501471 -0.19 0.851 -.1077159 .0888572
50 | .1313747 .0342221 3.84 0.000 .0643006 .1984488
51 | .0487631 .0302823 1.61 0.107 -.010589 .1081153
52 | .0069189 .0326689 0.21 0.832 -.057111 .0709488
53 | -.001618 .0304502 -0.05 0.958 -.0612992 .0580632
54 | .0384879 .0291089 1.32 0.186 -.0185644 .0955402
55 | .0731123 .0608473 1.20 0.230 -.0461462 .1923708
56 | .0656505 .0853148 0.77 0.442 -.1015634 .2328643
57 | .0310206 .0492127 0.63 0.528 -.0654345 .1274757
58 | .1449909 .0387659 3.74 0.000 .0690112 .2209706
59 | -.0699147 .1006199 -0.69 0.487 -.267126 .1272967
60 | -.0279 .0339965 -0.82 0.412 -.094532 .0387319
62 | .007089 .037765 0.19 0.851 -.0669291 .0811072
63 | .0946544 .0403222 2.35 0.019 .0156244 .1736843
65 | .0081776 .0327049 0.25 0.803 -.0559229 .0722781
66 | .1662942 .0322711 5.15 0.000 .103044 .2295444
67 | -.0116125 .0298762 -0.39 0.698 -.0701689 .0469438
68 | -.0035924 .0297088 -0.12 0.904 -.0618206 .0546359
69 | -.0474068 .0880717 -0.54 0.590 -.2200242 .1252106
70 | .0902161 .0298148 3.03 0.002 .0317802 .1486521
71 | -.0949128 .0310808 -3.05 0.002 -.15583 -.0339956
74 | .0455349 .0264831 1.72 0.086 -.006371 .0974408
75 | .1209061 .0643097 1.88 0.060 -.0051386 .2469508
76 | .1207171 .0442349 2.73 0.006 .0340184 .2074159
77 | .0385638 .0349209 1.10 0.269 -.0298798 .1070074
|
_cons | -.3673088 .1241373 -2.96 0.003 -.6106136 -.1240041
-------------+----------------------------------------------------------------
sigma_u | .07688877
sigma_e | .06860304
rho | .5567657 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. est store random
.
. *Hausman test
. hausman fixed random
Note: the rank of the differenced variance matrix (16) does not equal the number of coefficients being tested (18); be sure this is what you expect, or there may be problems
computing the test. Examine the output of your estimators for anything unexpected and possibly consider scaling your variables so that the coefficients are on a
similar scale.
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference Std. err.
-------------+----------------------------------------------------------------
ESG | -2.39e-06 .0001875 -.0001899 .000049
SIZE | -.0109689 -.0100899 -.000879 .0020455
Age | .0692884 .0000215 .069267 .0525641
TDTA | .0103895 -.0041148 .0145043 .0044828
RDS | .0000673 .0000451 .0000221 .0000266
CR | .0009998 .0011442 -.0001443 .0003749
CAPEXTA | -.0738388 -.0509159 -.0229229 .0141775
HDI | -.0879332 .1542254 -.2421586 .0404251
GDPPCgrowth | .1709007 .1552501 .0156506 .0072427
KOFGI | .0048154 .0044576 .0003577 .0002476
FY |
2014 | -.0654977 .0035742 -.069072 .052518
2015 | -.129166 .0082835 -.1374495 .105065
2016 | -.200469 .0056978 -.2061667 .1576435
2017 | -.2714317 .0016247 -.2730564 .2102164
2018 | -.3578895 -.0152687 -.3426208 .2627555
2019 | -.4294352 -.0186997 -.4107355 .3153166
2020 | -.5104639 -.0290688 -.4813951 .3678556
2021 | -.5940772 -.0430519 -.5510253 .4204454
------------------------------------------------------------------------------
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(16) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 113.14
Prob > chi2 = 0.0000
.
. *Multi-level vs. single-level
. mixed winsor_g || ISO_Head:
Performing EM optimization ...
Performing gradient-based optimization:
Iteration 0: Log likelihood = 26294.384
Iteration 1: Log likelihood = 26294.384
Computing standard errors ...
Mixed-effects ML regression Number of obs = 31,006
Group variable: ISO_Head Number of groups = 77
Obs per group:
min = 1
avg = 402.7
max = 9,354
Wald chi2(0) = .
Log likelihood = 26294.384 Prob > chi2 = .
------------------------------------------------------------------------------
winsor_g | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
_cons | -.0568708 .0065113 -8.73 0.000 -.0696327 -.0441089
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
ISO_Head: Identity |
var(_cons) | .0028039 .0005443 .0019166 .0041021
-----------------------------+------------------------------------------------
var(Residual) | .010654 .0000857 .0104874 .0108233
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 1476.02 Prob >= chibar2 = 0.0000
. estat icc
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
ISO_Head | .2083469 .0320601 .1524014 .2780913
------------------------------------------------------------------------------
.
. *Multilevl model with year and industry fixed effects
. mixed winsor_g ESG SIZE Age TDTA RDS CR CAPEXTA HDI GDPPCgrowth KOFGI i.FY i.Industry_ID || ISO_Head:
Performing EM optimization ...
Performing gradient-based optimization:
Iteration 0: Log likelihood = 21310.829
Iteration 1: Log likelihood = 21310.829
Computing standard errors ...
Mixed-effects ML regression Number of obs = 22,590
Group variable: ISO_Head Number of groups = 61
Obs per group:
min = 1
avg = 370.3
max = 6,785
Wald chi2(46) = 2024.77
Log likelihood = 21310.829 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
winsor_g | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
ESG | .0002938 .0000409 7.19 0.000 .0002137 .0003739
SIZE | -.0093939 .000583 -16.11 0.000 -.0105366 -.0082513
Age | .0000485 .000025 1.94 0.052 -5.06e-07 .0000975
TDTA | -.0223034 .0035677 -6.25 0.000 -.0292959 -.0153109
RDS | .0000662 .0001153 0.57 0.566 -.0001597 .0002921
CR | .0007453 .0003997 1.86 0.062 -.0000382 .0015287
CAPEXTA | -.0269738 .0127314 -2.12 0.034 -.0519269 -.0020207
HDI | .2137668 .0862447 2.48 0.013 .0447302 .3828033
GDPPCgrowth | .1010101 .0409246 2.47 0.014 .0207993 .1812209
KOFGI | .0010835 .0008372 1.29 0.196 -.0005575 .0027245
|
FY |
2014 | .0065828 .0034156 1.93 0.054 -.0001117 .0132773
2015 | .011849 .0033438 3.54 0.000 .0052954 .0184027
2016 | .0117035 .0032994 3.55 0.000 .0052368 .0181702
2017 | .0032649 .0032144 1.02 0.310 -.0030351 .0095649
2018 | -.0084931 .0032685 -2.60 0.009 -.0148993 -.0020869
2019 | -.0121533 .0032326 -3.76 0.000 -.0184891 -.0058176
2020 | -.023709 .0038786 -6.11 0.000 -.0313109 -.016107
2021 | -.0340569 .0034152 -9.97 0.000 -.0407505 -.0273633
|
Industry_ID |
2 | .0601981 .0100782 5.97 0.000 .0404452 .0799511
3 | .0660787 .0939344 0.70 0.482 -.1180293 .2501867
4 | .0204559 .0045417 4.50 0.000 .0115544 .0293574
5 | -.0035117 .0045484 -0.77 0.440 -.0124265 .005403
6 | .0100505 .0060274 1.67 0.095 -.0017631 .0218641
7 | .0467232 .0040959 11.41 0.000 .0386955 .054751
8 | .0257573 .0043281 5.95 0.000 .0172743 .0342403
9 | .0309369 .0043936 7.04 0.000 .0223256 .0395482
10 | .0017321 .004921 0.35 0.725 -.0079128 .011377
11 | .0026584 .0044756 0.59 0.553 -.0061136 .0114305
12 | .0466072 .004337 10.75 0.000 .0381068 .0551076
13 | .0265765 .0044471 5.98 0.000 .0178603 .0352928
14 | .025399 .0041886 6.06 0.000 .0171895 .0336085
15 | .0328156 .0060624 5.41 0.000 .0209335 .0446977
16 | .0321594 .0056216 5.72 0.000 .0211413 .0431776
17 | .0149714 .0079179 1.89 0.059 -.0005475 .0304902
18 | .03626 .0061815 5.87 0.000 .0241444 .0483755
19 | .0454169 .0134931 3.37 0.001 .0189708 .0718629
21 | -.0092164 .0334052 -0.28 0.783 -.0746895 .0562566
22 | .0449322 .0044642 10.06 0.000 .0361825 .0536818
23 | .0356056 .0045374 7.85 0.000 .0267126 .0444987
24 | .042552 .0043619 9.76 0.000 .0340028 .0511011
25 | .0556 .0042607 13.05 0.000 .0472492 .0639508
26 | .077396 .0128278 6.03 0.000 .0522539 .1025381
27 | .018252 .005089 3.59 0.000 .0082777 .0282262
28 | -.0063825 .0043704 -1.46 0.144 -.0149483 .0021834
29 | .0132645 .0047977 2.76 0.006 .0038612 .0226678
30 | .0268071 .0129162 2.08 0.038 .0014919 .0521224
|
_cons | -.1352934 .0590556 -2.29 0.022 -.2510402 -.0195465
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
ISO_Head: Identity |
var(_cons) | .002443 .0006309 .0014727 .0040526
-----------------------------+------------------------------------------------
var(Residual) | .0087957 .0000829 .0086347 .0089598
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 974.72 Prob >= chibar2 = 0.0000
I do not understand why results differ that much depending on the model used! Does this mean that I should not use the random effects (GLS/ML) or multilevel model? Or is it more likely that the fixed effects model is inappropriate in this case? For example, I thought that the ESG variable within a company might not change enough over time, and, therefore, the firm-fixed effects model might not be appropriate.
So I would like to know the following:
1) Do I have fundamentally wrong intuitions or fundamentally wrong code?
2) How should I determine which of these models is most appropriate, and how can I justify my decision?
3) Does my research question, sample size, or a similar factor already make one model theoretically preferable?
4) Are there any other reasons (that I could test) why the models mentioned are or are not suitable?
5) As a previous paper uses a multilevel regression with random intercept modeling (and year and industry fixed effects) when analyzing the effect of time-invariant variables (like cultural values) on the described relationship, I planned on applying this multilevel model on all my regressions (with the idea of having one consistent approach for all hypotheses/regressions) but am now unsure if that is a good approach.
Thank you very much for your help! Please contact me anytime if this description is too unclear or contains too little information to answer my question!
Kind regards
Fabian Büchi
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