Hi everyone,
I have performed several negative binomial regressions to examine my panel data. I am researching the effect of CSR (ESG measures of performance provided by ASSET4) on the amount of institutional owners controlling for total assets (log), long term debt to assets ratio and return on assets. I am using a combined measure of environmental performance, governance performance and social performance and I also conduct analysis where I regress these three indicators without the average CSRP variable. According to several researchers, I should include industry as a control aswell when examining this relationship. There are signs of overdispersion, autocorrelation and heteroscedascisty in my data. Furthermore, by conducting a Hausman test, FE is indicated as the right option to use when doing regressions.
What I am unsure about, is whether I should be using fixed effects or random effects. Information on the internet is quite divergent and there are bias problems relating to random effects and fixed effects and xtnbreg mentioned specifically. Furthermore, I tested whether I should include time fixed effects as well by using testparm and got a significant result, however this impacts my findings quite a bit. I am not sure whether I should include year dummies and/ or industry dummies, as I can only find information regarding this when xtreg is used, but not xtnbreg.
Below, some analysis I have done are provided. I would like some guidance on what options to follow and why these are appropriate, as I am quite lost at the moment and would like to make a decision and do not always understand the reasoning behind certain options. Also I find it hard to interpret the findings, for instance iterations or the low coefficient with 'good' z-score value, when I go with different options, as I am not experienced in doing negative binomial regressions or count data regressions in general.
Thanks in advance and apologies for the many results I have included.
.
I have performed several negative binomial regressions to examine my panel data. I am researching the effect of CSR (ESG measures of performance provided by ASSET4) on the amount of institutional owners controlling for total assets (log), long term debt to assets ratio and return on assets. I am using a combined measure of environmental performance, governance performance and social performance and I also conduct analysis where I regress these three indicators without the average CSRP variable. According to several researchers, I should include industry as a control aswell when examining this relationship. There are signs of overdispersion, autocorrelation and heteroscedascisty in my data. Furthermore, by conducting a Hausman test, FE is indicated as the right option to use when doing regressions.
What I am unsure about, is whether I should be using fixed effects or random effects. Information on the internet is quite divergent and there are bias problems relating to random effects and fixed effects and xtnbreg mentioned specifically. Furthermore, I tested whether I should include time fixed effects as well by using testparm and got a significant result, however this impacts my findings quite a bit. I am not sure whether I should include year dummies and/ or industry dummies, as I can only find information regarding this when xtreg is used, but not xtnbreg.
Below, some analysis I have done are provided. I would like some guidance on what options to follow and why these are appropriate, as I am quite lost at the moment and would like to make a decision and do not always understand the reasoning behind certain options. Also I find it hard to interpret the findings, for instance iterations or the low coefficient with 'good' z-score value, when I go with different options, as I am not experienced in doing negative binomial regressions or count data regressions in general.
Thanks in advance and apologies for the many results I have included.
Code:
Conditional FE negative binomial regression Number of obs = 1,508
Group variable: ID Number of groups = 187
Obs per group:
min = 2
avg = 8.1
max = 12
Wald chi2(4) = 1005.49
Log likelihood = -7092.4252 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------
IOAmountLAG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
CSRP | .0025641 .0003451 7.43 0.000 .0018877 .0032405
AssetsLOG | .3066893 .0112647 27.23 0.000 .284611 .3287676
Longtermdebttoassetsratio | -.1643564 .0510454 -3.22 0.001 -.2644035 -.0643092
ROA | .2738025 .0596164 4.59 0.000 .1569565 .3906484
_cons | -1.11622 .1860415 -6.00 0.000 -1.480855 -.7515854
-------------------------------------------------------------------------------------------
Code:
Random-effects negative binomial regression Number of obs = 1,517
Group variable: ID Number of groups = 196
Random effects u_i ~ Beta Obs per group:
min = 1
avg = 7.7
max = 12
Wald chi2(4) = 1211.20
Log likelihood = -8721.4284 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------
IOAmountLAG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
CSRP | .0025812 .0003402 7.59 0.000 .0019144 .003248
AssetsLOG | .303675 .0103124 29.45 0.000 .283463 .3238871
Longtermdebttoassetsratio | -.2044821 .0499734 -4.09 0.000 -.3024282 -.1065359
ROA | .3170092 .059285 5.35 0.000 .2008127 .4332057
_cons | -1.064183 .1696876 -6.27 0.000 -1.396764 -.7316012
--------------------------+----------------------------------------------------------------
/ln_r | 2.149175 .1144246 1.924907 2.373443
/ln_s | 4.117728 .1280466 3.866762 4.368695
--------------------------+----------------------------------------------------------------
r | 8.577781 .9815089 6.854513 10.73429
s | 61.41955 7.864562 47.78738 78.94053
-------------------------------------------------------------------------------------------
LR test vs. pooled: chibar2(01) = 1720.08 Prob >= chibar2 = 0.000
Code:
Conditional FE negative binomial regression Number of obs = 1,508
Group variable: ID Number of groups = 187
Obs per group:
min = 2
avg = 8.1
max = 12
Wald chi2(15) = 1881.37
Log likelihood = -6905.4815 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------
IOAmountLAG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
CSRP | .0008846 .000333 2.66 0.008 .000232 .0015372
AssetsLOG | .2115616 .011534 18.34 0.000 .1889553 .2341679
Longtermdebttoassetsratio | -.2015839 .0422237 -4.77 0.000 -.2843409 -.1188269
ROA | .2220044 .0497289 4.46 0.000 .1245376 .3194712
1.Yr1 | -.3204323 .0214642 -14.93 0.000 -.3625014 -.2783632
1.Yr2 | -.2530504 .0205494 -12.31 0.000 -.2933265 -.2127743
1.Yr3 | -.2124784 .0182754 -11.63 0.000 -.2482975 -.1766592
1.Yr4 | -.1729895 .0170758 -10.13 0.000 -.2064575 -.1395215
1.Yr5 | -.1129992 .0162236 -6.97 0.000 -.1447969 -.0812015
1.Yr6 | -.2020783 .0160457 -12.59 0.000 -.2335272 -.1706293
1.Yr7 | -.1550496 .0148343 -10.45 0.000 -.1841243 -.125975
1.Yr8 | -.1120334 .0142217 -7.88 0.000 -.1399074 -.0841594
1.Yr9 | -.0985822 .0139772 -7.05 0.000 -.1259769 -.0711875
1.Yr10 | -.1435823 .0138142 -10.39 0.000 -.1706577 -.1165069
1.Yr11 | -.0070922 .0132745 -0.53 0.593 -.0331099 .0189254
1.Yr12 | 0 (omitted)
_cons | 1.019664 .2009242 5.07 0.000 .62586 1.413469
-------------------------------------------------------------------------------------------
Code:
Random-effects negative binomial regression Number of obs = 1,517
Group variable: ID Number of groups = 196
Random effects u_i ~ Beta Obs per group:
min = 1
avg = 7.7
max = 12
Wald chi2(15) = 2021.62
Log likelihood = -8547.0218 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------
IOAmountLAG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
CSRP | .0011649 .0003253 3.58 0.000 .0005274 .0018025
AssetsLOG | .2322487 .0106162 21.88 0.000 .2114413 .253056
Longtermdebttoassetsratio | -.2170431 .0420245 -5.16 0.000 -.2994096 -.1346765
ROA | .2649071 .0500815 5.29 0.000 .1667491 .363065
1.Yr1 | -.2947362 .0208167 -14.16 0.000 -.3355361 -.2539363
1.Yr2 | -.2292164 .0199877 -11.47 0.000 -.2683916 -.1900412
1.Yr3 | -.1923851 .0177932 -10.81 0.000 -.2272591 -.157511
1.Yr4 | -.1571183 .0166608 -9.43 0.000 -.189773 -.1244637
1.Yr5 | -.0997591 .0159177 -6.27 0.000 -.1309572 -.068561
1.Yr6 | -.1909155 .015803 -12.08 0.000 -.2218889 -.1599421
1.Yr7 | -.1471921 .0146709 -10.03 0.000 -.1759465 -.1184377
1.Yr8 | -.1052959 .0141022 -7.47 0.000 -.1329357 -.077656
1.Yr9 | -.093183 .0138849 -6.71 0.000 -.1203968 -.0659691
1.Yr10 | -.1413071 .0137671 -10.26 0.000 -.1682902 -.114324
1.Yr11 | -.0049756 .013236 -0.38 0.707 -.0309176 .0209664
1.Yr12 | 0 (omitted)
_cons | .660757 .1876681 3.52 0.000 .2929343 1.02858
--------------------------+----------------------------------------------------------------
/ln_r | 2.022788 .1107667 1.805689 2.239886
/ln_s | 3.589428 .1244353 3.345539 3.833316
--------------------------+----------------------------------------------------------------
r | 7.559367 .8373263 6.08416 9.392263
s | 36.21335 4.506218 28.37587 46.21556
-------------------------------------------------------------------------------------------
LR test vs. pooled: chibar2(01) = 2016.08 Prob >= chibar2 = 0.000
Code:
Conditional FE negative binomial regression Number of obs = 1,508
Group variable: ID Number of groups = 187
Obs per group:
min = 2
avg = 8.1
max = 12
Wald chi2(21) = 1958.68
Log likelihood = -6891.3078 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------
IOAmountLAG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
CSRP | .0005671 .0003336 1.70 0.089 -.0000868 .001221
AssetsLOG | .2056713 .0118557 17.35 0.000 .1824346 .2289079
Longtermdebttoassetsratio | -.2046538 .0451906 -4.53 0.000 -.2932258 -.1160818
ROA | .2337794 .0524947 4.45 0.000 .1308917 .3366671
1.Yr1 | -.3394409 .0219168 -15.49 0.000 -.382397 -.2964847
1.Yr2 | -.2668586 .0208005 -12.83 0.000 -.3076267 -.2260905
1.Yr3 | -.2178926 .0187049 -11.65 0.000 -.2545534 -.1812317
1.Yr4 | -.1804838 .017247 -10.46 0.000 -.2142873 -.1466803
1.Yr5 | -.1158919 .0163515 -7.09 0.000 -.1479403 -.0838435
1.Yr6 | -.2031608 .0160031 -12.70 0.000 -.2345262 -.1717953
1.Yr7 | -.1592172 .0149453 -10.65 0.000 -.1885095 -.1299249
1.Yr8 | -.1132372 .0145929 -7.76 0.000 -.1418388 -.0846357
1.Yr9 | -.0983507 .0140453 -7.00 0.000 -.1258789 -.0708225
1.Yr10 | -.1437807 .0136537 -10.53 0.000 -.1705414 -.11702
1.Yr11 | -.0100198 .0132106 -0.76 0.448 -.0359122 .0158726
1.Yr12 | 0 (omitted)
1.Ind1 | .1574301 .4053718 0.39 0.698 -.6370841 .9519442
1.Ind2 | -.0265892 .3097767 -0.09 0.932 -.6337405 .580562
1.Ind3 | .3656919 .3247828 1.13 0.260 -.2708707 1.002254
1.Ind4 | -.6574858 .376067 -1.75 0.080 -1.394564 .079592
1.Ind5 | .5353919 .3087592 1.73 0.083 -.069765 1.140549
1.Ind6 | .2540746 .302764 0.84 0.401 -.3393319 .8474811
1.Ind7 | 0 (omitted)
_cons | .944985 .3740042 2.53 0.012 .2119504 1.67802
-------------------------------------------------------------------------------------------
Code:
Random-effects negative binomial regression Number of obs = 1,517
Group variable: ID Number of groups = 196
Random effects u_i ~ Beta Obs per group:
min = 1
avg = 7.7
max = 12
Wald chi2(21) = 2075.67
Log likelihood = -8525.5143 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------
IOAmountLAG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
CSRP | .0014413 .0003354 4.30 0.000 .000784 .0020986
AssetsLOG | .2460312 .0111618 22.04 0.000 .2241546 .2679079
Longtermdebttoassetsratio | -.1937714 .0411262 -4.71 0.000 -.2743772 -.1131656
ROA | .2691561 .0487697 5.52 0.000 .1735692 .364743
1.Yr1 | -.2679108 .0217655 -12.31 0.000 -.3105705 -.2252512
1.Yr2 | -.2088733 .0206541 -10.11 0.000 -.2493547 -.1683919
1.Yr3 | -.1726793 .0184227 -9.37 0.000 -.2087872 -.1365714
1.Yr4 | -.139893 .0171796 -8.14 0.000 -.1735644 -.1062216
1.Yr5 | -.0870741 .0163152 -5.34 0.000 -.1190512 -.055097
1.Yr6 | -.1772471 .0161774 -10.96 0.000 -.2089542 -.1455401
1.Yr7 | -.1358885 .0150696 -9.02 0.000 -.1654244 -.1063526
1.Yr8 | -.1002982 .0144687 -6.93 0.000 -.1286564 -.07194
1.Yr9 | -.0899588 .0141648 -6.35 0.000 -.1177213 -.0621963
1.Yr10 | -.1390783 .0139516 -9.97 0.000 -.1664229 -.1117337
1.Yr11 | -.0031437 .0134104 -0.23 0.815 -.0294275 .0231401
1.Yr12 | 0 (omitted)
1.Ind1 | -.2243791 .185185 -1.21 0.226 -.5873351 .1385768
1.Ind2 | .0028774 .1455043 0.02 0.984 -.2823058 .2880606
1.Ind3 | -.0872357 .1552782 -0.56 0.574 -.3915754 .2171039
1.Ind4 | -.59714 .1799455 -3.32 0.001 -.9498267 -.2444533
1.Ind5 | -.418096 .1468534 -2.85 0.004 -.7059234 -.1302687
1.Ind6 | -.1590296 .141692 -1.12 0.262 -.4367409 .1186817
1.Ind7 | 0 (omitted)
_cons | .5578262 .2539453 2.20 0.028 .0601025 1.05555
--------------------------+----------------------------------------------------------------
/ln_r | 2.400519 .1300849 2.145558 2.655481
/ln_s | 4.022098 .1499044 3.728291 4.315905
--------------------------+----------------------------------------------------------------
r | 11.0289 1.434693 8.546807 14.23183
s | 55.81809 8.367378 41.60793 74.88138
-------------------------------------------------------------------------------------------
LR test vs. pooled: chibar2(01) = 1184.09 Prob >= chibar2 = 0.000