Separating managerial fixed effect from firm fixed effect

[Tracy Chen]

Dear all,

Sorry for bringing up a topic that has been discussed in this forum several times , but I cannot find any helpful insights after reading the previous posts. I am currently doing the research on analysing the effect of Chief Digital Officer (CDO) on firm financial performance by replicating the methodology proposed by Bertrand and Schoar (2003). So basically I choose the Chief Digital Officers that have been in at minimum of two firms during my sample period in order to separate managerial fixed effect from the firm fixed effect, and they should be at each firm for at least one full year. The dummy variable CDO is defined as 1 if for a firm i at time t it has the CDO j. But what troubles me is that I cannot separate managerial fixed effect from firm fixed effect by using the following command:

encode Company_id,gen(company)
gen lnassets = log(Totalassets)
areg ROA CDO* CF Leverage Investment Cashholdings lnassets i.Year, absorb(company) vce(robust)
testparm CDO*

or alternatively,

encode Company_id,gen(company)
gen lnassets = log(Totalassets)
areg ROA CF Leverage Investment Cashholdings lnassets i.CDO_id i.Year, absorb(company) vce(robust)

Once the above commands are applied, i.CDO_id will be omitted by Stata due to collinearity except one CDO in my case.

However, if I set the fixed effect the other way around, then it seems to work:

encode Company_id,gen(company)
gen lnassets = log(Totalassets)
areg ROA CDO* CF Leverage Investment Cashholdings lnassets i.company, absorb(Year) vce(robust)
testparm CDO*

The followings are my sample data:

* Example generated by -dataex-. For more info, type help dataex
clear
input long company int Year long CDO_id byte CDO double(CF Leverage Investment Cashholdings) float lnassets
 3 2012 2099971 0   .019565658615790543     .819335705812574  .08556931195453622  .10525674852851634  10.64137
 3 2013 2099971 0   .056068811723478815    .8298892119116839  .07916533928002549  .09198789423383243 10.606857
 3 2014 2099971 0    .08007633891296569    .8304290874449252   .0801558586139716  .08938014393065882 10.570445
 3 2015 2099971 0    .06584324766142947    .8647743376132606  .10480428662246843   .0783761692852602 10.504246
 3 2016 2099971 0  .0022532451628704386    .8744156778137361  .11486651971589518  .08689688954200343 10.494713
 3 2017 2099971 0 .00039416633819471815    .8901417238613067  .10726251478123769   .0811489948758376  10.40765
 3 2018 2099971 0    .10310338381005796    .8574792305300102   .0991306786315199  .08641802206019816 10.389642
 3 2019 2099971 1    .05906581368854614     .872597380506889  .10538077293839278  .06261502059416353  10.42371
 3 2020 2099971 1    .04822302064845678    .8850082947699293   .0822475217523051   .0616423531448855 10.451695
 3 2021 2099971 0    .03205509314308363    .9065814393939394  .10483551327784384 .058214427269124056  10.40314
 3 2022 2099971 0   .021671297285744816    .9377142411966345   .1945287454584313  .08993374652703569  10.55485
 3 2023 2099971 0    .04538862153075351    .9435356922866334   .2545981936844881   .0600237326125651  10.70994
14 2012 2099971 0     .5160075329566854    .6960208062418726  .30836522689994533  .33351558228540185 11.396054
14 2013 2099971 0     .4026939970717423    .6446269701678592   .2603806734992679   .3561346998535871 11.349182
14 2014 2099971 1      .338722326114496    .7011297317556353   .2038366411292755   .4428424926102431 11.346646
14 2015 2099971 0     .3454319453076445    .7196433304305024  .20267246737103792  .40149160969546305  11.26884
14 2016 2099971 0     .1936431275290432    .7368389423076923  .19109776791541574   .4678240438585041  11.22129
14 2017 2099971 0     .2565171317555634    .7180236747297993  .06344048039561992   .5836100317908867 11.251067
14 2018 2099971 0     .6566229556505083    .7225055344718533  .21482245469279504     .57882716958892 11.270968
14 2019 2099971 0     .6408929627439385    .7241248888972939  .19729450029568302   .6123595505617978 11.270255
14 2020 2099971 0    .41756382651491847    .7113567044470385  .16264226391879422   .7191633343586589  11.26861
14 2021 2099971 0     .6953204876130554    .6998270053719384  .19441604404246954   .7278018088871412   11.3241
14 2022 2099971 0     .7087039390088945    .7030557062929211  .20640088945362134   .5562261753494282  11.31378
14 2023 2099971 0     .9428074947113931    .6635833362095744  .23360531882744032   .5271985494106981  11.37912
 5 2012 1950347 0     2.723963599595551   .22739047189998873  .28816986855409504   .8149646107178968 11.751525
 5 2013 1950347 0             2.5859375    .2307477626658232         .2021484375         .6591796875 11.724158
 5 2014 1950347 0     3.119301648884578   .20047583759116971   .2793404461687682   .6372453928225025 11.594312
 5 2015 1950347 0           2.482421875   .21949965729952023         .2958984375         .4833984375 11.558434
 5 2016 1950347 0      2.12112676056338   .25271749950228944  .29389671361502345  .40938967136150234  11.59552
 5 2017 1950347 0     3.425373134328358    .2343519338647771   .2789179104477612   .5755597014925373 11.630015
 5 2018 1950347 0     2.555980861244019   .25034927041291527  .26507177033492824  .47751196172248805 11.628475
 5 2019 1950347 0    3.3746928746928746   .23354475438482947  .26597051597051596   .2076167076167076  11.69483
 5 2020 1950347 0     4.318620689655172   .22820849759088918  .21241379310344827                 .26 11.743934
 5 2021 1950347 0     2.142857142857143   .26716252571609433   .2753391859537111   .6089385474860335  11.50731
 5 2022 1950347 0     -.361998361998362    .3494741270509045    .343980343980344   .6027846027846028  11.49261
 5 2023 1950347 1     .5048923679060665   .34300162995778827  .26125244618395305   .7064579256360078 11.545993
40 2012 1950347 0     .9465064162592594    .2746583504475039  .11087502664023094  1.5405157548711257  8.650051
40 2013 1950347 0      .743973215362572   .24436980207378886  .07713608930785448  1.7030533135857742  9.375039
40 2014 1950347 0     .7950652701201807    .4087537292768794 .061704045701535495  1.5831079634029117  9.413333
40 2015 1950347 0      .782465142903872    .4989083905274559  .06520116939935397  1.4208662141718116  9.447694
40 2016 1950347 0     .7839686031991437    .5162744995717069  .05518225605042517  1.7742111607842714  9.499447
40 2017 1950347 0     .8035117849435984   .48894071267313727  .07370956679807515  1.8756823669140565  9.532275
40 2018 1950347 0    1.0551637674345713    .1077623881166026  .08196207490988873  1.9611290214252133  9.494501
40 2019 1950347 0     .8592905015544885   .20780431306551264  .07841229471473891  1.6242527367596946  9.510287
40 2020 1950347 0      .894177520994409   .24000384119286497   .1002624578668526   8.671119420549873  9.714252
40 2021 1950347 1      .804080800176485   .24035817629529388  .11388279562283815   9.435410223644832  9.775406
40 2022 1950347 0    .44947439537371414    .5360709969915317  .10706731117241601    2.97100126273797  9.798986
40 2023 1950347 0     .7434821319718191   .40172780501010896  .14807945943349873  3.6040586820551286  9.837464
 6 2012 2264218 0    .25860323886639675     .863571278163824   .5381723539618276   .5431607865818392 12.113667
 6 2013 2264218 0    .18001674574379012    .8576014423446896   .5133128663131454  .30873569634384596  11.92614
 6 2014 2264218 0     .2070433240435774    .8385130043614276   .5008360780339498   .2825437040790474 11.929205
 6 2015 2264218 0    .24778868290318673    .8536599370679161   .2838361807827457   .3865261117169514  11.97402
 6 2016 2264218 0    .29115313185885533    .8337826705609226  .27638021273003544   .5009285834880972  12.00596
 6 2017 2162824 0     .3031423290203327    .8048110164465595  .44057844949440034  .46232467108839836 12.026635
 6 2018 2162824 0    .32424006235385816    .8032854940102004   .4129829640351854   .5051775971495379  12.09441
 6 2019 2162824 1      .337879727216367    .7338748384714787  .41568505889646623  .36732796032238063 12.104283
 6 2020 2162824 1     .2503087299325544    .6233090797294527   .4103733257338273  1.4838985465944714 12.112668
 6 2021 2264218 1    .35435460062325735    .5388036329470717  .41987862883385274   .4151221912415942  12.11239
 6 2022 2264218 1    .25703659876595386    .6583206304933026    .298537739836024   .4708815822838306 12.164344
 6 2023 2264218 1    .21502418666413733    .6470914810930849  .26169022099971545   .6587309115052642 12.187868
29 2012 2162824 0      .884808189541449    .2629084720935743   .7488259194765448  2.3309060207904597  5.836272
29 2013 2162824 0    1.1791420354689248    .1916200248756219   .3085956223038824  1.4876178303243328   6.06461
29 2014 2162824 0    .34601320899118454   .34307363179096045   .4066441792567816  1.1310411292837097  6.512213
29 2015 2162824 0    .38401991923770606   .12454461660009655    .486042168770849  1.8013024116961678   6.95904
29 2016 2162824 0     .2788852631416155   .11106545933224302  .16840135475789114  3.7929818592350877  7.470373
29 2017 2162824 0     .6195984115442698  .057312129312595335   .6943285418647576  1.6682756306281115  7.922433
29 2018 2162824 0    .25839161371912667 .0029433332592618032   .4248411573798967  1.2344509454373696  8.208069
29 2019 2162824 0    .13615598766029258   .00492132055123276  .13327528941343395   .8192326020516018   8.47904
29 2020 2162824 0     .3133102168806674    .7312205856111069  .08095515433896332  1.2528397366421489  8.971106
29 2021 2162824 0     .7841970723908808    .3096225544427904 .012831187863245016   .8680410997685224  9.013521
29 2022 2162824 1     .7481750161418967   .09563065765382016  .16617038246800103  1.5976147973717194  9.195785
29 2023 2162824 1    .36904231021285017  .028555746879035726   .1816302868377275  2.2599183344255684  9.330026
 7 2012 2264218 1    1.5056396148555709    .7673364296009757   .2896836313617607   6.121045392022008 11.939108
 7 2013 2264218 1    1.6461935483870969    .7558330306711586  .25961290322580644  5.0286451612903225  11.94064
 7 2014 2264218 1    1.7513966480446928    .7482218541433234   .3034535297105129   5.659725749111224 11.977307
 7 2015 2264218 1    1.5107108081791627    .7189106137655344  .32643622200584227   5.540895813047712 11.990302
 7 2016 2264218 0    1.4595082337017822    .7194410991898401  .31017369727047145   5.686442589668396 11.975986
 7 2017 2264218 0       .93993993993994    .7638958923238044  .24532224532224534   7.606144606144606 12.107334
 7 2018 2264218 0     1.860054347826087    .7340508035746245   .2966485507246377   6.214900362318841 12.147394
 7 2019 2264218 0    1.6439801406702523    .7358726015478316   .3402978899462143  5.0570955730244105 12.197642
 7 2020 2264218 0     .9328015952143569    .6610729347922258    .294715852442672   6.573280159521436 12.161948
 7 2021 2264218 0    1.9556936647955092    .6485141453363975   .3107457898957498   4.416198877305534 12.147108
 7 2022 2264218 0    1.7526366251198466    .6399492947896025  .35570469798657717   6.503163950143816 12.338653
 7 2023 2264218 0    1.9511483067341378    .6366426647326979   .3042039704165045   9.068898404048268  12.47269
 2 2012 1978032 0    1.5195031814833078   .16474936519404518  .26389440709809187   7.787252903465391  8.634149
 2 2013 1978032 0    1.5425968817583058    .1554293377706365  .24219012891329886   9.215228732060666  8.761198
 2 2014 1978032 0    1.2391753504856835   .15500580213494414  .28583983213960945   4.605344926753874  8.833418
 2 2015 1978032 0    1.4269581282700161   .14638238541693657   .2390274953035972   4.702501125584139  8.862027
 2 2016 1978032 0     1.684368888693257    .2511203942709228  .20027322060756217   6.375870124316949  8.983475
 2 2017 1978032 0    1.1842438932759205    .4358656462267796   .1843197532023726   .9462965906381625  9.958983
 2 2018 1978032 0     1.997736345302202    .3597937076550918   .2208003271167294    .707416782751523  9.925169
 2 2019 1978032 0    1.7821980362118017   .31927706745850715  .22571678924973915   .5314162668679799  9.970802
 2 2020 1978032 0    1.8130954048909431   .31328328447842546   .1478652210812263   .9422601714676845  9.974347
 2 2021 1978032 0     1.245574772959363   .15779451805028843    .173656969931548   .9994507468478578 10.865173
 2 2022 1978032 1     2.101383248435017   .15987916559103815   .2912201037436326   .6124055929611577 10.825807
 2 2023 1978032 1    1.6038550762689494   .17173030802257896   .3607914707138275   .2740153593276698 10.795372
39 2012 1978032 0     .5356364768129473     .317668207498716  .16588857765328355  .49455337690631807  9.868171
39 2013 1978032 0     .5947567909033481    .2645251886958048  .19425142135186355  .44314592545799114  9.823416
39 2014 1978032 0     .7986301369863014   .29988340458608626  .21746575342465754   .8414383561643836  9.911058
39 2015 1978032 0    1.0397260273972602   .28836587719949514   .2054794520547945   1.140068493150685  9.932512
end
label values company company
label def company 2 "ADI", modify
label def company 3 "AES", modify
label def company 5 "ALL", modify
label def company 6 "ALLY", modify
label def company 7 "APX", modify
label def company 14 "CAT", modify
label def company 29 "LOB", modify
label def company 39 "TEL", modify
label def company 40 "TRMK", modify

I would really appreciate any advice on how to solve this problem. Specially, I wonder if it is correct to set the fixed effect in the second that I mentioned above (i.e., y controls i.company, absorb(Year) ).

[Carlo Lazzaro]

Tracy:
your data excerpt is partially inconsistent with your code.
However, why not going -xtreg-?:

xtset company Year
xtreg  CF  i.CDO Leverage Investment Cashholdings lnassets i.Year, robust fe
Fixed-effects (within) regression               Number of obs     =        100
Group variable: company                         Number of groups  =          9

R-squared:                                      Obs per group:
     Within  = 0.1095                                         min =          4
     Between = 0.2649                                         avg =       11.1
     Overall = 0.2479                                         max =         12

                                                F(8, 8)           =          .
corr(u_i, Xb) = 0.2540                          Prob > F          =          .

                                (Std. err. adjusted for 9 clusters in company)
------------------------------------------------------------------------------
             |               Robust
          CF | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       1.CDO |  -.1295614   .1980722    -0.65   0.531    -.5863167    .3271938
    Leverage |  -.9909433   1.099648    -0.90   0.394    -3.526736     1.54485
  Investment |   .0038172   .3852464     0.01   0.992    -.8845626    .8921971
Cashholdings |  -.0319724   .0183029    -1.75   0.119    -.0741789    .0102341
    lnassets |   .0551135   .1883533     0.29   0.777    -.3792299    .4894569
             |
        Year |
       2013  |  -.0287807   .0936342    -0.31   0.766    -.2447016    .1871402
       2014  |  -.0217297   .1129967    -0.19   0.852    -.2823005     .238841
       2015  |  -.0894876   .1265732    -0.71   0.500    -.3813658    .2023907
       2016  |  -.1732134   .1700954    -1.02   0.338     -.565454    .2190273
       2017  |  -.1037293   .1145581    -0.91   0.392    -.3679009    .1604422
       2018  |  -.0229875   .2105833    -0.11   0.916    -.5085934    .4626185
       2019  |  -.0016982   .1432139    -0.01   0.991      -.33195    .3285536
       2020  |   .1247603   .2125852     0.59   0.573    -.3654619    .6149826
       2021  |  -.0893284    .264236    -0.34   0.744    -.6986576    .5200009
       2022  |  -.3470427   .5190456    -0.67   0.523    -1.543964    .8498787
       2023  |  -.2627436   .4072321    -0.65   0.537    -1.201823    .6763354
             |
       _cons |   1.038644   1.479571     0.70   0.503    -2.373254    4.450541
-------------+----------------------------------------------------------------
     sigma_u |  .67243252
     sigma_e |  .51140967
         rho |  .63354646   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

[Tracy Chen]

Hi, Carlo
Thanks for your reply and apologise for any confusion and inconvenience caused by the inconsistent data excerpt earlier. I've put the modified data below.

* Example generated by -dataex-. For more info, type help dataex
clear
input long company int Year long CDO_id byte CDO double(ROA CF Leverage Investment Cashholdings) float lnassets
 3 2012 2099971 0   -.02180253406645948   .019565658615790543     .819335705812574  .08556931195453622  .10525674852851634  10.64137
 3 2013 2099971 0   .002821014080324664   .056068811723478815    .8298892119116839  .07916533928002549  .09198789423383243 10.606857
 3 2014 2099971 0   .019735153723759176    .08007633891296569    .8304290874449252   .0801558586139716  .08938014393065882 10.570445
 3 2015 2099971 0   .008390457910611462    .06584324766142947    .8647743376132606  .10480428662246843   .0783761692852602 10.504246
 3 2016 2099971 0   -.03128114273059462  .0022532451628704386    .8744156778137361  .11486651971589518  .08689688954200343 10.494713
 3 2017 2099971 0   -.03506281710558106 .00039416633819471815    .8901417238613067  .10726251478123769   .0811489948758376  10.40765
 3 2018 2099971 0    .03699148242673964    .10310338381005796    .8574792305300102   .0991306786315199  .08641802206019816 10.389642
 3 2019 2099971 1   .009004992867332383    .05906581368854614     .872597380506889  .10538077293839278  .06261502059416353  10.42371
 3 2020 2099971 1  .0013293645059676907    .04822302064845678    .8850082947699293   .0822475217523051   .0616423531448855 10.451695
 3 2021 2099971 0  -.012407851227133452    .03205509314308363    .9065814393939394  .10483551327784384 .058214427269124056  10.40314
 3 2022 2099971 0   -.01423246357167062   .021671297285744816    .9377142411966345   .1945287454584313  .08993374652703569  10.55485
 3 2023 2099971 0    .00555815978035224    .04538862153075351    .9435356922866334   .2545981936844881   .0600237326125651  10.70994
14 2012 2099971 0    .06385298415196133     .5160075329566854    .6960208062418726  .30836522689994533  .33351558228540185 11.396054
14 2013 2099971 0     .0446310780248775     .4026939970717423    .6446269701678592   .2603806734992679   .3561346998535871 11.349182
14 2014 2099971 1    .02895572796731262      .338722326114496    .7011297317556353   .2038366411292755   .4428424926102431 11.346646
14 2015 2099971 0    .03206453754052743     .3454319453076445    .7196433304305024  .20267246737103792  .40149160969546305  11.26884
14 2016 2099971 0 -.0008968729920753909     .1936431275290432    .7368389423076923  .19109776791541574   .4678240438585041  11.22129
14 2017 2099971 0   .009797042696395624     .2565171317555634    .7180236747297993  .06344048039561992   .5836100317908867 11.251067
14 2018 2099971 0    .07829675578596085     .6566229556505083    .7225055344718533  .21482245469279504     .57882716958892 11.270968
14 2019 2099971 0    .07766433405988299     .6408929627439385    .7241248888972939  .19729450029568302   .6123595505617978 11.270255
14 2020 2099971 0     .0382769010775752    .41756382651491847    .7113567044470385  .16264226391879422   .7191633343586589  11.26861
14 2021 2099971 0    .07837619122389573     .6953204876130554    .6998270053719384  .19441604404246954   .7278018088871412   11.3241
14 2022 2099971 0    .08182517115555936     .7087039390088945    .7030557062929211  .20640088945362134   .5562261753494282  11.31378
14 2023 2099971 0    .11814669166399927     .9428074947113931    .6635833362095744  .23360531882744032   .5271985494106981  11.37912
 5 2012 1950347 0   .018165061009712716     2.723963599595551   .22739047189998873  .28816986855409504   .8149646107178968 11.751525
 5 2013 1950347 0   .018458549222797927             2.5859375    .2307477626658232         .2021484375         .6591796875 11.724158
 5 2014 1950347 0   .026272366080070796     3.119301648884578   .20047583759116971   .2793404461687682   .6372453928225025 11.594312
 5 2015 1950347 0   .020744152270295062           2.482421875   .21949965729952023         .2958984375         .4833984375 11.558434
 5 2016 1950347 0    .01728201823036553      2.12112676056338   .25271749950228944  .29389671361502345  .40938967136150234  11.59552
 5 2017 1950347 0    .02836633399156749     3.425373134328358    .2343519338647771   .2789179104477612   .5755597014925373 11.630015
 5 2018 1950347 0   .019242933121898637     2.555980861244019   .25034927041291527  .26507177033492824  .47751196172248805 11.628475
 5 2019 1950347 0    .04040850354314297    3.3746928746928746   .23354475438482947  .26597051597051596   .2076167076167076  11.69483
 5 2020 1950347 0     .0442585346107138     4.318620689655172   .22820849759088918  .21241379310344827                 .26 11.743934
 5 2021 1950347 0   .016080048270313757     2.142857142857143   .26716252571609433   .2753391859537111   .6089385474860335  11.50731
 5 2022 1950347 0   -.01315453775423772     -.361998361998362    .3494741270509045    .343980343980344   .6027846027846028  11.49261
 5 2023 1950347 1  -.001818850254445541     .5048923679060665   .34300162995778827  .26125244618395305   .7064579256360078 11.545993
40 2012 1950347 0    .01193274734000043     .9465064162592594    .2746583504475039  .11087502664023094  1.5405157548711257  8.650051
40 2013 1950347 0   .009928430654033885      .743973215362572   .24436980207378886  .07713608930785448  1.7030533135857742  9.375039
40 2014 1950347 0   .010086172690015284     .7950652701201807    .4087537292768794 .061704045701535495  1.5831079634029117  9.413333
40 2015 1950347 0   .009152058665044652      .782465142903872    .4989083905274559  .06520116939935397  1.4208662141718116  9.447694
40 2016 1950347 0   .008119255264229854     .7839686031991437    .5162744995717069  .05518225605042517  1.7742111607842714  9.499447
40 2017 1950347 0   .007655483389456393     .8035117849435984   .48894071267313727  .07370956679807515  1.8756823669140565  9.532275
40 2018 1950347 0   .011258378830779606    1.0551637674345713    .1077623881166026  .08196207490988873  1.9611290214252133  9.494501
40 2019 1950347 0   .011146938144420786     .8592905015544885   .20780431306551264  .07841229471473891  1.6242527367596946  9.510287
40 2020 1950347 0   .009668109406567487      .894177520994409   .24000384119286497   .1002624578668526   8.671119420549873  9.714252
40 2021 1950347 1   .008375088004775731      .804080800176485   .24035817629529388  .11388279562283815   9.435410223644832  9.775406
40 2022 1950347 0    .00399029101531472    .44947439537371414    .5360709969915317  .10706731117241601    2.97100126273797  9.798986
40 2023 1950347 0    .00883919075915749     .7434821319718191   .40172780501010896  .14807945943349873  3.6040586820551286  9.837464
 6 2012 2264218 0   .006558923371374358    .25860323886639675     .863571278163824   .5381723539618276   .5431607865818392 12.113667
 6 2013 2264218 0  .0023880873471061807    .18001674574379012    .8576014423446896   .5133128663131454  .30873569634384596  11.92614
 6 2014 2264218 0  .0075842011198237825     .2070433240435774    .8385130043614276   .5008360780339498   .2825437040790474 11.929205
 6 2015 2264218 0   .008128338199405982    .24778868290318673    .8536599370679161   .2838361807827457   .3865261117169514  11.97402
 6 2016 2264218 0   .006516906088146194    .29115313185885533    .8337826705609226  .27638021273003544   .5009285834880972  12.00596
 6 2017 2162824 0  .0055579486443152176     .3031423290203327    .8048110164465595  .44057844949440034  .46232467108839836 12.026635
 6 2018 2162824 0   .007061033493785955    .32424006235385816    .8032854940102004   .4129829640351854   .5051775971495379  12.09441
 6 2019 2162824 1   .009493811031642346      .337879727216367    .7338748384714787  .41568505889646623  .36732796032238063 12.104283
 6 2020 2162824 1   .005956138665495567     .2503087299325544    .6233090797294527   .4103733257338273  1.4838985465944714 12.112668
 6 2021 2264218 1    .01680266206881404    .35435460062325735    .5388036329470717  .41987862883385274   .4151221912415942  12.11239
 6 2022 2264218 1   .008935180840970463    .25703659876595386    .6583206304933026    .298537739836024   .4708815822838306 12.164344
 6 2023 2264218 1   .005193694244164731    .21502418666413733    .6470914810930849  .26169022099971545   .6587309115052642 12.187868
29 2012 2162824 0   .046992700729927006      .884808189541449    .2629084720935743   .7488259194765448  2.3309060207904597  5.836272
29 2013 2162824 0     .0652066317342659    1.1791420354689248    .1916200248756219   .3085956223038824  1.4876178303243328   6.06461
29 2014 2162824 0   .014923178601397562    .34601320899118454   .34307363179096045   .4066441792567816  1.1310411292837097  6.512213
29 2015 2162824 0    .01959392830474757    .38401991923770606   .12454461660009655    .486042168770849  1.8013024116961678   6.95904
29 2016 2162824 0    .00784669630328481     .2788852631416155   .11106545933224302  .16840135475789114  3.7929818592350877  7.470373
29 2017 2162824 0    .03643282481545956     .6195984115442698  .057312129312595335   .6943285418647576  1.6682756306281115  7.922433
29 2018 2162824 0   .014016813746765042    .25839161371912667 .0029433332592618032   .4248411573798967  1.2344509454373696  8.208069
29 2019 2162824 0    .00374706929065406    .13615598766029258   .00492132055123276  .13327528941343395   .8192326020516018   8.47904
29 2020 2162824 0   .007563606228063122     .3133102168806674    .7312205856111069  .08095515433896332  1.2528397366421489  8.971106
29 2021 2162824 0    .02033203573724038     .7841970723908808    .3096225544427904 .012831187863245016   .8680410997685224  9.013521
29 2022 2162824 1   .017879157400265314     .7481750161418967   .09563065765382016  .16617038246800103  1.5976147973717194  9.195785
29 2023 2162824 1   .006556226307893865    .36904231021285017  .028555746879035726   .1816302868377275  2.2599183344255684  9.330026
 7 2012 2264218 1   .029267337077184277    1.5056396148555709    .7673364296009757   .2896836313617607   6.121045392022008 11.939108
 7 2013 2264218 1   .034940505297473515    1.6461935483870969    .7558330306711586  .25961290322580644  5.0286451612903225  11.94064
 7 2014 2264218 1     .0369886174365034    1.7513966480446928    .7482218541433234   .3034535297105129   5.659725749111224 11.977307
 7 2015 2264218 1     .0320317153067302    1.5107108081791627    .7189106137655344  .32643622200584227   5.540895813047712 11.990302
 7 2016 2264218 0    .03382779606401792    1.4595082337017822    .7194410991898401  .31017369727047145   5.686442589668396 11.975986
 7 2017 2264218 0   .015165897701936024       .93993993993994    .7638958923238044  .24532224532224534   7.606144606144606 12.107334
 7 2018 2264218 0   .036696323474830594     1.860054347826087    .7340508035746245   .2966485507246377   6.214900362318841 12.147394
 7 2019 2264218 0    .03408111092622566    1.6439801406702523    .7358726015478316   .3402978899462143  5.0570955730244105 12.197642
 7 2020 2264218 0   .016382134850836352     .9328015952143569    .6610729347922258    .294715852442672   6.573280159521436 12.161948
 7 2021 2264218 0    .04274773532469186    1.9556936647955092    .6485141453363975   .3107457898957498   4.416198877305534 12.147108
 7 2022 2264218 0    .03290505092969687    1.7526366251198466    .6399492947896025  .35570469798657717   6.503163950143816 12.338653
 7 2023 2264218 0    .03207102042066884    1.9511483067341378    .6366426647326979   .3042039704165045   9.068898404048268  12.47269
 2 2012 1978032 0    .11587113749382379    1.5195031814833078   .16474936519404518  .26389440709809187   7.787252903465391  8.634149
 2 2013 1978032 0    .10553327848944255    1.5425968817583058    .1554293377706365  .24219012891329886   9.215228732060666  8.761198
 2 2014 1978032 0     .0917417550938891    1.2391753504856835   .15500580213494414  .28583983213960945   4.605344926753874  8.833418
 2 2015 1978032 0    .09872503409584975    1.4269581282700161   .14638238541693657   .2390274953035972   4.702501125584139  8.862027
 2 2016 1978032 0     .1081096543934854     1.684368888693257    .2511203942709228  .20027322060756217   6.375870124316949  8.983475
 2 2017 1978032 0    .03439992840551766    1.1842438932759205    .4358656462267796   .1843197532023726   .9462965906381625  9.958983
 2 2018 1978032 0    .07373290017411371     1.997736345302202    .3597937076550918   .2208003271167294    .707416782751523  9.925169
 2 2019 1978032 0    .06371401268314651    1.7821980362118017   .31927706745850715  .22571678924973915   .5314162668679799  9.970802
 2 2020 1978032 0    .05686261933298594    1.8130954048909431   .31328328447842546   .1478652210812263   .9422601714676845  9.974347
 2 2021 1978032 0   .026574292137633466     1.245574772959363   .15779451805028843    .173656969931548   .9994507468478578 10.865173
 2 2022 1978032 1    .05464080703983015     2.101383248435017   .15987916559103815   .2912201037436326   .6124055929611577 10.825807
 2 2023 1978032 1    .06792938741961745    1.6038550762689494   .17173030802257896   .3607914707138275   .2740153593276698 10.795372
39 2012 1978032 0    .05759867398736144     .5356364768129473     .317668207498716  .16588857765328355  .49455337690631807  9.868171
39 2013 1978032 0    .06911868262824332     .5947567909033481    .2645251886958048  .19425142135186355  .44314592545799114  9.823416
39 2014 1978032 0    .08837832473203652     .7986301369863014   .29988340458608626  .21746575342465754   .8414383561643836  9.911058
39 2015 1978032 0    .11753849142746127    1.0397260273972602   .28836587719949514   .2054794520547945   1.140068493150685  9.932512
end
label values company company
label def company 2 "ADI", modify
label def company 3 "AES", modify
label def company 5 "ALL", modify
label def company 6 "ALLY", modify
label def company 7 "APX", modify
label def company 14 "CAT", modify
label def company 29 "LOB", modify
label def company 39 "TEL", modify
label def company 40 "TRMK", modify

I am kindly asking if it is possible for your to clarify why managerial effect is defined as "i.CDO" rather than "i.CDO_id" , and if that is the case, is the following approach of getting the managerial fixed for each separate executive correct? (I suspect this approach is incorrect because it is running the regression using a subset with very small observations, though this is the only way that I can think of to give managerial fixed effect for each executive) Thank you in advance!

xtset company Year

tempname memhold
postfile `memhold' cdo_id CDO_b CDO_pvalue using "result_post.dta", replace

levelsof CDO_id, local(levels)

foreach x of local levels {
    xtreg ROA CDO CF Leverage Investment Cashholdings lnassets i.Year if CDO_id == `x', fe vce(robust)
    matrix CDO_coef = e(b)
    matrix CDO_se = e(V)
    
    scalar CDO_b = CDO_coef[1, "CDO"]
    scalar CDO_se = sqrt(CDO_se[1, 1])
    
    scalar CDO_pvalue = 2 * (ttail(e(df_r), abs(CDO_b / CDO_se)))
    
    post `memhold' (`x') (CDO_b) (CDO_pvalue)
}
postclose `memhold'

use result_post.dta, clear
list

[Carlo Lazzaro]

Tracy:
if you want to collect more fixed effects than -xtreg- allows you to you should switch to the community-contributed module -reghdfe-.
However, this switch will not shelter you from perfect collinearity if you use the -fe- estimator.
Unlike CDO_id, CDO has some within-panel variation: that's why it is not wiped out by the -fe- machinery.
Performing different regressions on different CEO would be incorrect.
As an aside: have you already double-checked that -re- is out of debate here?

[Tracy Chen]

Hi, Carlo. Thanks for the classification provided above. Yes, I've checked with the Hausman specification test and it says I should use '-fe' (I wonder if it is correct to say that for most time we use fixed effect as it is difficult to assume that there is no correlation between the X’s and error term to use the random effects? ).

 hausman fixed random

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference       Std. err.
-------------+----------------------------------------------------------------
         CDO |    .0033992      .002211        .0011882               .
          CF |    .0163909     .0159659         .000425        .0002104
    Leverage |    -.009724    -.0098272        .0001032        .0016194
  Investment |   -.0006026    -.0009121        .0003095        .0001651
Cashholdings |   -.0018313    -.0024035        .0005723        .0005102
    lnassets |    -.025863    -.0131109       -.0127521         .003054
        Year |
       2013  |    .0047233     .0039605        .0007628               .
       2014  |    .0105673     .0090769        .0014904               .
       2015  |    .0149141     .0129507        .0019633               .
       2016  |    .0133406     .0105147        .0028258               .
       2017  |    .0154622     .0117376        .0037245               .
       2018  |     .014305     .0093856        .0049194               .
       2019  |    .0188453     .0127532        .0060921               .
       2020  |    .0009347    -.0065507        .0074855         .000964
       2021  |    .0206825     .0123391        .0083434        .0013695
       2022  |    .0220405     .0127479        .0092927        .0016784
       2023  |     .026671      .017355         .009316          .00164
------------------------------------------------------------------------------
                          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(17) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            =  33.29
Prob > chi2 = 0.0103
(V_b-V_B is not positive definite)

.

my questions are as follows:
1) is there anything wrong with sample construction? i.e., for one CDO that was in firm A in year 2014, and then worked in firm B during the years 2019-2020, is it problematic to have observations from the year 2012-2023 for these two firms (24 observations in total for this CDO), but in this case CDO_id will be time-invariant? Because according to what Bertrand and Schoar (2003) do, the reasons why they consider executives that have been in minimum of two firms to separately managerial FE from firm FE, and it should theoretically work in my case.
2) does the collinearity occur because of the choice of control variables on the firm level? or endogeneity of the research question: firms that have better performance are more likely to have a CDO, and it can be argued by saying the other round that CDOs are more likely to join a company with better performance?

Thank you in advance!

Best regards,
Tracy

[Carlo Lazzaro]

Tracy:
1) as your -hausman- outcomes is a bit limping, I would go -re- and then check it via the community-contributed module -xtoverid- (that allows non-default standard errors).
2) I share your concerns about the risk of reverse causation-driven endogeneity, that is worth investigating in the literature.

[Tracy Chen]

Hi, Carlo. Thank you very much!
Thank you for clarifying the test. May I ask if the following is the right way to use -xtoverid- and thus I should reject the null hypothesis that -re- is the right way to go?

 xi: xtreg ROA CDO CF Leverage Investment Cashholdings lnassets i.Year, re robust
i.Year            _IYear_2012-2023    (naturally coded; _IYear_2012 omitted)

Random-effects GLS regression                   Number of obs     =        480
Group variable: company                         Number of groups  =         43

R-squared:                                      Obs per group:
     Within  = 0.2284                                         min =          3
     Between = 0.0010                                         avg =       11.2
     Overall = 0.0252                                         max =         12

                                                Wald chi2(17)     =      77.54
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                               (Std. err. adjusted for 43 clusters in company)
------------------------------------------------------------------------------
             |               Robust
         ROA | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         CDO |    .002211   .0055704     0.40   0.691    -.0087067    .0131288
          CF |   .0159659   .0034715     4.60   0.000      .009162    .0227698
    Leverage |  -.0098272    .017492    -0.56   0.574    -.0441108    .0244564
  Investment |  -.0009121    .000293    -3.11   0.002    -.0014863   -.0003379
Cashholdings |  -.0024035   .0011364    -2.11   0.034    -.0046309   -.0001762
    lnassets |  -.0131109   .0057358    -2.29   0.022    -.0243529   -.0018689
 _IYear_2013 |   .0039605   .0066784     0.59   0.553     -.009129      .01705
 _IYear_2014 |   .0090769   .0061747     1.47   0.142    -.0030254    .0211792
 _IYear_2015 |   .0129507   .0061957     2.09   0.037     .0008073    .0250941
 _IYear_2016 |   .0105147   .0077718     1.35   0.176    -.0047177    .0257472
 _IYear_2017 |   .0117376   .0088802     1.32   0.186    -.0056672    .0291425
 _IYear_2018 |   .0093856   .0092808     1.01   0.312    -.0088045    .0275757
 _IYear_2019 |   .0127532   .0084986     1.50   0.133    -.0039037    .0294101
 _IYear_2020 |  -.0065507    .009703    -0.68   0.500    -.0255682    .0124668
 _IYear_2021 |   .0123391   .0114671     1.08   0.282    -.0101359    .0348142
 _IYear_2022 |   .0127479   .0111066     1.15   0.251    -.0090207    .0345165
 _IYear_2023 |    .017355   .0100948     1.72   0.086    -.0024305    .0371405
       _cons |   .1711898   .0536629     3.19   0.001     .0660125    .2763671
-------------+----------------------------------------------------------------
     sigma_u |  .05618831
     sigma_e |     .03449
         rho |  .72632943   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(company)
Sargan-Hansen statistic 135.468  Chi-sq(12)   P-value = 0.0000

[Carlo Lazzaro]

Tracy:
yes, your interpretation is correct.
Then you have to stick with -xtreg,fe- without doing -hausman- again (by the way, if you need non-defaut standard errors, it is not correct to go -hausman- with default standard errors and then replace them with their non.default counterparts after -hausman- verdict).

[Tracy Chen]

Hi, Carlo, thank you so much!