Unbalanced panel data fixed effect regression (age and gender dependent variable)

[Jahan Ismat]

Dear stata experts,

I hope everyone is doing well.

I am trying to analyze the relationship between CEO age, Gender, and financial reporting quality (FRQ). I am investigating the relationship by including both CEO age and CEO gender as independent variable in the same model where FRQ is the dependent variable. I estimated OLS including Industry Fixed Effects and Year Fixed Effects. The co-efficient for both age and gender is positive and significant for the main analysis and a battery of additional analysis for alternative measures of FRQ. But when I include firm fixed effect instead of industry fixed effect, the co-efficient becomes insignificant/ and inconsistent between alternative measures of FRQ.

One colleague suggested using logit model for CEO gender, and using sample of observations from years around CEO change.

Please advise what may be the cause of such results and what can possibly be done to get consistent results, if any.

For your kind information, T= 20, N=15,000, Number of Firm =1,300 Number of CEOs= 2,900.

The example data is following

* Example generated by -dataex-. For more info, type help dataex
clear
input long gvkey double(fyear tenure age) float(acc_con FRQ1 FRQ2 fin) str6 gender float growth
1004 1994 2 64 .013411057 -.01445761 -.016000718 .01452747 "MALE" 10.702777
1013 1993 5 45 .031962927 -.0241131 -.028054986 0 "MALE" 15.678555
1013 1994 4 46 .04998015 -.02394609 -.028043434 0 "MALE" 22.56567
1034 1994 5 66 .011116134 -.03049344 -.01667558 .27759245 "MALE" 38.74079
1055 1993 2 42 .070407435 -.11691124 -.04107639 0 "MALE" 49.57965
1055 1994 1 43 .05772815 -.11715856 -.0616904 .10737058 "MALE" 67.636154
1078 1993 6 52 .007690612 -.015379924 -.010814613 .04156209 "MALE" 7.080198
1078 1994 3 53 .0045946483 -.015231054 -.010987644 .012655032 "MALE" 8.898433
1161 1993 5 57 -.01414187 -.031472735 -.07418257 .0030794654 "MALE" 8.834067
1161 1994 2 58 -.021501655 -.03203603 -.06765337 .017183205 "MALE" 29.50827
1203 1994 1 56 .029618626 -.01499509 -.018464886 .012009954 "MALE" 37.433224
1209 1993 1 58 -.010534966 -.04317003 -.01868584 .05802793 "MALE" 3.431447
1209 1994 8 59 -.01024618 -.04322805 -.019265603 .025336564 "MALE" 4.7360053
1213 1993 7 56 -.004830632 -.034713276 -.033446636 0 "MALE" 15.877007
1213 1994 1 57 -.004890278 -.029907364 -.037015453 .0435788 "MALE" 14.58028
1230 1993 2 51 -.02156891 -.01885471 -.036723576 .073747486 "MALE" 1.1611264
1230 1994 1 52 -.017615708 -.02071672 -.036124714 .0790411 "MALE" 16.598972
1239 1993 1 74 .005957008 -.04369544 -.02168542 .05336348 "MALE" 5.19607
1239 1994 10 42 -.003036958 -.04351002 -.02147372 .009465625 "MALE" 5.934635
1240 1993 2 53 -.00747036 -.006110306 -.006830883 .07650471 "MALE" 10.910533
1240 1994 8 54 -.007783341 -.006318838 -.006808233 .008235846 "MALE" 5.414398
1243 1993 1 64 .007643901 -.01943049 -.018918635 .04220184 "MALE" -4.791996
1243 1994 6 47 .009993883 -.019494485 -.01931703 .03393733 "MALE" 13.606194
1254 1993 5 54 -.008314948 -.0235259 -.01498338 .04680045 "MALE" 31.61668
1254 1994 1 55 .0025703476 -.02380211 -.015753035 .016039006 "MALE" 23.20782
1281 1994 3 53 .03755007 -.018731136 -.01907864 0 "MALE" 18.326897
1300 1993 1 59 .005551617 -.033754118 -.0427384 .012097146 "MALE" -1.7854177
1300 1994 2 60 .013976213 -.035933506 -.04201439 .00061832 "MALE" 8.370677
1318 1994 7 57 .005905546 -.02642074 -.02026653 .0858917 "MALE" 26.456324
1356 1993 1 58 -.017036399 -.015539997 -.020128276 .0645 "MALE" -4.5893693
1356 1994 3 59 -.007621051 -.01529318 -.01886772 .0400625 "MALE" 9.368473
1359 1993 1 52 -.01908353 -.0353285 -.017224668 0 "MALE" -4.1098723
1359 1994 2 56 -.02041266 -.03547517 -.01744214 .4069658 "MALE" 18.715744
1372 1994 1 62 .02987902 -.016497795 -.1599977 0 "MALE" 22.10399
1392 1993 3 53 -.16459185 -.05125584 -.0549377 0 "MALE" -33.437263
1468 1993 6 54 .04606384 -.0092680175 -.011176224 .01247034 "MALE" 5.878594
1468 1994 10 55 .07297094 -.00992416 -.011045543 .017547315 "MALE" 5.591244
1478 1993 7 56 -.01029666 -.04210322 -.01988368 .032735065 "MALE" 5.476011
1478 1994 5 57 .011259664 -.04260417 -.01947458 .3986064 "MALE" 7.96358
1485 1993 2 64 .003382936 -.027342737 -.02338306 .03948744 "MALE" 4.997758
1485 1994 3 47 .011513405 -.028275266 -.023375256 .032351054 "MALE" 7.33621
1500 1994 1 53 .03912275 -.0306782 -.026986754 .05085216 "MALE" 26.326643
1533 1993 5 66 -.13091263 -.033014085 -.01854372 0 "MALE" -9.290528
1533 1994 3 67 -.16093872 -.032555066 -.02210931 0 "MALE" -10.525212
1543 1993 1 57 .007236285 -.02892241 -.02098217 .4562579 "MALE" 3.281221
1543 1994 2 58 .0015006282 -.0271884 -.01976661 .08855277 "MALE" 7.347172
1573 1993 6 46 .02321819 -.006236822 -.009950805 .01443536 "MALE" -1.5103563
1573 1994 1 47 .02568195 -.007725106 -.009926908 .07537439 "MALE" -2.176112
1587 1994 2 56 -.003257459 -.02397682 -.023035357 .07217398 "MALE" 7.345129
1598 1993 7 58 -.05253353 -.018448846 -.014669897 0 "MALE" -4.854134
1598 1994 1 59 -.04168556 -.018238805 -.016049441 .6096134 "MALE" 10.3482
1602 1993 5 58 -.002075554 -.0414236 -.02186679 .03005002 "MALE" 25.689886
1608 1994 6 60 .005315556 -.016698197 -.015609668 .018919285 "MALE" 16.718466
1609 1993 1 55 .005403719 -.007548312 -.006660404 .04609282 "MALE" .221519
1609 1994 5 56 .005422147 -.00700167 -.006490586 .014940646 "MALE" 2.8102305
1632 1993 3 59 .008193967 -.017593134 -.01603907 .11790854 "MALE" 17.451326
1632 1994 2 60 -.021119174 -.017529614 -.01599627 .0005944567 "MALE" 16.081642
1651 1993 3 59 -.002851426 -.02318044 -.02245915 0 "MALE" -2.531175
1651 1994 8 60 .032060675 -.02317815 -.02207526 0 "MALE" 29.626524
1655 1993 1 49 -.002706926 -.007599068 -.021033186 0 "MALE" -.8516766
1655 1994 2 50 -.009628813 -.007193484 -.02007553 0 "MALE" 10.700308
1661 1993 15 64 .04682803 -.0391083 -.0449363 .10999902 "MALE" 22.975056
1661 1994 8 65 .010503584 -.03740831 -.04505412 .0003532633 "MALE" 20.030285
1663 1993 2 56 -.020768566 -.008518427 -.010187315 .063343845 "MALE" .9794869
1663 1994 3 57 -.017010279 -.008511785 -.010707838 .016495556 "MALE" 4.7673697
1678 1993 2 71 -.0007349245 -.03924968 -.07645191 .1729608 "MALE" 9.46671
1678 1994 6 72 -.008750218 -.036414284 -.07194993 .11935943 "MALE" 16.101542
1686 1994 4 61 .05421029 -.009567019 -.016902126 .1393233 "MALE" 9.926294
1690 1993 1 54 -.0005384435 -.017170332 -.021260686 0 "MALE" 12.56483
1690 1994 1 51 .04814596 -.017739693 -.02544909 .05607566 "MALE" 15.191186
1704 1993 6 55 .04080482 -.02438253 -.0187445 .004914511 "MALE" 43.74121
1704 1994 5 56 .08200854 -.02493898 -.01862703 .0579057 "MALE" 53.67915
1722 1993 5 75 .012343374 -.009090712 -.011072364 .06027717 "MALE" 6.281319
1722 1994 6 76 .015124732 -.009157775 -.010944296 .0013720363 "MALE" 15.93061
1743 1994 1 54 .04216493 -.015524905 -.01144775 .19330633 "MALE" 8.763382
1755 1993 1 58 -.07493015 -.027585715 -.09116664 .065627135 "MALE" -19.75309
1755 1994 5 56 -.008476923 -.02952896 -.06928208 .007752338 "MALE" -13.60577
1762 1993 1 59 -.0289508 -.5080832 -1.906927 0 "MALE" -.9569397
1762 1994 5 53 -.033236474 -.4950471 -1.8890734 0 "MALE" 9.000559
1766 1993 1 54 -.00880902 -.01926175 -.014858779 0 "MALE" 16.726738
1766 1994 4 55 -.016598823 -.019477237 -.0164081 0 "MALE" 10.888645
1773 1993 7 52 .014554508 -.017431075 -.016635697 .05185998 "MALE" 56.36936
1773 1994 6 53 .06159448 -.017644696 -.016280554 .02512343 "MALE" 83.3595
1789 1993 3 59 .007127542 -.019053923 -.021647915 .12300976 "MALE" -9.01937
1789 1994 2 60 -.003746348 -.020484246 -.021882944 .034961145 "MALE" 17.017687
1794 1993 1 61 .003208979 -.04008762 -.025585845 .06142133 "MALE" .20072167
1794 1994 2 62 .012914873 -.04424621 -.023868106 .013241616 "MALE" -1.1070228
1848 1993 3 65 -.007173192 -.007174946 -.006254306 .05252365 "MALE" -1.7939782
1848 1994 2 66 -.0037506786 -.0071143 -.006333144 .05190734 "MALE" -12.53127
1849 1993 2 53 -.0226009 -.02776194 -.021665547 .035164423 "MALE" 22.44852
1849 1994 5 54 -.0204152 -.025128 -.021587146 .08424735 "MALE" 8.190647
1865 1993 1 58 .03848515 -.015646547 -.014545733 0 "MALE" 16.185265
1865 1994 2 59 .023734903 -.015853211 -.01426912 0 "MALE" 26.2795
1878 1993 6 45 -.04476048 -.02813105 -.020186406 0 "FEMALE" 13.868937
1878 1994 8 46 -.035700817 -.0286049 -.020080864 0 "FEMALE" 11.119124
1891 1993 2 64 -.007423002 -.03060707 -.02072413 0 "MALE" 14.573182
1891 1994 3 65 .011815777 -.0305058 -.020702455 0 "MALE" 11.045914
1913 1993 3 66 -.02111615 -.006276383 -.008573839 .06162294 "MALE" -.5413818
1913 1994 4 67 -.011529914 -.00640573 -.009197468 .05700187 "MALE" 9.506653
1919 1993 2 69 .02883697 -.015631061 -.016447838 0 "MALE" 27.228184
end

[Carlo Lazzaro]

Jahan:
an idea might be:

. xtset gvkey fyear

Panel variable: gvkey (unbalanced)
 Time variable: fyear, 1993 to 1994
         Delta: 1 unit

. encode gender, g(num_gender)

. xtreg FRQ1 i.num_gender i.fyear c.age##c.age growth acc_con , fe vce(cluster gvkey)
note: 2.num_gender omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =        100
Group variable: gvkey                           Number of groups  =         57

R-squared:                                      Obs per group:
     Within  = 0.0784                                         min =          1
     Between = 0.0133                                         avg =        1.8
     Overall = 0.0092                                         max =          2

                                                F(5,56)           =       3.36
corr(u_i, Xb) = -0.1140                         Prob > F          =     0.0100

                                 (Std. err. adjusted for 57 clusters in gvkey)
------------------------------------------------------------------------------
             |               Robust
        FRQ1 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
  num_gender |
       MALE  |          0  (omitted)
             |
       fyear |
       1994  |   .0003788   .0003541     1.07   0.289    -.0003306    .0010881
             |
         age |  -.0012543    .001456    -0.86   0.393     -.004171    .0016625
             |
 c.age#c.age |   .0000107   .0000124     0.86   0.391    -.0000142    .0000357
             |
      growth |  -5.52e-06   .0000257    -0.21   0.831     -.000057     .000046
     acc_con |   -.027696   .0104838    -2.64   0.011    -.0486976   -.0066944
       _cons |   .0014356   .0418143     0.03   0.973    -.0823284    .0851996
-------------+----------------------------------------------------------------
     sigma_u |  .06549004
     sigma_e |  .00174614
         rho |   .9992896   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

[Jahan Ismat]

Dear Carlo,

Thank you for the kind response. But unfortunately, I did not get consistent coefficients.

Regards,
Ismat