Omitted because of collinearity

[Henk Janssen]

Dear,

When using the following data

* Example generated by -dataex-. For more info, type help dataex
clear
input double ESGscore float(ESGcompensation tenure) double femaledummy float(independent boardsize newfirmage Democratic logsales roa_w logtobin_w leverage) double year
                 . .  .                  0 .8181818 11 43 1   7.37419  .05524752   .12475272  .10165016 2014
                 . .  .                  0 .8181818 11 44 1  7.416138    .094931 -.016281042  .10269745 2015
             24.84 0  . .08333333333333333 .8333333 12 45 1  7.477378  .09853068    .1741487  .10458081 2016
             23.81 0  . .08333333333333333 .8333333 12 46 1  7.466399  .08296714    .3389418  .11621959 2017
             22.62 0  0 .08333333333333333 .8333333 12 47 1  7.626473  .10117321   .08878828  .09339573 2018
             70.36 0  2 .09090909090909091 .9090909 11 77 0 10.621083  .18364143    .3576642   .4246824 2015
             70.27 0  3 .15384615384615385 .9230769 13 78 0 10.601125   .1527675    .3279516   .4747825 2016
             72.02 0  4 .15384615384615385 .9230769 13 79 0  10.65034  .13248113    .3400276   .4876839 2017
             69.36 0  5 .16666666666666666 .9166667 12 80 0 10.704165   .0925388    .2206872     .56172 2018
 71.34000000000002 0  6                 .2        0 10 81 0  10.73134  .10040837    .1878603   .5574465 2019
             63.25 1  .                 .2       .9 10 58 0  8.213719  .07676775   .21915583  .29520902 2018
             62.58 1  0 .18181818181818182        0 11 59 0  8.152258 .068340935     .225777   .3145051 2019
             77.27 0  . .36363636363636365 .8181818 11 81 1 10.217934  .09202623    .6417528   .3662164 2017
             72.39 0  .  .3333333333333333 .8333333 12 82 1 10.328036    .112575    .8903543  .29127774 2018
 65.69000000000001 0  .                 .1       .8 10 41 1   8.59822       .056    .2571971      .5105 2012
 65.79999999999998 0  .                 .1       .7 10 42 1 8.5752735  .05579894    .4196974  .47452155 2013
 63.76999999999999 0  0 .09090909090909091 .7272727 11 43 1  8.613594 .073798776    .4057164   .5872047 2014
             80.48 0  1                 .2       .6 10 44 1  8.291797  .04321077    .6225287   .7275651 2015
             71.73 0  2  .2222222222222222 .6666667  9 45 1  8.359838  .04321077   1.4030088   .4320988 2016
 69.35000000000001 0  3                .25      .75  8 46 1  8.580919  .06468926   1.2907536   .3940678 2017
             68.12 0  4  .2222222222222222 .7777778  9 47 1  8.775703  .12949955   1.5674034   .2743635 2018
             78.76 1  0 .16666666666666666 .9166667 12 54 0 9.2533045  .14402303     .765121     .34414 2014
 79.16999999999999 1  1                 .2       .9 10 55 0  9.199775  .16095217    .7700632  .33713534 2015
             73.57 1  2                .25     .875  8 56 0 9.1616125  .16982825    .8828155   .3447852 2016
             79.04 1  3                .25     .875  8 57 0  9.010376  .13681555    .8072674  .21458586 2017
 84.77999999999999 1  4                .25     .875  8 58 0  9.097194  .14923117    .8526819   .1987976 2018
                 . .  .  .2222222222222222 .8888889  9 49 1  8.251221  .14258662   .17025746   .3058247 2010
                 . .  .                 .3       .8 10 50 1 8.3705015  .14142445     .252262  .25156882 2011
                 . .  0                 .3       .8 10 51 1  8.446127  .14459582   .25676554  .18746594 2012
                 . .  1  .2727272727272727 .8181818 11 52 1  8.509967  .15690304   .41635615  .14919493 2013
                 . .  2                 .4       .9 10 53 1  8.588211   .1983498    .6560078  .12991425 2014
 55.67999999999999 0  3 .45454545454545453 .9090909 11 54 1  8.630165   .2525639    .7763644  .10500536 2015
             64.86 0  4 .45454545454545453 .9090909 11 55 1  8.687948  .18359767    .5901425  .29753062 2016
 60.86999999999999 0  5  .4444444444444444 .8888889  9 56 1  8.978786  .16294228    .4026812  .23919925 2017
             54.26 0  6 .45454545454545453 .9090909 11 57 1  9.019664  .10749634    .2950791   .1927236 2018
                 . .  .  .1111111111111111 .7777778  9 40 1  7.451241  .08765724    .2051185   .2197327 2011
                 . .  0                 .1       .8 10 41 1  7.352441  .14945073    .5058599  .27173635 2012
                 . .  1 .14285714285714285 .8571429  7 42 1  7.400743  .13658576    .4850742   .2291917 2013
                 . .  2 .14285714285714285 .8571429  7 43 1  7.446702  .14374375    .5901712  .26651448 2014
 34.88999999999999 0  3 .14285714285714285 .8571429  7 44 1   7.54163  .17541023    .6101473  .25745597 2015
              39.5 0  4 .14285714285714285 .8571429  7 45 1  7.571268  .11684445    .4182765   .3666088 2016
 37.67000000000001 0  5 .14285714285714285 .7142857  7 46 1  7.624082  .09757508   .23310487   .3813571 2017
39.300000000000004 0  6 .14285714285714285 .8571429  7 47 1  7.706523  .08998518    .2245757     .35237 2018
             50.32 0  7  .2857142857142857        0  7 48 1  7.697621  .07229212   .28666762   .4298165 2019
 66.64999999999999 1  .                .25 .9166667 12 92 0  10.57903  .15441585    .8198145  .29134193 2016
                67 1  0 .23076923076923078 .8461539 13 93 0 10.609897   .1555391    .9738825   .3011097 2017
 72.66999999999999 1  1                .25 .9166667 12 94 0   10.6407  .15354924    .8560433  .28065014 2018
 74.06999999999998 1  2                .25        0 12 95 0 10.510777  .14460029   1.0402052  .28471854 2019
 52.63999999999999 0  .                  0 .7777778  9 43 1   6.97714  .16074465    .9323655  .04778805 2010
             46.99 0  .                  0 .7777778  9 44 1  7.257653   .2039374    .6521157 .013800863 2011
48.730000000000004 0  .                  0 .7777778  9 45 1  7.357927   .1783866      .80136          0 2012
             47.07 0  .                  0      .75  8 46 1  7.491087  .19587673    .7419222          0 2013
             43.57 0  .               .125     .875  8 47 1  7.736962   .2333378    1.345916          0 2014
             47.31 0  .               .125     .875  8 48 1  8.088991  .29167736   1.4949583          0 2015
             41.54 0  0               .125     .875  8 49 1  8.098339  .29167736   1.3172176          0 2016
 55.72000000000001 0  1  .1111111111111111 .7777778  9 50 1  8.202866  .29167736   1.4328263          0 2017
             55.49 0  2  .1111111111111111 .7777778  9 51 1  8.260493  .29167736    1.248179          0 2018
 55.11000000000001 0  3  .2222222222222222        0  9 52 1  8.124683  .29167736   1.0762497          0 2019
 68.46000000000001 1 15 .07692307692307693 .7692308 13 49 1  10.43005  .17052774   .23008296   .1577297 2010
 73.16999999999999 1 16 .15384615384615385 .7692308 13 50 1  10.55753   .1661897  .020101056    .154768 2011
 69.93000000000004 1 17 .15384615384615385 .7692308 13 51 1 10.537177  .16677792  -.07162579    .186713 2012
             69.98 1 18 .10526315789473684 .9473684 19 52 1 10.011624   .1438228   .05197859  .13561304 2013
 74.15999999999998 1 19 .14285714285714285 .9285714 14 53 1  9.281451   .1422054 -.029052453  .15519208 2014
             76.76 1 20 .14285714285714285 .9285714 14 54 1  8.800264  .05588536  -.17600115    .193888 2015
 70.58000000000001 1 21 .18181818181818182 .9090909 11 55 1  8.468423  .04321077    .1664449  .23779742 2016
             77.38 1 22 .16666666666666666 .9166667 12 56 1  8.606302  .04321077    .1561371   .3018778 2017
 76.59000000000002 1 23 .16666666666666666 .9166667 12 57 1  8.751949  .11864881   .09665885   .3112957 2018
             78.64 1 24 .18181818181818182        0 11 58 1  8.778788  .12744468    .4281915   .3641539 2019
             44.99 0  0  .3333333333333333 .7777778  9 47 1  8.496541  .07093683    .2410163  .07349521 2015
 52.77999999999999 1  1                 .4       .9 10 48 1  8.545722  .07710854    .4223332  .11761354 2016
             64.86 1  2                 .3       .9 10 49 1  8.604032  .04490374    .3076631    .309028 2017
             62.92 1  3                 .3       .9 10 50 1  8.770625   .0836113   .14714135  .25885597 2018
             38.56 1  6               .125        0  8 36 0  6.530162  .06068184    .3098805   .3795676 2019
63.149999999999984 1  5                .25 .9166667 12 68 0  9.703822  .08566877   .19364943   .3509643 2016
 61.03999999999999 1  6                .25 .9166667 12 69 0  9.643739  .08386336    .2442706   .3570218 2017
 61.72000000000002 1  7                .25 .9166667 12 70 0  9.692501  .07303918   .23051265   .3712887 2018
                 . . 16                  0 .5555556  9 24 1  5.436426  .11913456    .2167348  .22050823 2010
                 . . 17  .1111111111111111 .7777778  9 25 1  5.718438  .14718068     .427489  .19572096 2011
                 . . 18               .125     .875  8 26 1  5.903152  .18160243    .9738351  .13114357 2012
                 . . 19               .125     .875  8 27 1  5.942854   .1570837    .6841882  .11564601 2013
                 . . 20  .1111111111111111 .8888889  9 28 1  5.699219   .0466808    .1498511  .21033834 2014
                 . . 21               .125      .75  8 29 1  5.667747   .0631241   .27523154  .15416007 2015
             19.42 0 22               .125     .875  8 30 1  5.743365  .08574598     .501839  .09524463 2016
19.710000000000004 0 23               .125     .875  8 31 1   5.87225  .08169091   .42095006  .14467356 2017
             21.23 0 24               .125     .875  8 32 1  6.118696  .08737051   .18997724  .16285902 2018
19.180000000000003 0  .               .125     .875  8 14 1  7.812359  .14534338    .7824795   .3059801 2010
             12.28 0  . .14285714285714285 .8571429  7 15 0     8.003  .16774504    .7361237  .29260954 2011
25.729999999999997 0  . .14285714285714285 .8571429  7 16 0  8.111992   .1640335     .821292  .28010777 2012
             29.59 0  .                .25     .875  8 17 0  8.187058   .1588553    .9790312   .2407432 2013
             32.43 0  .                .25     .875  8 18 0  8.299525  .16152874    .9056726   .2669422 2014
             33.37 0  .  .3333333333333333 .8888889  9 19 0  8.287602  .16411975    .8777345   .2914114 2015
             30.75 0  0               .375     .875  8 20 0   8.25325  .14184132    .7473257   .3297666 2016
24.979999999999997 0  1                 .3       .8 10 21 0   8.36641  .14399664    .9679301  .27889574 2017
             42.07 0  2               .375     .875  8 22 0  8.485883  .14719321    .8264899   .3039281 2018
 46.90999999999998 0  . .15384615384615385 .9230769 13 28 1  9.619332  .15195695   .48613095   .3072713 2010
 47.48000000000001 0  . .16666666666666666 .9166667 12 29 1  9.653872  .13017945    .5043692   .4384604 2011
 50.02999999999999 0  0 .14285714285714285 .8571429 14 30 1  9.756436  .12983903    .6149842   .4885815 2012
 67.06999999999996 0  1 .15384615384615385 .9230769 13 31 1  9.834994  .11457089    .6768623   .4858677 2013
 64.41999999999999 0  2 .16666666666666666 .9166667 12 32 1  9.906632  .12978017    .8677925   .4450869 2014
             68.27 0  3 .15384615384615385 .9230769 13 33 1  9.983315  .14964513     .840564    .440874 2015
end
format %ty year

And running the following commands:

-reg ESGscore c.ESGcompensation##c.tenure femaledummy independent boardsize newfirmage Democratic logsales roa_w logtobin_w leverage i.year, cluster(gvkey)
-reg ESGscore c.ESGcompensation##c.tenure femaledummy independent boardsize newfirmage Democratic logsales roa_w logtobin_w leverage i.year i.SIC, cluster(gvkey)
-xtreg ESGscore c.ESGcompensation##c.tenure femaledummy independent boardsize newfirmage Democratic logsales roa_w logtobin_w leverage i.year, fe vce(cluster gvkey)

With the last command, that includes firm fixed effects, the variable for the age of the firm (newfirmage) is dropped because of collinearity. What could be an explanation for this? Previously, when running a firm fixed effects regression using the firm age variable, this problem did not occur.

[Clyde Schechter]

Well, within any given firm, the firm age is colinear with year: age = year_of_founding - year, But age_of_founding is a fixed attribute of the firm, and so is colinaer with the fixed effects. Putting all of that together, you have a colinearity among age, i.year, and the firm fixed effects. So something has to go, and Stata chose to drop the age variable.

[Richard Williams]

Yes, age variables can be tricky. On the one hand, the value of age does vary across time. On the other hand, age at time t is perfectly correlated with age at time t-1 (assuming all cases are updated at the same interval, e.g. data is collected every year). This has screwed me up more than once.