time-invariant moderator (interaction) in quadric regression fe model

[louisa linkemeyer]

Hello everybody

I'm currently writing a paper about the effect of the Corporate Social Responsibility Score on the Return on Assets of firms. The main relationship is found to be inverted U-shaped. Now I want to investigate the influence of some moderators. One of them is the time-invariant variable consistency which describes the consistency of a firms CSR-action and is measured by the kurtosis of the firms CSR-Score over time, there fore consistency is the same for a firm in every year.
As we have a fixed effects model (suggested b Sargaa-Hansen-Test, used instead of Hausmann-Test because we have autocollinerarity in our data), we wondered how to investigate the moderating effect of consistency in pur quadric regression model. I found other forum-posts were was stated, that it doesn't matter if the moderator itself gets omitted because of collinearity as long as we got values for the moderating-effect/interaction effect.

The latest code looks like this:

xtreg roa c.csr_score##c.csr_score##c.consistency ln_firmsize ln_adi ln_rdi slack lev_w industry_growth industry_concentration i.fyear, fe cluster(cusipnr)

where:
roa = return on assets, dependent variable (time variant)
csr_score = CSR score, independent variable (time variant, continuous)
consistency= moderating variable (time-invariant, continuous)

we also inserted some control variables in our model which are the other variables.

with this code we get the following results:

is this model appropriate to investigate an interaction effects between a time variant and a time-invariant variable?

As we are hypothizing for a quadric (inverted u-shape) relationship, which row of interaction terms do we have to interpret? Obviously both are not statistically significant with very low coefficients, but it would be just nice to know which values have to be used for interpretation.


Hopefully there is somebody out there who can help out, we would be so thankful! If there is any needed information missing, please let me know.

Many thanks in advance,
Louisa

[Clyde Schechter]

Yes the code and results are appropriate to your model. Whether your model is fit for purpose is a substantive question, about which I lack the expertise to offer an opinion. But this is how you code the interaction between a continuous moderating variable and a quadratic continuous variable.

As for interpretation, because of the interaction you are not actually hypothesizing a quadratic relationship. You are hypothesizing many quadratic relationships between roa and csr_score, a different quadratic relationship for each value of the consistency variable. Interpreting such a model is fairly complicated and doing it from the regression output directly requires a lot of tedious and error-prone calculations. For that reason, I suggest you use the -margins- command. First you have to pick out series of values for the csr_score and consistency variables that span the interesting range of those variables. As I have no sense of how these variables run, let me assume that for csr_score a good set of values would be 0 10 20 30 40 50 and that for consistency a good set of values would be 2 4 6 8. Then after running your regression you would run

margins, at(consistency = (2(2)8) csr_score = (0(10)50))
marginsplot, xdimension(csr_score)

The table in the margins output and the graph from -marginsplot- will show you the expected values of roa as functions of csr_score, at the different values of consistency. It is often also helpful in this context to look at the marginal effects of csr_score conditional on csr_score and consistency. Those would be:

margins, dydx(csr_score) at(consistency = (2(2)8) csr_score = (0(10)50))
marginsplot, xdimension(csr_score)

[louisa linkemeyer]

Hello Clyde,

many thanks to you for your fast response! This helps a lot Do you know if there is any literature which states that it's appropriate to use a fe model with a time invariant moderating/interacting variable?

Thank you as well for the codes for the graphs, great! Unfortunately I tried the following (adjusted your code to our data)

margins, at(consistency = (-4(2)4) csr_score = (0(20)80))
marginsplot, xdimension(csr_score)

but state was not able to put the predicted values out, as you can see here:

do you have any idea what could have gone wrong? (Of course I ran the regression directly before using the margins code)

I tried the code with another regression using a time variant moderator and it worked pretty good.

Very thankful for any help Best regards

[Clyde Schechter]

To try to diagnose the non-estimability problem you are encountering, I need to see example data (use the -dataex- command for that) as well as the exact regression command and the exact and complete regression output you got. If you are running version 17, 16 or a fully updated version 15.1 or 14.2, -dataex- is already part of your official Stata installation. If not, run -ssc install dataex- to get it. Either way, run -help dataex- to read the simple instructions for using it. -dataex- will save you time; it is easier and quicker than typing out tables. It includes complete information about aspects of the data that are often critical to answering your question but cannot be seen from tabular displays or screenshots. It also makes it possible for those who want to help you to create a faithful representation of your example to try out their code, which in turn makes it more likely that their answer will actually work in your data.

I can't think of any references that talk about the acceptability of such models. There are plenty of papers out there using them. In fact just about any paper that looks at effect moderation in panel data will have done this. I'm sure you can find several of those in your field easily.

[louisa linkemeyer]

Hello again and thank you for the answer, so I tried to prepare some example data and the regression, I hope this is sufficient.

We have a panel data set with different firms (cusipnr) and years. roa is the variable for return on assets, csr_pace, relatedness and consistency are the moderating variables which we would like to investigate. The other variables are the control variables.

* Example generated by -dataex-. For more info, type help dataex
clear
input long cusipnr int fyear float(roa csr_score csr_pace relatedness consistency ln_firmsize ln_rdi ln_adi slack lev_w industry_growth industry_concentration)
 2 2015    .19638057  17.06594          .   4.316243   2.736909  5.450412  -3.435509  -5.275619          0          0  .8972727  .5207492
 2 2016    .20806924 18.633266          .   4.316243   2.736909  5.547246  -3.062339  -5.214351          0          0 1.0325423  .4491171
 2 2017    .18363097 19.130655          .   4.316243   2.736909  5.692991  -3.128042  -5.141984          0          0 1.0667765  .4664789
 2 2018    .13813242 24.212416   5.935795   4.316243   2.736909  5.730739 -3.1280496  -6.002548          0          0 1.0312803  .4377039
 5 2015    .04397461  50.32922 -16.514132   4.810818 -2.1841028  7.577327 -4.5815945  -2.782363   .3688441  1.2396765         .         1
 5 2016    .04625817  54.46924          .   4.810818 -2.1841028  7.632643  -4.588121 -2.9312544   .3040446   .9823621  1.030919         1
 5 2017    .04705083  57.19421          .   4.810818 -2.1841028  7.937053  -4.780053  -3.193862   .3176735  1.2044955 1.2515575         1
 5 2018    .03829314  69.11864          .   4.810818 -2.1841028  7.932506 -4.7628202  -3.273795   .3025409   1.117513  .9961001         1
 5 2019    .03829879 74.217224   13.95653   4.810818 -2.1841028  7.933295  -4.851385  -3.344254   .3109087  1.1916764 1.0074697         1
 5 2020   .020336537  73.47199   8.916965   4.810818 -2.1841028   8.02247  -5.041852  -3.427351   .3710106  1.6563888  .8463466         1
 5 2021   .032963477  73.92408   7.917933   4.810818 -2.1841028  8.036347  -4.755436   -3.27076   .3374308   1.284112 1.2235985         1
 8 2017    -.4051047 12.490838          .          .  1.7463065 4.6823072  -2.852931  -5.193133  .39780965  1.0654055 1.6981722  .1915441
 8 2018     -.739716  14.49408          .          .  1.7463065  4.487242  -3.119621  -4.710386   .4972546  2.2369246  1.307601  .2294221
 8 2019    -.3798774 14.745724  1.1204895          .  1.7463065  4.844903 -3.9930444  -4.844903   .6648858   3.234834  1.304022 .22279187
 8 2020    -.3647513 13.859795 -.05041949          .  1.7463065  5.335965 -3.5598266  -5.240654   .4685395  1.1067435 1.2673837 .24075544
 8 2021   -.25935647 13.890784          .          .  1.7463065  5.621317 -4.3276863  -5.284845   .3704177   .7290346 1.2333057    .39117
14 2007     .0514454 12.221898  -42.10529  4.1329384  3.1969914  8.473784  -3.431005 -4.5129714  .06142953   .3410671 1.1477077   .418588
14 2010     .0405562  31.85556          .  4.1329384  3.1969914  8.600965 -3.2091565 -4.6231537  .08148026  .27008727         .  .4025807
14 2011    .08037535  41.66358 -11.722534  4.1329384  3.1969914   8.88975  -3.270799 -4.6955595  .19424845   .4907185 1.1772008  .4139956
14 2012   .067613766  54.56546  -5.312147  4.1329384  3.1969914  8.951803 -3.1925855  -4.777415   .1341138    .371403 1.0797285  .4252602
14 2013    .07076836  54.83744   15.31076  4.1329384  3.1969914  9.040595  -3.172995  -4.937952   .1112125    .311755 1.0878597   .411657
14 2014     .0554902  51.78242   2.834122  4.1329384  3.1969914  8.908681  -3.088598  -4.817676  .13488555   .3166304  .9550692   .417706
14 2015    .04097642  49.42811          .  4.1329384  3.1969914 8.7797575  -3.137141  -4.849895  .14286374   .4351196  .8619233  .4121684
14 2016   .022334134  50.15047  -2.856758  4.1329384  3.1969914  8.877438 -3.1867404  -5.031555  .22459684   .6107128 1.0579144  .3479807
14 2017   .023382716  56.62341   8.602795  4.1329384  3.1969914  8.983653  -3.205691  -5.231799  .20298053   .5655862 1.1066555  .3452723
14 2018    .03743575  50.61585 -.18208694  4.1329384  3.1969914  8.939371   -3.06669  -5.194584  .16722177   .4976304 1.1307391 .54856783
14 2019   .016134644  56.16477   4.390232  4.1329384  3.1969914  8.956699  -3.117803  -5.211912   .1742851   .5440465 1.0503434 .56095743
14 2020    .05022224  56.20768  3.3555744  4.1329384  3.1969914  9.048315  -3.211752  -5.235008  .16373086   .6035571  .9805646  .5339019
14 2021    .09769008  74.03995          .  4.1329384  3.1969914  9.125011  -3.119151   -5.13233   .1669226   .4893879 1.2536585  .6083341
23 2016 -.0010018456   25.9221          .          . -.28325605  7.815379   -5.06478  -5.018098   .3895032  1.0557926 1.2824277  .1739138
23 2017   -.10750277  25.16907          .          . -.28325605  7.524689  -2.576908 -4.4023237   .3964325   .9296913 1.0908631  .1730324
23 2018   -.05594496  22.35269          .          . -.28325605  7.069414  -2.721125 -3.6749055  .22283468   .3793037   1.62485 .17692553
23 2019   -.59105796 18.387827  -6.093458          . -.28325605  6.673585 -1.7340232 -2.6976485   .3751452  1.0753567 1.3181446  .1778406
33 2016    .04442384 28.129354   8.567928 -1.5388618   -.303599  5.688726 -2.6636295  -.4065384   .1590433   .3254599  1.233927 .16190542
33 2017  -.070279196  24.18009   7.307666 -1.5388618   -.303599  7.291153  -3.421892  -1.648183   .1774114  .27671626 1.2767423 .15090197
33 2018    .04276374 17.196304          . -1.5388618   -.303599  7.499991  -3.386776  -1.686757  .13605218   .1978276 1.2535667  .1441372
33 2019   .018124895 15.264187          . -1.5388618   -.303599  7.560919  -3.398916 -1.3782147   .1828263  .28784028 1.2603662  .1474435
33 2020   -.00265309  18.15678          . -1.5388618   -.303599  7.769878 -3.5386305 -1.5803823   .3445056   .6535868 1.1554825 .15121265
33 2021  -.035508953     19.24    .359808 -1.5388618   -.303599   7.60596 -3.3442245 -1.2844726  .29001695   .5288762 1.2179762 .24604855
34 2010   -.26415285  31.76407          .   2.793515  -2.123696  7.993721 -4.2584352  -3.620483 .017182596  .03764922         .  .3455047
34 2011  .0046371683   49.0158          .   2.793515  -2.123696  7.946264  -3.904968 -3.6037576  .02343363   .0509988  1.265931  .3267821
34 2012       .37479  39.18911  -3.914822   2.793515  -2.123696   7.93641  -4.134202  -3.484391  .02012655  .04952995 1.1824448  .2841207
34 2013   .030971376   37.0914  -2.736967   2.793515  -2.123696  8.000819  -4.297051  -3.880157  .01883757  .04927434 1.1625855 .24832855
34 2014   .036336284  48.53192          .   2.793515  -2.123696  8.148041 -4.5210366  -4.242036  .11502632   .1891677  1.198014  .2193918
36 2017  -.063374825  21.70317          .  -1.936413  1.3215555  5.827253 -3.8957314  -5.296625   .3642219  1.1088784         .  .6969197
36 2018   .026118876 27.356094   3.058881  -1.936413  1.3215555   5.82811 -3.6998785  -5.086173   .3092583    .906772  .9799531   .710729
36 2019   .008302194  26.38933          .  -1.936413  1.3215555  5.894835  -3.664821  -5.307049   .3478991  1.0774859 1.0995514  .6599063
36 2020    .01791349  27.25223  1.0707105  -1.936413  1.3215555  5.844813  -3.898903  -6.201488   .3278157   .9680838  .6197662  .7445267
36 2021   .028219223 24.799137          .  -1.936413  1.3215555   5.78074  -3.924442  -6.291566  .27585888   .7444744  .9403766         1
40 2005   .032863658  38.51499  -27.69521   .5995823  1.1845474 11.888838  -7.021304  -5.189338  .17932186   .5589687  .8448224  .3364634
40 2006    .02718062 36.198936   -31.2052   .5995823  1.1845474 12.508523  -7.101351  -5.175499  .18498415  .51753503 1.2136565  .3446204
40 2007    .04335665  49.87153   -5.77181   .5995823  1.1845474 12.526865  -5.634224   -4.38655  .20771357  .55574816  1.522356  .5932505
40 2010    .07398468  67.79414  16.114553   .5995823  1.1845474 12.500562  -5.296412 -4.4978676   .2196411   .5926447         .  .5106827
40 2011    .01458882  69.01931          .   .5995823  1.1845474  12.50745  -5.419877 -4.7414575  .22674814   .6135747 1.0117916  .5129313
40 2012    .02667499    69.352   3.460953   .5995823  1.1845474 12.514715  -5.361663 -4.5388064  .24368103   .7561985   1.01422 .51748633
40 2013    .06569422 70.215576  12.860456   .5995823  1.1845474  12.53461  -5.229422 -4.4426765  .24943572   .8219545  .9830278  .5302172
40 2014   .021254726  66.51443 -1.3213755   .5995823  1.1845474 12.587344  -5.131467 -4.4941874   .2595747   .9501795  .9574131  .5604888
40 2015   .033141118  66.34599   2.721413   .5995823  1.1845474 12.905878   -5.47162 -4.7083387  .29432145  1.0283686 1.0473092  .5747091
40 2016    .03213305   59.5466          .   .5995823  1.1845474 12.908727  -5.500803 -4.6744275  .28151333  1.0030698 1.0354123  .5980662
40 2017    .06631434  61.76279  4.1198106   .5995823  1.1845474 13.003798   -5.68858  -4.768438  .28365874  1.1667247 1.0763835  .5703876
40 2018   .036419086  63.51772          .   .5995823  1.1845474 13.184143  -6.099079  -4.647147   .3125799   .9588025  .9928784  .8487262
40 2019   .025201706 66.652245  10.593143   .5995823  1.1845474 13.220703  -6.069218 -4.5012226   .3137987  1.0226955 1.0070066  .8545038
40 2020  -.009844777  67.80942    3.78154   .5995823  1.1845474 13.172602  -6.074226 -4.6060476   .3347091  1.1318154  .9886045  .8362852
55 2013    .14137955  43.46735   -33.2762   5.334289  2.3503118 10.281856 -2.2131393  -3.842505   .4894856  3.2776046 1.1086869 .26778266
55 2014    .06439903  59.38638  -5.682236   5.334289  2.3503118  10.22365 -2.0214405  -3.723862   .3835263   8.617106 1.3551962 .27578223
55 2015    .09696513  65.13353   6.844884   5.334289  2.3503118  10.87899  -2.481707 -4.3222117  .55117816   8.028137 1.1579565  .2917908
55 2016    .09006187  72.01221    12.4185   5.334289  2.3503118 11.098908  -2.672516  -4.460341  .55129427   7.946937 1.1767914 .20782527
55 2017     .0750007  75.92739          .   5.334289  2.3503118 11.167417  -2.590258  -4.426897   .4372757   7.331371 1.6981722  .1915441
55 2018    .09581817  72.02344   6.512732   5.334289  2.3503118 10.991241  -1.708301 -3.9881756   .5897358  -4.772674  1.307601  .2294221
55 2019    .08844751 75.811104          .   5.334289  2.3503118 11.397683  -2.574182 -4.3946176   .7094877  -8.209496  1.304022 .22279187
55 2020   .030657856  78.49215          .   5.334289  2.3503118  11.92215  -2.966057  -4.426608  .52061236   6.658229 1.2673837 .24075544
55 2021     .0787694  79.43053   9.707477   5.334289  2.3503118 11.894979  -2.902048  -4.245286   .4429294   5.034722 1.2333057    .39117
64 2019    .04552026 15.908957          .          .          .  6.581214 -1.7237304  -8.190653 .021798827 .034497246 1.1503124  .4509397
67 2016    -.4836346  16.96303 -13.794436          . -1.9045488  6.329994  -2.508727   -5.85999          0          0 1.1767914 .20782527
67 2017    -.7526619 25.688423  -8.847367          . -1.9045488   5.95196  -1.765537 -3.2046885          0          0 1.6981722  .1915441
67 2018    -.4538895  21.92274          .          . -1.9045488  6.291943  -1.765102  -2.608076          0          0  1.307601  .2294221
67 2019    -.3003883  44.66124   12.17288          . -1.9045488  6.663366  -1.912919 -3.0179164 .008121984  .01401017  1.304022 .22279187
67 2020    -.3597984  38.51894          .          . -1.9045488  6.662642  -1.258052  -2.728858  .05680947   .0790212 1.2673837 .24075544
67 2021    -.2397725 37.023396          .          . -1.9045488  6.551255  -1.440961  -2.818358  .08016602   .1191176 1.2333057    .39117
77 2017   -.07277151  30.92537          .  1.9133438 -2.4441466  6.007495 -2.0970535  -6.923786  .12682058  3.5366514  1.170393  .7551558
77 2018  -.063103504  38.66709   5.914056  1.9133438 -2.4441466  5.936816 -1.8893706  -6.853106   .3460989   2.695283 1.1532891  .6842193
77 2019   -.03749592  31.05715          .  1.9133438 -2.4441466  6.082632 -2.0485153  -6.775779   .3647899   3.205149  1.242983  .6460786
77 2020   .007795456 36.018578   .6849728  1.9133438 -2.4441466  6.196295 -2.2886019  -7.805733   .4348508   3.483995 1.0269183  .6816548
77 2021  -.013145233 36.276577          .  1.9133438 -2.4441466   6.17399 -2.2088246  -7.783428  .39043695   2.896674  1.313438   .580654
90 2006     .1689709  19.29672          .   4.723263  -1.049143  6.714515 -1.2070436  -2.418591          0          0  1.210701  .3403699
90 2007    .27885205  20.60276    -20.811   4.723263  -1.049143  6.805304  -.8525646  -2.510743          0          0 1.2524844  .3193658
90 2010    .03118007  23.12704   -9.11326   4.723263  -1.049143  9.503458 -3.0388694 -3.6983225          0          0         .  .3380032
90 2011    .08172027  18.78308          .   4.723263  -1.049143  9.493789  -3.022989  -3.656058          0          0 1.1470146  .3468503
90 2012     .0809155 11.309568 -35.164585   4.723263  -1.049143  9.560997  -3.157423  -3.579583          0          0 1.0281603  .4002011
90 2013   .072081074 32.784096    2.61755   4.723263  -1.049143  9.547669 -3.1777685  -3.553708    .333143   .7086983  1.003063   .381912
90 2014    .05662553 33.575905  -2.702307   4.723263  -1.049143  9.598727  -3.251338  -3.394169  .29323205   .5978156 1.0709003  .4399855
90 2015    .05848797  46.18123  13.039525   4.723263  -1.049143  9.632401  -3.161601  -3.372819  .26745787  .50557756 1.0281149  .4325918
90 2016    .05535182  43.18066  -9.348376   4.723263  -1.049143   9.76721 -2.9023616   -3.30418   .2800252    .535914 1.0903251  .3762313
90 2017   .014623956 36.320972   3.244347   4.723263  -1.049143  9.834566  -2.860087  -3.272122   .2351618   .4639611 1.1100184  .3464299
90 2018    .10165405  43.33405  13.431443   4.723263  -1.049143  9.788918  -2.784944  -3.341612   .1497617  .23518535  1.119816  .3838807
90 2019    .07573696  50.06056    7.95735   4.723263  -1.049143  9.895707  -2.989954 -3.5206826  .14537667  .23022257 1.0995812 .41853705
90 2020    .09507118   54.3444  19.494137   4.723263  -1.049143 10.047977   -3.00046  -3.433252    .165693  .25902772  1.068727  .4331855
90 2021    .10771871  61.34533          .   4.723263  -1.049143  10.12887  -2.930685 -3.5276384   .1524585  .22143303  1.127538  .4690302
92 2014    .08108482 17.136501 -37.909817   4.745368 -1.1800754  7.681607 -4.1177235  -5.093843   .1630921   .3039106         .         1
92 2015    .09141422  32.43112 -26.737314   4.745368 -1.1800754  7.795482  -4.079474  -5.310575  .14504445  .25911763 1.1308544         1
end
label values cusipnr cusipnr
label def cusipnr 2 "000360206", modify
label def cusipnr 5 "00081T108", modify
label def cusipnr 8 "000899104", modify
label def cusipnr 14 "001084102", modify
label def cusipnr 23 "00163U106", modify
label def cusipnr 33 "00183L102", modify
label def cusipnr 34 "00184X105", modify
label def cusipnr 36 "00191G103", modify
label def cusipnr 40 "00206R102", modify
label def cusipnr 55 "00287Y109", modify
label def cusipnr 64 "00401C108", modify
label def cusipnr 67 "004225108", modify
label def cusipnr 77 "004397105", modify
label def cusipnr 90 "00507V109", modify
label def cusipnr 92 "00508Y102", modify

 xtreg roa c.csr_score##c.csr_score##c.consistency ln_firmsize ln_adi ln_rdi slack lev_w industry_growth industry_concentrati
> on i.fyear, fe cluster(cusipnr)
note: consistency omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =      4,416
Group variable: cusipnr                         Number of groups  =        606

R-squared:                                      Obs per group:
     Within  = 0.0749                                         min =          3
     Between = 0.0713                                         avg =        7.3
     Overall = 0.0471                                         max =         16

                                                F(26,605)         =       4.40
corr(u_i, Xb) = -0.3013                         Prob > F          =     0.0000

                                                       (Std. err. adjusted for 606 clusters in cusipnr)
-------------------------------------------------------------------------------------------------------
                                      |               Robust
                                  roa | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------------------+----------------------------------------------------------------
                            csr_score |    .001772   .0005536     3.20   0.001     .0006847    .0028592
                                      |
              c.csr_score#c.csr_score |  -.0000184   5.17e-06    -3.56   0.000    -.0000286   -8.26e-06
                                      |
                          consistency |          0  (omitted)
                                      |
            c.csr_score#c.consistency |  -.0006745   .0002693    -2.50   0.013    -.0012034   -.0001455
                                      |
c.csr_score#c.csr_score#c.consistency |   7.38e-06   2.61e-06     2.83   0.005     2.26e-06    .0000125
                                      |
                          ln_firmsize |   -.003396   .0062653    -0.54   0.588    -.0157004    .0089084
                               ln_adi |  -.0045337    .005554    -0.82   0.415    -.0154412    .0063737
                               ln_rdi |  -.0487821    .008959    -5.45   0.000    -.0663766   -.0311876
                                slack |  -.1150484   .0319061    -3.61   0.000    -.1777086   -.0523881
                                lev_w |   .0001941   .0007528     0.26   0.797    -.0012842    .0016725
                      industry_growth |   .0269596   .0120662     2.23   0.026     .0032629    .0506563
               industry_concentration |  -.0014657   .0170921    -0.09   0.932    -.0350329    .0321014
                                      |
                                fyear |
                                2004  |   .0265101   .0091279     2.90   0.004     .0085839    .0444363
                                2005  |    .026324   .0113385     2.32   0.021     .0040564    .0485917
                                2006  |   .0292448   .0124297     2.35   0.019     .0048342    .0536555
                                2007  |   .0217059   .0125761     1.73   0.085    -.0029923     .046404
                                2011  |    .026565   .0137926     1.93   0.055    -.0005222    .0536521
                                2012  |   .0140146   .0139053     1.01   0.314     -.013294    .0413231
                                2013  |   .0177353   .0141622     1.25   0.211    -.0100778    .0455484
                                2014  |   .0227091   .0142315     1.60   0.111      -.00524    .0506581
                                2015  |   .0174202   .0148292     1.17   0.241    -.0117026    .0465431
                                2016  |   .0199863   .0148575     1.35   0.179    -.0091923    .0491649
                                2017  |   .0167473    .015588     1.07   0.283     -.013866    .0473605
                                2018  |   .0343683   .0159241     2.16   0.031     .0030951    .0656415
                                2019  |   .0268363     .01695     1.58   0.114    -.0064518    .0601243
                                2020  |   .0244969   .0181309     1.35   0.177    -.0111102    .0601041
                                2021  |    .046595   .0183382     2.54   0.011     .0105808    .0826092
                                      |
                                _cons |  -.1899549   .0600566    -3.16   0.002    -.3078996   -.0720102
--------------------------------------+----------------------------------------------------------------
                              sigma_u |   .1305783
                              sigma_e |  .08189417
                                  rho |  .71770186   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------------------

sum consistency

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
 consistency |      4,829   -.1423454    1.858059  -5.954534   5.746652

 sum csr_score

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
   csr_score |      4,850    42.64924     21.8346   .7918259   95.10387

[Clyde Schechter]

OK, it seems that -margins- is getting confused by the (appropriate) omission of consistency (which is time-invariant within cusipnr). And it is not colinear with anything else. By rephrasing the regression command slightly, you avoid this problem:

xtreg roa  c.csr_score##c.csr_score c.csr_score##c.csr_score#c.consistency ln_firmsize ln_adi ln_rdi ///
    slack lev_w industry_growth industry_concentration i.fyear, fe cluster(cusipnr)

This does not change the model: you are still modeling a quadratic relationship to csr_score moderated by consistency. But by avoiding the explicit omission of the consistency variable, you remove the stumbling block to running -margins-:

. margins, at(csr_score = (20(20)60) consistency = (-2(1)3))

Predictive margins                                          Number of obs = 92
Model VCE: Robust

Expression: Linear prediction, predict()
1._at:  csr_score   = 20
        consistency = -2
2._at:  csr_score   = 20
        consistency = -1
3._at:  csr_score   = 20
        consistency =  0
4._at:  csr_score   = 20
        consistency =  1
5._at:  csr_score   = 20
        consistency =  2
6._at:  csr_score   = 20
        consistency =  3
7._at:  csr_score   = 40
        consistency = -2
8._at:  csr_score   = 40
        consistency = -1
9._at:  csr_score   = 40
        consistency =  0
10._at: csr_score   = 40
        consistency =  1
11._at: csr_score   = 40
        consistency =  2
12._at: csr_score   = 40
        consistency =  3
13._at: csr_score   = 60
        consistency = -2
14._at: csr_score   = 60
        consistency = -1
15._at: csr_score   = 60
        consistency =  0
16._at: csr_score   = 60
        consistency =  1
17._at: csr_score   = 60
        consistency =  2
18._at: csr_score   = 60
        consistency =  3

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         _at |
          1  |  -.0431656    .063464    -0.68   0.496    -.1675529    .0812216
          2  |  -.0606716   .0525997    -1.15   0.249    -.1637652     .042422
          3  |  -.0781775   .0494046    -1.58   0.114    -.1750087    .0186536
          4  |  -.0956835   .0552261    -1.73   0.083    -.2039246    .0125577
          5  |  -.1131894   .0677795    -1.67   0.095    -.2460348     .019656
          6  |  -.1306954   .0841025    -1.55   0.120    -.2955333    .0341426
          7  |   .0710921    .090131     0.79   0.430    -.1055615    .2477456
          8  |    .049018   .0569692     0.86   0.390    -.0626397    .1606757
          9  |   .0269439    .025928     1.04   0.299    -.0238739    .0777618
         10  |   .0048699   .0200972     0.24   0.809    -.0345198    .0442596
         11  |  -.0172042   .0494004    -0.35   0.728    -.1140272    .0796189
         12  |  -.0392782   .0823516    -0.48   0.633    -.2006844    .1221279
         13  |   .0732546   .1101161     0.67   0.506    -.1425689    .2890782
         14  |   .0595503    .074591     0.80   0.425    -.0866454    .2057459
         15  |   .0458459   .0456096     1.01   0.315    -.0435472    .1352391
         16  |   .0321416   .0409246     0.79   0.432    -.0480691    .1123523
         17  |   .0184373   .0659361     0.28   0.780    -.1107951    .1476696
         18  |   .0047329   .1004911     0.05   0.962    -.1922261    .2016919
------------------------------------------------------------------------------

I don't know why this happens in this circumstance but not more generally.

[louisa linkemeyer]

thanks a lot, Clyde! It worked very good with this little adjustment