[Siegfried Fiegler]

Thank you! Does that mean i.Year in both FE and RE? In this case, the Hausman results that Random is better. Do you have a source on this approach?

What is the advantage of your proposed code over Hausman?

[Carlo Lazzaro]

Siegfried:
1) -hausman. test (Hausman, J. A. 1978. Specification tests in econometrics. Econometrica 46: 1251–1271. https://doi.org/10.2307/1913827.) compare the coefficients that are shared between the -fe- and the -re- estimator. I fail to get why -i.year- should be kicked out from the set of the preductors before running -hausman- (if that is what you mean): if you decide to include -i.year- in .fe- specif8cation only, the -hausman- machinery will simly not take it into account.
2) if your interested in the difference between -hausman- and the community-contributed module -xtoverid-, see the following toy-example:

. use https://www.stata-press.com/data/r17/nlswork.dta
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtset idcode year

Panel variable: idcode (unbalanced)
 Time variable: year, 68 to 88, but with gaps
         Delta: 1 unit

. quietly xtreg ln_wage c.age##c.age, vce(cluster idcode) fe

. estimates store fe

. quietly xtreg ln_wage c.age##c.age, vce(cluster idcode) re

. estimates store re

. hausman fe re ///-hausman- does not support non-default standard errors///
hausman cannot be used with vce(robust), vce(cluster cvar), or p-weighted data
r(198);

. quietly xtreg ln_wage c.age##c.age, vce(cluster idcode) re

. xtoverid ///-xtoverid- does not support -fvvarlist- notation///
cage#c:  operator invalid
r(198);

. g sq_age=age^2 ///this is the work-around that allows for squared term creation by hand ///


. quietly xtreg ln_wage age sq_age, vce(cluster idcode) re

. xtoverid ///-xtoverid- null: -re- is the way to go///

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(idcode)
Sargan-Hansen statistic  60.741  Chi-sq(2)    P-value = 0.0000
///-xtoverid- outcome points you out to -fe- specification///
.

[Siegfried Fiegler]

Wait

[Siegfried Fiegler]

xtreg ESGScore RELINT CENSUSPOPINT percentwhite percenturbanipol age_int repint TOTALASSETS RETURNONASSETS TOTALDEBTTOTALCAPITALSTD MRKTVALUETOBOOK TobinsQ i.Year, fe
estimates store fixed
xtreg ESGScore RELINT CENSUSPOPINT percentwhite percenturbanipol age_int repint TOTALASSETS RETURNONASSETS TOTALDEBTTOTALCAPITALSTD MRKTVALUETOBOOK TobinsQ i.Year, re
hausman fixed

. hausman fixed

Note: the rank of the differenced variance matrix (24) does not equal the number
        of coefficients being tested (29); be sure this is what you expect, or
        there may be problems computing the test.  Examine the output of your
        estimators for anything unexpected and possibly consider scaling your
        variables so that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed          .          Difference          S.E.
-------------+----------------------------------------------------------------
      RELINT |     8.27648    -2.663957        10.94044        3.851563
CENSUSPOPINT |   -3.38e-07     3.93e-07       -7.32e-07        1.94e-06
percentwhite |    16.90004     1.686267        15.21377        6.523651
percenturb~l |   -20.07824     .3500672       -20.42831        12.17013
     age_int |   -.2138276     .0922228       -.3060504        .2647666
      repint |    4.309962      .264448        4.045514        2.040134
 TOTALASSETS |    2.27e-08     3.68e-08       -1.41e-08        2.16e-09
RETURNONAS~S |   -.0033905     .0053493       -.0087398        .0026836
TOTALDEBTT~D |   -.0085192     -.004429       -.0040902        .0012337
MRKTVALUET~K |     .002212     .0023169       -.0001049               .
     TobinsQ |   -.0101047    -.1598556        .1497509        .0480765
        Year |
       2003  |    .3960878     .1123887         .283699               .
       2004  |    4.095441      3.47511        .6203314        .1680503
       2005  |    7.673055     6.613837        1.059218        .2969452
       2006  |     8.95613     7.470588        1.485542        .4144061
       2007  |    17.22758     15.27563        1.951952        .5282034
       2008  |    22.26464     19.82632        2.438324        .6375119
       2009  |    24.94106     22.24356        2.697499         .734646
       2010  |    27.82836     24.76911        3.059246        .8328412
       2011  |    30.49884     27.11185        3.386993        .8976187
       2012  |    30.93711     27.24393        3.693177        .9601135
       2013  |    31.38636     27.39014        3.996225        1.036738
       2014  |    32.48303     28.16678        4.316251        1.115143
       2015  |    35.52905      30.8692        4.659848        1.188819
       2016  |    38.23312     33.19154        5.041581        1.266043
       2017  |    40.78256      35.4611        5.321459        1.335637
       2018  |    42.36351     36.58236         5.78115        1.405341
       2019  |    44.68547     38.58843        6.097047        1.479787
       2020  |    48.24414     41.76166        6.482482        1.557262
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                 chi2(24) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       68.14
                Prob>chi2 =      0.0000
                (V_b-V_B is not positive definite)

This is the result i get when using hausman!

[Carlo Lazzaro]

Siegfried:
with 568 panels default standard errors are, in all likelihood, misleading.
Go cluster-robust and then -xtoverid-.

[Siegfried Fiegler]

I do a lot of regressions. So I change dependent and independent variables. Do I have to test for each model separately, whether FE or RE? Basically I split the ESG score into E S and G. Additionally, am I looking at individual religion types in the US?

Do you think the insignificance issue with i.Year can come from the fact that my panel is unbalanced since I am considering the change in the S&P 500 in terms of constituents?

[Carlo Lazzaro]

Siegfried:
1) doing a lot of regressions hunting for significant predictors is not the way to go. Your regression should give a fair nad true view of the data generating process you're investigating.
2) you should apply the estimator that is consistent (and possibly efficient) with your dataset;
3) to test the joint significance of -i.year-, see -testparm-.

[Siegfried Fiegler]

Carlo:
Thank you!

[Siegfried Fiegler]

I don't understand why the Random Effects Tobit Model is not an option, since it takes into account that the ESG score can only range from 0-1?

[Carlo Lazzaro]

Siegfried_
is ESG censored from right and/or left?

[Siegfried Fiegler]

Yes it only ranges from 0 to one. The command xtoverid command doesnt work for me too.

2002b:  operator invalid

I always get this error message.

[Carlo Lazzaro]

Siegfried:
1) therefore, your variable is not censored. It simply varies between 0 and 1, bounds included.
2) the -xi:- prefix is the fix here (pun unintended ):

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xi: xtreg ln_wage i.race i.year, re vce(cluster idcode)
i.race            _Irace_1-3          (naturally coded; _Irace_1 omitted)
i.year            _Iyear_68-88        (naturally coded; _Iyear_68 omitted)

Random-effects GLS regression                   Number of obs     =     28,534
Group variable: idcode                          Number of groups  =      4,711

R-squared:                                      Obs per group:
     Within  = 0.1058                                         min =          1
     Between = 0.0975                                         avg =        6.1
     Overall = 0.0907                                         max =         15

                                                Wald chi2(16)     =    1321.80
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                             (Std. err. adjusted for 4,711 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    _Irace_2 |  -.1279049   .0127384   -10.04   0.000    -.1528717   -.1029381
    _Irace_3 |   .0900274   .0609305     1.48   0.140    -.0293942    .2094489
   _Iyear_69 |    .085839    .010195     8.42   0.000     .0658571    .1058209
   _Iyear_70 |   .0702121   .0103353     6.79   0.000     .0499553    .0904689
   _Iyear_71 |   .1200453   .0108527    11.06   0.000     .0987745    .1413161
   _Iyear_72 |   .1329282    .011754    11.31   0.000     .1098907    .1559657
   _Iyear_73 |   .1480458   .0117481    12.60   0.000     .1250199    .1710717
   _Iyear_75 |   .1615023   .0117297    13.77   0.000     .1385124    .1844921
   _Iyear_77 |   .2215681   .0121434    18.25   0.000     .1977674    .2453688
   _Iyear_78 |   .2603374   .0125917    20.68   0.000     .2356582    .2850166
   _Iyear_80 |   .2685209   .0128514    20.89   0.000     .2433326    .2937093
   _Iyear_82 |   .2858463    .012884    22.19   0.000      .260594    .3110985
   _Iyear_83 |   .3132819   .0134049    23.37   0.000     .2870088     .339555
   _Iyear_85 |   .3656784   .0129719    28.19   0.000     .3402539    .3911028
   _Iyear_87 |   .3814745   .0133834    28.50   0.000     .3552436    .4077054
   _Iyear_88 |   .4370321   .0144939    30.15   0.000     .4086246    .4654395
       _cons |     1.4612   .0106163   137.64   0.000     1.440393    1.482008
-------------+----------------------------------------------------------------
     sigma_u |  .36492114
     sigma_e |  .30294584
         rho |  .59200363   (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(idcode)
Sargan-Hansen statistic  75.575  Chi-sq(14)   P-value = 0.0000

.