Religiosity

[Siegfried Fiegler]

Hello all,
I am investigating the effects of religiosity on corporate ESG scores. The dependent variable is the ESG score and the independent variable is a percentage of church followers in the county where the company is located. My problem is that, according to my supervisor, I need to integrate time-fixed effects to be able to factor out the change over time in the coefficient for religion. However, as soon as I use xtreg in conjunction with i.Year, all my explanatory variables become insignificant. Is it possible that the question is such that I only need to calculate time fixed effects but not entity fixed effects?

[Carlo Lazzaro]

Siegfied:
as you're surely aware of, the FAQ the recommend to share what you typed and what Stata gave you back. This laudable habit help interested listers to reply more positively. Thanks.
That said, when you go -xtreg,fe- adding -i.timevar- in the right-hand side of your regression equation is the way to go.
Please, be also advised that -xtreg,fe- focusses on the within-panel variation; hence, if your time-varying variables do not change that much as time goes by (say, if the panel-specific percentage of church attendance is basically the same), no wonder that -i.timevar- predates their statistical significance.
Last but by no means least, please consider that the main goal of each and every regression is to give a fair and true view of the data generating process you're investigating: non-significant coefficients are as informative as your significant counterparts.

[Siegfried Fiegler]

Thank you Carlo! I try to use dataex. The point is religious adherence changes over time and time variable is significant but all other variables get insignificant except for the case i use reg instead of xtreg. How can i show regression output using dataex?

[Siegfried Fiegler]

Another point is: When i substract in every year the mean religiosity in whole US from religiosity and take it ^2. Then this variable gets significant. Is this a sign for a u shaped relation?

[Siegfried Fiegler]

* Example generated by -dataex-. To install: ssc install dataex
clear
input float Year str47 NAME long ISIN double(RELINT ESGScore)
2006 "ARCHER DANIELS MIDLAND" 56 .6740355253219548 28.96
2006 "PTC" 430 .6863699913024846 36.63
2006 "MOLSON COORS BEVERAGE COMPANY B" 383 .3718380689620968 7.8
2006 "DILLARDS 'A'" 176 .6883617877960262 21.33
2006 "UNITED PARCEL SER.'B'" 571 .7795824527740507 46.3
2006 "ODP" 543 .4940392076969147 40.97
2006 "BAKER HUGHES A" 68 .6095748662948601 12.84
2006 "WHOLE FOODS MARKET DEAD - DELIST.29/08/17" 605 .4973936140537276 23.11
2006 "BARR PHARMACEUTICALS DEAD - DELIST.02/01/09" 71 .732740628719327 18.39
2006 "EBAY" 196 .4595679044723511 44.63
2006 "MONSANTO DEAD - DELIST.07/06/18" 385 .6022433519363375 39.78
2006 "AFFILIATED CMP.SVS.'A' DEAD - DELIST.18/02/10" 17 .6564605951309233 57.11
2006 "HESS" 273 .6218161702155953 52.1
2006 "APOLLO EDUCATION GP.'A' DEAD - DELIST.02/02/17" 51 .4155288815498359 10.87
2006 "AMAZON.COM" 36 .39777146577835154 19.38
2006 "PACCAR" 431 .39777146577835154 24.03
2006 "HP" 261 .4595679044723511 87.41
2006 "REYNOLDS AMERICAN DEAD - DELIST.25/07/17" 474 .5980128288269029 25.56
2006 "EMC DEAD - DELIST.07/09/16" 193 .702066624164587 44.23
2006 "WINDSTREAM HOLDINGS DEAD - DELIST.22/09/20" 606 .6883617877960262 36.33
2006 "EMBARQ DEAD - DELIST.13/07/09" 201 .5553025841712955 29.97
2006 "COMPUWARE DEAD - DELIST.16/12/14" 144 .5004290163517027 48.7
2006 "AIR PRDS.& CHEMS." 19 .5635939002037063 47.01
2006 "FAMILY DOLLAR STORES DEAD - DELIST.07/07/15" 217 .5774142026901217 40.46
2006 "TELLABS DEAD - DELIST.04/12/13" 534 .6954863190650933 19.98
2006 "ORACLE" 425 .46893423795700073 61.89
2006 "THERMO FISHER SCIENTIFIC" 544 .702066624164587 11.34
2006 "EASTMAN CHEMICAL" 195 .5682632923126221 29.73
2006 "HEALTH MAN.ASSOCS. DEAD - DELIST.27/01/14" 268 .3753322184085839 20.64
2006 "HOSPIRA DEAD - DELIST.03/09/15" 281 .5989710807800321 23.71
2006 "JONES GROUP DEAD - DELIST.09/04/14" 309 .6218161702155953 24.3
2006 "PROCTER & GAMBLE" 454 .5749150156974778 55.57
2006 "MEDCO HEALTH SLTN. DEAD - T/OVER 02/04/12" 372 .732740628719327 42.38
2006 "CONSTELLATION BRANDS 'A'" 149 .4599243640899644 19.71
2006 "CARDINAL HEALTH" 114 .43331772685051106 31.96
2006 "NEWMONT" 404 .36913568973541544 66.45
2006 "BEMIS DEAD - DELIST.11/06/19" 80 .5523081481456771 26.29
2006 "STANLEY BLACK & DECKER" 513 .5744977653026524 23.12
2006 "D R HORTON" 161 .5876270413398714 30.91
2006 "NETAPP" 399 .4595679044723511 9.63
2006 "LOWE'S COMPANIES" 347 .5503865838050857 29.07
2006 "MEADWESTVACO DEAD - DELIST.02/07/15" 371 .8513031959533635 15.87
2006 "TARGET" 530 .5987061023712172 72.26
2006 "SNAP-ON" 507 .4440478861331911 17.2
2006 "LOCKHEED MARTIN" 344 .5004644095897675 38.5
2006 "MOODY'S" 388 .6218161702155953 32.28
2006 "PPG INDUSTRIES" 428 .7110529899597111 30.76
2006 "MOLEX DEAD - ACQD.BY 322739" 382 .6954863190650933 22.36
2006 "VULCAN MATERIALS" 592 .47570566534996317 23.68
2006 "KLA" 312 .4595679044723511 16
2006 "KATE SPADE & COMPANY DEAD - DELIST.12/07/17" 314 .6218161702155953 19.06
2006 "UNIVISION COMMS.'A' DEAD - DELIST.09/04/07" 575 .5995135068893376 13.6
2006 "MICROSOFT" 377 .39777146577835154 50.51
2006 "BURL.NTHN.SANTA FE C DEAD - DELIST.26/02/10" 99 .5876270413398714 .
2006 "COGNIZANT TECH.SLTN.'A'" 141 .732740628719327 45.23
2006 "BROADCOM 'A' DEAD - ACQD.SEE 54332K" 94 .47703648805618215 29.02
2006 "MICRON TECHNOLOGY" 379 .45500667095184255 32.95
2006 "BAUSCH & LOMB DEAD - MERGER" 73 .5441095590591374 15.28
2006 "DELL DEAD - DELIST.30/10/13" 168 .4083368837833419 77.45
2006 "ITT" 288 .7135865569114657 51.66
2006 "SIGMA ALDRICH DEAD - DELIST.19/11/15" 502 .567097985744482 27.16
2006 "OMNICOM GROUP" 424 .6218161702155953 36.43
2006 "NOVELLUS SYSTEMS DEAD - ACQD.BY 946387" 415 .4595679044723511 22.52
2006 "FIDELITY NAT.INFO.SVS." 221 .5782214641571031 16.77
2006 "ILLINOIS TOOL WORKS" 291 .6740355253219548 22.77
2006 "HARMAN INTL.INDS. DEAD - DELIST.13/03/17" 265 .7135865569114657 12.79
2006 "VIATRIS" 589 .5695936858653994 25.28
2006 "IMS HEALTH DEAD - DELIST.08/03/10" 287 .7135865569114657 13.13
2006 "HOME DEPOT" 278 .5605307817459106 42.57
2006 "PARAMOUNT GLOBAL B" 588 .6218161702155953 36.54
2006 "WYETH DEAD - DELIST.15/10/09" 610 .6145440578460679 26.5
2006 "ST.JUDE MEDICAL DEAD - DELIST.05/01/17" 487 .5897020101547241 27.3
2006 "CAMPBELL SOUP" 113 .6042627692222595 27.54
2006 "TERADYNE (XSC)" 538 .702066624164587 20.45
2006 "BIOMET DEAD - 26/09/07" 85 .37050684094429087 30.91
2006 "LSI DEAD - ACQD.BY 54332K" 329 .4595679044723511 21.94
2006 "NEW YORK TIMES 'A'" 401 .6218161702155953 47.09
2006 "UNISYS" 569 .6797127842903166 45.8
2006 "SHERWIN-WILLIAMS" 500 .634991908073431 39.27
2006 "PEPSICO" 441 .7334323406219454 71.42
2006 "HILLSHIRE BRANDS DEAD - DELIST.28/08/14" 275 .6740355253219548 50.12
2006 "LABORATORY CORP.OF AM. HDG." 331 .46807627081871317 29.69
2006 "TEREX" 539 .7135865569114657 24.12
2006 "YUM! BRANDS" 616 .6073460578918457 19.64
2006 "DOVER" 185 .6954863190650933 19.3
2006 "MEREDITH DEAD - DELIST.02/12/21" 376 .49009158015250875 24.2
2006 "WALT DISNEY" 177 .5995135068893376 54.29
2006 "ALLTEL DEAD - MERGER" 29 .6883617877960262 8.72
2006 "ALLERGAN DEAD - DELIST.17/03/15" 27 .47703648805618215 30.21
2006 "FLUOR" 226 .6564605951309233 33.61
2006 "CORNING" 154 .4005899608135195 67.04
2006 "ANALOG DEVICES" 45 .702066624164587 43.14
2006 "SUPERVALU DEAD - DELIST.23/10/18" 522 .5987061023712172 13.06
2006 "GAP" 240 .4110478520393386 58.49
2006 "TRANE DEAD - MERGER" 554 .622551929950717 16.26
2006 "ELI LILLY" 341 .4701380908489199 45.54
2006 "SANMINA" 490 .4595679044723511 28.38
2006 "ELECTRONIC DATA SYSTEMS DEAD - DELIST.05/09/08" 200 .5605440616607638 27.35
2006 "STRYKER" 517 .3968753516674042 35.17
2006 "UST DEAD - DELIST.20/01/09" 564 .7135865569114657 15.

[Siegfried Fiegler]

(1)
VARIABLES ESGScore

RELINT -3.071
(2.667)
POPINT 1.48e-06
(1.67e-06)
age_int 0.216
(0.331)
repint 4.910
(3.603)
TOTALASSETS 2.13e-08***
(5.96e-09)
RETURNONASSETS 0.000731
(0.0188)
TOTALDEBTTOTALCAPITALSTD -0.00811*
(0.00471)
MRKTVALUETOBOOK 0.00233
(0.00199)
TobinsQ -0.00687
(0.148)
2003.Year 0.0420
(0.826)
2004.Year 3.400***
(0.834)
2005.Year 6.620***
(0.844)
2006.Year 7.565***
(0.885)
2007.Year 15.51***
(0.939)
2008.Year 20.22***
(1.000)
2009.Year 22.56***
(1.045)
2010.Year 25.17***
(1.106)
2011.Year 27.48***
(1.172)
2012.Year 27.55***
(1.231)
2013.Year 27.63***
(1.310)
2014.Year 28.32***
(1.392)
2015.Year 31.00***
(1.471)
2016.Year 33.36***
(1.556)
2017.Year 35.58***
(1.641)
2018.Year 36.83***
(1.727)
2019.Year 38.85***
(1.810)
2020.Year 42.04***
(1.905)
Constant 14.33
(11.75)

Observations 6,162
Number of ISIN 568
R-squared 0.598
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1

[Carlo Lazzaro]

Siegfried:
1) just press the #-shaped toggle available from the advanced editor.
Copy and paste Stata codes and out put in between.
2) the way you coded -regress- differs from -xtreg,fe-. Hence, the results differ too.
3) do you mean that you centered that variable around its mean, get the squared term, put them in the right-hand side of your regression equation? It's difficult to reply about a non-linear relationship without seeing your regression results and knowing the range of .religiosity.

[Siegfried Fiegler]

xtreg ESGScore RELINT POPINT age_int repint TOTALASSETS RETURNONASSETS TOTALDEBTTOTALCAPITALSTD MRKTVALUETOBOOK TobinsQ i.Year, fe

[Siegfried Fiegler]

Religiosity ranges from 0 to 100. It´s in percent.

Fixed-effects (within) regression               Number of obs     =      6,162
Group variable: ISIN                            Number of groups  =        568

R-sq:                                           Obs per group:
     within  = 0.5983                                         min =          1
     between = 0.1574                                         avg =       10.8
     overall = 0.2993                                         max =         19

                                                F(27,5567)        =     307.06
corr(u_i, Xb)  = -0.1051                        Prob > F          =     0.0000

------------------------------------------------------------------------------------------
                ESGScore |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
                  RELINT |  -3.070892   2.667061    -1.15   0.250    -8.299373    2.157589
                  POPINT |   1.48e-06   1.67e-06     0.89   0.375    -1.79e-06    4.75e-06
                 age_int |   .2161095     .33057     0.65   0.513    -.4319366    .8641556
                  repint |   4.909647   3.602801     1.36   0.173    -2.153249    11.97254
             TOTALASSETS |   2.13e-08   5.96e-09     3.57   0.000     9.60e-09    3.30e-08
          RETURNONASSETS |   .0007307   .0188066     0.04   0.969    -.0361375    .0375989
TOTALDEBTTOTALCAPITALSTD |   -.008105    .004712    -1.72   0.085    -.0173424    .0011324
         MRKTVALUETOBOOK |   .0023257   .0019906     1.17   0.243    -.0015766     .006228
                 TobinsQ |  -.0068682    .148204    -0.05   0.963    -.2974058    .2836694
                         |
                    Year |
                   2003  |   .0420041   .8259005     0.05   0.959    -1.577083    1.661091
                   2004  |   3.400249   .8337769     4.08   0.000     1.765721    5.034777
                   2005  |   6.620376    .843873     7.85   0.000     4.966056    8.274697
                   2006  |   7.564786   .8850379     8.55   0.000     5.829767    9.299806
                   2007  |   15.50584   .9394462    16.51   0.000     13.66416    17.34752
                   2008  |   20.22065   .9998844    20.22   0.000     18.26049    22.18082
                   2009  |   22.56212     1.0453    21.58   0.000     20.51293    24.61132
                   2010  |   25.17464   1.105956    22.76   0.000     23.00654    27.34275
                   2011  |   27.47555   1.171507    23.45   0.000     25.17894    29.77216
                   2012  |   27.55243   1.231247    22.38   0.000      25.1387    29.96615
                   2013  |   27.62574   1.310126    21.09   0.000     25.05738     30.1941
                   2014  |   28.31833   1.392489    20.34   0.000     25.58851    31.04815
                   2015  |   31.00481   1.471009    21.08   0.000     28.12106    33.88856
                   2016  |   33.35789   1.555701    21.44   0.000     30.30811    36.40767
                   2017  |   35.58137   1.641221    21.68   0.000     32.36393     38.7988
                   2018  |   36.82949   1.727129    21.32   0.000     33.44365    40.21534
                   2019  |   38.84809   1.810449    21.46   0.000      35.2989    42.39728
                   2020  |   42.04408   1.905038    22.07   0.000     38.30946     45.7787
                         |
                   _cons |   14.32956   11.74517     1.22   0.223    -8.695547    37.35467
-------------------------+----------------------------------------------------------------
                 sigma_u |  15.860316
                 sigma_e |  9.3066227
                     rho |  .74387126   (fraction of variance due to u_i)
------------------------------------------------------------------------------------------
F test that all u_i=0: F(567, 5567) = 26.43                  Prob > F = 0.0000

.
end of do-file

[Siegfried Fiegler]

. xtreg ESGScore DIFFREL2 POPINT age_int repint TOTALASSETS RETURNONASSETS TOTALDEBTTOTALCAPITA
> LSTD MRKTVALUETOBOOK TobinsQ i.Year, fe

Fixed-effects (within) regression               Number of obs     =      6,162
Group variable: ISIN                            Number of groups  =        568

R-sq:                                           Obs per group:
     within  = 0.5998                                         min =          1
     between = 0.1578                                         avg =       10.8
     overall = 0.2999                                         max =         19

                                                F(27,5567)        =     309.07
corr(u_i, Xb)  = -0.1018                        Prob > F          =     0.0000

------------------------------------------------------------------------------------------
                ESGScore |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
                DIFFREL2 |    49.3714   10.24404     4.82   0.000     29.28908    69.45372
                  POPINT |   8.46e-07   1.58e-06     0.54   0.591    -2.24e-06    3.94e-06
                 age_int |   .4250619   .3122881     1.36   0.174    -.1871447    1.037269
                  repint |     3.2753   3.572792     0.92   0.359    -3.728766    10.27937
             TOTALASSETS |   2.20e-08   5.94e-09     3.70   0.000     1.03e-08    3.36e-08
          RETURNONASSETS |   .0029361   .0187641     0.16   0.876    -.0338488     .039721
TOTALDEBTTOTALCAPITALSTD |    -.00806   .0046994    -1.72   0.086    -.0172726    .0011525
         MRKTVALUETOBOOK |   .0025693   .0019873     1.29   0.196    -.0013267    .0064652
                 TobinsQ |  -.0065889   .1477278    -0.04   0.964     -.296193    .2830153
                         |
                    Year |
                   2003  |   .1546286   .8213135     0.19   0.851    -1.455466    1.764723
                   2004  |   3.619247    .821888     4.40   0.000     2.008025    5.230468
                   2005  |    6.90843   .8142308     8.48   0.000      5.31222    8.504641
                   2006  |   7.923941   .8332297     9.51   0.000     6.290486    9.557397
                   2007  |   15.90518   .8611017    18.47   0.000     14.21709    17.59328
                   2008  |   20.67177   .8944356    23.11   0.000     18.91833    22.42521
                   2009  |   23.05079   .9089467    25.36   0.000      21.2689    24.83268
                   2010  |   25.70438   .9387952    27.38   0.000     23.86397    27.54478
                   2011  |   28.02793   .9729079    28.81   0.000     26.12065    29.93521
                   2012  |   28.12324   .9996285    28.13   0.000     26.16358     30.0829
                   2013  |   28.19005   1.040715    27.09   0.000     26.14984    30.23026
                   2014  |   28.84036   1.088021    26.51   0.000     26.70741     30.9733
                   2015  |   31.47424   1.134005    27.75   0.000     29.25115    33.69733
                   2016  |   33.75845   1.183719    28.52   0.000      31.4379      36.079
                   2017  |   35.89617   1.238919    28.97   0.000     33.46741    38.32494
                   2018  |   37.05779   1.294672    28.62   0.000     34.51973    39.59585
                   2019  |   38.99747   1.350448    28.88   0.000     36.35006    41.64488
                   2020  |   42.10428   1.415934    29.74   0.000      39.3285    44.88006
                         |
                   _cons |   5.690477   11.51416     0.49   0.621    -16.88176    28.26272
-------------------------+----------------------------------------------------------------
                 sigma_u |  15.859581
                 sigma_e |  9.2883735
                     rho |  .74460085   (fraction of variance due to u_i)
------------------------------------------------------------------------------------------
F test that all u_i=0: F(567, 5567) = 26.61                  Prob > F = 0.0000

. 
end of do-file

This is the regression with the squared centered values. Here, religiosity becomes significant again.

[Carlo Lazzaro]

Siegfried:
I would go:

 
 xtreg ESGScore c.RELINT##c.RELINT POPINT c.age_int##c.age_int repint TOTALASSETS RETURNONASSETS TOTALDEBTTOTALCAPITALSTD MRKTVALUETOBOOK TobinsQ i.Year, fe vce(cluster ISIN)

[Siegfried Fiegler]

. xtreg ESGScore c.RELINT##c.RELINT POPINT c.age_int##c.age_int repint TOTALASSETS RETURNONASSETS TOTALDEBTTOTALCAPITALSTD
>  MRKTVALUETOBOOK TobinsQ i.Year, fe vce(cluster ISIN)

Fixed-effects (within) regression               Number of obs     =      6,162
Group variable: ISIN                            Number of groups  =        568

R-sq:                                           Obs per group:
     within  = 0.6000                                         min =          1
     between = 0.1326                                         avg =       10.8
     overall = 0.2732                                         max =         19

                                                F(29,567)         =      62.80
corr(u_i, Xb)  = -0.1803                        Prob > F          =     0.0000

                                             (Std. Err. adjusted for 568 clusters in ISIN)
------------------------------------------------------------------------------------------
                         |               Robust
                ESGScore |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
                  RELINT |  -17.93297   12.80083    -1.40   0.162    -43.07581     7.20987
                         |
       c.RELINT#c.RELINT |    18.0052   12.37083     1.46   0.146     -6.29305    42.30345
                         |
                  POPINT |   2.77e-06   4.09e-06     0.68   0.499    -5.26e-06    .0000108
                 age_int |  -8.902095   5.500836    -1.62   0.106     -19.7066    1.902408
                         |
     c.age_int#c.age_int |   .1145074   .0678021     1.69   0.092    -.0186666    .2476814
                         |
                  repint |   1.511503   6.383629     0.24   0.813    -11.02694    14.04995
             TOTALASSETS |   2.21e-08   1.13e-08     1.96   0.050    -2.69e-11    4.42e-08
          RETURNONASSETS |   .0002761   .0252303     0.01   0.991    -.0492802    .0498324
TOTALDEBTTOTALCAPITALSTD |  -.0078834   .0060678    -1.30   0.194    -.0198014    .0040346
         MRKTVALUETOBOOK |   .0019899   .0021516     0.92   0.355    -.0022362     .006216
                 TobinsQ |   .0243825   .2681313     0.09   0.928    -.5022695    .5510344
                         |
                    Year |
                   2003  |    .348037   .5750812     0.61   0.545    -.7815126    1.477587
                   2004  |   3.997179   .7951492     5.03   0.000     2.435382    5.558977
                   2005  |   7.433529   1.100031     6.76   0.000     5.272895    9.594163
                   2006  |   8.567237   1.381236     6.20   0.000     5.854273     11.2802
                   2007  |     16.669   1.643766    10.14   0.000     13.44038    19.89761
                   2008  |   21.53212   1.885824    11.42   0.000     17.82807    25.23618
                   2009  |   24.04741   2.064466    11.65   0.000     19.99247    28.10234
                   2010  |   26.80872   2.218014    12.09   0.000     22.45219    31.16524
                   2011  |   29.24516   2.369133    12.34   0.000     24.59181    33.89851
                   2012  |   29.41056   2.549686    11.53   0.000     24.40258    34.41854
                   2013  |   29.51079   2.774377    10.64   0.000     24.06148     34.9601
                   2014  |   30.23087   2.963425    10.20   0.000     24.41024    36.05151
                   2015  |   32.90999   3.184169    10.34   0.000     26.65578    39.16419
                   2016  |    35.2343   3.378758    10.43   0.000     28.59789    41.87071
                   2017  |   37.41042   3.541114    10.56   0.000     30.45511    44.36572
                   2018  |   38.59678   3.769936    10.24   0.000     31.19203    46.00152
                   2019  |   40.53351   3.929018    10.32   0.000     32.81631    48.25072
                   2020  |   43.64094   4.125188    10.58   0.000     35.53843    51.74346
                         |
                   _cons |   194.0679   109.4649     1.77   0.077    -20.93833    409.0741
-------------------------+----------------------------------------------------------------
                 sigma_u |  16.485207
                 sigma_e |  9.2881619
                     rho |  .75904401   (fraction of variance due to u_i)
------------------------------------------------------------------------------------------

. 
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The problem is that since I install i.Year the RELINT is no longer significant and I would have needed exactly this result. The reason why I center and square is that this means that if the deviation is very high or very low, the ESG score also increases. That means low religiosity and high religiosity compared to the average leads to higher ESG scores.

Do I understand it correctly that when I include i.Year the trend over the years is taken out and the focus is really on the difference between the units of study then. The goal is to show that companies in counties with high religiosity achieve better ESG scores.

THANK YOU.

[Carlo Lazzaro]

Siegfied:
1) regardless of centering around the mean (or not), you should plug both the linear and the squared terms in the roght-hand side of your regression equation;
2) not quite. TH e-fe- estimator focusses on within-panel variation (that is within the same panel) as time goes by. As per your results, other things being equal, -timevar- seems to have a remarkable bearing on the variation of the conditional mean of the regressand.

[Siegfried Fiegler]

Thanks for your good answers. I still have three questions:
1. do you integrate i.Year into the Random and Fixed model when you run the Hausman test or do you leave i.Year out of it completely?
2. if I want to show that companies in religious counties have higher ESG scores, isn't Fixed Effects the wrong way to go since it cuts out differences between groups?
3. wouldn't a Tobit Random Effects Regression be the right way to include that the ESG score can only be between 0 and 1? Thanks in advance.

[Carlo Lazzaro]

Siegfried;
1) keep -i.year- in when running -hausman-. That said, you should switch from -hausman- to the community-contributed module -xtoverid- as you have non-default standard errors. Be also informed that -xtoverid- does not allow for -fvvarlist- notation (as it was shared before -fvvarlist- became a built-in Stata command); hence you should prefix your -xtreg- code with -xi-;
2) theoretically speaking, -re- ought to be your first choice. However, it depends on which estimator is the right one for your data. The -fe- estimator is consistent even if -re- is the way to go (but, in this case is less efficient); conversely, if -fe- is the way to go, the -re- estimator is inconsistent;
3) if your variable actually ranges between 0 and 1 (bounds included), there's no censoring and, as such, -tobit- has no role.