How to test for reversed causality in a balanced panel dataset?

[Qi vd Kolk]

Hi all,

I have a balanced panel dataset and my independent variable is the overall ESG score of a firm and the dependent variable is financial performance measured with ROA and several accounting control variables such as firm size, cash, leverage, R&D and PPE. The literature that I follow does not use lagged variables to examine the relation between ESG and firm performance, but I do think that there may be reversed causality in this association.
I'm wondering how you can test for reverse causality between de independent and dependent variable, so that I know whether to use lagged variables or not?

I'm using Stata 17 on a macOS Catalina!

Below a sample of my data

* Example generated by -dataex-. For more info, type help dataex
clear
input str45 name int year str9 cusip double ESG_score float(ROA CASH_ net_ppe RandD)
"ANI PHARMACEUTICALS - ESG Combined Score"     2016 "00182C103" 19.25   12.184697  .08475705  .03406388   22.593336
"ANI PHARMACEUTICALS - ESG Combined Score"     2017 "00182C103" 21.63   -2.610776  .07556693  .04950526   .05128872
"ANI PHARMACEUTICALS - ESG Combined Score"     2018 "00182C103" 18.12  .035982016   .0998783  .08845714   .07633846
"ANI PHARMACEUTICALS - ESG Combined Score"     2019 "00182C103" 19.99   13.340952  .13645688  .08877403     .095891
"ANI PHARMACEUTICALS - ESG Combined Score"     2020 "00182C103" 21.78  -.04889091   17.05154  .08948373    .0767526
"ABBVIE - ESG Combined Score"                  2016 "00287Y109" 74.88    90.06187   77.15699   39.39545     178.095
"ABBVIE - ESG Combined Score"                  2017 "00287Y109" 70.79    75.00071  131.42429   39.59822     178.095
"ABBVIE - ESG Combined Score"                  2018 "00287Y109" 50.58    95.81817  122.80968    48.5746    .3283058
"ABBVIE - ESG Combined Score"                  2019 "00287Y109"  56.9    88.44751   .4480054  37.098133     178.095
"ABBVIE - ESG Combined Score"                  2020 "00287Y109" 48.59   30.657856    56.1153   40.79966   169.38232
"ACORDA THERAPEUTICS - ESG Combined Score"     2016 "00484M601" 23.68  -.02578939   .1181054  .02555994    .3915254
"ACORDA THERAPEUTICS - ESG Combined Score"     2017 "00484M601" 24.94  -.18644807   .2563238 .030609306    .7197542
"ACORDA THERAPEUTICS - ESG Combined Score"     2018 "00484M601" 27.45   .02591589   .2258765  .04656504    .2256588
"ACORDA THERAPEUTICS - ESG Combined Score"     2019 "00484M601"  37.7   -.3413278  .07763362   .2075444    .3122687
"ACORDA THERAPEUTICS - ESG Combined Score"     2020 "00484M601"  37.3  -1.5741607  .11280426   .0406904    .1774435
"ACTIVISION BLIZZARD - ESG Combined Score"     2016 "00507V109" 53.16    55.35182  174.81306  14.783406   .14497578
"ACTIVISION BLIZZARD - ESG Combined Score"     2017 "00507V109" 43.41   14.623956  174.81306  15.748875    .1523443
"ACTIVISION BLIZZARD - ESG Combined Score"     2018 "00507V109" 51.78   101.65405  174.81306  15.811606       .1468
"ACTIVISION BLIZZARD - ESG Combined Score"     2019 "00507V109" 59.86    75.73696  174.81306  24.439405   .15379873
"ACTIVISION BLIZZARD - ESG Combined Score"     2020 "00507V109" 35.62    95.07118  174.81306   19.55948   .14222112
"ACUITY BRANDS - ESG Combined Score"           2016 "00508Y102"  30.4   .09864315  .14016283  .09084125  .014310455
"ACUITY BRANDS - ESG Combined Score"           2017 "00508Y102" 41.05   .11094633  .10729066  .09922058  .014835525
"ACUITY BRANDS - ESG Combined Score"           2018 "00508Y102" 41.33   .11697003  .04319459  .09592479  .017363658
"ACUITY BRANDS - ESG Combined Score"           2019 "00508Y102" 62.56   .10414828  .14531586  .08741016   .02033926
"ACUITY BRANDS - ESG Combined Score"           2020 "00508Y102" 55.18   .07111149   .1605808  .09562677  .024652015
"ADTRAN - ESG Combined Score"                  2016 "00738A106" 52.79   .05279849  .11974042   330.9382 .0010180313
"ADTRAN - ESG Combined Score"                  2017 "00738A106" 47.36   .03563027  .12917916   330.9382   .19558254
"ADTRAN - ESG Combined Score"                  2018 "00738A106" 53.51  -.03079804  .16799277   330.9382   .23531535
"ADTRAN - ESG Combined Score"                  2019 "00738A106" 35.93  -.09719364    .135334  .15071966    .2380858
"ADTRAN - ESG Combined Score"                  2020 "00738A106" 50.83    4.523673  .11444437  .12880103    .2236619
"ADVANSIX - ESG Combined Score"                2016 "00773T101" 29.14   .03773328 .015690248   .6358037  .011549914
"ADVANSIX - ESG Combined Score"                2017 "00773T101" 47.45   .13967688  .05277861   .5832878 .0087534245
"ADVANSIX - ESG Combined Score"                2018 "00773T101" 48.11  .064027004   8.991655    .649713   .00970502
"ADVANSIX - ESG Combined Score"                2019 "00773T101" 51.71  .033453103 .009535838   .7215925  .010683325
"ADVANSIX - ESG Combined Score"                2020 "00773T101" 57.44   .03647043 .009328743   .6964921  .010190713
"ALSP.HLTHCR.SLTN. - ESG Combined Score"       2016 "01988P108" 29.78 -.006693877  .02521033   .0388319   .12123758
"ALSP.HLTHCR.SLTN. - ESG Combined Score"       2017 "01988P108" 31.17  -.04644256 .036840066  .03914826   .12191434
"ALSP.HLTHCR.SLTN. - ESG Combined Score"       2018 "01988P108" 37.03    .1143303  .05476784  .03831954    .1533799
"ALSP.HLTHCR.SLTN. - ESG Combined Score"       2019 "01988P108" 33.89  -.05682871  .04044871  .05813293   .14365429
"ALSP.HLTHCR.SLTN. - ESG Combined Score"       2020 "01988P108" 33.64   .24006124   .1820334  .05784274   .13712718
"ANSYS - ESG Combined Score"                   2016 "03662Q105" 53.66   .09485218  .29368734 .019523833   .18522963
"ANSYS - ESG Combined Score"                   2017 "03662Q105" 43.07   .08813196  .29966486 .019409694    .1851139
"ANSYS - ESG Combined Score"                   2018 "03662Q105" 45.86   .12840772  .23795088  .01887804   .18073244
"ANSYS - ESG Combined Score"                   2019 "03662Q105"  55.5   .09326421  .18022616  .03912201   .19672246
"ANSYS - ESG Combined Score"                   2020 "03662Q105" 55.52   .07303769   .1536332  .03942925   .21136717
"APPLIED OPTOELECTRONICS - ESG Combined Score" 2016 "03823U102" 17.54    .0969043  .15582126   .4470678    .1218965
"APPLIED OPTOELECTRONICS - ESG Combined Score" 2017 "03823U102" 17.98     1.63253  1.8308815   .4369757   .09249887
"APPLIED OPTOELECTRONICS - ESG Combined Score" 2018 "03823U102"    17   -4.596864  .11919715   .5016944    .1865777
"APPLIED OPTOELECTRONICS - ESG Combined Score" 2019 "03823U102" 17.91  -1.4148557  .12847856  .54909444   .22737227
"APPLIED OPTOELECTRONICS - ESG Combined Score" 2020 "03823U102"  17.1  -.12157112  .09031728  .54242575   .18494777
"AVANOS MEDICAL - ESG Combined Score"          2016 "05350V106" 52.43   .01921035  .05487981  .12588088   .02581172
"AVANOS MEDICAL - ESG Combined Score"          2017 "05350V106"  45.5  .036112756   .1000501  .05004781   .06245912
"AVANOS MEDICAL - ESG Combined Score"          2018 "05350V106" 53.75  .031362496  .20971964   .0840515  .064080946
"AVANOS MEDICAL - ESG Combined Score"          2019 "05350V106"  52.2  -.02550567   .1140809  .13808624   .05404243
"AVANOS MEDICAL - ESG Combined Score"          2020 "05350V106" 45.97 -.016260162  .06665471   .1336681   .04882485
"AXON ENTERPRISE - ESG Combined Score"         2016 "05464C101" 17.37   .06218296  .14614093  .08629473   .11410837
"AXON ENTERPRISE - ESG Combined Score"         2017 "05464C101"  25.5   15.400223  .22213054   .0921943    .1610626
"AXON ENTERPRISE - ESG Combined Score"         2018 "05464C101"  18.9   .04058843   .4856742  .05266281   .18296085
"AXON ENTERPRISE - ESG Combined Score"         2019 "05464C101" 18.83 .0010429983  .20369212  .06317471   .18973176
"AXON ENTERPRISE - ESG Combined Score"         2020 "05464C101" 29.11    -1.24835  .11255424  .09254155    .1809023
"BIOGEN - ESG Combined Score"                  2016 "09062X103" 73.86    .1618583  .10169692   .1093597    .1734243
"BIOGEN - ESG Combined Score"                  2017 "09062X103" 60.66   .10734972  .06653814  .13454758   .19338596
"BIOGEN - ESG Combined Score"                  2018 "09062X103" 80.09   .17520335  .04842441   .1424024   .21549258
"BIOGEN - ESG Combined Score"                  2019 "09062X103" 76.29   .22679043   .1122186  .14151245   .17363453
"BIOGEN - ESG Combined Score"                  2020 "09062X103" 56.06   .16250117  .05407228   .1561727   .30385435
"BIO-TECHNE - ESG Combined Score"              2016 "09073M104" 34.54   .09249093  .05686799  .11717796   .09055094
"BIO-TECHNE - ESG Combined Score"              2017 "09073M104" 45.33   .04882882  .05879276  .08671695     .095051
"BIO-TECHNE - ESG Combined Score"              2018 "09073M104" 50.88   .07918017  .07656907  .09123012   .08604915
"BIO-TECHNE - ESG Combined Score"              2019 "09073M104" 65.97   .05098253  .05353718  .08174389   .08741243
"BIO-TECHNE - ESG Combined Score"              2020 "09073M104" 56.83     .113088  .07231495  .12245776    .0882534
"BLACKBAUD - ESG Combined Score"               2016 "09227Q100" 35.09  .031685762 .012900222  .03836713    .1229723
"BLACKBAUD - ESG Combined Score"               2017 "09227Q100" 48.66   .03747415 .016954392 .024009535   .11405596
"BLACKBAUD - ESG Combined Score"               2018 "09227Q100" 38.84  .027760083 .019108465 .024782317    .1164392
"BLACKBAUD - ESG Combined Score"               2019 "09227Q100" 47.89  .005975023 .015961159  .07022007   .11790458
"BLACKBAUD - ESG Combined Score"               2020 "09227Q100"  54.4    3.774085 .017483937 .062525496   .10966263
"BOSTON SCIENTIFIC - ESG Combined Score"       2016 "101137107" 71.58    19.17551  10.831123   90.07516   .11054138
"BOSTON SCIENTIFIC - ESG Combined Score"       2017 "101137107" 74.39    5.461611   9.872912   89.11879    .1101901
"BOSTON SCIENTIFIC - ESG Combined Score"       2018 "101137107" 72.01    79.57522   6.952712   84.86118    .1133055
"BOSTON SCIENTIFIC - ESG Combined Score"       2019 "101137107" 83.82    138.3006   7.099624   79.01194    109.3619
"BOSTON SCIENTIFIC - ESG Combined Score"       2020 "101137107" 47.49   -2.664327   56.34077   82.59415   .13739534
"BOTTOMLINE TECHS. - ESG Combined Score"       2016 "101388106" 21.99  -.03009403   1.488374    .078159   .13795103
"BOTTOMLINE TECHS. - ESG Combined Score"       2017 "101388106" 27.72  -.05366846   .2017511  .08957484   .15168913
"BOTTOMLINE TECHS. - ESG Combined Score"       2018 "101388106" 29.62   1.4667405   .1916134  .04543468   .14542142
"BOTTOMLINE TECHS. - ESG Combined Score"       2019 "101388106" 30.15    14.09383  .13771668  .08149826    .1596447
"BOTTOMLINE TECHS. - ESG Combined Score"       2020 "101388106" 34.49  -1.1636072  .24564734   .1158274    .1651188
"BRADY NONVOTING A - ESG Combined Score"       2016 "104674106"  30.4   .07673636  .13528052  .09812982  .031945568
"BRADY NONVOTING A - ESG Combined Score"       2017 "104674106"  40.6   .09107114  .12753862  .09341254  .035590973
"BRADY NONVOTING A - ESG Combined Score"       2018 "104674106"  34.8    .0861551  .17165454   .9266925   .03855089
"BRADY NONVOTING A - ESG Combined Score"       2019 "104674106" 34.85   .11341666   .2411389  .09508964   .03891629
"BRADY NONVOTING A - ESG Combined Score"       2020 "104674106" 37.12   .09835654  .19050282  .13739315   .03760477
"CTS - ESG Combined Score"                     2016 "126501105" 36.39    .0664095  .21982937  .15860823   .06060316
"CTS - ESG Combined Score"                     2017 "126501105" 37.22  .026770627    .210437  .16351242   .05944779
"CTS - ESG Combined Score"                     2018 "126501105" 35.63    .0848596  .18406977   .1812759   .05378303
"CTS - ESG Combined Score"                     2019 "126501105" 43.06   .05618369  14.460157  .20157176   .05536686
"CTS - ESG Combined Score"                     2020 "126501105"  34.6   .05540461   14.85986  .19282517   .06253036
"CABOT - ESG Combined Score"                   2016 "127055101" 67.72    20.63712   27.70083  178.67036   .02198258
"CABOT - ESG Combined Score"                   2017 "127055101" 79.07     33.3795   38.78116  180.74792   .02061097
"CABOT - ESG Combined Score"                   2018 "127055101" 78.62   -15.65097   24.23823   179.5014  .020357804
"CABOT - ESG Combined Score"                   2019 "127055101" 76.82    21.74515    23.4072   186.7036  .017980222
"CABOT - ESG Combined Score"                   2020 "127055101" 73.88   -32.96399   20.91413  195.56787   .02180566
end

Thanks in advance!

[Jared Greathouse]

I don't know if you can "test" for it, it's more something that you gotta theoretically argue in many cases. I would present lagged results just in case.

[Maxence Morlet]

Like Jared says, you cannot prove the absence of reverse causality, you have to argue it.

If there is theoretical reason to suspect it, then I suggest with your data that you use Kripfganz's xtdpdgmm command

[Qi vd Kolk]

Thanks Jared and Maxence