Panel Data Regression Fixed Effects Interpretation

[Anton Bernabe]

Hello everyone.

I am asking for your help in interpreting my results. I am currently using a panel dataset wherein I am testing the effect on our DEPENDENT variable StockReturn from the INDEPENDENT variable ESG (rating) and we've also included CONTROL variables such as EPS, ROE, ROA FirmSize, and Profitability. Our dataset involves 5 countries from the ASEAN region, and we have a total of 765 observations spread across a 5 year period (2016-2020). Our preferred method was to use a Fixed Effects model given that we have a panel dataset and from performing a Hausman Test. I am unsure about our initial results as my independent variable (ESG) came out insignificant and 2 control variables (EPS, ROE) also came out insignificant. All the other variables that were included however did come out significant. Another problem that arose was when I tested for Random Effects, the coefficients remained the same for some variables if compared to the Fixed Effects model.

I will be attaching my dataset here for your reference in seeing the format of my data. I will also include my DO file to show the commands I tried executing.

I thank you in advance.

[Carlo Lazzaro]

Anton:
as per FAQ, please share what you typed and what Stata gave you back via CODE delimiters. Thanks.

[Anton Bernabe]

My apologies Carlo,

Here are the commands which I used

For Fixed Effects

egen CName1=group(CompanyName)
xtset CName1 Year, yearly
xtreg StockReturn ESG, fe
xtreg StockReturn ESG EPS ROE ROA FirmSize Profitability, fe

For Random Effects

xtreg StockReturn ESG EPS ROE ROA FirmSize Profitability, re

The Hausman Test which I used

xtreg StockReturn ESG EPS ROE ROA FirmSize Profitability, fe
estimates store fixed
xtreg StockReturn ESG EPS ROE ROA FirmSize Profitability, re
estimates store random
hausman fixed ., sigmamore
hausman fixed random

Here is also a sample of my data

* Example generated by -dataex-. To install: ssc install dataex
clear
input str45 CompanyName str11 Country int Year double(ESG StockReturn EPS ROE ROA FirmSize Profitability)
"AKR Corporindo Tbk PT"              "Indonesia"   2016 23.6108616213128    -.152503206095184  .003799078708741               .18006   .06892000000000001  20.87559593355994             .0522964
"AKR Corporindo Tbk PT"              "Indonesia"   2017 37.8874272049311   .08191403416967359  .003775830734967               .15657               .06514 20.894002805117076   .06644409999999999
"AKR Corporindo Tbk PT"              "Indonesia"   2018 39.8720998372689    -.292024274276639   .00332956948028                 .125                 .055 20.923968742201303             .0491242
"AKR Corporindo Tbk PT"              "Indonesia"   2019 49.0013011237909   -.0374721824360396  .002442164869565   .08933999999999999               .03871   21.0603325378142             .0302156
"AKR Corporindo Tbk PT"              "Indonesia"   2020 49.6546886007341    -.163186495637418  .002579438760807   .08589000000000001                .0347 21.065783960026106             .0328819
"AMMB Holdings Bhd"                  "Malaysia"    2016  38.526599565818   -.0141880633504147   .10945641025641               .08792  .009729999999999999  24.21422677478142   .31782710000000003
"AMMB Holdings Bhd"                  "Malaysia"    2017 56.2711680078656  .062170969635390004  .098584990958409   .08492000000000001               .00987  24.17309842431941             .3314325
"AMMB Holdings Bhd"                  "Malaysia"    2018 58.7870418545088  .020303391641259202  .097314862765407                .0696                .0083 24.268879413208243             .2620689
"AMMB Holdings Bhd"                  "Malaysia"    2019 75.1400558365468 -.052890696344777596  .123191176470588   .08800000000000001                .0108  24.35888533614588             .3076996
"AMMB Holdings Bhd"                  "Malaysia"    2020 76.3122205705755   -.0447936859828365  .106318108045444   .07400000000000001  .009300000000000001 24.399945332555404             .2713992
"Aboitiz Power Corp"                 "Philippines" 2016 49.0901584113826    .0382520724661339  .051162686567164               .18572               .07665 22.368339997025267   .20668050000000002
"Aboitiz Power Corp"                 "Philippines" 2017 45.7042728590398  .027917015227601597  .055632882019411               .19905                 .067 22.676648627996496             .2243366
"Aboitiz Power Corp"                 "Philippines" 2018 52.0936409093142    -.125126353770077  .063429977789783               .21133               .06486 22.663047796549943             .1710044
"Aboitiz Power Corp"                 "Philippines" 2019 54.4021915903995    .0152820512270442  .058989136649514   .19579999999999997               .06337  22.73193209654813             .1649864
"Aboitiz Power Corp"                 "Philippines" 2020 48.1424037562298  -.18776057792128298  .046686870681145               .13125               .04154  22.81958436826272             .1378808
"Advanced Info Service PCL"          "Thailand"    2016 69.2060851973735    .0339894503971627  .365611604664076               .82316   .25414000000000003 22.353052698334356             .2521465
"Advanced Info Service PCL"          "Thailand"    2017 63.5196625974822   .35753328610459595  .287807198660714                .6744               .13408 22.786837873421437             .2015548
"Advanced Info Service PCL"          "Thailand"    2018 64.8542358837938  -.06252958626776689  .310808602150538    .6476000000000001               .10747 22.918687378130144             .1906985
"Advanced Info Service PCL"          "Thailand"    2019 73.2585793061168     .279547634705931   .30881255799567               .55048   .10332000000000001 22.953507403482877   .17474920000000002
"Advanced Info Service PCL"          "Thailand"    2020 67.9176551029324    -.145142133334564   .35251814516129   .49200000000000005               .10752  22.95319090468397             .1724193
"Airports of Thailand PCL"           "Thailand"    2016 57.9858611422304     .152272975434622  .038480913823019   .17024999999999998               .11796 22.297987997805595   .37907310000000005
"Airports of Thailand PCL"           "Thailand"    2017 57.6233337452828     .732146677031523  .043789015606242                .1637               .11798 22.424572378422898             .3767425
"Airports of Thailand PCL"           "Thailand"    2018 61.1563237209247 -.039461753054809395  .054651608910891   .18286999999999998                .1375 22.464683685608076             .4157886
"Airports of Thailand PCL"           "Thailand"    2019 68.9135926443712   .17171386609625197  .056483164432821               .16807               .12964  22.60495412113655             .3986143
"Airports of Thailand PCL"           "Thailand"    2020 65.5448621701759    -.159256266347242   .01075917721519               .02918               .02323 22.467643642678244              .138576
"Alliance Bank Malaysia Bhd"         "Malaysia"    2016 29.8911243266143    .0856777239364699  .086784615384615               .11182                .0096 23.336328632695984   .27183620000000003
"Alliance Bank Malaysia Bhd"         "Malaysia"    2017 41.3257114494399     .141062657625128  .075947106690778                 .105  .009340000000000001  23.26017852075283   .27237500000000003
"Alliance Bank Malaysia Bhd"         "Malaysia"    2018 35.4476761656928    .0223902614710709   .08251683065769                .0933                .0091 23.329655111444993             .2598839
"Alliance Bank Malaysia Bhd"         "Malaysia"    2019 45.9442575430708  -.31603761705648004  .086115196078431   .09609999999999999                .0097 23.324697504247773   .26729949999999997
"Alliance Bank Malaysia Bhd"         "Malaysia"    2020 41.9785923868653     .106463878366032  .067567818223974                .0724                .0072 23.380719331932582             .2049692
"Alliance Global Group Inc"          "Philippines" 2016 15.3546702054164  -.19111458290100403  .028707036247335               .10597               .03254  22.99938331047538             .1029292
"Alliance Global Group Inc"          "Philippines" 2017 8.31015748265623     .251956181543725    .0295994673016   .10414999999999999               .03149    23.004777769652             .1081063
"Alliance Global Group Inc"          "Philippines" 2018 7.73179867838155     -.24998947812601  .030384176721292   .09641999999999999               .02836  23.10997970774143             .1119989
"Alliance Global Group Inc"          "Philippines" 2019 10.7125430539609 -.020168067159687803  .028956165427864               .09034                .0263  23.15399546385555             .0997958
"Alliance Global Group Inc"          "Philippines" 2020 30.7667270090209   -.0865300402290023  .036170187561698                .1007                .0287  23.28008100472611             .1015193
"Aneka Tambang Tbk PT"               "Indonesia"   2016 74.4231103756053     1.85031847126315 -.008739057671382  -.07629999999999999 -.044000000000000004 21.549652479256366            -.1368135
"Aneka Tambang Tbk PT"               "Indonesia"   2017 73.2253884536015    -.301675977650408  .000200220489978 .0035299999999999997               .00215  21.53150754685779 .0071170999999999995
"Aneka Tambang Tbk PT"               "Indonesia"   2018 69.6165925763521     .226691447529826  .000418761518614                .0074               .00455 21.502809748532453  .010787999999999999
"Aneka Tambang Tbk PT"               "Indonesia"   2019 64.6227244301084     .116445820495623  .000505477565217               .04575               .02762 21.569805096052725             .0647274
"Aneka Tambang Tbk PT"               "Indonesia"   2020 71.0765001812675   1.3143087368349402  .001009613832853               .04099  .024390000000000002  21.38366821464217             .0059248
"Astra Agro Lestari Tbk PT"          "Indonesia"   2016 26.1991893944568     .118097054277649  .027175231048241               .05454  .030899999999999997 21.196266230264516  .047407700000000004
"Astra Agro Lestari Tbk PT"          "Indonesia"   2017 33.6513609881273  -.18814716544897198  .084324801781737                .1412               .08776  21.32060515930863             .1421231
"Astra Agro Lestari Tbk PT"          "Indonesia"   2018 33.3256935409399   -.0706899598814588   .07737698562477               .11422               .08178  21.32544960529238             .1137214
"Astra Agro Lestari Tbk PT"          "Indonesia"   2019 30.8838461252297     .258301078729621  .055795176347826               .07764               .05535  21.37559128362614   .07537630000000001
"Astra Agro Lestari Tbk PT"          "Indonesia"   2020 36.4585182394865  -.14609464800251198  .006246752161383                 .045  .031400000000000004 21.376945978935492             .0120965
"Astra International Tbk PT"         "Indonesia"   2016 35.2460627674041     .412390390473874               .03                 .189                 .077 23.633658633749256                 .079
"Astra International Tbk PT"         "Indonesia"   2017 32.2469571240015                 .023               .03                 .142                  .06 23.700214752194633                 .084
"Astra International Tbk PT"         "Indonesia"   2018 33.8067274539761                 .017               .04                 .197                 .083  23.79722497887473                 .091
"Astra International Tbk PT"         "Indonesia"   2019 33.8897556186313                -.133               .04                 .166                 .068 23.925130770358777                 .091
"Astra International Tbk PT"         "Indonesia"   2020 33.5799143781922                -.097               .04                 .152                 .062  23.94557979312937                 .092
"Astro Malaysia Holdings Bhd"        "Malaysia"    2016 56.6473005681295   -.0145928592268647  .028884337349398               .95056   .09026999999999999 21.268637804464987   .11237920000000001
"Astro Malaysia Holdings Bhd"        "Malaysia"    2017 59.2577226014124    .0684864756935721  .027612917795845              1.01903               .09474  21.07360676236993              .111121
"Astro Malaysia Holdings Bhd"        "Malaysia"    2018 55.9367708676478  -.47303261921454104   .03828695986665              1.20704                .1175 21.296022688869172             .1393365
"Astro Malaysia Holdings Bhd"        "Malaysia"    2019 60.0845706163255    .0282976406159667  .022589154860772    .7472799999999999               .07063  21.15373912279879             .0844893
"Astro Malaysia Holdings Bhd"        "Malaysia"    2020 58.1782958602361    -.239146037977544  .030940170940171    .9093899999999999               .10519 21.068911408992875             .1334129
"Axiata Group Bhd"                   "Malaysia"    2016  49.840377966552    -.240877767874833  .058634032634033   .11538999999999999               .04854 23.312670987046832             .1284595
"Axiata Group Bhd"                   "Malaysia"    2017 64.6149017859094     .181111713239176  .010166127773442               .06369  .023700000000000002  23.48648896430137             .0233826
"Axiata Group Bhd"                   "Malaysia"    2018 60.2639832590746    -.269008363104168  .028860039564787  .045579999999999996               .01568  23.60567345481491             .0372701
"Axiata Group Bhd"                   "Malaysia"    2019 61.6672403393274    .0776134792117822 -.063295399515738               .05686               .01794 23.475443135840937            -.1993665
"Axiata Group Bhd"                   "Malaysia"    2020 62.6388712612508    -.079372326115418   .03074834922964                .0866               .02229  23.49026782673479             .0592902
"Ayala Corp"                         "Philippines" 2016 70.4797436967981   -.0264476457017832  .729750746268657                 .113               .02931  23.55567192800707   .11074429999999999
"Ayala Corp"                         "Philippines" 2017 72.5928424146429   .39982455561932495  .843474444601384   .11835000000000001                .0305 23.620318271632183             .1144903
"Ayala Corp"                         "Philippines" 2018 68.1092439617897  -.10662541408152601  .784142905736639                .1697                .0313 23.700536782821352   .10484170000000001
"Ayala Corp"                         "Philippines" 2019 69.8854767005057    -.118689352695534  .761504478749762               .11634               .02867 23.848326226682524             .0947933
"Ayala Corp"                         "Philippines" 2020 73.7723939262123    .0618786607339539  2.06286100691017                .1139                .0277 23.989742049609003   .24330490000000002
"Ayala Land Inc"                     "Philippines" 2016 86.3714213733835 -.058774766324397695   .02602473347548               .14651               .04242  22.97117638482672             .1745291
"Ayala Land Inc"                     "Philippines" 2017 87.0101742305025     .411177335719735  .029509675336468   .14858000000000002               .04272   23.0990084766565             .1771103
"Ayala Land Inc"                     "Philippines" 2018 87.6730733208073   -.0789004613886745  .034815214998899               .16094  .045579999999999996 23.122429062584814             .1822492
"Ayala Land Inc"                     "Philippines" 2019 86.7940460399743   .13377002878331498  .037708785972937               .16518  .047060000000000005  23.27178515217709             .1790147
"Ayala Land Inc"                     "Philippines" 2020 85.5487297272057  -.09501542903955579  .044322211253702               .16663                 .048 23.371276237770864               .19987
"BDO Unibank Inc"                    "Philippines" 2016 44.1836046245141   .07961946011462649  .130155437100213               .13235  .012849999999999999  24.47978720124567               .34076
"BDO Unibank Inc"                    "Philippines" 2017 48.6342454945842     .545134841652599    .1295994673016                .1255               .01198 24.559305851792413             .3156503
"BDO Unibank Inc"                    "Philippines" 2018 58.5279240659991    -.195138339771528  .127253336534806                 .102  .011000000000000001 24.660780187271843             .2778696
"BDO Unibank Inc"                    "Philippines" 2019 58.4821371322226     .218172971872266  .139424814179531   .10468999999999999                .0115 24.786547518587685             .2508447
"BDO Unibank Inc"                    "Philippines" 2020 53.9948127595904    -.316661518741093  .195809674234946               .12694               .01423  24.85983921523111             .2731174
"BEC World PCL"                      "Thailand"    2016 44.5115616103711    -.429258372351985  .041403387007218               .35942               .18499  19.85445381756475             .1882413
"BEC World PCL"                      "Thailand"    2017 40.7783038575127    -.199347871267018  .016996372767857               .16415               .08152 19.872498154855286             .0993245
"BEC World PCL"                      "Thailand"    2018 37.6218062500308    -.632061068680825   .00093732718894               .00919               .00417 19.939195428163444  .005528999999999999
"BEC World PCL"                      "Thailand"    2019 35.2049268017761     .224066390060425  -.00510640272193 -.052930000000000005              -.02305 19.940990604887155             -.032608
"BEC World PCL"                      "Thailand"    2020   44.52239473245      .36440677967848 -.006672715053763              -.04299               -.0196 19.700354089808673 -.047792799999999996
"BTS Group Holdings PCL"             "Thailand"    2016 35.7695483127627  .013185875113525002   .00995584045584               .02871               .02092 21.325094339201776    .7724245999999999
"BTS Group Holdings PCL"             "Thailand"    2017 49.9840540441016    .0100924110501637  .005501747233547               .04208               .02321 21.733253230445875             .3272829
"BTS Group Holdings PCL"             "Thailand"    2018 59.0654109202283   .19748642914757902  .006178376644209               .04764               .01974  21.92088718247609             .1868357
"BTS Group Holdings PCL"             "Thailand"    2019 62.0672368192866   .43586973049051303  .007762925598991               .07241  .022949999999999998  22.23422585858372             .0645382
"BTS Group Holdings PCL"             "Thailand"    2020 76.3396825794418  -.26568201985033096  .011430360415394               .17427               .05142  22.42588148425652   .20735430000000002
"Bangkok Bank PCL"                   "Thailand"    2016 63.5127454893768   .08718948459042711   .46214908384231   .09976000000000002               .01222  25.08264838921058             .3292488
"Bangkok Bank PCL"                   "Thailand"    2017 56.6469494488178     .312267559612004  .453768694196428   .08589000000000001  .011009999999999999  25.14500436386059             .3105612
"Bangkok Bank PCL"                   "Thailand"    2018 58.3150825297417    .0382524259674375  .542752995391705               .08456               .01097 25.292146059062354   .31294869999999997
"Bangkok Bank PCL"                   "Thailand"    2019 65.1881447566706    -.184930781852019  .593763996288277   .08675000000000001               .01141 25.310234264942967   .31891780000000003
"Bangkok Bank PCL"                   "Thailand"    2020 66.6240268964569    -.226013513480258  .608140793010753               .08522               .01131  25.38527689550399             .3181808
"Bangkok Dusit Medical Services PCL" "Thailand"    2016 44.5803881031576    .0526611546244846  .014378400888395               .15763               .08097  21.77889103329745             .1276485
"Bangkok Dusit Medical Services PCL" "Thailand"    2017 40.3570735757411   -.0809498286952873       .0147890625               .15333               .08015  21.84075179302747   .12335760000000001
"Bangkok Dusit Medical Services PCL" "Thailand"    2018 44.0754592985645   .20472358817146202  .015667281105991                 .172   .08897000000000001  22.08305812535681   .14201840000000002
"Bangkok Dusit Medical Services PCL" "Thailand"    2019 43.5071836766101    .0675241360057581  .018254562326013   .13781000000000002               .07177 22.165150655918364   .11879429999999999
"Bangkok Dusit Medical Services PCL" "Thailand"    2020 60.9849851873585    -.188732394404629  .020057459677419               .12169               .07019 22.163208234204607             .1875807
"Bangkok Expressway and Metro PCL"   "Thailand"    2016 13.3831799581402   .47619855727028404  .004812881732371               .09619  .035769999999999996  21.50636167032384             .2257481
"Bangkok Expressway and Metro PCL"   "Thailand"    2017 15.7579172807844    .0500095877038214  .004756696428571               .08874               .03239  21.58388578935236             .1988574
"Bangkok Expressway and Metro PCL"   "Thailand"    2018 15.5945090115447     .280178882995743  .006277419354839                .1374                .0344  21.86853615422858   .20610050000000002
"Bangkok Expressway and Metro PCL"   "Thailand"    2019 18.1767101913398     .138945878230176  .006669656665636   .09824999999999999               .03231 21.918266690383707   .34052059999999995
"Bangkok Expressway and Metro PCL"   "Thailand"    2020 27.1402585284863  -.23108296767446798   .00635752688172                .1463                .0504 21.978644384389142             .3374181
end
format %ty Year

Thank you.

[Carlo Lazzaro]

Anton:
what did Stata give you back? Thanks.

[Anton Bernabe]

Carlo, here are my results for both Fixed and Random Effects. Thanks.

[Carlo Lazzaro]

Anton:
according to bith the outcome tables, your dataset does niot show any evidence of a panel-wise effect.
Go pooled OLS, then.

[Anton Bernabe]

Anton:
according to bith the outcome tables, your dataset does niot show any evidence of a panel-wise effect.
Go pooled OLS, then.

Dear Carlo, here are my results from the Pooled OLS which you recommended. I received only 1 statistically significant variable in contrast to the results I had when I ran the Fixed Effects model. Is this fine? How would you interpret this?

Thank you again.

[Carlo Lazzaro]

Anton:
if you go pooled OLS, you have to apply -vce(cluster panelid)- standard errors, as th eobservations each one of your 153 panels is composed of are not independent.

[Anton Bernabe]

Anton:
if you go pooled OLS, you have to apply -vce(cluster panelid)- standard errors, as th eobservations each one of your 153 panels is composed of are not independent.

My apologies Carlo, is this the right command? I am not experienced with Pooled OLS models.

regress StockReturn ESG EPS ROE ROA FirmSize Profitability i.Year, cluster(CompanyName)

Here are my results as well. I also wanted to ask, can time-fixed effects apply for Pooled OLS? I wanted to incorporate that into the model. Would these results now be acceptable?

Thanks again Carlo.

[Carlo Lazzaro]

Anton:
yes, your code is correct and you can add -i.year- in the right-hand side of your regression equation.
You may want to test the joint statistical significance of -i.year- via -testparm-:

testparm i.year

[Anton Bernabe]

Anton:
yes, your code is correct and you can add -i.year- in the right-hand side of your regression equation.
You may want to test the joint statistical significance of -i.year- via -testparm-:

testparm i.year

Thanks Carlo, you’ve been a great help. I forgot to ask what do you mean in my initial results (from the fixed and random effects model) that there is no panel-wise effect? Which led me to use a Pooled OLS model. Thanks again.

[Carlo Lazzaro]

Anton:
1) the F-test appearing as a footnote of the -xtreg,fe. outcome table does noit reach statistical significance;
2) the -sigma_u- the -xtreg,re- code gives back is zero.

[Anton Bernabe]

Greetings again Carlo,

I now have everything I need, all that is left is the interpretation which I am unsure of. I wanted to incorporate into the model a Time-Fixed Effects, a Country-Fixed Effects, and also an Industry-Fixed Effects and that is where my doubt lies in interpreting these Fixed Effects. Please correct me if I am wrong, but from my understanding (for example for Time-Fixed Effects) and as shown in my results, there is a 0.822 increase in the effect of all independent variables on the dependent variable in 2017 with 2016 as the base year? Would that be correct?

Also pasting my code for reference

reg StockReturn ESG EPS ROE ROA FirmSize Profitability i.Year, cluster(CompanyName)

And my results:

[Anton Bernabe]

Anton:
yes, your code is correct and you can add -i.year- in the right-hand side of your regression equation.
You may want to test the joint statistical significance of -i.year- via -testparm-:

testparm i.year

Thank you for this suggestion Carlo, upon testing for joint statistical significance for Time-Fixed Effects in my POLS, my results indicate there a Time-Fixed Effects would be needed for my model.

[Carlo Lazzaro]

Anton:
correct.