How to use explicit coding for multiple dummies in regression (no factor notation)

Hi. I would like to run a fixed effects regression containing a continuous-categorical interaction without Stata's factor notation. I have a group-variable consisting of 4 groups, I created dummies for each group. Furthermore there are time demeaned versions of all variables, since I also want to show the equivalence of xtreg and reg with this explicit dummy modelling.

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input long(id year group) double(x y group_1 group_2 group_3 group_4 tdm_y tdm_x tdm_group_1 tdm_group_2 tdm_group_3 tdm_group_4)
 1 2003 4 10.999889592640102  5.968150671105832 0 0 1 0  -7.632118122419342   .28228607680648565                  0 -.2 .19999999999999996   0
 1 2004 4  8.328235403168947 24.058973410865292 0 0 1 0  10.458704617340118  -2.3893681126646698                  0 -.2 .19999999999999996   0
 1 2005 4  9.886130336672068 15.034143149387091 0 0 1 0  1.4338743558619171   -.8314731791615486                  0 -.2 .19999999999999996   0
 1 2006 3 14.544738274998963 12.875743181211874 0 1 0 0  -.7245256123133004   3.8271347591653466                  0  .8                -.8   0
 1 2007 4  9.829023971688002 10.064333555055782 0 0 1 0  -3.535935238469392   -.8885795441456139                  0 -.2 .19999999999999996   0
 2 2003 3 13.903502221219242   22.0061635307502 0 1 0 0  12.629190189763904    2.960886503569782                -.2  .4                -.2   0
 2 2004 3  14.14438186911866  9.102296619676054 0 1 0 0   -.274676721310243    3.201766151469201                -.2  .4                -.2   0
 2 2005 3 11.087349823210388  7.205982017330825 0 1 0 0  -2.170991323655471   .14473410556092858                -.2  .4                -.2   0
 2 2006 4  9.106897765304893  4.266130877658725 0 0 1 0  -5.110842463327572  -1.8357179523445666                -.2 -.6                 .8   0
 2 2007 2  6.470946909394115  4.304293659515679 1 0 0 0  -5.072679681470618   -4.471668808255345                 .8 -.6                -.2   0
 3 2003 1  14.35299803270027   12.0510651380755 0 0 0 1  3.6845534422900528    3.421853056177497                -.2 -.6                  0  .8
 3 2004 3   8.01228899974376   6.32412321283482 0 1 0 0  -2.042388482950628   -2.918855976779014                -.2  .4                  0 -.2
 3 2005 3  5.607205715496093  5.406369740376249 0 1 0 0  -2.960141955409199  -5.3239392610266805                -.2  .4                  0 -.2
 3 2006 2 14.477269400376827 16.859409702010453 1 0 0 0   8.492898006225005    3.546124423854053                 .8 -.6                  0 -.2
 3 2007 3 12.205962734296918 1.1915906856302172 0 1 0 0  -7.174921010155231   1.2748177577741444                -.2  .4                  0 -.2
 4 2003 4  6.422942955978215 17.521327186841518 0 0 1 0  1.5138552070129663   -3.848384694196284                -.2   0                 .4 -.2
 4 2004 1 10.492846560664475  8.797215961385518 0 0 0 1  -7.210256018443033    .2215189104899764                -.2   0                -.6  .8
 4 2005 2 14.540912385564297 10.223599948221818 1 0 0 0  -5.783872031606734    4.269584735389799                 .8   0                -.6 -.2
 4 2006 4 10.854833531193435  20.52378309890628 0 0 1 0   4.516311119077727    .5835058810189366                -.2   0                 .4 -.2
 4 2007 4   9.04510281747207 22.971433703787625 0 0 1 0   6.963961723959073   -1.226224832702428                -.2   0                 .4 -.2
 5 2003 2 11.478934793267399  7.063208252657205 1 0 0 0  -6.493024631636217   2.7495535844936967 .19999999999999996   0                  0 -.2
 5 2004 1  8.198206170927733  24.02761984267272 0 0 0 1  10.471386958379298   -.5311750378459692                -.8   0                  0  .8
 5 2005 2  8.077200108673424 18.209860706701875 1 0 0 0   4.653627822408453   -.6521811001002789 .19999999999999996   0                  0 -.2
 5 2006 2  7.197676312644035 17.159377050120384 1 0 0 0  3.6031441658269614  -1.5317048961296678 .19999999999999996   0                  0 -.2
 5 2007 2  8.694888658355922 1.3210985693149269 1 0 0 0 -12.235134314978495 -.034492550417780876 .19999999999999996   0                  0 -.2
 6 2003 4 14.842192034702748  9.880503366002813 0 0 1 0  -5.355816191295162    5.719433007761836                  0 -.4                 .6 -.2
 6 2004 1  6.542023008223623 11.946134496247396 0 0 0 1  -3.290185061050579   -2.580736018717289                  0 -.4                -.4  .8
 6 2005 3  5.910439998842776 14.006331592099741 0 1 0 0 -1.2299879651982337   -3.212319028098136                  0  .6                -.4 -.2
 6 2006 4  6.419069077819586 17.456539871636778 0 0 1 0  2.2202203143388033   -2.703689949121326                  0 -.4                 .6 -.2
 6 2007 3 11.900071015115827 22.892088460503146 0 1 0 0   7.655768903205171   2.7773119881749153                  0  .6                -.4 -.2
 7 2003 2 11.192564833909273 15.458780684275553 1 0 0 0    5.91783843934536   -.6911614798009396                 .8 -.4                -.2 -.2
 7 2004 3  13.91394117148593 10.710537718841806 0 1 0 0  1.1695954739116132    2.030214857775718                -.2  .6                -.2 -.2
 7 2005 4 11.729990926105529  13.55200918042101 0 0 1 0   4.011066935490817  -.15373538760468364                -.2 -.4                 .8 -.2
 7 2006 1 12.370777379255742 1.4619622146710753 0 0 0 1  -8.078980030259117    .4870510655455291                -.2 -.4                -.2  .8
 7 2007 3 10.211357257794589 6.5214214264415205 0 1 0 0 -3.0195208184886724   -1.672369055915624                -.2  .6                -.2 -.2
 8 2003 2 11.598384496755898  9.928798832697794 1 0 0 0 -1.9868512556422502   -.7759733335115016                 .6   0                -.4 -.2
 8 2004 4  13.21805460145697 4.9436184170190245 0 0 1 0 -6.9720316713210195    .8436967711895704                -.4   0                 .6 -.2
 8 2005 4 12.862815517000854 20.798189070774242 0 0 1 0   8.882538982434198   .48845768673345447                -.4   0                 .6 -.2
 8 2006 2 14.798219173680991 3.8221805705688894 1 0 0 0  -8.093469517771155   2.4238613434135914                 .6   0                -.4 -.2
 8 2007 1  9.394315362442285  20.08546355064027 0 0 0 1   8.169813462300226  -2.9800424678251147                -.4   0                -.4  .8
 9 2003 4  8.117022020742297 13.670653913868591 0 0 1 0   2.041816918645054  -.39942419808357954                -.2 -.2                 .6 -.2
 9 2004 1  9.094749526120722  16.55794105026871 0 0 0 1   4.929104055045173    .5783033072948456                -.2 -.2                -.4  .8
 9 2005 3  5.104671118315309  4.292462347075343 0 1 0 0  -7.336374648148194  -3.4117751005105674                -.2  .8                -.4 -.2
 9 2006 2  6.838495240081102 15.826383995590732 1 0 0 0   4.197547000367194   -1.677950978744775                 .8 -.2                -.4 -.2
 9 2007 4 13.427293188869953   7.79674366931431 0 0 1 0  -3.832093325909227    4.910846970044076                -.2 -.2                 .6 -.2
10 2003 2  7.311617820523679 18.113858660217375 1 0 0 0  -.8208987989928573   -.7380057526752353                 .6 -.2                -.4   0
10 2004 2  7.390999556519091  9.973495616577566 1 0 0 0  -8.961261842632666   -.6586240166798234                 .6 -.2                -.4   0
10 2005 3 5.7669116533361375  24.23391027841717 0 1 0 0   5.299152819206938   -2.282711919862777                -.4  .8                -.4   0
10 2006 4  7.457236780319363  24.18495926540345 0 0 1 0   5.250201806193218   -.5923867928795516                -.4 -.2                 .6   0
10 2007 4 12.321352055296302   18.1675634754356 0 0 1 0  -.7671939837746322    4.271728482097387                -.4 -.2                 .6   0
11 2003 1 13.474531651008874  6.430418661329895 0 0 0 1  -2.922792157623917    4.293661816045642                -.4   0                -.4  .8
11 2004 2  9.975272670853883  5.544698366429657 1 0 0 0 -3.8085124525241554    .7944028358906507                 .6   0                -.4 -.2
11 2005 4  8.879090298432857 14.826141291996464 0 0 1 0   5.472930473042652   -.3017795365303755                -.4   0                 .6 -.2
11 2006 2  7.464489941485226  6.688035803381354 1 0 0 0 -2.6651750155724585  -1.7163798934780061                 .6   0                -.4 -.2
11 2007 4  6.110964613035321  13.27675997163169 0 0 1 0  3.9235491526778787   -3.069905221927911                -.4   0                 .6 -.2
12 2003 1  8.899944352451712  19.63229178218171 0 0 0 1    6.14511804538779    .2167819868773222                -.4 -.4                  0  .8
12 2004 3 10.719353139866143   4.20152026345022 0 1 0 0    -9.2856534733437   2.0361907742917538                -.4  .6                  0 -.2
12 2005 2  7.168927628081292 10.109979525441304 1 0 0 0 -3.3771942113526165  -1.5142347374930978                 .6 -.4                  0 -.2
12 2006 3  9.447680020239204 11.789406940806657 0 1 0 0 -1.6977667959872633    .7645176546648145                -.4  .6                  0 -.2
12 2007 2  7.179906687233597  21.70267017208971 1 0 0 0    8.21549643529579  -1.5032556783407927                 .6 -.4                  0 -.2
13 2003 2  10.02299563260749  23.14269889611751 1 0 0 0   3.400277739856392    .5502983699552715                 .6   0                -.2 -.4
13 2004 1  8.539045718498528  22.04943898250349 0 0 0 1  2.3070178262423724   -.9336515441536903                -.4   0                -.2  .6
13 2005 1   11.4998515881598 16.854671062901616 0 0 0 1    -2.8877500933595   2.0271543255075812                -.4   0                -.2  .6
13 2006 4   8.74713956611231 23.754174483474344 0 0 1 0   4.011753327213228   -.7255576965399086                -.4   0                 .8 -.4
13 2007 2  8.554453807882965 12.911122356308624 1 0 0 0  -6.831298799952492   -.9182434547692537                 .6   0                -.2 -.4
14 2003 3 10.336879454553127 14.412975532468408 0 1 0 0   5.497914508450776    .9897633562795818                -.6  .8                -.2   0
14 2004 2 12.403343603946269  8.408280147705227 1 0 0 0  -.5067808763124049    3.056227505672723                 .4 -.2                -.2   0
14 2005 2  7.211029378231615   8.68311578524299 1 0 0 0 -.23194523877464235  -2.1360867200419307                 .4 -.2                -.2   0
14 2006 4  9.127461186144501  .5006075138226151 0 0 1 0  -8.414453510195017  -.21965491212904453                -.6 -.2                 .8   0
14 2007 2  7.656866868492216  12.57032614084892 1 0 0 0  3.6552651168312877  -1.6902492297813296                 .4 -.2                -.2   0
15 2003 3 11.299730534665287 21.776085341116413 0 1 0 0  12.356352236820385   .11513391556218266                -.4  .8                -.4   0
15 2004 2  6.838284907862544 .15751959872432053 1 0 0 0  -9.262213505571708    -4.34631171124056                 .6 -.2                -.4   0
15 2005 4 13.636441114358604 1.8014280998613685 0 0 1 0   -7.61830500443466      2.4518444952555                -.4 -.2                 .6   0
15 2006 2 12.465680041350424 4.1052806249354035 1 0 0 0  -5.314452479360625   1.2810834222473204                 .6 -.2                -.4   0
15 2007 4  11.68284649727866 19.258351856842637 0 0 1 0   9.838618752546608   .49824987817555666                -.4 -.2                 .6   0
16 2003 3 11.180178732611239 18.379607645329088 0 1 0 0  3.8959328655619174    .2271306086331606                  0  .8                -.2 -.6
16 2004 1   8.72238060226664 24.296890891855583 0 0 0 1   9.813216112088412   -2.230667521711439                  0 -.2                -.2  .4
16 2005 4 10.298356858547777 11.661809420911595 0 0 1 0 -2.8218653588555753   -.6546912654303014                  0 -.2                 .8 -.6
16 2006 1 13.746823428664356 1.8596128327772021 0 0 0 1 -12.624061946989968    2.793775304686278                  0 -.2                -.2  .4
16 2007 1  10.81750099780038 16.220453107962385 0 0 0 1  1.7367783281952143  -.13554712617769837                  0 -.2                -.2  .4
17 2003 3  13.39767764788121  18.96482923766598 0 1 0 0  11.088690563337877    2.957943143788725                  0  .4                -.2 -.2
17 2004 3  8.124481649138033  3.427652025129646 0 1 0 0  -4.448486649198458  -2.3152528549544513                  0  .4                -.2 -.2
17 2005 4 12.082903222180903   9.91461486555636 0 0 1 0  2.0384761912282556   1.6431687180884182                  0 -.6                 .8 -.2
17 2006 1  7.650178060866892  5.624633230036125 0 0 0 1  -2.251505444291979  -2.7895564432255924                  0 -.6                -.2  .8
17 2007 3 10.943431940395385 1.4489640132524073 0 1 0 0  -6.427174661075696    .5036974363029003                  0  .4                -.2 -.2
18 2003 3  9.812898004893214  9.897317207651213 0 1 0 0   2.839224358322099  -1.4390531536191702                -.2  .8                -.4 -.2
18 2004 4    7.6503273146227  1.623207499505952 0 0 1 0  -5.434885349823162  -3.6016238438896835                -.2 -.2                 .6 -.2
18 2005 4  10.64590434776619  5.647160822991282 0 0 1 0 -1.4109320263378322   -.6060468107461929                -.2 -.2                 .6 -.2
18 2006 1 14.131882230285555 1.3657277275342494 0 0 0 1 -5.6923651217948645   2.8799310717731714                -.2 -.2                -.4  .8
18 2007 2 14.018743894994259 16.757050988962874 1 0 0 0    9.69895813963376    2.766792736481875                 .8 -.2                -.4 -.2
19 2003 3  7.741666215006262  7.443544565467164 0 1 0 0  -3.081732599530369  -3.5355291082523763                -.2  .4                  0 -.2
19 2004 3  8.214827564079314 2.5180395576171577 0 1 0 0  -8.007237607380375   -3.062367759179324                -.2  .4                  0 -.2
19 2005 2 14.856408843770623 1.7976024304516613 1 0 0 0  -8.727674734545872    3.579213520511985                 .8 -.6                  0 -.2
19 2006 3 11.199933101888746 22.011014219606295 0 1 0 0  11.485737054608762  -.07726222136989236                -.2  .4                  0 -.2
19 2007 1 14.373140891548246 18.856185051845387 0 0 0 1   8.330907886847854   3.0959455682896078                -.2 -.6                  0  .8
20 2003 2   9.66532702324912 20.415147190215066 1 0 0 0   6.414050456369296    .1497084335424006                 .6 -.2                -.4   0
20 2004 2   9.06832593260333 24.553509341785684 1 0 0 0  10.552412607939914   -.4472926571033895                 .6 -.2                -.4   0
20 2005 3 11.592303242068738 2.5899911241140217 0 1 0 0 -11.411105609731749    2.076684652362019                -.4  .8                -.4   0
20 2006 4  6.523466168437153  2.476045733783394 0 0 1 0 -11.525051000062376   -2.992152421269566                -.4 -.2                 .6   0
20 2007 4 10.728670582175255 19.970790279330686 0 0 1 0   5.969693545484915    1.213051992468536                -.4 -.2                 .6   0
end
label values group group
label def group 1 "4", modify
label def group 2 "1", modify
label def group 3 "2", modify
label def group 4 "3", modify

Here are my three basic minimal models:

Code:

xtset id year

* Fixed effects interaction (implicit coding)
xtreg y c.x##i.group, fe
margins, dydx(x) post
estimates store FE_1

* Fixed effects interaction (explicit coding): dummies instead of factor
gen int_x_group = x*group_1*group_2*group_3*group_4
xtreg y x group_1 group_2 group_3 group_4 int_x_group, fe
margins, dydx(x) post
estimates store FE_2

* OLS time demeaning = FE
gen tdm_int_x_group = tdm_x*tdm_group_1*tdm_group_2*tdm_group_3*tdm_group_4
reg tdm_y tdm_x tdm_group_1 tdm_group_2 tdm_group_3 tdm_group_4 tdm_int_x_group
margins, dydx(tdm_x) post
estimates store OLS_tdm

estimates table FE_1 FE_2 OLS_tdm



-----------------------------------------------------
    Variable |    FE_1         FE_2       OLS_tdm    
-------------+---------------------------------------
           x | -.06871007   -.00823415              
       tdm_x |                           -.06124972  
-----------------------------------------------------

I use implicit coding (factor notation) as a reference model. Neither of my explicit FE or TDM reg estimates is the same. How can I fix this? Thank you very much

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How to use explicit coding for multiple dummies in regression (no factor notation)

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Home / Data Cleaning / Data management / Data Processing / How to use explicit coding for multiple dummies in regression (no factor notation)
How to use explicit coding for multiple dummies in regression (no factor notation)