Different results using xtreg, fe and reghdfe, absorb

[Ankita Marwaha]

Apologies for a long post. Posting here first time, so trying to be as descriptive about my problem as possible.

I'm using Stata 15.1 to run certain regressions of a dependent variable on 12 independent variables, 2 of which are dummies. I have about 13000 observations of about firms and 11 years. The following is a sample of my data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float id double fyear float depvar double indepvar float(avg_acc bign btm) double ib float(lev ln_mve negearn) double(returns returns_sd) float roa double turnover
 1 2008 .21098053  .5637141535615172  .008471157 1   .3294921      693     .2857335  8.957575 0   -.009528047869725224 .043552877898948815   .09318274  .008361675741150975
 1 2009 .19782035  .5812519272278756    .0576721 1  .29263046      -31     .3815029  9.055287 1    .005355215185532733  .06399085279101045 -.004072517  .010527989189140498
 1 2010   .196463  .5812519272278756 .0035066006 1  .26797697      684    .22586633  9.396472 0   .0068172405747016175  .04030163330312947  .070544556   .01009467148128897
 1 2011 .19716935  .6583745239445751  .027382135 1   .3355041     1012    .21331567   9.46035 0    .002321546803264377 .057455056678877264   .11173678  .012597314028069377
 1 2012 .19436316  .6920832995705375  .007118451 1   .4155719     1153    .20045558 9.4310465 0    .000574310337576796 .048660550088320056   .10943432  .009339219935238362
 1 2013 .18369286  .6920832995705375   .04005241 1   .3133838      724    .25257346  9.733144 0   .0073712712373190485 .028140228933663403    .0677522  .009011035441420972
 1 2014   .180157   .715292459478506   .01911181 1   .2861167      504    .25500876   9.82644 0    .002056485512293875 .028562754063788047    .0465331 .0067959762928076085
 1 2015 .17802577  .7040169133192389  .012033694 1   .3323942      438    .22128627  9.436385 0  .00011126648795017797   .0269186764339904   .05361679  .007689854548778385
 1 2016 .17573275  .7040169133192389   .04242502 1   .3010673      462    .24506536  9.553448 0    .003445337727988282 .030085134101758067   .05921559  .006401633309200406
 1 2017 .17838474   .723684210526316  .024329456 1  .22055374      684     .2137432  9.994423 0    .008917151643030453 .021258123519906528    .0811773  .005766246012412012
 1 2018 .17764647  .6660412757973732   .09027046 1  .22186323      316    .21063107  9.932306 0  -.0002192192306906423  .03571619570176653   .03699801   .00796381507301703
 2 2008 .14732866  .3602941176470588    .0455329 1   .4634591 -273.829     .4979979  6.274389 1    .004488017717552073   .1523623373863852   -.1327424  .031082197126001118
 2 2009 .18914294  .3035714285714285   .00719254 1   .7137276  134.662    .47676665   6.55574 0    .009821480704256548  .11954877456868047    .0589544   .02977910908870399
 2 2010 .18234695                 .4   .05607961 1   .5380657   38.543     .4342996  6.910154 0    .010715832983036168  .10333402652174215  .017685564  .030142837908118964
 3 2014 .14020246  .2490118577075098  .004523543 1  .05402936     2882    .40903795 10.529575 0     .01575231987785978  .04715140656536541   .06584268  .017945348266512156
 3 2015 .11068071 .29090909090909095   .02811112 1   .2130214     7610     .4246824 10.183115 0  -.0028670972365384493 .051643774805462055    .1571827  .016255052791908385
 3 2016 .14916953 .29090909090909095   .07504778 1  .15980203     2676     .4747825  10.07262 0    .003643968411219808  .05328928039386283   .05219019  .015726902717724443
 3 2017 .14504911 .29090909090909095   .05496537 1    .158686     1919     .4876839 10.116204 0    .002807587695525189  .04086280597844709   .03733754  .011680605379864574
 3 2018  .1349146 .21538461538461545  .035011556 1 -.01142647     1412       .56172  9.601722 0  -.0062770233815535904 .058583369794131965   .02330802  .015764765104278922

My problem is that I am running the following two regression commands (which to me are equivalent) and getting different coefficients and standard errors:

xtset id fyear
xtreg depvar indepvar avg_accruals bign btm ib lev ln_mve negearn returns returns_sd roa turnover, fe vce(robust)

reghdfe depvar indepvar avg_accruals bign btm ib lev ln_mve negearn returns returns_sd roa turnover, absorb(id fyear) vce(robust)

Some of the ways that I have tried to investigate the problem are as below:

The following are the first half of the results that I am getting - is there a reason why the degrees of freedom for F values are different?

xtreg:

Fixed-effects (within) regression               Number of obs     =     13,398
Group variable: id                              Number of groups  =      1,538

R-sq:                                           Obs per group:
     within  = 0.2122                                         min =          2
     between = 0.0148                                         avg =        8.7
     overall = 0.0273                                         max =         12

                                                F(12,1537)        =      59.05
corr(u_i, Xb)  = -0.2804                        Prob > F          =     0.0000

                                  (Std. Err. adjusted for 1,538 clusters in id)

reghdfe:

HDFE Linear regression                            Number of obs   =     13,398
Absorbing 2 HDFE groups                           F(  12,  11837) =      32.01
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.9124
                                                  Adj R-squared   =     0.9008
                                                  Within R-sq.    =     0.0436
                                                  Root MSE        =     0.0167

I also tried running the following xtreg command which I know is incorrect, but just to try:

xtreg depvar indepvar avg_accruals bign btm ib lev ln_mve negearn returns returns_sd roa turnover i.id i.fyear, fe vce(robust)

this gave me the same coefficients as my reghdfe command, but with different SEs. Is my initial command of

xtreg depvar indepvar controls, fe vce(robust)

somehow missing estimating the fixed effects??

[Andrew Musau]

xtreg does not automatically include the year fixed effects, so both commands are not equivalent. So you want

xtreg depvar indepvar avg_accruals bign btm ib lev ln_mve negearn returns returns_sd roa turnover i.fyear, fe vce(robust)

[FernandoRios]

Hi Anika
I think the problem that you have is a misunderstanding I had as well when starting working with panel FE models.
Namely, -xtreg,fe- does not control for time fixed effect, unless you add the "i.time" to the model specification.
in contrast, reghdfe adds the fixed effects as long as you add both time and individual FE in "abs"
Regarding the standard errors, there is an additional correction (this is documented in the Stata Manual) when using robust or cluster xtreg. This is different from how reghdfe estimates (robust) standard errors.
HTH
Fernando

[Ankita Marwaha]

Thank you Andrew and Fernando for letting me know, noted!