Time Fixed-Effects [xtreg,fe vs. reghdfe]

[Vincent KH Lee]

I have a question about diff-in-diff results with different commands.

x1 is the time-variant binary variable, if it is before the treatment it's 0, if its after the treatment its 1.

1. 
xtreg y i.x1##i.x2 i.date, fe robust 

gen treat = (x1 == 1 & x2 == 1)

2. 
xtdidreg (y) (treat), group(id) time(date) 

3. 
reghdfe y i.x1##i.x2, absorb(id date) vce(robust)

The first two diff-in-diff regression commands give me exactly same results in terms of ATET and i.x1#i.x2.

However, with xtreg, "i.x1" is not omitted, and this sounds a little awkward, since I have controlled for the time-fixed effect in the first command.

When I run the same diff-in-diff with reghdfe, only the interaction term is left, and non-interacted terms are omitted as expected.

So my question is, why is command using

 xtreg y i.x1##i.x2 i.date, fe robust

returning some value for i.x1? (which is totally unexpected, considering its original value when estimated solely e.g. xtreg i.x1, fe robust)

Thank you.

[Jared Greathouse]

These commands are likely doing different things under the hood as far as presentation goes- but if the ATT is the same, I don't see why it matters very much.



You don't give your example data/the results, so I can't comment further, but that's likely the issue.

EDIT: Nevermind. Under the hood, xtdidreg uses time and unit FE. Your third command, unlike the first two, does not. So this likely explains the differences.

[Vincent KH Lee]

Thank you for the reply.

Here are some results regarding the matter.


1. xtreg with time fixed effect.

Fixed-effects (within) regression               Number of obs     =    126,672
Group variable: id                              Number of groups  =      1,218

R-squared:                                      Obs per group:
Within  = 0.3549                                         min =        104
Between = 0.0183                                         avg =      104.0
Overall = 0.0453                                         max =        104

F(104,1217)       =     516.57
corr(u_i, Xb) = -0.0205                         Prob > F          =     0.0000

(Std. err. adjusted for 1,218 clusters in id)

Robust
ln_OFF  Coefficient  std. err.      t    P>t     [95% conf. interval]

FC 
Post     .8484489   .0098513    86.13   0.000     .8291215    .8677762

over 
Competitive            0  (omitted)

FC#over 
Post#Competitive    -.0738441    .008204    -9.00   0.000    -.0899396   -.0577486

date 
3069    -.0234435   .0036636    -6.40   0.000    -.0306311   -.0162559
3070    -.0330616   .0038225    -8.65   0.000     -.040561   -.0255621
3071    -.0464528   .0042592   -10.91   0.000     -.054809   -.0380966
3072     .0142889   .0052425     2.73   0.007     .0040035    .0245743
3073    -.0893196   .0055157   -16.19   0.000    -.1001409   -.0784984
3074     .0305656   .0041074     7.44   0.000     .0225072    .0386239
3075     .0101663   .0039318     2.59   0.010     .0024525      .01788
3076     .0424484   .0036935    11.49   0.000      .035202    .0496948
3077     .0078064   .0043448     1.80   0.073    -.0007176    .0163305
3078     .0868084   .0050886    17.06   0.000     .0768251    .0967918
3079     .0044045    .005164     0.85   0.394    -.0057269    .0145359
3080     .0595264   .0050988    11.67   0.000      .049523    .0695298
3081     .0201319   .0074393     2.71   0.007     .0055367    .0347271
3082     .0174062   .0050331     3.46   0.001     .0075317    .0272808
3083     .0111077    .004516     2.46   0.014     .0022476    .0199678
3084    -.0032333   .0050638    -0.64   0.523    -.0131681    .0067014
3085     .1035966   .0060528    17.12   0.000     .0917215    .1154717
3086     .0976943   .0049776    19.63   0.000     .0879287      .10746
3087     .0402426   .0047892     8.40   0.000     .0308466    .0496385
3088    -.0088539   .0054759    -1.62   0.106    -.0195972    .0018894
3089     .0467458   .0054523     8.57   0.000     .0360488    .0574428
3090     .0053473   .0052373     1.02   0.307    -.0049278    .0156224
3091     .0097629   .0056622     1.72   0.085    -.0013459    .0208718
3092      .004486   .0054775     0.82   0.413    -.0062603    .0152324
3093     .0261269   .0050716     5.15   0.000     .0161769    .0360769
3094     .0162182   .0055287     2.93   0.003     .0053714     .027065
3095     -.007476   .0055681    -1.34   0.180    -.0184002    .0034482
3096     .0023746   .0053647     0.44   0.658    -.0081506    .0128997
3097    -.0079741   .0052097    -1.53   0.126    -.0181951    .0022468
3098     .0504102   .0071989     7.00   0.000     .0362864    .0645339
3099     .0123666   .0058064     2.13   0.033     .0009751    .0237582
3100      .012247   .0052193     2.35   0.019     .0020071    .0224869
3101     .0208429   .0051306     4.06   0.000     .0107771    .0309086
3102     .0437478   .0051812     8.44   0.000     .0335827     .053913
3103    -.0472256   .0052696    -8.96   0.000    -.0575642   -.0368871
3104     -.086758    .009557    -9.08   0.000     -.105508    -.068008
3105    -.0171379   .0054514    -3.14   0.002    -.0278331   -.0064427
3106     .0430576   .0054028     7.97   0.000     .0324578    .0536574
3107    -.0051916   .0050485    -1.03   0.304    -.0150963    .0047132
3108    -.0148988   .0052219    -2.85   0.004    -.0251438   -.0046539
3109    -.0276678   .0054835    -5.05   0.000    -.0384261   -.0169096
3110    -.0353024   .0057263    -6.16   0.000     -.046537   -.0240678
3111     .0195842    .005266     3.72   0.000     .0092529    .0299156
3112     .0098852   .0062524     1.58   0.114    -.0023815    .0221519
3113    -.0122257   .0061547    -1.99   0.047    -.0243007   -.0001508
3114    -.0706925   .0057345   -12.33   0.000    -.0819431   -.0594419
3115    -.0453573   .0077529    -5.85   0.000    -.0605678   -.0301468
3116    -.0654352   .0073142    -8.95   0.000    -.0797851   -.0510853
3117    -.0237825   .0054427    -4.37   0.000    -.0344607   -.0131043
3118     .1351882   .0055964    24.16   0.000     .1242086    .1461679
3119     .6674334   .0081739    81.65   0.000     .6513968      .68347
3120    -.0112277   .0044752    -2.51   0.012    -.0200076   -.0024478
3121    -.0231867   .0053556    -4.33   0.000    -.0336939   -.0126795
3122    -.0643617   .0050951   -12.63   0.000    -.0743579   -.0543655
3123    -.1145721   .0093972   -12.19   0.000    -.1330086   -.0961357
3124    -.0059702   .0051989    -1.15   0.251      -.01617    .0042296
3125    -.0500152   .0054337    -9.20   0.000    -.0606755   -.0393548
3126    -.0298146   .0049851    -5.98   0.000     -.039595   -.0200342
3127    -.0646914   .0056753   -11.40   0.000    -.0758259   -.0535569
3128    -.0428028   .0068511    -6.25   0.000     -.056244   -.0293616
3129     -.876342   .0085777  -102.17   0.000    -.8931706   -.8595133
3130    -.8266008   .0087786   -94.16   0.000    -.8438236   -.8093779
3131    -.8838929   .0087349  -101.19   0.000      -.90103   -.8667557
3132    -.8160397   .0076634  -106.48   0.000    -.8310748   -.8010047
3133    -.8444588   .0099651   -84.74   0.000    -.8640095   -.8249082
3134    -.8330202   .0084397   -98.70   0.000    -.8495781   -.8164623
3135    -.8632482   .0087911   -98.20   0.000    -.8804955   -.8460009
3136    -.8427622   .0093915   -89.74   0.000    -.8611876   -.8243369
3137    -.6987716   .0094882   -73.65   0.000    -.7173866   -.6801567
3138    -.7271565   .0085106   -85.44   0.000    -.7438536   -.7104595
3139    -.7370376   .0089173   -82.65   0.000    -.7545327   -.7195426
3140    -.7982379     .00916   -87.14   0.000     -.816209   -.7802667
3141    -.7480058   .0097701   -76.56   0.000     -.767174   -.7288375
3142    -.8562893   .0093299   -91.78   0.000    -.8745939   -.8379848
3143    -.8771425    .009329   -94.02   0.000    -.8954452   -.8588398
3144    -.8738573   .0090901   -96.13   0.000    -.8916912   -.8560233
3145    -.8256514   .0085571   -96.49   0.000    -.8424398   -.8088631
3146    -.8254862   .0091005   -90.71   0.000    -.8433406   -.8076318
3147    -.8577879   .0087985   -97.49   0.000    -.8750498    -.840526
3148    -.8553055   .0082971  -103.09   0.000    -.8715837   -.8390274
3149    -.8940692   .0085779  -104.23   0.000    -.9108983     -.87724
3150    -.8125704   .0103076   -78.83   0.000    -.8327931   -.7923478
3151    -.8668659   .0087955   -98.56   0.000    -.8841218   -.8496099
3152    -.8505619   .0084984  -100.08   0.000    -.8672351   -.8338888
3153    -.8282254   .0086122   -96.17   0.000    -.8451219   -.8113289
3154    -.7951754    .007175  -110.83   0.000    -.8092521   -.7810988
3155    -.8727308   .0076656  -113.85   0.000    -.8877702   -.8576915
3156    -.8962792   .0074175  -120.83   0.000    -.9108318   -.8817267
3157    -.8933396   .0084234  -106.05   0.000    -.9098655   -.8768137
3158    -.8297725   .0090092   -92.10   0.000    -.8474478   -.8120972
3159    -.9730041   .0107696   -90.35   0.000    -.9941332    -.951875
3160     -.901572   .0090566   -99.55   0.000    -.9193402   -.8838038
3161    -.9210881   .0100153   -91.97   0.000    -.9407372   -.9014389
3162    -.9537892   .0100102   -95.28   0.000    -.9734283     -.93415
3163     -.816505   .0093232   -87.58   0.000    -.8347963   -.7982136
3164    -.9155536   .0098286   -93.15   0.000    -.9348365   -.8962707
3165    -.9154131   .0098828   -92.63   0.000    -.9348024   -.8960238
3166    -.9363869   .0098447   -95.12   0.000    -.9557014   -.9170725
3167    -.8486302   .0093263   -90.99   0.000    -.8669276   -.8303328
3168    -.8616797   .0108798   -79.20   0.000    -.8830249   -.8403344
3169    -.9175595   .0097108   -94.49   0.000    -.9366113   -.8985076
3170    -.8577555   .0074374  -115.33   0.000    -.8723471    -.843164
3171            0  (omitted)

_cons    16.26473   .0039452  4122.71   0.000     16.25699    16.27247

sigma_u   .47809263
sigma_e   .16070603
rho   .89848061   (fraction of variance due to u_i)

2. xtdidreg

Number of groups and treatment time

Time variable: date
Control:       treat = 0
Treatment:     treat = 1

Control  Treatment

Group        
id        763        455

Time         
Minimum       3068       3129
Maximum       3068       3129


Difference-in-differences regression    Number of obs = 126,672
Data type: Longitudinal

(Std.    err. adjusted for 1,218 clusters in id)
    
Robust
ln_OFF  Coefficient  std. err.    t    P>t     [95% conf. interval]
    
ATET         
treat 
(1 vs 0)    -.0738441    .008204    -9.00   0.000    -.0899396   -.0577486
    
Note: ATET estimate adjusted for panel    effects and time effects.

3. reghdfe

HDFE Linear regression                            Number of obs   =    126,672
Absorbing 2 HDFE groups                           F(   1, 125350) =    1501.82
Prob > F        =     0.0000
R-squared       =     0.9039
Adj R-squared   =     0.9029
Within R-sq.    =     0.0120
Root MSE        =     0.1607


Robust
ln_OFF  Coefficient  std. err.      t    P>t     [95% conf. interval]

FC 
Post            0  (omitted)

over 
Competitive            0  (omitted)

FC#over 
Post#Competitive    -.0738441   .0019055   -38.75   0.000    -.0775788   -.0701094

_cons    16.27677   .0005308  3.1e+04   0.000     16.27573    16.27781


Absorbed degrees of freedom:

Absorbed FE  Categories  - Redundant  = Num. Coefs 
-
date        104           0         104     
id       1218           1        1217

@Jared, for the third command, reghdfe, I've specified to absorb time (date) and id level fixed effect, and the reghdfe command is the only command that returns the expected result (as per my understanding goes).

Here, FC is binary time variant, and over is binary group identifier.

So, to re-address my question, why does FC in the xtreg command not omitted like the one in reghdfe?

Thank you.

[Jared Greathouse]

🤷🤷🤷🤷 I don't know honestly. Considering the point estimates are the same, this tells me something with the SEs are being calculated differently under the hood. I'm unsure what the issue is here.

[Vincent KH Lee]

Thank you for the reply though!

I'll have to well go open up the under the hood and see how exactly all three command works I guess...

[Jared Greathouse]

I wouldn't worry about this too much. Unless the implications are wildly different, then unless you just wanna know the underlying machinations (which I'm definitely guilty of in my own work!!!!), I wouldn't lose sleep over it. Stata already makes me lose sleep in other ways, I try not to add other reasons to the list.

But, you could email the author of the command. Presumably he's better insight than a mere mortal like myself.

[Vincent KH Lee]

I agree. I don't really think this is going to be a main game changer, but I'll definitely try sending an email to the authors of above commands when I have extra time Thanks a bunch.