2 way clustering in fixed effects panel data regression

[Titir Bhattacharya]

Hi,

I'm trying a fixed effects regression with panel data where I cluster across two dimensions. Following the discussion here, I tried two-way clustering in the two ways and got non-identical results. This has left me confused as to which method is the correct one. For demonstration, I use a sample data given by

use "http://www.stata-press.com/data/r14/nlswork.dta", clear

Method 1:

use "http://www.stata-press.com/data/r14/nlswork.dta", clear
reghdfe ln_wage hours age i.race i.year,a(idcode) vce (cluster occ_code year)
(dropped 548 singleton observations)
note: 2bn.race is probably collinear with the fixed effects (all partialled-out values are close to zero; tol =
>  1.0e-09)
note: 3bn.race is probably collinear with the fixed effects (all partialled-out values are close to zero; tol =
>  1.0e-09)
(MWFE estimator converged in 1 iterations)
Warning: VCV matrix was non-positive semi-definite; adjustment from Cameron, Gelbach & Miller applied.
warning: missing F statistic; dropped variables due to collinearity or too few clusters
note: 2.race omitted because of collinearity
note: 3.race omitted because of collinearity

HDFE Linear regression                            Number of obs   =     27,775
Absorbing 1 HDFE group                            F(  16,     12) =          .
Statistics robust to heteroskedasticity           Prob > F        =          .
                                                  R-squared       =     0.6555
                                                  Adj R-squared   =     0.5948
Number of clusters (occ_code) =         13        Within R-sq.    =     0.1066
Number of clusters (year)    =         15         Root MSE        =     0.3031

                         (Std. Err. adjusted for 13 clusters in occ_code year)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       hours |   .0007912   .0013155     0.60   0.559     -.002075    .0036573
         age |   .0123773    .008567     1.44   0.174    -.0062886    .0310433
             |
        race |
      black  |          0   7.23e-10     0.00   1.000    -1.57e-09    1.57e-09
      other  |          0   1.85e-09     0.00   1.000    -4.04e-09    4.04e-09
             |
        year |
         69  |    .074031   .0289008     2.56   0.025     .0110616    .1370005
         70  |   .0475113   .0335979     1.41   0.183    -.0256922    .1207148
         71  |   .0867244   .0357381     2.43   0.032     .0088578    .1645911
         72  |    .085603   .0452419     1.89   0.083    -.0129706    .1841766
         73  |   .0889179   .0482453     1.84   0.090    -.0161995    .1940353
         75  |   .0790484   .0628044     1.26   0.232    -.0577907    .2158875
         77  |    .110587   .0820362     1.35   0.203    -.0681546    .2893286
         78  |    .133743   .0908718     1.47   0.167    -.0642497    .3317356
         80  |   .1167207    .097275     1.20   0.253    -.0952233    .3286646
         82  |   .1137017   .1244713     0.91   0.379    -.1574979    .3849013
         83  |   .1261455   .1254465     1.01   0.334    -.1471791      .39947
         85  |    .151498   .1362975     1.11   0.288    -.1454688    .4484649
         87  |   .1422716   .1548657     0.92   0.376    -.1951518     .479695
         88  |   .1837026   .1757012     1.05   0.316    -.1991175    .5665227
             |
       _cons |   1.181475   .1358746     8.70   0.000     .8854294     1.47752
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
      idcode |      4149           0        4149     |
-----------------------------------------------------+

clear

Method 2:

use "http://www.stata-press.com/data/r14/nlswork.dta", clear
egen occ_year=group(occ_code year)
areg ln_wage hours age i.race i.year,a(idcode) cluster(occ_year)
note: 2.race omitted because of collinearity
note: 3.race omitted because of collinearity

Linear regression, absorbing indicators         Number of obs     =     28,323
                                                F(  16,    175)   =      17.61
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6648
                                                Adj R-squared     =     0.5980
                                                Root MSE          =     0.3031

                             (Std. Err. adjusted for 176 clusters in occ_year)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       hours |   .0007912   .0005501     1.44   0.152    -.0002944    .0018768
         age |   .0123773   .0152226     0.81   0.417    -.0176661    .0424208
             |
        race |
      black  |          0  (omitted)
      other  |          0  (omitted)
             |
        year |
         69  |    .074031   .0427223     1.73   0.085    -.0102861    .1583482
         70  |   .0475113     .05194     0.91   0.362    -.0549982    .1500208
         71  |   .0867244   .0607844     1.43   0.155    -.0332405    .2066893
         72  |    .085603   .0725549     1.18   0.240    -.0575924    .2287983
         73  |   .0889179   .0877736     1.01   0.312    -.0843132     .262149
         75  |   .0790484    .113218     0.70   0.486    -.1444001    .3024969
         77  |    .110587   .1410838     0.78   0.434    -.1678578    .3890318
         78  |    .133743   .1569636     0.85   0.395    -.1760424    .4435283
         80  |   .1167207   .1853747     0.63   0.530    -.2491371    .4825784
         82  |   .1137017   .2147943     0.53   0.597     -.310219    .5376224
         83  |   .1261455   .2315117     0.54   0.587    -.3307688    .5830597
         85  |    .151498   .2606477     0.58   0.562    -.3629195    .6659155
         87  |   .1422716   .2896411     0.49   0.624    -.4293677    .7139108
         88  |   .1837026   .2959214     0.62   0.536    -.4003315    .7677367
             |
       _cons |   1.179466   .2917784     4.04   0.000     .6036086    1.755324
-------------+----------------------------------------------------------------
      idcode |   absorbed                                    (4697 categories)



clear

As can be seen, these two methods give nonidentical results, with the standard error from Method 1 being higher than that from Method 2. I also found the Method 2 standard error to be higher than the robust standard error (result not shown here).

Can anyone suggest which amongst these two is the correct way to do two-way clustering and why?

Thanks,

[Carlo Lazzaro]

Titir:
I think you should prefer the community-contributed programme -reghdfe- to accomplish what you have in mind.

[Titir Bhattacharya]

Titir:
I think you should prefer the community-contributed programme -reghdfe- to accomplish what you have in mind.

Thank you Carlo for your response. Can you please tell me why reghdfe is more suited compared to the other method? I tried looking it up but could not really understand in which ways they are different. That is, if one is clustering the standard error along occ_code and year, what is the other doing?

Thanks,

[Carlo Lazzaro]

Titir:
the main differences between -areg- and the community-contributed programme -reghdfe- are:
- -areg- is not conceived from a number of groups that increase with sample size;
- -areg- can't cluster the standard errors on more than one -clusterid- at a time.

[Titir Bhattacharya]

Titir:
the main differences between -areg- and the community-contributed programme -reghdfe- are:
- -areg- is not conceived from a number of groups that increase with sample size;
- -areg- can't cluster the standard errors on more than one -clusterid- at a time.

thank you Carlo for your response. Much appreciated.