interpreting REGHDFE with absorb specifications

[tom berk]

Hi all, I am using panel data with fixed effect. In checking the robustness of my results, I estimate my model with two specifications. I am wondering which of the two is most intuitive/informative to use (i should only choose one).
1.

reghdfe Y X1 Z1 Z2, absorb(county state#year) vce(cluster PERMCO)

2.

reghdfe Y X1 Z1 Z2, absorb(state#year) vce(cluster PERMCO)

As you see, the first model includes county and state by year effects. The second only state by year.
The results are as following:

1

HDFE Linear regression                            Number of obs   =    106,089
Absorbing 2 HDFE groups                           F(  11,  11820) =    1126.78
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.5108
                                                  Adj R-squared   =     0.5003
                                                  Within R-sq.    =     0.4693
Number of clusters (PERMCO)  =     11,821         Root MSE        =     0.1999

                            (Std. Err. adjusted for 11,821 clusters in PERMCO)
------------------------------------------------------------------------------
             |               Robust
         ROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   prot_perc |   .0820807   .0518339     1.58   0.113    -.0195222    .1836836
      totpop |  -2.56e-08   1.17e-08    -2.18   0.029    -4.87e-08   -2.63e-09
         Edu |  -.1081303   .0907921    -1.19   0.234    -.2860978    .0698373
        Male |  -.1102668    .243603    -0.45   0.651    -.5877688    .3672351
       Money |   3.07e-07   3.10e-07     0.99   0.322    -3.00e-07    9.14e-07
    Minority |  -.0183953   .0502177    -0.37   0.714    -.1168302    .0800396
     Married |   -.006168   .0604787    -0.10   0.919    -.1247162    .1123802
             |
      Size_w |
         L1. |    .029529   .0007727    38.22   0.000     .0280144    .0310435
             |
 Liquidity_w |   .0386051    .000815    47.37   0.000     .0370075    .0402028
             |
        Loss |
         D1. |  -.0630033    .001485   -42.43   0.000    -.0659142   -.0600924
             |
  Leverage_w |  -.1230631   .0038557   -31.92   0.000    -.1306209   -.1155053
       _cons |  -.0133236    .138057    -0.10   0.923    -.2839381    .2572909

2

HDFE Linear regression                            Number of obs   =    106,308
Absorbing 1 HDFE group                            F(  11,  11852) =    1139.66
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.4992
                                                  Adj R-squared   =     0.4923
                                                  Within R-sq.    =     0.4755
Number of clusters (PERMCO)  =     11,853         Root MSE        =     0.2013

                            (Std. Err. adjusted for 11,853 clusters in PERMCO)
------------------------------------------------------------------------------
             |               Robust
         ROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   prot_perc |   .0100529   .0164292     0.61   0.541    -.0221511    .0422568
      totpop |   9.15e-10   9.00e-10     1.02   0.309    -8.49e-10    2.68e-09
         Edu |  -.1176459   .0235673    -4.99   0.000    -.1638417   -.0714502
        Male |  -.0226447   .0866049    -0.26   0.794    -.1924045     .147115
       Money |   1.75e-07   2.38e-07     0.73   0.463    -2.92e-07    6.42e-07
    Minority |  -.0509284   .0155635    -3.27   0.001    -.0814354   -.0204215
     Married |   .0278872   .0392895     0.71   0.478    -.0491267    .1049011
             |
      Size_w |
         L1. |   .0291427   .0007839    37.18   0.000     .0276062    .0306793
             |
 Liquidity_w |   .0389049   .0008103    48.01   0.000     .0373166    .0404932
             |
        Loss |
         D1. |  -.0633705   .0014821   -42.76   0.000    -.0662757   -.0604653
             |
  Leverage_w |  -.1229857   .0037679   -32.64   0.000    -.1303714      -.1156
       _cons |  -.0792589   .0484973    -1.63   0.102    -.1743215    .0158037
------------------------------------------------------------------------------

How should i interpret both specifications. To my understanding, in the first specification, I control for effects that happen within a certain county and also for state effects that occur during my sample period. The second only does the latter, but excludes potential effects on county level. Is it right that, by choosing the first specification, I control for more within variation? And is that a good thing?

[tom berk]

Does anyone know an answer to this question or maybe has a source where i could learn more about this matter?

[Carlo Lazzaro]

Tom:
I read your query several times and what I found baffling is your choice of an interaction as a fixed effect: this is neither intuitive to grasp, nor easy to disseminate.
In my opinion, if you want to collect two fixed effects, the easiest approach to understand and disseminate is a two-way -fe- specification (unlike -xtreg-, the community-contributed programme -reghdfe- allows you to retrieve the estimates of both the -fe-):

 
 reghdfe Y X1 Z1 Z2, absorb(county year) vce(cluster PERMCO)