-reghdfe- and degree of freedom

[Michelle Zhang]

Hi all,

I am having problem understanding degree of freedom reported from -reghdfe-. I use pooled individual-level data across years with -reghdfe- absorbing multiple fixed effects (e.g. time, state, industry, industry#time). My naïve thought is that e(N) = e(df_r) + e(df_m) + absorbed df. Am I wrong about how df is calculated in -reghdfe- ? In reported data, I find, e(df_r) = 31, and e(df_m) = 67, e(df_a) = 6433, and all these df do not sum up to e(N) = 411418.

I am trying to do a F-test of no pre-trend, and need df of N-K, which I suppose should be e(df_r), but get confused on df calculation based on results reported by -reghdfe-. Any help would be appreciated! Thank you!

(attached below ereturn list and table results)

scalars:
    e(report_constant) =  1
          e(converged) =  1
                 e(ic) =  6
         e(sumweights) =  643393987.7511139
        e(r2_a_within) =  .0704817963078309
               e(r2_a) =  .3799237769984229
          e(r2_within) =  .0706355863023422
                 e(r2) =  .3897671179698056
               e(ll_0) =  -1795488.799942529
                 e(ll) =  -1780419.720321791
                  e(F) =  .
               e(rmse) =  18.47805467413722
                e(mss) =  88298809.44856453
                e(rss) =  138243670.3493461
         e(tss_within) =  148750768.0645063
                e(tss) =  226542479.7979107
               e(df_m) =  67
               e(df_r) =  31
               e(rank) =  67
                  e(N) =  411418
             e(N_full) =  411672
     e(num_singletons) =  254
    e(drop_singletons) =  1
        e(df_a_nested) =  32
     e(df_a_redundant) =  269
       e(df_a_initial) =  6702
               e(df_a) =  6433
    e(N_hdfe_extended) =  4
             e(N_hdfe) =  4
           e(N_clust1) =  32
      e(N_clustervars) =  1
            e(N_clust) =  32

HDFE Linear regression                            Number of obs   =    411,418
Absorbing 4 HDFE groups                           F(  67,     31) =          .
Statistics robust to heteroskedasticity           Prob > F        =          .
                                                  R-squared       =     0.3898
                                                  Adj R-squared   =     0.3799
                                                  Within R-sq.    =     0.0706
Number of clusters (state_code_census) =         32Root MSE       =    18.4781

                       (Std. Err. adjusted for 32 clusters in state_code_census)
--------------------------------------------------------------------------------
               |               Robust
re_caring_wo~M |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
      years_23 |
            1  |   .9919705   .3724542     2.66   0.012     .2323452    1.751596
            2  |   1.598075   .4209958     3.80   0.001     .7394489    2.456702
            3  |   1.851101   .5539009     3.34   0.002     .7214124    2.980789
            4  |   1.116223   .5319318     2.10   0.044     .0313412    2.201105
            5  |   2.542907   .5741966     4.43   0.000     1.371825    3.713988
            6  |   1.233233   .4338037     2.84   0.008     .3484844    2.117981
            7  |   1.496063    .461687     3.24   0.003     .5544461     2.43768
            8  |   .9271761    .417414     2.22   0.034     .0758546    1.778498
            9  |   .7132363   .4386013     1.63   0.114    -.1812968    1.607769
           10  |  -.0872098   .4454745    -0.20   0.846    -.9957611    .8213415
           11  |   2.082407   .4088558     5.09   0.000      1.24854    2.916274
           12  |   2.092709   .5877807     3.56   0.001     .8939223    3.291496
           13  |   1.957509   .4706451     4.16   0.000     .9976224    2.917396
           14  |   .9445423   .5272858     1.79   0.083    -.1308642    2.019949
           15  |   1.241498   .5292371     2.35   0.026     .1621121    2.320884
           16  |   .5044626   .4324811     1.17   0.252    -.3775884    1.386514
           17  |   .6128867   .6191473     0.99   0.330    -.6498726    1.875646
           18  |  -.5033032   .4995753    -1.01   0.322    -1.522194    .5155873
           19  |   .5111114   .4870344     1.05   0.302    -.4822018    1.504425
           20  |   .4739347   .2758336     1.72   0.096    -.0886316    1.036501
           21  |   .4482408   .3361083     1.33   0.192    -.2372566    1.133738
           24  |   .2357569   .2252456     1.05   0.303    -.2236345    .6951482
           25  |  -.4283681   .2676664    -1.60   0.120    -.9742772    .1175411
           26  |  -.5689729   .2627846    -2.17   0.038    -1.104926   -.0330202
           27  |   .0488333   .3822994     0.13   0.899    -.7308714    .8285381
           28  |  -.3546079    .255738    -1.39   0.175    -.8761891    .1669733
           29  |   .1542909   .2606191     0.59   0.558    -.3772452     .685827
           30  |  -.5390402   .2975555    -1.81   0.080    -1.145909    .0678282
           31  |  -.3836032   .3365146    -1.14   0.263    -1.069929    .3027228
           32  |  -.1585311   .3447817    -0.46   0.649     -.861718    .5446559
           33  |  -.6677153   .3043337    -2.19   0.036    -1.288408   -.0470226
           34  |  -.2069282   .3688007    -0.56   0.579    -.9591021    .5452457
           35  |  -.3109342   .3688873    -0.84   0.406    -1.063285    .4414165
           36  |  -.3936873   .3332719    -1.18   0.246      -1.0734    .2860252
           37  |  -.5215181   .2906202    -1.79   0.082    -1.114242    .0712058
           38  |  -.6520205   .2759389    -2.36   0.025    -1.214802   -.0892393
           39  |   -.719748   .2384159    -3.02   0.005    -1.206001   -.2334955
           40  |  -.8269267   .2480615    -3.33   0.002    -1.332852   -.3210019
           41  |  -.8462573   .2063203    -4.10   0.000     -1.26705   -.4254644
           42  |  -.9774718   .1983986    -4.93   0.000    -1.382108   -.5728353
           43  |  -.6844414   .2327311    -2.94   0.006      -1.1591   -.2097831
           44  |  -.7927493   .2247374    -3.53   0.001    -1.251104   -.3343945
           45  |  -.8344636   .2860695    -2.92   0.007    -1.417906    -.251021
           46  |  -.9340013   .2908262    -3.21   0.003    -1.527145   -.3408573
           47  |     -.7944   .4395029    -1.81   0.080    -1.690772    .1019722
           48  |  -.6527734   .2688042    -2.43   0.021    -1.201003   -.1045435
           49  |  -.9472554   .3183957    -2.98   0.006    -1.596628    -.297883
           50  |  -.7739992   .2552812    -3.03   0.005    -1.294649   -.2533497
           51  |  -.6591308   .2749931    -2.40   0.023    -1.219983   -.0982786
           52  |  -.7478838   .2499912    -2.99   0.005    -1.257744   -.2380234
           53  |  -.9599688   .2617877    -3.67   0.001    -1.493888   -.4260493
           54  |  -1.261569   .3325019    -3.79   0.001    -1.939711   -.5834266
           55  |   .2361319   .6036391     0.39   0.698    -.9949982    1.467262
           56  |          0  (omitted)
               |
           age |  -.0488436   .0341683    -1.43   0.163    -.1185304    .0208431
          age2 |   .0005306   .0003901     1.36   0.184    -.0002651    .0013263
       edu_ref |   1.964396    .037998    51.70   0.000     1.886899    2.041894
        lnwage |   .0459319   .0261057     1.76   0.088    -.0073111    .0991749
   usual_hours |   .0938964   .0050051    18.76   0.000     .0836883    .1041045
        nchild |  -.0189383   .0887455    -0.21   0.832    -.1999361    .1620594
dummy_youngkid |   .1336484   .1054411     1.27   0.214    -.0814002     .348697
               |
      race_ref |
            2  |  -5.101245   .6336882    -8.05   0.000    -6.393661    -3.80883
            3  |  -2.006494    .753452    -2.66   0.012     -3.54317    -.469819
            4  |  -2.752406   .4684655    -5.88   0.000    -3.707848   -1.796965
            5  |  -3.377558   .2411825   -14.00   0.000    -3.869453   -2.885663
               |
2.workstat_ref |    .272921   .2093059     1.30   0.202    -.1539612    .6998031
               |
property_group |
            2  |  -.2092973   .3389107    -0.62   0.541    -.9005102    .4819155
            3  |    .339929   .1931255     1.76   0.088    -.0539531    .7338112
               |
         _cons |   32.52504   .5508157    59.05   0.000     31.40164    33.64844
--------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------------+
       Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------------+---------------------------------------|
 state_code_census |        32          32           0    *|
              year |        33           1          32     |
           ind1990 |       235           1         234     |
      ind1990#year |      6402         235        6167    ?|
-----------------------------------------------------------+
? = number of redundant parameters may be higher
* = FE nested within cluster; treated as redundant for DoF computation

Best regards,
Michelle

[Clyde Schechter]

Because you are using cluster robust standard errors, the df calculations are different. In particular, the denominator degrees of freedom (e(df_r)) in this situation is limited by the number of clusters minus 1, which, in your situation is 31. e(N) plays no role in it. Consequently, you will not be able to do any F test that involves more than 31 df--which is why your omnibus F statistic is missing. I do not know what variables are involved in your test of pre-trend, but suffice it to say, if there are more than 31 of them, you will not be able to get an F statistic for it.

[Michelle Zhang]

Because you are using cluster robust standard errors, the df calculations are different. In particular, the denominator degrees of freedom (e(df_r)) in this situation is limited by the number of clusters minus 1, which, in your situation is 31. e(N) plays no role in it. Consequently, you will not be able to do any F test that involves more than 31 df--which is why your omnibus F statistic is missing. I do not know what variables are involved in your test of pre-trend, but suffice it to say, if there are more than 31 of them, you will not be able to get an F statistic for it.

Thank you Mr. Schechter. Your explanation was very helpful! My pre-trend test is basically turning off the first 23 time periods before policy shock (since the time are relative to policy year and thus actually distribute between -23 to 33, and I add 23 so that they could be positive and used in fixed effects of "categories"). As you have explained, it would still have the problem of over 31 "controls" even dropping the first 23 years, and still would deliver an invalid F-test.

I would then try to collapse every three years into one "relative time" and try again. Thank you so much for your help!