Standard errors attached to incorrect coefficients

[NilsEnevoldsen]

. clear

. input w x y unity

             w          x          y      unity
  1. 1    -1.10565   -1.223344       1
  2. 1   -1.109139   -1.127615       1
  3. 0   -.8497003   -1.207231       1
  4. 1   -.2734231   -1.294683       1
  5. 0    .0063879   -.8343916       1
  6. 1    .7669702   -.8245103       1 
  7. end

. reghdfe y i.w##i.unity x, a(unity)
(converged in 1 iterations)
note: 1bn.w omitted because of collinearity
note: 1bn.unity omitted because of collinearity

HDFE Linear regression                            Number of obs   =          6
Absorbing 1 HDFE group                            F(   2,      3) =       2.07
                                                  Prob > F        =     0.2726
                                                  R-squared       =     0.6044
                                                  Adj R-squared   =     0.3407
                                                  Within R-sq.    =     0.6044
                                                  Root MSE        =     0.1666

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         1.w |          0   .1442878     0.00   1.000     -.459188     .459188
     1.unity |          0  (omitted)
             |
     w#unity |
        1 1  |   -.094956          .        .       .            .           .
             |
           x |   .2046129   .1006242     2.03   0.135    -.1156182    .5248439
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
       unity |         1           0           1     |
-----------------------------------------------------+

. reghdfe y i.unity##i.w x, a(unity)
(converged in 1 iterations)
note: 1bn.unity omitted because of collinearity
note: 1bn.unity#1bn.w omitted because of collinearity

HDFE Linear regression                            Number of obs   =          6
Absorbing 1 HDFE group                            F(   2,      3) =       2.29
                                                  Prob > F        =     0.2488
                                                  R-squared       =     0.6044
                                                  Adj R-squared   =     0.3407
                                                  Within R-sq.    =     0.6044
                                                  Root MSE        =     0.1666

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     1.unity |          0  (omitted)
         1.w |   -.094956   .1442878    -0.66   0.557     -.554144    .3642321
             |
     unity#w |
        1 1  |          0  (omitted)
             |
           x |   .2046129   .1006242     2.03   0.135    -.1156182    .5248439
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
       unity |         1           0           1     |
-----------------------------------------------------+

Note that reghdfe y i.w##i.unity x, a(unity) omits 1bn.w because of collinearity, but wrongly attaches the standard error of 1.w#1.unity to it.

Reversing the order of the interaction, as in reghdfe y i.unity##i.w x, a(unity), sidesteps the issue.

(This contrived example is a reduced testcase of a more meaningful regression I run that uses triple interactions.)

[sergiocorreia]

AFAIK, this is because the betas are computed with qrsolve() and the variance with invsym(), so they decide to drop different regressors.

If I compute inv(X'X) first and then use that to select the columns used to call qrsolve, this might sidestep the issue, but I still need to dig a bit deeper.

[sergiocorreia]

I just added a commit aimed at tackling this (it also fixes some corner-case bugs, and tries to be more methodical when dealing with omitted variables)

Let me know how it goes..

[NilsEnevoldsen]

Great. Are you going to release, or should I install from GitHub?

[sergiocorreia]

GitHub. Release schedule on SSC is slower so until not much happens in terms of commits + issues), I will keep the old version there.

[NilsEnevoldsen]

I think this fixed all my tables. Thanks!