pweights in reghdfe allow colinear variable to generate a coefficient?

[Claire Duquennois]

Hi,

This is my first post here. This question pertains to the use of pweight in reghdfe. I have a variable that is colinear with the fixed effects (see the output of the first regression. But when I add in the probability weights, reghdfe does manage do output a coefficient (see second regression output below). I was hoping someone could point me to some resources/an explanation to help me understand why this is happening.

Thank you,

Claire

[Andrew Musau]

reghdfe is from SSC (FAQ Advice #12). The estimation samples across the 2 regressions slightly differ. Try

reghdfe approve covratehat [pw=weight_cumulative], absorb(`fe4') vce(cluster statecty)
reghdfe approve covratehat if e(sample), absorb(`fe4') vce(cluster statecty)

and see whether the difference in observations explains it.

[Claire Duquennois]

Thanks for your response Andrew. Restricting it to the same sample does not change the inconsistency. Conceptually the covratehat variable should, by construction, be colinear with the statecty_cd_yr fixed effect, for all samples and subsamples, so I am struggling to understand how reghdfe is generating a coefficient when the pweights are added.

Thanks,
Claire

[Andrew Musau]

What you observe is not generally reproducible. Consider:

webuse grunfeld, clear
gen covar= company*0.25 +0.005
reghdfe invest covar, absorb(company)
reghdfe invest covar [pw=mvalue], absorb(company)

Res.:

. reghdfe invest covar, absorb(company)
note: covar 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)
note: covar omitted because of collinearity

HDFE Linear regression                            Number of obs   =        200
Absorbing 1 HDFE group                            F(   0,    190) =          .
                                                  Prob > F        =          .
                                                  R-squared       =     0.7602
                                                  Adj R-squared   =     0.7489
                                                  Within R-sq.    =     0.0000
                                                  Root MSE        =   108.6848

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       covar |          0  (omitted)
       _cons |   145.9583   7.685174    18.99   0.000      130.799    161.1175
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
     company |        10           0          10     |
-----------------------------------------------------+

.
. reghdfe invest covar [pw=mvalue], absorb(company)
note: covar 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)
note: covar omitted because of collinearity

HDFE Linear regression                            Number of obs   =        200
Absorbing 1 HDFE group                            F(   0,    190) =          .
                                                  Prob > F        =          .
                                                  R-squared       =     0.5872
                                                  Adj R-squared   =     0.5677
                                                  Within R-sq.    =     0.0000
                                                  Root MSE        =   222.2123

------------------------------------------------------------------------------
             |               Robust
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       covar |          0  (omitted)
       _cons |   370.6729   34.08355    10.88   0.000     303.4421    437.9036
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
     company |        10           0          10     |
-----------------------------------------------------+

.

Here are some ideas to push this forward:

1. Update reghdfe so that we are sure that it is not a bug in an older version that was subsequently corrected.

ssc install reghdfe, replace

2. If you have the latest version, check whether the issue is reproducible in the older version, specifying the -old- option. In this case, you are checking whether the issue was due to the latest upgrade.

reghdfe approve covratehat [pw=weight_cumulative], absorb(`fe4') vce(cluster statecty) old

3. You can run the same estimation with one of the fixed effects absorbed using the official regress command. Check whether regress replicates the issue.

regress approve covratehat [pw=weight_cumulative], absorb(statecty) cluster(statecty)

For an illustration of the above:

webuse grunfeld, clear
gen covar= company*0.25 +0.005
regress invest covar [pw=mvalue], absorb(company)

Res.:

regress invest covar [pw=mvalue], absorb(company)
(sum of wgt is 216,336.22038269)
note: covar omitted because of collinearity

Linear regression, absorbing indicators         Number of obs     =        200
                                                F(0, 190)         =       0.00
                                                Prob > F          =          .
                                                R-squared         =     0.5872
                                                Adj R-squared     =     0.5677
                                                Root MSE          =     222.21

------------------------------------------------------------------------------
             |               Robust
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       covar |          0  (omitted)
       _cons |   370.6729   34.08355    10.88   0.000     303.4421    437.9036
------------------------------------------------------------------------------

.

4. If you make no progress with 1-3 and are able to share your dataset, you can email it to me and I will investigate further.