Workaround for "svy: xtreg , fe"

Jack Jameson

Join Date: Apr 2021

Posts: 20
#1

Workaround for "svy: xtreg , fe"

27 May 2022, 09:57

Dear Stata users,

I am using a survey dataset, which I declare as survey data

Code:

svyset clusterID [pweight=pw], strata(strataID) singleunit(centered)

I would like to run a fixed effects model, but xtreg is not supported by svy. In addition, my weights change through time so I cannot simply add pweights to xtreg. I also have a large number of panels, so a normal regression with individual level dummies is not feasible.

For now, this is the best approximation I've found:

Code:

areg y x [pweight=pw], absorb(panelID) vce(cluster clusterID)

However, my standard errors are unexpectedly large, which may be due to the fact that I am not accounting for strata. This is an aspect of svyset that I don't really understand, even after reading the help files.

Is there a way that I can build upon the areg specification in order to take strata into account, and best approximate a theoretical "svy: xtreg , fe" command?

Any information would be greatly appreciated.

Thank you in advance,
Jack

Last edited by Jack Jameson; 27 May 2022, 10:19.
Tags: areg, fixed effects, survey data, svyset

Andrew Musau

Join Date: Oct 2014
Posts: 9944

27 May 2022, 10:19

-svy- estimation will differ from including weights in the presence of stratification. An alternative command to areg is:

Code:

ssc install reghdfe

Code:

webuse nhanes2f, clear
svyset psuid [pweight=finalwgt], strata(stratid)
svy: regress zinc age c.age#c.age weight female black orace rural i.region
reghdfe zinc age c.age#c.age weight female black orace rural [pweight=finalwgt], absorb(region)

You may get closer to the -svy- standard errors by clustering at the strata level.

Code:

reghdfe zinc age c.age#c.age weight female black orace rural [pweight=finalwgt], absorb(region) cluster(stratid)

Res.:

Code:

. svyset psuid [pweight=finalwgt], strata(stratid)

      pweight: finalwgt
          VCE: linearized
  Single unit: missing
     Strata 1: stratid
         SU 1: psuid
        FPC 1: <zero>

.
. svy: regress zinc age c.age#c.age weight female black orace rural i.region
(running regress on estimation sample)

Survey: Linear regression

Number of strata   =        31                Number of obs     =        9,189
Number of PSUs     =        62                Population size   =  104,176,071
                                              Design df         =           31
                                              F(  10,     22)   =        39.57
                                              Prob > F          =       0.0000
                                              R-squared         =       0.0708

------------------------------------------------------------------------------
             |             Linearized
        zinc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.1656289   .0837319    -1.98   0.057    -.3364013    .0051436
             |
 c.age#c.age |   .0008381   .0008655     0.97   0.340    -.0009271    .0026033
             |
      weight |   .0530054   .0139419     3.80   0.001     .0245708      .08144
      female |  -6.126299   .4503075   -13.60   0.000    -7.044707   -5.207891
       black |  -2.639637   .9309377    -2.84   0.008    -4.538297   -.7409767
       orace |  -4.621847   1.866237    -2.48   0.019    -8.428063   -.8156321
       rural |   -.430827   .6720359    -0.64   0.526    -1.801453    .9397992
             |
      region |
         MW  |   .1015875   .8366954     0.12   0.904    -1.604864    1.808039
          S  |   -.443779    .873074    -0.51   0.615    -2.224425    1.336867
          W  |   .8625159   1.560477     0.55   0.584    -2.320099    4.045131
             |
       _cons |   92.21343   1.999375    46.12   0.000     88.13568    96.29119
------------------------------------------------------------------------------

.
. reghdfe zinc age c.age#c.age weight female black orace rural [pweight=finalwgt], absorb(region) cluster(stratid)
(MWFE estimator converged in 1 iterations)

HDFE Linear regression                            Number of obs   =      9,189
Absorbing 1 HDFE group                            F(   7,     30) =     123.83
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.0708
                                                  Adj R-squared   =     0.0698
                                                  Within R-sq.    =     0.0692
Number of clusters (stratid) =         31         Root MSE        =    14.2125

                               (Std. Err. adjusted for 31 clusters in stratid)
------------------------------------------------------------------------------
             |               Robust
        zinc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.1656289     .08583    -1.93   0.063    -.3409172    .0096595
             |
 c.age#c.age |   .0008381   .0009528     0.88   0.386    -.0011077    .0027839
             |
      weight |   .0530054   .0108136     4.90   0.000     .0309211    .0750897
      female |  -6.126299   .4577537   -13.38   0.000    -7.061157   -5.191441
       black |  -2.639637   .6833685    -3.86   0.001    -4.035261   -1.244012
       orace |  -4.621847   .8036171    -5.75   0.000    -6.263052   -2.980642
       rural |   -.430827   .6572918    -0.66   0.517    -1.773196    .9115419
       _cons |   92.34905   1.908838    48.38   0.000     88.45068    96.24742
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
      region |         4           0           4     |
-----------------------------------------------------+

.

Last edited by Andrew Musau; 27 May 2022, 10:38.

Comment

Jack Jameson

Join Date: Apr 2021

Posts: 20
#3

30 May 2022, 04:56

Hi Andrew,

Thanks for your suggestion. Why should I cluster at the strata level instead of PSUs? Don't svy commands cluster at the PSU level? When using my data, I find that clustering at the strata level inflates standard errors even more than clustering at the PSU level.
Comment
Andrew Musau

Join Date: Oct 2014

Posts: 9944
#4

30 May 2022, 06:06

In the absence of stratification, using -pweights- and clustering on the PSU variable is equivalent to -svy- estimation. With stratification, there is no equivalent strategy. In my example, the PSU variable has only 2 levels, so there will be significant bias if I cluster using the PSU variable.
Comment

Andrew Musau

Join Date: Oct 2014
Posts: 9944

30 May 2022, 06:26

It appears that regress with the -svy- prefix still allows the -absorb()- option. So this may solve your problem.

Code:

webuse nhanes2f, clear
svyset psuid [pweight=finalwgt], strata(stratid)
svy: regress zinc age c.age#c.age weight female black orace rural i.region
svy: regress zinc age c.age#c.age weight female black orace rural, absorb(region)

Res.:

Code:

.
. svyset psuid [pweight=finalwgt], strata(stratid)

      pweight: finalwgt
          VCE: linearized
  Single unit: missing
     Strata 1: stratid
         SU 1: psuid
        FPC 1: <zero>

.
. svy: regress zinc age c.age#c.age weight female black orace rural i.region
(running regress on estimation sample)

Survey: Linear regression

Number of strata   =        31                Number of obs     =        9,189
Number of PSUs     =        62                Population size   =  104,176,071
                                              Design df         =           31
                                              F(  10,     22)   =        39.57
                                              Prob > F          =       0.0000
                                              R-squared         =       0.0708

------------------------------------------------------------------------------
             |             Linearized
        zinc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.1656289   .0837319    -1.98   0.057    -.3364013    .0051436
             |
 c.age#c.age |   .0008381   .0008655     0.97   0.340    -.0009271    .0026033
             |
      weight |   .0530054   .0139419     3.80   0.001     .0245708      .08144
      female |  -6.126299   .4503075   -13.60   0.000    -7.044707   -5.207891
       black |  -2.639637   .9309377    -2.84   0.008    -4.538297   -.7409767
       orace |  -4.621847   1.866237    -2.48   0.019    -8.428063   -.8156321
       rural |   -.430827   .6720359    -0.64   0.526    -1.801453    .9397992
             |
      region |
         MW  |   .1015875   .8366954     0.12   0.904    -1.604864    1.808039
          S  |   -.443779    .873074    -0.51   0.615    -2.224425    1.336867
          W  |   .8625159   1.560477     0.55   0.584    -2.320099    4.045131
             |
       _cons |   92.21343   1.999375    46.12   0.000     88.13568    96.29119
------------------------------------------------------------------------------

.
. svy: regress zinc age c.age#c.age weight female black orace rural, absorb(region)
(running regress on estimation sample)

Survey: Linear regression

Number of strata   =        31                Number of obs     =        9,189
Number of PSUs     =        62                Population size   =  104,176,071
                                              Design df         =           31
                                              F(   7,     25)   =        63.23
                                              Prob > F          =       0.0000
                                              R-squared         =       0.0708

------------------------------------------------------------------------------
             |             Linearized
        zinc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.1656289   .0845041    -1.96   0.059    -.3379761    .0067184
             |
 c.age#c.age |   .0008381   .0008667     0.97   0.341    -.0009295    .0026057
             |
      weight |   .0530054   .0139078     3.81   0.001     .0246402    .0813706
      female |  -6.126299   .4403543   -13.91   0.000    -7.024408   -5.228191
       black |  -2.639637   1.121315    -2.35   0.025    -4.926574   -.3526995
       orace |  -4.621847   1.557779    -2.97   0.006    -7.798959   -1.444736
       rural |   -.430827   .6325575    -0.68   0.501    -1.720937    .8592825
       _cons |   92.34905   2.235011    41.32   0.000     87.79071    96.90738
------------------------------------------------------------------------------

Last edited by Andrew Musau; 30 May 2022, 06:31.

Comment

Jack Jameson

Join Date: Apr 2021

Posts: 20
#6

30 May 2022, 07:51

Thanks again Andrew, this is really helpful. I had no idea that this option existed for -reg-. Is it written anywhere in the help files? I can't seem to find it...

This seems to massively inflate my SEs, not sure why this is could be happening

Last edited by Jack Jameson; 30 May 2022, 08:02.
Comment
Andrew Musau

Join Date: Oct 2014

Posts: 9944
#7

30 May 2022, 09:40

The -absorb()- option is undocumented, but it essentially turns regress into areg. I do not think that your standard errors change much compared to the case where you include the fixed effects as indicators. There is a small adjustment due to different degrees of freedom from explicitly including indicators and absorbing them. Try to do a comparison with a small subset of your data.
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