Fixed effects and survey weights

[Giulia Ferrero]

Hi all,

I am working with a panel dataset where the panel variable is woman and the time variable is year. I would like to run a regression with both province and year fixed effects (but not woman FE!). I am clustering standard errors at the province level, accordingly:

xtreg birth_male i.gender age i.province i.year if no_child==0, vce(cluster province)

birth_male is a binary variable while gender, the regressor of interest has four categories.

Now, given that I would like to run this regression with survey weights which are not supported by xtreg, I tried to run the command below. My aim was to check whether the outputs of the two regressions are identical, as expected.

reg birth_male i.gender age i.province i.year if no_child==0, vce(cluster province)

surprisingly, this is not the case and I am not getting why. Probably the issue is that the second command ignores the panel structure of the data. How can I solve this problem?

Any clue?

Many thanks!

[Andrew Musau]

EDITED:

but not woman FE!

If you imply that all individuals in the sample are women, then the first regression controls for individual effects. Better to use this terminology than "woman FE" which can be confusing.

birth_male is a binary variable while gender, the regressor of interest has four categories.

This is confusing as well. Gender is considered to be binary; male and female. So how do you have 4 categories? In any case, gender is usually considered to be time invariant, so it will drop out of the estimation.

I would like to run a regression with both province and year fixed effects (but not woman FE!)

Probably the comparison that you want is:

xtset province
xtreg birth_male i.gender age i.year if no_child==0, vce(cluster province)
reg birth_male i.gender age i.province i.year if no_child==0, vce(cluster province)

Since your outcome is binary, a more appropriate estimator is xtlogit which can estimate a conditional FE logit model, unless you want to estimate a linear probability model. See

help xtlogit

[Carlo Lazzaro]

Giulia:
as an aside to Andrew0s excellent reply, please note:
1) if women do not change -province- during the timespan your panel stretches over, the -fe- estimator will wipe this predictor out;
2) there's no way that -xtreg,fe- and -regress- can give you back the same sample estimates (exception made for the constant; see Constant in a Fixed Effects Model - Statalist) if you do not add -i.panelvar- in the righ-hand side of your -regress-equation, as in the following toy-example:

. xtreg ln_wage c.age##c.age if idcode<=40, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =        276
Group variable: idcode                          Number of groups  =         34

R-squared:                                      Obs per group:
     Within  = 0.0860                                         min =          1
     Between = 0.2647                                         avg =        8.1
     Overall = 0.1424                                         max =         15

                                                F(2, 33)          =       2.56
corr(u_i, Xb) = 0.2088                          Prob > F          =     0.0923

                                (Std. err. adjusted for 34 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0471642   .0489821     0.96   0.343    -.0524907    .1468191
             |
 c.age#c.age |  -.0005725   .0007691    -0.74   0.462    -.0021372    .0009922
             |
       _cons |    1.05726   .7447384     1.42   0.165    -.4579212    2.572442
-------------+----------------------------------------------------------------
     sigma_u |  .33403602
     sigma_e |  .26421062
         rho |  .61514812   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. reg ln_wage c.age##c.age i.idcode if idcode<=40, vce(cluster idcode)

Linear regression                               Number of obs     =        276
                                                F(1, 33)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.5969
                                                Root MSE          =     .26421

                                (Std. err. adjusted for 34 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0471642   .0522412     0.90   0.373    -.0591214    .1534498
             |
 c.age#c.age |  -.0005725   .0008203    -0.70   0.490    -.0022414    .0010963
             |
      idcode |
          2  |  -.3720612   .0137092   -27.14   0.000    -.3999529   -.3441696
          3  |  -.5229158   .0333729   -15.67   0.000    -.5908135   -.4550182
          4  |  -.1295612   .0399275    -3.24   0.003    -.2107943   -.0483281
          5  |  -.2307167   .0298778    -7.72   0.000    -.2915037   -.1699298
          6  |  -.3054527   .0277416   -11.01   0.000    -.3618933    -.249012
          7  |  -.6488146   .0236138   -27.48   0.000    -.6968572    -.600772
          9  |   .0172563   .0043347     3.98   0.000     .0084372    .0260754
         10  |  -.6596642   .0304618   -21.66   0.000    -.7216392   -.5976893
         12  |   .7359191   .0717112    10.26   0.000     .5900216    .8818166
         13  |   .1302922   .0365034     3.57   0.001     .0560253     .204559
         14  |  -.0918187   .0717112    -1.28   0.209    -.2377162    .0540788
         15  |   .3402376   .0562453     6.05   0.000     .2258058    .4546694
         16  |   .0495111   .0279818     1.77   0.086    -.0074183    .1064405
         17  |   .1451495   .0020694    70.14   0.000     .1409393    .1493596
         18  |  -.6431574   .0561833   -11.45   0.000    -.7574631   -.5288516
         19  |  -.1083449   .0270679    -4.00   0.000    -.1634151   -.0532748
         20  |  -.0045038   .0284922    -0.16   0.875    -.0624716    .0534641
         21  |  -.1997627   .0062445   -31.99   0.000    -.2124673    -.187058
         22  |   .0615259   .0247813     2.48   0.018      .011108    .1119438
         23  |  -.2576115   .0539656    -4.77   0.000    -.3674053   -.1478176
         24  |  -.0641354   .0281672    -2.28   0.029    -.1214419   -.0068288
         25  |   .0198243   .0349148     0.57   0.574    -.0512104    .0908591
         26  |   -.199603   .0191288   -10.43   0.000    -.2385208   -.1606853
         27  |   .0591226   .0154214     3.83   0.001     .0277475    .0904976
         29  |  -.1046513   .0405522    -2.58   0.014    -.1871553   -.0221473
         30  |  -.5672304   .0130348   -43.52   0.000    -.5937498   -.5407109
         33  |  -.4128276    .032045   -12.88   0.000    -.4780236   -.3476316
         35  |  -.9723965   .0512393   -18.98   0.000    -1.076644   -.8681493
         36  |  -.1954419   .0288021    -6.79   0.000    -.2540401   -.1368437
         37  |    -.60211   .0611493    -9.85   0.000    -.7265192   -.4777007
         38  |  -.4755675   .0274881   -17.30   0.000    -.5314925   -.4196425
         39  |   .1111017   .0823492     1.35   0.186     -.056439    .2786424
         40  |  -.1794198   .0663681    -2.70   0.011    -.3144467   -.0443929
             |
       _cons |    1.21754   .7810231     1.56   0.129    -.3714631    2.806544
------------------------------------------------------------------------------

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