Interpreting fixed effects for a panel

[Adrienne Wold]

Hi,
I am working with a panel data set which is xtset at the district year level. With district and year fixed effects, does the interpretation amount to examining variation within districts in the same year?

Thanks.

[Carlo Lazzaro]

Adrienne:
not quite.
Under the -fe- specification, coefficients report variation of time varying predictors within the same panel as years go by (that is, along the entire time span -t-).
If you want to compare variation between different panels as time stretches over, you should go -be- or, more frequently, -re-.

[Adrienne Wold]

I'm not sure I understand then what the difference between controlling for district and year fixed effects via something like i.district and i.year versus using the xt option with "fe" specified is.

[Carlo Lazzaro]

Adrienne:
you probably meant what's the difference between:

regress <regressand> <regressors> i.panelid i.time

vs

 xtset panelid time
xtreg <regressand> <regressors> i.time, fe

Despite the coefficient will be the same (set aside for -paneild- which will be not estimated in -xtreg,fe-), the second approach gives you an insight about the existence of a panel-wise effect (sigma_u) along with its significance (F-test appearing as a footnote of the -xtreg, fe- outcome table), something that you cannot get from -regress-, as you can see from the following toy-example:

. use "http://www.stata-press.com/data/r15/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. regress ln_wage i.idcode i.year age if idcode<=4

      Source |       SS           df       MS      Number of obs   =        50
-------------+----------------------------------   F(18, 31)       =      1.19
       Model |  2.96881764        18  .164934314   Prob > F        =    0.3290
    Residual |  4.31127709        31  .139073454   R-squared       =    0.4078
-------------+----------------------------------   Adj R-squared   =    0.0639
       Total |  7.28009473        49  .148573362   Root MSE        =    .37293

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      idcode |
          2  |    -.34821   .1544058    -2.26   0.031    -.6631228   -.0332973
          3  |  -1.996997   2.662102    -0.75   0.459     -7.42639    3.432395
          4  |  -1.597003   2.699068    -0.59   0.558    -7.101788    3.907781
             |
        year |
         69  |  -.0536729   .6925589    -0.08   0.939    -1.466156     1.35881
         70  |  -.5622491   .9779883    -0.57   0.570    -2.556869    1.432371
         71  |  -.9270145   1.387092    -0.67   0.509    -3.756008    1.901979
         72  |  -1.063298   1.819443    -0.58   0.563    -4.774076     2.64748
         73  |  -1.228195   2.258252    -0.54   0.590     -5.83393     3.37754
         75  |  -1.704501   3.144409    -0.54   0.592    -8.117565    4.708562
         77  |  -2.312608   4.040225    -0.57   0.571     -10.5527    5.927484
         78  |  -2.367822   4.486708    -0.53   0.601    -11.51852     6.78288
         80  |  -3.040105   5.376662    -0.57   0.576    -14.00588     7.92567
         82  |  -3.763953   6.275703    -0.60   0.553    -16.56333    9.035427
         83  |  -3.803244   6.719895    -0.57   0.575    -17.50856    9.902073
         85  |  -4.165837   7.616051    -0.55   0.588    -19.69888     11.3672
         87  |  -4.750318   8.512544    -0.56   0.581    -22.11177    12.61113
         88  |  -5.133582   9.297175    -0.55   0.585     -24.0953    13.82813
             |
         age |   .2626399   .4488774     0.59   0.563    -.6528517    1.178131
       _cons |  -2.287519   7.228638    -0.32   0.754    -17.03042    12.45539
------------------------------------------------------------------------------

. xtset idcode year
       panel variable:  idcode (unbalanced)
        time variable:  year, 68 to 88, but with gaps
                delta:  1 unit

. xtreg ln_wage i.year age if idcode<=4, fe

Fixed-effects (within) regression               Number of obs     =         50
Group variable: idcode                          Number of groups  =          4

R-sq:                                           Obs per group:
     within  = 0.1909                                         min =         11
     between = 0.0349                                         avg =       12.5
     overall = 0.0044                                         max =         15

                                                F(15,31)          =       0.49
corr(u_i, Xb)  = -0.9582                        Prob > F          =     0.9290

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        year |
         69  |  -.0536729   .6925589    -0.08   0.939    -1.466156     1.35881
         70  |  -.5622491   .9779883    -0.57   0.570    -2.556869    1.432371
         71  |  -.9270145   1.387092    -0.67   0.509    -3.756008    1.901979
         72  |  -1.063298   1.819443    -0.58   0.563    -4.774076     2.64748
         73  |  -1.228195   2.258252    -0.54   0.590     -5.83393     3.37754
         75  |  -1.704501   3.144409    -0.54   0.592    -8.117565    4.708562
         77  |  -2.312608   4.040225    -0.57   0.571     -10.5527    5.927484
         78  |  -2.367822   4.486708    -0.53   0.601    -11.51852     6.78288
         80  |  -3.040105   5.376662    -0.57   0.576    -14.00588     7.92567
         82  |  -3.763953   6.275703    -0.60   0.553    -16.56333    9.035427
         83  |  -3.803244   6.719895    -0.57   0.575    -17.50856    9.902073
         85  |  -4.165837   7.616051    -0.55   0.588    -19.69888     11.3672
         87  |  -4.750318   8.512544    -0.56   0.581    -22.11177    12.61113
         88  |  -5.133582   9.297175    -0.55   0.585     -24.0953    13.82813
             |
         age |   .2626399   .4488774     0.59   0.563    -.6528517    1.178131
       _cons |  -3.321529   8.616061    -0.39   0.702     -20.8941    14.25104
-------------+----------------------------------------------------------------
     sigma_u |  .96166721
     sigma_e |  .37292553
         rho |  .86927679   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(3, 31) = 4.30                       Prob > F = 0.0120

.

In sum, when you have panel data analysis and you want to go -fe- (provided that this is the right specification for your model), you should start from -xtreg,fe- instead from -regress- with -i.panelid-.