year dummies in xtreg and pooled OLS

[Timea De Wispelaere]

Hello,

I ran both a fixed effects model and pooled OLS model on the same dataset. I am now wondering if, including year dummies and thus time effects, is comparable in both regressions. In the literature they mention "time fixed effects" to control for variables that are constant acreoss firms but change over time in the fixed effects model and "aggregate time effects" in the pooled OLS model. I am now wondering if the regression happens in a different way concerning these time dummies. And if so, what is the difference?

Kind regards,
Timea

[Carlo Lazzaro]

Timea:
the main issue here is that pooled OLS and -xtreg,fe- are different estimators.
Besides, I'm not clear whether, by "aggregate time effects", you mean -c.time- vs -i.time-.
As usual, sharing what you typed and what Stata gave you back (as per FAQ) would help enormously interested listers in replying more positively to your queries.

[Timea De Wispelaere]

Hi Carlo, what I meant was i.time

[Carlo Lazzaro]

Timea:
if you mean:

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. reg ln_wage i.year i.idcode c.age##c.age if idcode<=4

      Source |       SS           df       MS      Number of obs   =        50
-------------+----------------------------------   F(19, 30)       =      3.05
       Model |  4.79792411        19  .252522321   Prob > F        =    0.0031
    Residual |  2.48217063        30  .082739021   R-squared       =    0.6590
-------------+----------------------------------   Adj R-squared   =    0.4431
       Total |  7.28009473        49  .148573362   Root MSE        =    .28764

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        year |
         69  |    .224994   .5374605     0.42   0.678    -.8726469    1.322635
         70  |   .1649135   .7700301     0.21   0.832    -1.407698    1.737525
         71  |   .1712431    1.09509     0.16   0.877    -2.065229    2.407715
         72  |   .3136266   1.433598     0.22   0.828    -2.614171    3.241424
         73  |   .4386164   1.777538     0.25   0.807      -3.1916    4.068833
         75  |    .575746   2.473349     0.23   0.818    -4.475507    5.626999
         77  |    .651904   3.179439     0.21   0.839    -5.841377    7.145185
         78  |   .9314592     3.5311     0.26   0.794    -6.280009    8.142927
         80  |   .9700889    4.23391     0.23   0.820    -7.676708    9.616886
         82  |   1.063147   4.948233     0.21   0.831    -9.042493    11.16879
         83  |   1.379563   5.299088     0.26   0.796    -9.442619    12.20175
         85  |   1.854813   6.012334     0.31   0.760    -10.42401    14.13364
         87  |   2.153058   6.728032     0.32   0.751    -11.58742    15.89353
         88  |   2.571633   7.355941     0.35   0.729     -12.4512    17.59447
             |
      idcode |
          2  |   -.394374   .1194999    -3.30   0.002    -.6384254   -.1503226
          3  |   .1010589   2.101252     0.05   0.962     -4.19027    4.392388
          4  |   .5522662   2.131432     0.26   0.797    -3.800699    4.905231
             |
         age |   .2364322   .3462718     0.68   0.500    -.4707491    .9436135
             |
 c.age#c.age |  -.0056102   .0011932    -4.70   0.000    -.0080471   -.0031734
             |
       _cons |  -1.093667   5.581352    -0.20   0.846    -12.49231    10.30497
------------------------------------------------------------------------------

. xtreg ln_wage i.year c.age##c.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  = 0.5342                                         min =         11
     between = 0.0151                                         avg =       12.5
     overall = 0.2227                                         max =         15

                                                F(16,30)          =       2.15
corr(u_i, Xb)  = -0.6249                        Prob > F          =     0.0342

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        year |
         69  |    .224994   .5374605     0.42   0.678    -.8726469    1.322635
         70  |   .1649135   .7700301     0.21   0.832    -1.407698    1.737525
         71  |   .1712431    1.09509     0.16   0.877    -2.065229    2.407715
         72  |   .3136266   1.433598     0.22   0.828    -2.614171    3.241424
         73  |   .4386164   1.777538     0.25   0.807      -3.1916    4.068833
         75  |    .575746   2.473349     0.23   0.818    -4.475507    5.626999
         77  |    .651904   3.179439     0.21   0.839    -5.841377    7.145185
         78  |   .9314592     3.5311     0.26   0.794    -6.280009    8.142927
         80  |   .9700889    4.23391     0.23   0.820    -7.676708    9.616886
         82  |   1.063147   4.948233     0.21   0.831    -9.042493    11.16879
         83  |   1.379563   5.299088     0.26   0.796    -9.442619    12.20175
         85  |   1.854813   6.012334     0.31   0.760    -10.42401    14.13364
         87  |   2.153058   6.728032     0.32   0.751    -11.58742    15.89353
         88  |   2.571633   7.355941     0.35   0.729     -12.4512    17.59447
             |
         age |   .2364322   .3462718     0.68   0.500    -.4707491    .9436135
             |
 c.age#c.age |  -.0056102   .0011932    -4.70   0.000    -.0080471   -.0031734
             |
       _cons |  -1.036501   6.663463    -0.16   0.877    -14.64511    12.57211
-------------+----------------------------------------------------------------
     sigma_u |  .38900632
     sigma_e |  .28764391
         rho |  .64651254   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(3, 30) = 8.22                       Prob > F = 0.0004

set aside the _cons, the results are perfecty the same, as you do the same regression with two different approaches.

Conversely, what above does not hold for pooled OLS vs -xtreg,fe- (because they are two different beasts):

. reg ln_wage i.year c.age##c.age if idcode<=4, vce(cluster idcode)

Linear regression                               Number of obs     =         50
                                                F(2, 3)           =          .
                                                Prob > F          =          .
                                                R-squared         =     0.3789
                                                Root MSE          =     .37015

                                 (Std. Err. adjusted for 4 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        year |
         69  |   .1486743   .0549624     2.71   0.073    -.0262406    .3235891
         70  |    .277369   .2887149     0.96   0.408    -.6414508    1.196189
         71  |   .1301287   .2621698     0.50   0.654    -.7042125      .96447
         72  |   .1961925   .2197171     0.89   0.438    -.5030453    .8954304
         73  |   .2437975   .1144552     2.13   0.123      -.12045     .608045
         75  |   .2229619   .0470414     4.74   0.018     .0732552    .3726686
         77  |   .0565625   .2272149     0.25   0.819    -.6665367    .7796618
         78  |   .2544722   .4275434     0.60   0.594    -1.106162    1.615106
         80  |   .2037513    .589187     0.35   0.752    -1.671305    2.078807
         82  |   .0580069   .6546599     0.09   0.935    -2.025413    2.141427
         83  |   .3523115   .6776646     0.52   0.639     -1.80432    2.508943
         85  |   .6482934   .7762536     0.84   0.465    -1.822092    3.118679
         87  |   .7630092   .8329341     0.92   0.427    -1.887759    3.413777
         88  |     1.0182    .886308     1.15   0.334    -1.802428    3.838827
             |
         age |   .2887857    .133158     2.17   0.119    -.1349825     .712554
             |
 c.age#c.age |  -.0050776   .0021492    -2.36   0.099    -.0119174    .0017622
             |
       _cons |  -2.402156   1.992439    -1.21   0.314    -8.742986    3.938675
------------------------------------------------------------------------------