Results insignificant after using year dummy variables.

[Sania Zaffer]

Hi everyone!
I have a question regarding year dummy variables. I am trying to investigate the impact of Trade liberalisation on female labour force participation rate in 14 developing Asian countries and am therefore running a Fixed Effects regression. The first regression I run is without any year dummy variables and solely includes the Control Variables and the explanatory variable. The code is shown below.

xtreg FLFPR FR FUR GDPpc TO, fe robust

This gave me the following result where TO is significant at the 5% level.

Fixed-effects (within) regression               Number of obs     =        403
Group variable: CountryNum                      Number of groups  =         14

R-sq:                                           Obs per group:
     within  = 0.0876                                         min =         26
     between = 0.2218                                         avg =       28.8
     overall = 0.1360                                         max =         29

                                                F(4,13)           =       2.91
corr(u_i, Xb)  = -0.4371                        Prob > F          =     0.0639

                            (Std. Err. adjusted for 14 clusters in CountryNum)
------------------------------------------------------------------------------
             |               Robust
       FLFPR |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          FR |  -.7364388   .7314433    -1.01   0.332    -2.316626    .8437484
         FUR |    .083618   .2047825     0.41   0.690    -.3587877    .5260237
       GDPpc |   .0001044   .0000646     1.62   0.130    -.0000352     .000244
          TO |  -.0282203   .0121169    -2.33   0.037    -.0543972   -.0020434
       _cons |   54.80075   3.269936    16.76   0.000     47.73648    61.86501
-------------+----------------------------------------------------------------
     sigma_u |  19.497251
     sigma_e |  2.4764401
         rho |  .98412337   (fraction of variance due to u_i)
------------------------------------------------------------------------------

However, when I add a dummy variable for each year (minus 1) that is in my sample, i.e, from 1990 to 2018, the coefficient on TO becomes insignificant.

xtreg FLFPR FR FUR GDPpc TO y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 y17 y18 y19 y20 y21 y22 y23 y24 y25 y26 y27 y28, fe robust

Fixed-effects (within) regression               Number of obs     =        403
Group variable: CountryNum                      Number of groups  =         14

R-sq:                                           Obs per group:
     within  = 0.1396                                         min =         26
     between = 0.0039                                         avg =       28.8
     overall = 0.0003                                         max =         29

                                                F(13,13)          =          .
corr(u_i, Xb)  = -0.1276                        Prob > F          =          .

                            (Std. Err. adjusted for 14 clusters in CountryNum)
------------------------------------------------------------------------------
             |               Robust
       FLFPR |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          FR |  -1.708764     .96501    -1.77   0.100    -3.793541    .3760136
         FUR |   .0074997   .1827171     0.04   0.968    -.3872366     .402236
       GDPpc |   .0001995   .0000496     4.02   0.001     .0000923    .0003066
          TO |  -.0247951   .0168391    -1.47   0.165    -.0611737    .0115836
          y1 |   3.389236   2.208276     1.53   0.149    -1.381454    8.159926
          y2 |   3.233488   2.046978     1.58   0.138     -1.18874    7.655715
          y3 |   2.842947    1.78705     1.59   0.136    -1.017741    6.703634
          y4 |    2.85432   1.773783     1.61   0.132    -.9777045    6.686345
          y5 |   2.955971   1.664716     1.78   0.099    -.6404285    6.552371
          y6 |     2.5787   1.498052     1.72   0.109    -.6576454    5.815045
          y7 |   2.636164   1.457976     1.81   0.094    -.5136015     5.78593
          y8 |   2.565584   1.569233     1.63   0.126    -.8245376    5.955705
          y9 |   3.053849   1.642985     1.86   0.086    -.4956048    6.603303
         y10 |   2.601952   1.472541     1.77   0.101    -.5792797    5.783184
         y11 |    2.50133   1.517437     1.65   0.123    -.7768944    5.779554
         y12 |   2.761161   1.551812     1.78   0.099    -.5913241    6.113647
         y13 |   2.263491   1.601462     1.41   0.181    -1.196258    5.723241
         y14 |   2.026965   1.640635     1.24   0.239    -1.517411    5.571341
         y15 |   1.769197   1.743178     1.01   0.329     -1.99671    5.535105
         y16 |   1.714858    1.81088     0.95   0.361     -2.19731    5.627027
         y17 |    1.45597   1.706395     0.85   0.409    -2.230472    5.142411
         y18 |   1.589595   1.560558     1.02   0.327    -1.781786    4.960976
         y19 |   1.325755   1.502858     0.88   0.394    -1.920973    4.572483
         y20 |   1.340527   1.423183     0.94   0.363    -1.734073    4.415128
         y21 |   1.286046    1.29986     0.99   0.341    -1.522132    4.094223
         y22 |   1.401393   1.278901     1.10   0.293    -1.361506    4.164291
         y23 |   .9731538   1.114448     0.87   0.398    -1.434464    3.380772
         y24 |   .4656153   .7664366     0.61   0.554     -1.19017    2.121401
         y25 |   .2296892   .6472401     0.35   0.728    -1.168588    1.627966
         y26 |   .3651207   .6224359     0.59   0.568    -.9795703    1.709812
         y27 |   .2646698   .4753703     0.56   0.587    -.7623053    1.291645
         y28 |   .3260597   .3253869     1.00   0.335     -.376896    1.029015
       _cons |   55.61924   3.822775    14.55   0.000     47.36063    63.87784
-------------+----------------------------------------------------------------
     sigma_u |  19.066549
     sigma_e |  2.4973914
         rho |  .98313287   (fraction of variance due to u_i)
------------------------------------------------------------------------------

This is also the case for some other variables that I am using as explanatory variables in separate regressions for the same research.
Does anyone have any insight on why this might be the outcome and what it implies in terms of the yearly trends and the relationship between the explanatory and outcome variables?

Additionally I also wanted to confirm whether it is necessary/helpful to add year dummy variables when one is using a Fixed Effects model?

Thank you!

[Jared Greathouse]

Using FE for time, units, and both at once changes the estimand you're estimating. I direct everyone to this paper on the matter which hasn't really caused econ instructors to change their thinking much, but here it is. The short answer is "no, don't use both".

I wouldn't hunt statistical significance with a shotgun, thus spoke the Book of Kennedy, verse 7. In my opinion, statistical significance is stupid and is easily influenced by this like sample size, estimator and various other aspects of your data. You have a very small sample size, so it isn't surprising that your results are quite sensitive to small changes in your model.

In short, if I were you, I'd focus on the substantive meaning of my results. Abandon statistical significance, and consider the implications of adding unit or time dummies in your model.




Oh, and don't add in 30 year variables, just use i.year, Stata's time series notation.