HI Statalisters,

This is my first time using the forum so apologies for any mistakes in the way I ask my question. I am running a panel data of 115 countries for 21 years (1995-2015) to look at the effect of gender inequality on GDP per capita growth. Per the literature I am lagging all of my explanatory variables by 1 year. Hausman test indicated I should use a fixed effects model. Before doing the Hausman test I had absentmindedly been running an re model which was giving me coefficients that largely agreed with the literature and mostly of high significance (particularly my main explanatory variable, l1gii). However now that I run an fe model my inequality coefficient (l1gii) is much smaller in magnitude and highly insignificant, especially the case when I include year dummies. How else might my model be misspecified?

Code:
xtreg growth l1gii l1income l1inf l1LL l1cath l1mus l1prot l1pop l1trade l1fin l1fisc l1eth l1ling l1rel l1educ i.(year), fe robust
Code:
note: l1LL omitted because of collinearity
note: l1eth omitted because of collinearity
note: l1ling omitted because of collinearity
note: l1rel omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =      1,639
Group variable: country                         Number of groups  =        106

R-sq:                                           Obs per group:
     within  = 0.2248                                         min =          1
     between = 0.0414                                         avg =       15.5
     overall = 0.0006                                         max =         20

                                                F(30,105)         =      15.65
corr(u_i, Xb)  = -0.9609                        Prob > F          =     0.0000

                              (Std. Err. adjusted for 106 clusters in country)
------------------------------------------------------------------------------
             |               Robust
      growth |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       l1gii |  -.4159595   3.737908    -0.11   0.912    -7.827541    6.995622
    l1income |  -1.860856   .5161013    -3.61   0.000    -2.884189   -.8375223
       l1inf |  -.0091544   .0058696    -1.56   0.122    -.0207927    .0024838
        l1LL |          0  (omitted)
      l1cath |   .1741005   .0344523     5.05   0.000      .105788     .242413
       l1mus |    .188407   .1767898     1.07   0.289    -.1621346    .5389485
      l1prot |   .3607714     .10124     3.56   0.001     .1600311    .5615117
       l1pop |   1.936552   2.402572     0.81   0.422    -2.827305    6.700408
     l1trade |   .0167205   .0109988     1.52   0.131    -.0050881     .038529
       l1fin |  -.0302813   .0148705    -2.04   0.044    -.0597668   -.0007957
      l1fisc |  -.0044199   .0142309    -0.31   0.757    -.0326372    .0237973
       l1eth |          0  (omitted)
      l1ling |          0  (omitted)
       l1rel |          0  (omitted)
      l1educ |   .0347149   .0134619     2.58   0.011     .0080225    .0614073
             |
        year |
       1997  |  -1.020149   .5962938    -1.71   0.090    -2.202489    .1621918
       1998  |  -1.220308   .6580708    -1.85   0.066    -2.525141    .0845252
       1999  |  -1.684301   .6181221    -2.72   0.008    -2.909923   -.4586788
       2000  |  -1.128799    .651677    -1.73   0.086    -2.420954    .1633564
       2001  |  -2.095758   .5877275    -3.57   0.001    -3.261113    -.930403
       2002  |  -2.432149   .6708015    -3.63   0.000    -3.762224   -1.102073
       2003  |  -1.477883    .679521    -2.17   0.032    -2.825248   -.1305185
       2004  |    .351459   .6526041     0.54   0.591    -.9425344    1.645452
       2005  |  -.0377926    .674156    -0.06   0.955     -1.37452    1.298934
       2006  |   .8318328   .6862415     1.21   0.228    -.5288572    2.192523
       2007  |   .8639896   .7570659     1.14   0.256    -.6371321    2.365111
       2008  |  -.9147457   .7613802    -1.20   0.232    -2.424422    .5949306
       2009  |  -5.147295   .8443502    -6.10   0.000    -6.821486   -3.473105
       2010  |   .1432391   .8004739     0.18   0.858    -1.443953    1.730431
       2011  |  -.8019953   .8775833    -0.91   0.363    -2.542081    .9380903
       2012  |  -1.123839   .9056955    -1.24   0.217    -2.919666    .6719874
       2013  |  -1.283278   .9934092    -1.29   0.199    -3.253025    .6864688
       2014  |  -.8084123   .8947158    -0.90   0.368    -2.582468    .9656438
       2015  |  -.8589373   .9814056    -0.88   0.383    -2.804883    1.087009
             |
       _cons |  -30.83163   39.49629    -0.78   0.437    -109.1455    47.48222
-------------+----------------------------------------------------------------
     sigma_u |  8.3846694
     sigma_e |  3.0279314
         rho |   .8846326   (fraction of variance due to u_i)
-------------------------------------------------------------------
For comparative sake, here is my random effects model, which has coefficients much closer to what I expected:

Code:
xtreg growth l1gii l1income l1inf l1LL l1cath l1mus l1prot l1pop l1trade l1fin l1fisc l1eth l1ling l1rel l1educ i.(year), re robust
Code:
Random-effects GLS regression                   Number of obs     =      1,639
Group variable: country                         Number of groups  =        106

R-sq:                                           Obs per group:
     within  = 0.2026                                         min =          1
     between = 0.2517                                         avg =       15.5
     overall = 0.2177                                         max =         20

                                                Wald chi2(34)     =     351.13
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

                              (Std. Err. adjusted for 106 clusters in country)
------------------------------------------------------------------------------
             |               Robust
      growth |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       l1gii |  -5.751412    1.74489    -3.30   0.001    -9.171334   -2.331491
    l1income |  -1.499993   .2333249    -6.43   0.000    -1.957301   -1.042684
       l1inf |  -.0087819   .0061215    -1.43   0.151    -.0207798     .003216
        l1LL |  -.2229272   .5587782    -0.40   0.690    -1.318112     .872258
      l1cath |   -.002218   .0061923    -0.36   0.720    -.0143546    .0099186
       l1mus |  -.0030427   .0068987    -0.44   0.659    -.0165639    .0104785
      l1prot |  -.0023174   .0081364    -0.28   0.776    -.0182645    .0136297
       l1pop |   .2547697   .1420859     1.79   0.073    -.0237135    .5332529
     l1trade |   .0123383   .0051784     2.38   0.017     .0021888    .0224879
       l1fin |  -.0185212   .0125342    -1.48   0.139    -.0430878    .0060453
      l1fisc |   .0130483   .0098959     1.32   0.187    -.0063473    .0324439
       l1eth |  -.0292718   .8429514    -0.03   0.972    -1.681426    1.622883
      l1ling |  -.8033331   .7638123    -1.05   0.293    -2.300378    .6937115
       l1rel |  -.3975609   .7580992    -0.52   0.600    -1.883408    1.088286
      l1educ |   .0388791   .0088905     4.37   0.000     .0214541    .0563041
             |
        year |
       1997  |  -.9222909   .5993069    -1.54   0.124    -2.096911    .2523291
       1998  |  -1.109369   .6492041    -1.71   0.087    -2.381785    .1630481
       1999  |  -1.624904   .5971916    -2.72   0.007    -2.795378   -.4544303
       2000  |  -1.158781   .6287846    -1.84   0.065    -2.391176    .0736141
       2001  |  -2.084703   .5416363    -3.85   0.000    -3.146291   -1.023116
       2002  |  -2.489275   .6352981    -3.92   0.000    -3.734436   -1.244113
       2003  |  -1.678445   .6368031    -2.64   0.008    -2.926556   -.4303335
       2004  |   .0755202   .5863944     0.13   0.898    -1.073792    1.224832
       2005  |  -.3382007   .5485007    -0.62   0.538    -1.413242     .736841
       2006  |   .4936469    .563494     0.88   0.381    -.6107811    1.598075
       2007  |   .4837315    .596708     0.81   0.418    -.6857947    1.653258
       2008  |  -1.342811   .5740375    -2.34   0.019    -2.467904   -.2177184
       2009  |  -5.620564   .5967645    -9.42   0.000    -6.790201   -4.450927
       2010  |  -.4340173   .5686492    -0.76   0.445    -1.548549    .6805147
       2011  |  -1.367447   .6433871    -2.13   0.034    -2.628463   -.1064319
       2012  |  -1.786086   .5798817    -3.08   0.002    -2.922633   -.6495383
       2013  |  -2.014462   .7817502    -2.58   0.010    -3.546664   -.4822598
       2014  |  -1.493345   .5152251    -2.90   0.004    -2.503168   -.4835225
       2015  |    -1.5867   .5979239    -2.65   0.008    -2.758609   -.4147906
             |
       _cons |    11.0207   3.682578     2.99   0.003     3.802984    18.23842
-------------+----------------------------------------------------------------
     sigma_u |  1.3768448
     sigma_e |  3.0279314
         rho |  .17133855   (fraction of variance due to u_i)
------------------------------------------------------------------------------

Many thanks