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  • Insignificant and unexpected coefficients in fe model, especially with year dummies

    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

  • #2
    The random and fixed effects models are very different conceptually. Fixed effects only looks at change over time within a panel (within effect). Random includes both change over time and differences across panels (between). While many use a Hausman to choose between the two (essentially testing if between effects equal within effects), it is quite possible that between effects should differ from within - the choice is not just a statistical issue.

    So one could interpret the lack of within significance as the right answer, or one could look at both between and within and think that some of what differs across countries is stable and important. The xtreg documentation goes into this somewhat. Mundlak and hybrid estimators like xthybrid are alternatives perhaps worth considering.

    Comment


    • #3
      Ah this makes sense, thank you very much Phil

      Comment


      • #4
        Hellie:
        as an aside to Phil's helpful insight, you can also test whether -i.year- are jointly statistically significant vi a-testparm-, as you can see from the following toy-example:
        Code:
        . use "http://www.stata-press.com/data/r15/nlswork.dta"
        (National Longitudinal Survey. Young Women 14-26 years of age in 1968)
        
        . xtreg ln_wage age i.year, fe robust
        
        Fixed-effects (within) regression Number of obs = 28,510
        Group variable: idcode Number of groups = 4,710
        
        R-sq: Obs per group:
        within = 0.1060 min = 1
        between = 0.0914 avg = 6.1
        overall = 0.0805 max = 15
        
        F(15,4709) = 69.49
        corr(u_i, Xb) = 0.0467 Prob > F = 0.0000
        
        (Std. Err. adjusted for 4,710 clusters in idcode)
        ------------------------------------------------------------------------------
        | Robust
        ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
        -------------+----------------------------------------------------------------
        age | .0125992 .0123091 1.02 0.306 -.0115323 .0367308
        |
        year |
        69 | .0748621 .0156425 4.79 0.000 .0441955 .1055287
        70 | .0478697 .0265729 1.80 0.072 -.0042256 .0999649
        71 | .0865577 .0385328 2.25 0.025 .0110155 .1621
        72 | .0856757 .0505004 1.70 0.090 -.0133288 .1846802
        73 | .0880069 .0626993 1.40 0.160 -.0349132 .2109269
        75 | .0778607 .0865126 0.90 0.368 -.0917446 .247466
        77 | .108365 .1111117 0.98 0.329 -.1094659 .3261959
        78 | .1309518 .1237306 1.06 0.290 -.1116181 .3735217
        80 | .1142649 .1480678 0.77 0.440 -.1760172 .4045471
        82 | .1090451 .1724619 0.63 0.527 -.2290608 .4471511
        83 | .1211272 .1846402 0.66 0.512 -.2408539 .4831083
        85 | .1465637 .2092454 0.70 0.484 -.2636552 .5567825
        87 | .1382642 .2341219 0.59 0.555 -.3207242 .5972527
        88 | .1799741 .2500607 0.72 0.472 -.3102618 .67021
        |
        _cons | 1.203731 .235213 5.12 0.000 .7426037 1.664859
        -------------+----------------------------------------------------------------
        sigma_u | .4058746
        sigma_e | .30300411
        rho | .64212421 (fraction of variance due to u_i)
        ------------------------------------------------------------------------------
        
        . testparm(i.year)
        
        ( 1) 69.year = 0
        ( 2) 70.year = 0
        ( 3) 71.year = 0
        ( 4) 72.year = 0
        ( 5) 73.year = 0
        ( 6) 75.year = 0
        ( 7) 77.year = 0
        ( 8) 78.year = 0
        ( 9) 80.year = 0
        (10) 82.year = 0
        (11) 83.year = 0
        (12) 85.year = 0
        (13) 87.year = 0
        (14) 88.year = 0
        
        F( 14, 4709) = 7.76
        Prob > F = 0.0000
        
        .
        Kind regards,
        Carlo
        (Stata 18.0 SE)

        Comment


        • #5
          Thank you, I have now added this test to my work!

          Comment

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