Misspecification Tests for Fixed Effect Model

[Hellie Flint]

Hi all,

I am running a fixed effects model and I would like to check for omitted variables and/or misspecification (apologies if the two things aren't related, I'm relatively new to this). I am aware that -estat ovtest- only works after -regress- therefore is not valid for my use. Is there an equivalent test that can be used after -xtreg, fe-?

Is the following code an alternative, if so, how do I interpret my results?

predict yhat, xb
(839 missing values generated)

. gen yhat2 = yhat^2
(839 missing values generated)

. gen yhat3 = yhat^3
(839 missing values generated)

. gen yhat4 = yhat^4
(839 missing values generated)

. xtreg Growth lagGII lagIncomeln Inflation Landlocked Catholic Muslim Protestant Populationln CivilLiberty Trade FinancialFreedom FiscalFreedom Ethnic Linguistic Religious Education yhat2 yhat3 yhat4 i.Year, fe
>  robust
note: Landlocked omitted because of collinearity
note: Ethnic omitted because of collinearity
note: Linguistic omitted because of collinearity
note: Religious omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =      1,576
Group variable: CountryID                       Number of groups  =        102

R-sq:                                           Obs per group:
     within  = 0.2410                                         min =          1
     between = 0.0425                                         avg =       15.5
     overall = 0.0024                                         max =         20

                                                F(34,101)         =      16.72
corr(u_i, Xb)  = -0.9843                        Prob > F          =     0.0000

                                (Std. Err. adjusted for 102 clusters in CountryID)
----------------------------------------------------------------------------------
                 |               Robust
          Growth |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
          lagGII |   -2.29081   4.028734    -0.57   0.571    -10.28273    5.701114
     lagIncomeln |  -2.995378   1.397931    -2.14   0.035    -5.768496   -.2222597
       Inflation |  -.0067965   .0055327    -1.23   0.222     -.017772    .0041789
      Landlocked |          0  (omitted)
        Catholic |    .154141   .0451405     3.41   0.001     .0645944    .2436877
          Muslim |   .3246629   .1655551     1.96   0.053    -.0037538    .6530797
      Protestant |   .4809566   .1046587     4.60   0.000     .2733418    .6885714
    Populationln |    .287302   2.491611     0.12   0.908    -4.655384    5.229988
    CivilLiberty |   .1738866   .2514914     0.69   0.491    -.3250047    .6727779
           Trade |   .0103646   .0101007     1.03   0.307    -.0096725    .0304016
FinancialFreedom |  -.0240899   .0132607    -1.82   0.072    -.0503956    .0022159
   FiscalFreedom |  -.0047965    .015768    -0.30   0.762     -.036076     .026483
          Ethnic |          0  (omitted)
      Linguistic |          0  (omitted)
       Religious |          0  (omitted)
       Education |   .0231017   .0133602     1.73   0.087    -.0034013    .0496047
           yhat2 |  -.0114126   .0070675    -1.61   0.109    -.0254326    .0026074
           yhat3 |   .0001151   .0001728     0.67   0.507    -.0002276    .0004578
           yhat4 |   5.45e-06   9.70e-06     0.56   0.575    -.0000138    .0000247
                 |
            Year |
           1997  |  -.1794508   .5120041    -0.35   0.727    -1.195129    .8362276
           1998  |   -.586099   .5675585    -1.03   0.304    -1.711982    .5397843
           1999  |  -.6324539   .5195774    -1.22   0.226    -1.663156     .398248
           2000  |  -.0884756   .4613851    -0.19   0.848     -1.00374    .8267884
           2001  |   -.977025   .5689921    -1.72   0.089    -2.105752    .1517023
           2002  |  -.7009456   .5378715    -1.30   0.195    -1.767938    .3660467
           2003  |   .1681193   .5069165     0.33   0.741    -.8374667    1.173705
           2004  |   1.281764   .5657085     2.27   0.026     .1595502    2.403977
           2005  |   .8275233   .6226402     1.33   0.187    -.4076273    2.062674
           2006  |   1.806341   .6409772     2.82   0.006      .534815    3.077868
           2007  |   1.816851   .7305531     2.49   0.015     .3676303    3.266072
           2008  |   -.168887   .8027915    -0.21   0.834    -1.761409    1.423635
           2009  |  -4.114535   .8494684    -4.84   0.000    -5.799652   -2.429418
           2010  |   .3352618   .7783314     0.43   0.668    -1.208738    1.879262
           2011  |  -.1494889   .8832861    -0.17   0.866    -1.901691    1.602713
           2012  |  -.6098704   .9740913    -0.63   0.533    -2.542206    1.322465
           2013  |  -.4966572   .9738118    -0.51   0.611    -2.428438    1.435124
           2014  |  -.1605135   .9199332    -0.17   0.862    -1.985414    1.664387
           2015  |  -.3977542   .9944349    -0.40   0.690    -2.370446    1.574937
                 |
           _cons |   5.797258   47.91696     0.12   0.904     -89.2571    100.8516
-----------------+----------------------------------------------------------------
         sigma_u |  11.997763
         sigma_e |  2.7717223
             rho |  .94933386   (fraction of variance due to u_i)
----------------------------------------------------------------------------------

. test yhat2=yhat3=yhat4=0

 ( 1)  yhat2 - yhat3 = 0
 ( 2)  yhat2 - yhat4 = 0
 ( 3)  yhat2 = 0

       F(  3,   101) =    1.69
            Prob > F =    0.1747

Many thanks for any help you can offer!

[Carlo Lazzaro]

Hellie:
your approach is correct.
-test- outcome shows no model misspecification.

[Hellie Flint]

Great thanks for your help Carlo!

[Hellie Flint]

A quick follow up question if I may: does the outcome show 'no model misspecification' because the null hypothesis is that the model is correctly specified and we are rejecting the null, as the p value is greater than 0.05? Sorry I know this is really basic but I just want to double check that the interpretation is related to the P-value rather than the F-value

[Carlo Lazzaro]

Hellie:
a bit of confusion here.
The null assumes that the model is correctly specified; hence, a p-value higher than the arbitrary 0.05 cut-off, is not enough to reject the null
Put differently, the -test- outcome tells you that there's no evidence that the model is misspecified.
As an aside, how can you interpret the F-test without tables that reports the related p-value given the values of the F-test and the degrees of freedom for numerator and denominator?

[Hellie Flint]

Ah yes sorry that was my careless error, I meant to say fail to reject in #4. I understand now, thank you again for your help