Wanting to use time-invariant variables - despite xtoverid suggesting fe

[em lowthian]

Hi all,

Sorry for the frequent posts - but i'm not entirely sure after reading Longhi & Nandi's chapter on Xtreg, re, fe how I would solve this problem. I also have searched a few terms but I can't see a similar post.

I have ran a re model, which is clustered -

xtreg selfesteem dvage ypsex divorcemo emotabusemo physpunishtmo, re vce(cluster clusterhh)

Random-effects GLS regression                   Number of obs     =        834
Group variable: youth_pidp                      Number of groups  =        795

R-sq:                                           Obs per group:
     within  = 0.0005                                         min =          1
     between = 0.0331                                         avg =        1.0
     overall = 0.0300                                         max =          2

                                                Wald chi2(5)      =      24.32
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0002

                             (Std. Err. adjusted for 626 clusters in clusterhh)
-------------------------------------------------------------------------------
              |               Robust
   selfesteem |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        dvage |  -.1344853   .0794991    -1.69   0.091    -.2903008    .0213301
        ypsex |  -.1276481   .2528637    -0.50   0.614    -.6232518    .3679557
    divorcemo |   -.978547   .4455818    -2.20   0.028    -1.851871   -.1052227
  emotabusemo |   .2393315    .064738     3.70   0.000     .1124474    .3662155
physpunishtmo |  -.0460084   .0814713    -0.56   0.572    -.2056893    .1136724
        _cons |   23.01266   1.562677    14.73   0.000     19.94987    26.07545
--------------+----------------------------------------------------------------
      sigma_u |  .82554565
      sigma_e |  3.4511155
          rho |  .05412488   (fraction of variance due to u_i)
-------------------------------------------------------------------------------

Checking for consistency, the xtoverid test suggests I should use a fe regression

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(clusterhh)
Sargan-Hansen statistic   9.897  Chi-sq(4)    P-value = 0.0422

However, I do not want to omit the sex variable as it is of interest to me for controlling/being a confounder.

Is there anyway I can use the random effects? Is there something I can do to incorporate sex, whilst still having a reliable, powerful model? I am not a statistician so any responses which can lead in me in the right direction in a way that I can understand would be really helpful.

Many thanks in advance.

[Carlo Lazzaro]

Em:
you may want to take a look at the following link: net describe mundlak, from(http://fmwww.bc.edu/RePEc/bocode/m).

[em lowthian]

Many thanks Carlo - this looks useful. Do you know with Mundlak, whether you report the values of the mean of the variables, or the normal variables?

[Sebastian Kripfganz]

If you just want to "control" for it, you do not have to worry at all. All time-invariant variables are automatically controlled for when you use the fixed-effects approach. That is the whole purpose of this estimator.

[em lowthian]

Ok, that is useful thank you sebastian - although a random effects model is more powerful?

[Jeff Wooldridge]

Your example is a bit puzzling. You practically have a single cross section because there are only 39 units where you observe two periods. FE will use only those 39 observations; the others will be effectively discarded. You can still use the Mundlak approach and include the time-constant variable, especially if you're interested in that variable. I suspect the estimates on the other variables are much less significant, as they are based on a much smaller data set.

[em lowthian]

Hi Jeff - thanks for your post. Sorry about my example - If I can elaborate anywhere with explanation or code do please let me know.

Oh I see. I thought it was the other way around whereby if you have 834 observations and 795 groups I had 795 cases where I observed over two periods. That is not ideal at all, completely disappointing for a longitudinal analysis. It also suggests why I simply cannot use the FE model.
What would you say about the reliability of the model? I understand that this is not a great example.

I agree, with only 39 observations I guess I am still only looking at association rather than causality! Disappointing but unfortunately this is the way it goes with data sometimes I suppose. Whats interesting is that I'm still seeing similar findings to other studies so that will aid the discussion.

Em