Decreasing R2?

[Sean O'Connor]

Hi Folks!

While running a robust random effects regression I've noticed that adding an additional variable to my regression has resulted in a smaller R^2. My first regression examined the effects the investment share, oil exports and political rights(scale variable) have on GDP. All variables bad PR are in log format. Anyway I decided to add additional variables in the model , oil production. Anyway adding this additional variable has resulted in my r2 reducing. Below shows the output.

 xtreg  log_rgdpl  log_ki  log_exports PR, re robust
  Random-effects GLS regression                   Number of obs      =      1625
Group variable: id                              Number of groups   =        65
  R-sq:  within  = 0.4017                         Obs per group: min =        25
       between = 0.5872                                        avg =      25.0
       overall = 0.5073                                        max =        25
  Random effects u_i ~ Gaussian                   Wald chi2(3)       =     83.58
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000
                                      (Std. Err. adjusted for 65 clusters in id)
------------------------------------------------------------------------------
             |               Robust
   log_rgdpl |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      log_ki |   .0715439     .04157     1.72   0.085    -.0099317    .1530195
 log_exports |   .1007198   .0113213     8.90   0.000     .0785305    .1229091
          PR |  -.0086778   .0119547    -0.73   0.468    -.0321086    .0147529
       _cons |   8.546594   .1662514    51.41   0.000     8.220747     8.87244
-------------+----------------------------------------------------------------
     sigma_u |  .71276532
     sigma_e |  .15705413
         rho |   .9536963   (fraction of variance due to u_i)
------------------------------------------------------------------------------

 . xtreg  log_rgdpl  log_ki  log_exports log_oilp  PR, re robust
  Random-effects GLS regression                   Number of obs      =      1625
Group variable: id                              Number of groups   =        65
  R-sq:  within  = 0.4455                         Obs per group: min =        25
       between = 0.5414                                        avg =      25.0
       overall = 0.4848                                        max =        25
  Random effects u_i ~ Gaussian                   Wald chi2(4)       =    122.88
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000
                                      (Std. Err. adjusted for 65 clusters in id)
------------------------------------------------------------------------------
             |               Robust
   log_rgdpl |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      log_ki |   .0284645   .0443018     0.64   0.521    -.0583655    .1152945
 log_exports |   .0728598   .0129074     5.64   0.000     .0475618    .0981578
    log_oilp |   .0509208    .014486     3.52   0.000     .0225288    .0793129
          PR |  -.0117452   .0113979    -1.03   0.303    -.0340847    .0105944
       _cons |   8.544471   .1809206    47.23   0.000     8.189873    8.899069
-------------+----------------------------------------------------------------
     sigma_u |  .66937021
     sigma_e |  .15124515
         rho |  .95142586   (fraction of variance due to u_i)
------------------------------------------------------------------------------

I don't think the problem has anything to do with multicolinearity, as when I examined the correlation matrix both exports and production correlation coefficient was 0.61.

[Jeph Herrin]

This is a known phenomenon with random effects models. Notice that the within R2 went up - what you expect to see when you add a level 1 variable - and the between R2 went down - because now there is less explained at level 2. The overall R2 is a weighted combination of these, and whether it goes up or down depends on how much each level contributes.

hth,
Jeph