Fixed effects and random effeccts

[Jana Schue]

Hello everyone,

I am doing a multiple regression with the -xtreg- including clusters on the company level.

The Hausman test showed that fixed effects are more appropriate for my analysis. I ran the regression and found significant results.
Now I wanted to run the same regression with random effects to run a robustness test. The results are insignificant.

Can someone help me to interpret this result?


Thanks in advance and best regards
Jana

[Maarten Buis]

If the effects were the same, then the random effects model has more statistical power than the fixed effects model. So, in that case the p-value in the random effects model is lower ("more significant") than in the fixed effects model. So, your description indicates that the effects are different. That is no surprise: that is what the Hausman test tested.

Notice, that I needed infer all that based on what you told me and what I knew about fixed versus random effects models and the Hausman test. There is a much more direct way of conveying the same information: just look at and report the coefficients.

[Jana Schue]

Hello Maarten,

thanks for your help so far.
I understand the point but I am still struggling how to interpret this result.

Here are the results of my fixed effects model:

Fixed-effects (within) regression               Number of obs     =        755
Group variable: group_id                        Number of groups  =        183

R-squared:                                      Obs per group:
     Within  = 0.6532                                         min =          1
     Between = 0.3361                                         avg =        4.1
     Overall = 0.4269                                         max =          7

                                                F(14,182)         =     110.95
corr(u_i, Xb) = 0.2352                          Prob > F          =     0.0000

                                      (Std. err. adjusted for 183 clusters in group_id)
---------------------------------------------------------------------------------------
                      |               Robust
      ln_totalplatact | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------+----------------------------------------------------------------
educational_diversity |  -.1413744   .5944932    -0.24   0.812    -1.314359    1.031611
     gender_diversity |   2.400842    1.16173     2.07   0.040     .1086511    4.693034
 background_diversity |   2.061145   1.224011     1.68   0.094    -.3539319    4.476222
     tenure_diversity |   .7944632   .5457399     1.46   0.147    -.2823275    1.871254
      total_countries |    .053175   .0135032     3.94   0.000      .026532    .0798179
             itraffic |   .3246415   .1619315     2.00   0.046     .0051372    .6441459
               growth |   .1352508   .0675846     2.00   0.047     .0019007    .2686009
             firm_age |   .2610166   .0838637     3.11   0.002     .0955464    .4264867
             TMT_size |    .048028    .092543     0.52   0.604    -.1345672    .2306232
                      |
                 year |
                2015  |   .3659694   .1260428     2.90   0.004     .1172765    .6146624
                2016  |   .3049189   .1584625     1.92   0.056    -.0077408    .6175787
                2017  |   .7216528   .1878165     3.84   0.000     .3510751    1.092231
                2018  |   1.143606   .2602899     4.39   0.000     .6300318    1.657179
                2019  |   1.056926   .2799153     3.78   0.000     .5046296    1.609223
                2020  |          0  (omitted)
                      |
                _cons |   5.778787   2.271327     2.54   0.012     1.297268     10.2603
----------------------+----------------------------------------------------------------
              sigma_u |  2.7721208
              sigma_e |  .98473439
                  rho |  .88795216   (fraction of variance due to u_i)
---------------------------------------------------------------------------------------

and here are the results of my random effects model:

Random-effects GLS regression                   Number of obs     =        755
Group variable: group_id                        Number of groups  =        183

R-squared:                                      Obs per group:
     Within  = 0.6446                                         min =          1
     Between = 0.5144                                         avg =        4.1
     Overall = 0.5357                                         max =          7

                                                Wald chi2(23)     =    1618.73
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                      (Std. err. adjusted for 183 clusters in group_id)
---------------------------------------------------------------------------------------
                      |               Robust
      ln_totalplatact | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------------+----------------------------------------------------------------
educational_diversity |  -.1368343   .5416414    -0.25   0.801    -1.198432    .9247634
     gender_diversity |   1.398078   .9385112     1.49   0.136    -.4413706    3.237526
 background_diversity |   1.269721   .9235437     1.37   0.169    -.5403911    3.079834
     tenure_diversity |   .5535224   .3884783     1.42   0.154    -.2078811    1.314926
      total_countries |   .0771377   .0112801     6.84   0.000     .0550292    .0992463
             itraffic |   .3391795   .1627408     2.08   0.037     .0202133    .6581456
               growth |   .1284586   .0659203     1.95   0.051    -.0007428      .25766
             firm_age |   .7174352   .1264173     5.68   0.000     .4696619    .9652086
             TMT_size |    .153483   .0892033     1.72   0.085    -.0213521    .3283182
                      |
                 year |
                2015  |  -.1631712   .1717689    -0.95   0.342    -.4998321    .1734897
                2016  |  -.9475196   .3183013    -2.98   0.003    -1.571379   -.3236605
                2017  |  -1.059348   .4178311    -2.54   0.011    -1.878282   -.2404143
                2018  |  -1.167866   .5419608    -2.15   0.031     -2.23009   -.1056422
                2019  |  -1.891476   .6559343    -2.88   0.004    -3.177084   -.6058685
                2020  |  -3.438568   .7696345    -4.47   0.000    -4.947024   -1.930112
                      |
       industry_dummy |
                   2  |  -.3791976   .8309988    -0.46   0.648    -2.007925     1.24953
                   3  |  -.1586964   .9222799    -0.17   0.863    -1.966332    1.648939
                   4  |  -1.132413    .880291    -1.29   0.198    -2.857751     .592926
                   5  |   -.803474   .8036669    -1.00   0.317    -2.378632    .7716842
                   6  |   .5326954   .6673684     0.80   0.425    -.7753225    1.840713
                   7  |  -1.634871   1.149168    -1.42   0.155      -3.8872    .6174573
                   8  |   -.334755    .685029    -0.49   0.625    -1.677387    1.007877
                   9  |  -1.593011   1.228879    -1.30   0.195    -4.001569    .8155473
                      |
                _cons |   5.512513   2.588456     2.13   0.033     .4392328    10.58579
----------------------+----------------------------------------------------------------
              sigma_u |  2.1118576
              sigma_e |  .98473439
                  rho |  .82140602   (fraction of variance due to u_i)
---------------------------------------------------------------------------------------

Could you help me how to interpret them?
As I think the test can not confirm the relationship between gender diversity and ln totalplatact.
How do I evaluate and or reason this?

Best regards
Jana

[Maarten Buis]

Fixed effects regression controls for unobserved company level variables that remain constant over time. Interpretation of fixed effects models thus gets a bit "arm-wavy": People just speculate what those unobserved variables might be and build a hopefully plausible story of where those differences might come from.

[Carlo Lazzaro]

Jana:

I am doing a multiple regression with the -xtreg- including clusters on the company level.
The Hausman test showed that fixed effects are more appropriate for my analysis

What you report is simply impossible to achieve, as -hausman- test does not support non-defaut standard errors.

[Jana Schue]

Hi Carlo,

you are right. I performed the -hausman- test before including the clusters on company-level. I tested afterwards for autocorrelation and heteroskedasticity to see that I have to include the clusters on company level.
Sorry for my misleading explanation.

Best regards
Jana

[Carlo Lazzaro]

Jana:
this is not correct.
You should test before ruinning -hausman- and, if you nees to invoke non-default standard errors due to autocorrelation and/or heteroskedasticity, you should check via the community-contributed module -xtoverid- if -re- is the way to go.

[Jana Schue]

Hi Carlo,

thanks for the clarification.
I did the test and the results are "Sargan-Hansen statistic 55.607 Chi-sq(14) P-value = 0.0000".
Does this indicate fixed effects or random effects are more appropriate?

Best regards
Jana

[Carlo Lazzaro]

Jana:
go fixed (-fe-), as the -xtoverid- null is that -re- is the way to go.
Since your test clearly rejects the null, go -fe-.