How do I choose between robust RE and FE

[Kamilla Issak]

Hello!
I'm doing RE/FE models with clustered SE's on panel data to then choose between them using xtoverid (since apparently Hausman test doesn’t allow clustered SE's). I get the following error:

. xtoverid
0b: operator invalid
r(198);

Can somebody please help me out?

Here's my code:

xtreg depvar indepvars, fe cluster(CO_ID)
est store fixed
xtreg depvar indepvars, re cluster(CO_ID)
est store random
xtoverid

Or maybe can anybody suggest any other test that I can use?

P.S: Initially, I firstly did the RE/FE Hausman test and then based on the model that the test chooses checked for heteroscedasticity and did robust RE/FE. Somehow, this is not the right way to go about it. Is that true?

[Maxence Morlet]

In classical panel data with two sources of variation (unit and time), economists (I don't know what field you're in) would just through two-way fixed-effects at the data they have and use cluster-robust standard errors. For the level of clustering, see the QJE paper by Abadie et al. (2023) "When should you adjust standard errors for clustering?".

You can consult Wooldridge (2021) for an extended two-way fixed effects model.

[Kamilla Issak]

Maxence Morlet Thank you for your answer! You guessed right, I am researching The Effect on Nonconventional Factors on Firm Performance (like CEO attractiveness and facial asymmetry). I eyeballed through the literature and some of them indeed use two-way fixed effects, however, after validating the FE choice using a test. Besides, I was advised by my thesis supervisor to do a test first.

[Maxence Morlet]

Fair enough, then try the Mundlak (1978) test. It sounds like you're in the management field, perhaps not that obsessed with causality yet

[Kamilla Issak]

Maxence Morlet yet..maybe Can I ask another question: what is the intuition behind performing the Hausman test first and based on the favored model (after the heteroscedasticity test) using cluster-robust standard errors being wrong?

[Maxence Morlet]

Nothing wrong, just theory vs practice (the real world ).

The Hausman test however makes very unrealistic distribution assumptions, see Hayashi (2000).

Regarding FE vs RE: RE assumes regressors are uncorrelated with the unobserved heterogeneity (the fixed-effects, often called alpha_i). No economist will ever believe that, so if you have time-varying variables in economics, my advice would be to use fixed-effects and not make that unrealistic assumption.

Even if the Hausman test indicates the RE model is appropriate, you could question the power of the test? Its robustness? Were distributional assumptions met? etc.

Regarding standard errors; there will almost inevitably be heteroscedasticity of unknown form in your model. Same logic regarding tests for heteroscedasticity; if you fail to reject the null of homoscedasticity, was the test powerful enough? Do you have enough observations? Is it a type 2 error? etc.

In panel data, there will probably be correlation amongst observations across time within a certain cluster.

I had an econometrics professor who used to say: just use cluster-robust standard errors automatically, just like you brush your teeth every morning, regardless of whether you've had breakfast, nothing, only coffee,...

But I really recommend the paper of Abadie et al. (2023) on clustered standard errors. It is really informative.

[Kamilla Issak]

Maxence Morlet I am so lucky to get a reply from you! Thank you so much. I will check out all the literature you pointed out.

[Maxence Morlet]

You're very welcome! Let me know if you have any other questions.

[Nick Cox]

Cross-posted on Stack Overflow and Reddit. https://stackoverflow.com/questions/...bust-re-and-fe
https://www.reddit.com/r/stata/comme..._error_urgent/

Please note our policy on cross-posting, which is that you should tell us about it.

[Andrew Musau]

Hello!
I'm doing RE/FE models with clustered SE's on panel data to then choose between them using xtoverid (since apparently Hausman test doesn’t allow clustered SE's). I get the following error:

. xtoverid
0b: operator invalid
r(198);

Can somebody please help me out?

Here's my code:

xtreg depvar indepvars, fe cluster(CO_ID)
est store fixed
xtreg depvar indepvars, re cluster(CO_ID)
est store random
xtoverid

You are probably using factor variable notation whereas xtoverid does not support factor variables. Use the -xi- prefix instead. Here are some notes:

1. You will only want to compare the RE and FE estimates using the test of overidentifying restrictions in case you want to estimate an RE model. FE is consistent in all cases, so you need not do any test if you choose to estimate an FE model.

2. You run xtoverid immediately after estimating the random effects model. You do not need to estimate the FE model in this sequence.

webuse nlswork, clear
xtreg ln_wage hours tenure i.year, re cluster(idcode)
*REPLICATES THE ERROR
xtoverid
xi: xtreg ln_wage hours tenure i.year, re cluster(idcode)
xtoverid

Res.:

. xtreg ln_wage hours tenure i.year, re cluster(idcode)

Random-effects GLS regression                   Number of obs     =     28,036
Group variable: idcode                          Number of groups  =      4,698

R-sq:                                           Obs per group:
     within  = 0.1322                                         min =          1
     between = 0.2004                                         avg =        6.0
     overall = 0.1497                                         max =         15

                                                Wald chi2(16)     =    2127.88
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

                             (Std. err. adjusted for 4,698 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       hours |   .0007958   .0004501     1.77   0.077    -.0000864     .001678
      tenure |   .0254145   .0011415    22.26   0.000     .0231771    .0276519
             |
        year |
         69  |   .0795902   .0102815     7.74   0.000     .0594389    .0997416
         70  |   .0512423   .0104708     4.89   0.000     .0307199    .0717647
         71  |   .0941771   .0109301     8.62   0.000     .0727545    .1155996
         72  |   .1034008   .0116803     8.85   0.000     .0805079    .1262938
         73  |   .1106309   .0117177     9.44   0.000     .0876646    .1335973
         75  |   .1138813   .0117957     9.65   0.000      .090762    .1370005
         77  |   .1642916   .0123885    13.26   0.000     .1400107    .1885726
         78  |   .1915684   .0129508    14.79   0.000     .1661853    .2169515
         80  |   .1961758   .0131747    14.89   0.000     .1703539    .2219976
         82  |   .1959882   .0134366    14.59   0.000     .1696529    .2223235
         83  |   .2079875   .0143194    14.52   0.000     .1799219    .2360531
         85  |   .2486962   .0140576    17.69   0.000     .2211439    .2762486
         87  |   .2515615   .0148809    16.90   0.000     .2223954    .2807276
         88  |   .2888409   .0165733    17.43   0.000     .2563578    .3213239
             |
       _cons |   1.398854   .0198687    70.40   0.000     1.359912    1.437795
-------------+----------------------------------------------------------------
     sigma_u |  .33389046
     sigma_e |  .29770265
         rho |  .55710861   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. *REPLICATES THE ERROR

. 
. xtoverid
68b:  operator invalid
r(198);

. 
. xi: xtreg ln_wage hours tenure i.year, re cluster(idcode)
i.year            _Iyear_68-88        (naturally coded; _Iyear_68 omitted)

Random-effects GLS regression                   Number of obs     =     28,036
Group variable: idcode                          Number of groups  =      4,698

R-sq:                                           Obs per group:
     within  = 0.1322                                         min =          1
     between = 0.2004                                         avg =        6.0
     overall = 0.1497                                         max =         15

                                                Wald chi2(16)     =    2127.88
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

                             (Std. err. adjusted for 4,698 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       hours |   .0007958   .0004501     1.77   0.077    -.0000864     .001678
      tenure |   .0254145   .0011415    22.26   0.000     .0231771    .0276519
   _Iyear_69 |   .0795902   .0102815     7.74   0.000     .0594389    .0997416
   _Iyear_70 |   .0512423   .0104708     4.89   0.000     .0307199    .0717647
   _Iyear_71 |   .0941771   .0109301     8.62   0.000     .0727545    .1155996
   _Iyear_72 |   .1034008   .0116803     8.85   0.000     .0805079    .1262938
   _Iyear_73 |   .1106309   .0117177     9.44   0.000     .0876646    .1335973
   _Iyear_75 |   .1138813   .0117957     9.65   0.000      .090762    .1370005
   _Iyear_77 |   .1642916   .0123885    13.26   0.000     .1400107    .1885726
   _Iyear_78 |   .1915684   .0129508    14.79   0.000     .1661853    .2169515
   _Iyear_80 |   .1961758   .0131747    14.89   0.000     .1703539    .2219976
   _Iyear_82 |   .1959882   .0134366    14.59   0.000     .1696529    .2223235
   _Iyear_83 |   .2079875   .0143194    14.52   0.000     .1799219    .2360531
   _Iyear_85 |   .2486962   .0140576    17.69   0.000     .2211439    .2762486
   _Iyear_87 |   .2515615   .0148809    16.90   0.000     .2223954    .2807276
   _Iyear_88 |   .2888409   .0165733    17.43   0.000     .2563578    .3213239
       _cons |   1.398854   .0198687    70.40   0.000     1.359912    1.437795
-------------+----------------------------------------------------------------
     sigma_u |  .33389046
     sigma_e |  .29770265
         rho |  .55710861   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(idcode)
Sargan-Hansen statistic 391.395  Chi-sq(16)   P-value = 0.0000

[Kamilla Issak]

Thank you Nick Cox for pointing this out, I will definitely take it into account the next time. Thank you Andrew Musau for the resolution and explanation, it indeed worked! Statalist helps me so much, I am sincerely grateful!

[Andrew Musau]

Even if the Hausman test indicates the RE model is appropriate, you could question the power of the test? Its robustness? Were distributional assumptions met? etc.

If the Hausman test selects RE over FE, it implies that the difference in RE coefficients and FE coefficients is not systematic. In this sense, the FE results will not much differ from the RE results, so you will prefer RE because of efficiency.

[Nitin Jain]

Hello!
I'm doing RE/FE models with clustered SE's on panel data to then choose between them using xtoverid (since apparently Hausman test doesn’t allow clustered SE's). I get the following error:

. xtoverid
0b: operator invalid
r(198);

Can somebody please help me out?

Here's my code:

xtreg depvar indepvars, fe cluster(CO_ID)
est store fixed
xtreg depvar indepvars, re cluster(CO_ID)
est store random
xtoverid

Or maybe can anybody suggest any other test that I can use?

P.S: Initially, I firstly did the RE/FE Hausman test and then based on the model that the test chooses checked for heteroscedasticity and did robust RE/FE. Somehow, this is not the right way to go about it. Is that true?

You may want to read up on Mundlak model. Check this link - https://ideas.repec.org/c/boc/bocode/s457601.html