Issues with RE vs. FE

[Joost Pracht]

Hi All,

My unbalanced panel consist of 6618 individuals accumulating to 23288 observations. My key variable is a dummy variable, 1 for being self-employed, 0 when organizationally employed. Unfortunately, only 4% of the individuals (276) switch in the observed period (2008-2017). Using FE will throw away a lot of data and information. Is there any argument that I can make that justifies using a RE estimator, even though the Hausman test is suggesting the FE? That brings me to my second question: Do I perform the Hausman test correctly in one of the two examples:

. quietly xtreg mhi5 selfemp age partner children urbanity income1 tenure hours stress t
> imepressure ownpace autonomous jobexist i.profession i.industry i.year if mainsample==
> 1, fe
. estimate store fe
. quietly xtreg mhi5 selfemp age partner children urbanity income1 tenure hours stress t
> imepressure ownpace autonomous jobexist i.profession i.industry i.year if mainsample==
> 1, re
. estimate store re
. hausman fe re
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
selfemp | -.6397109 -1.118332 .4786208 .5425021
age | .0992662 .1369822 -.037716 .1603685
partner | .6375024 2.364401 -1.726898 .4006339
children | -1.208196 -.371029 -.8371672 .3286044
urbanity | .0949526 -.3546126 .4495652 .2531054
income1 | -.1119805 -.0263154 -.0856651 .0383413
tenure | -.0779686 .0029308 -.0808994 .0166017
hours | -.008133 .0115307 -.0196637 .0040017
stress | -.096136 -.548203 .452067 .0777594
timepressure | -.6650375 -1.220604 .5555666 .0669468
ownpace | .2948356 .6540685 -.3592329 .0824091
autonomous | .4887014 .787014 -.2983125 .0613924
jobexist | -.3226005 -1.017642 .6950419 .0581616
profession |
2 | -2.104472 -.7490098 -1.355462 .7649729
3 | -1.903829 -1.910996 .0071671 .7170875
4 | -2.372971 -1.689078 -.6838927 .797724
5 | -2.472012 -3.086166 .6141535 .8133822
6 | -1.454968 -1.75216 .2971919 1.033679
7 | -1.53831 -2.93549 1.39718 .9910714
8 | -2.994782 -4.530754 1.535972 .9255954
9 | -.2310861 -3.011064 2.779978 2.463292
industry |
2 | -.567905 -2.785585 2.21768 4.184788
3 | .7022447 -2.268898 2.971143 1.626532
4 | -.1194474 -4.387646 4.268199 1.923663
5 | 1.61684 -.7812754 2.398115 1.918581
6 | -2.057382 -3.152176 1.094794 1.53994
7 | -2.351767 -4.235134 1.883367 1.657942
8 | 1.401435 -1.676582 3.078017 1.716534
9 | -1.32821 -3.22144 1.89323 1.684676
10 | -1.407675 -3.286806 1.879131 1.563357
11 | -.4955917 -3.215038 2.719447 1.625408
12 | 1.040028 -2.173712 3.21374 1.724948
13 | -.2168061 -2.783409 2.566603 1.555117
14 | .4798685 -3.563843 4.043711 1.636106
15 | -.4958086 -3.283848 2.788039 1.482181
year |
2009 | .2772957 .2922297 -.0149341 .1791564
2010 | .3587313 .4430665 -.0843351 .3357557
2011 | .4692276 .4263205 .0429071 .4894618
2012 | .7942335 .785973 .0082605 .6506854
2013 | 1.003127 1.006724 -.0035976 .8085903
2015 | 1.968987 1.829539 .1394476 1.077926
2016 | 1.257863 .8903368 .3675262 1.291754
2017 | 1.860241 1.131941 .7282992 1.452363
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(43) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 448.65
Prob>chi2 = 0.0000

-------------------------------------------------------------------------------------------------------------------------------------------------------------

. quietly xtreg mhi5 selfemp if mainsample==1, fe
. estimate store fe
. quietly xtreg mhi5 selfemp if mainsample==1, re
. estimate store re
. hausman fe re
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
selfemp | .4867794 .7960378 -.3092584 .5305123
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 0.34
Prob>chi2 = 0.5599




Thanks in advance!!

[Carlo Lazzaro]

Joost:
welcome to this forum.
You tested via -hausman- (taht you performed correctly) -fe- vs- re- specification on the grounds of two very different models: please note that any regression model should give the fairest and truest view of the data generating process, regardless -fe- or -re- specification.
I would skim through the literarature in your research field and see what others did in the past when presented with the same research issue.