Hausman-test interpretation for RE vs FE

[Ana Quiroga]

Hello,
I have a queston on how to interpret a Hausman-test.

• Dependent variable (y) is suffering from an accident or injury on a scale 0-10 (pl05)
• Independent variable (x) is work stress (yes/no 1/0) (pw604)
• Panel data for years 2010 and 2016

Pools OLS coefficient= 0.084 p-value=0.00
FE coefficient=0.084 p-value=0.00 (same as Pooled OLS)
RE coefficient=0.620 p-value= 0.875

Hausman-test results (also in attachment):
Chi2=4.83
Prob>Chi2= 0.1847

In this case, Ho would be rejected, which would mean both models are the same, but they are clearly different based on the estimated coefficients and p-values.

My questions are:

1. Why does the test reject Ho when RE and FE seem clearly different?
2. Does rejecting the null Hypothesis mean that RE is preferred over FE?

Thank you!

[Ana Quiroga]

Sorry, because p is 0.1847 we would fail to reject Ho, which would mean the two models are not systematically different... but they do seem different... any idea as to why this is?
And would RE be preferred?

[Carlo Lazzaro]

Ana:
I would take one step aside.
If you have, as it seems, an ordered regressand, why using -xtreg-?

[Ana Quiroga]

Dear Carlo,
This is part of an assignment for a course, other methods like ordered logit haven't been covered, so in this case the method used within the course's scope was linear regression for panel data.

[Carlo Lazzaro]

Ana:
as you may already know thanks to FAQ, the policy of this forum about assignments is: please do not post, please do not reply.
However, as you've challenged yourself with -xtreg- I think a temporary waiver can apply.
The results of -hausman- tell you that there's no enough evidence to claim that your model are different. Hence, as per your data, you should stick with -re- specification.
As an aside (and despite your reasonable justification), I still doubt that the assigned analysis is consistent with the -xtreg- framework.

[Ana Quiroga]

Carlo,
I'm assisting in this course, a student came up to me with this question since we didn't cover the Hausman-test fully during the semester and was curious about the interpretation, so I became curious myself.
This part is actually not required for the assignment as it wasn't covered, so I'm trying to help by providing a bit more information (for me and the student).
Regarding the methods chosen for this analysis, I agree, but its within the course's scope so I guess in this case it works.
Thank you so much for your help!

Ana

[Carlo Lazzaro]

Ana:
thanks for providing further clarification.
For the future, I take the liberty to advise you to report all the details concerning your query from the very start, as per it subject it seemed to be posted by a student (and, as as such, at major risk of being side-tracked due to FAQ recommendation about class/homeworks) rather than an assitant professor.
I remain a bit queasy about the choice of the assignment, though: there are datasets more suitable to -xtreg- in Stata (eg, nlswork.dta).

[Ana Quiroga]

Carlo:
Thank you for the advise, I'm new at the forum and just getting familiar with all the requirements/recommendations. I appreciate it.

Best,
Ana