Panel Regression: Hausmann Test Discussion

[mab23]

Dear Community,

I run a panel regression model and wanted to decide whether fixed effect or random effect specification is appropriate.
In most of my previous regression models the answer was quite obvious.
Unfortunately, right now the answer is kind of ambigious.

The Null Hypothesis for the Hausmann Test is rejected for the cross section but not rejected for the period.
When I run a Redundant Fixed Effects - Likelihood Ratio Test, the result shows that I need a period fixed effect.

Now my question: What is the appropriate model specification.
Do I use a cross section radom effect model or a period fixed effect model.
In my opinion both specifications are justified, but I am quite sure that this is the wrong answer.

What is your opinion for this case??