Cross-section or Period in panel data

[raining123]

Hi everyone,

My unbalanced panel data has cross-section=139 & period=36, I tested for fixed/random effects using Hausman test and the results as follows:
- Cross-section: reject the null hyppothesis --> choosing fixed effect.
- Period: not reject the null hyppothesis --> choosing random effect.
I do not know how to choose between them, because two-way effect is not accepted in unbalanced data.
Please help me on this!
Thank you very much!