I am facing some problems with a panel dataset, and I hope somebody could help me.

I have a pretty large data set (approx. 5000 firms, 15 years, annual data), and I want perform a panel regression with these data. One of the independent variables is time-varying, but not cross sectional varying! It is an interest rate. For every firm, the interest rate is the same in the same year. My question is about whether I should use random/fixed crossectional/time effects?

Intitially I thought I have to use time period fixed or random effects, this because my cross sectional dimension is relatively large compared to the time period. And all the firms are in the same country. But I am not sure whether this thought is correct.

If I estimate a random effects model (random time effects) all the estimates are exactly the same as with a 'normal' pooled OLS estimation. I do not understand why?

I also tried fixed effects model but my statistical programm (Eviews) cannot estimate a model with time fixed effects, I receive the error: "near singular matrix", which makes sense I guess, since the interest rate is not cross-sectional varying...?

A fixed cross-sectional effects model is possible, but I am really doubting if this the correct estimation method..

I would really appreciate anybody's help with this.

Kind regards,