Good morning everyone,
My dataset includes some daily market quality metrics (spread, price and volume -> independent variables) and two dummy variables (X1 and X2 -> regressors) for 100 different listed firms over 2 months:
SPREAD PRICE VOLUME DUMMY X1 DUMMY X2
STOCK A DAY 1
STOCK B DAY 1
STOCK C DAY 1
STOCK A DAY 2
STOCK B DAY 2
STOCK C DAY 2
I'm currently working at a fixed-effect panel regression with by-stock-clustered standard errors (SPREAD = alfa + beta1X1 + beta2X2). I've performed a Sargan-Hansen test to check whether opting for a FE estimator was a good idea and I actually end up concluding that, for almost all my independent variables, a FE estimator is appropriate. I have two different questions:
1) Does it make any sense to run a random-effect panel regression with by-stock-clustered standard errors when the Sargan-Hansen test suggests to do so and to compare the results with the original fixed-effect panel regression with by-stock-clustered standard errors as a robustness check?
2) Is there anything else I could test? I am not interested in presenting the model without clustered standard errors, but I would like to further check (if there is anything else to do) my model.

Thanks for any help!