Minimum observations to run 2 stage REpanel data model with i.year and i.sector

Dear Statalist,

I am new to STATA and panel data and really need help.

I have an unbalanced panel dataset with 229 observations (43 firms over 7 years).
I have 1 endogenous (2 instruments) and 18 exogenous regressors.
I am using xtivreg indepvar exogenousregressors (endogenousregressor = IV1 IV2), , re vce(cluster id) small command.
I would like to further add i.year (6 dummies) and i.sector (4 dummies).
The problem is that when I add these variables I am afraid that I may be correcting potential bias (year dummies are statistically significant) at the expense of precision.
Can anyone tell me how can I calculate the minimum number of observations needed in order to be able to include these year and sector dummies without hampering precision? Is there a rule of thumb of some sort?
(I am working with a subsample that I believe is approx. 50% of my final sample size, but since collecting the data takes a lot of time - hand-collected - I would like to know how many more data do I need until I get reliable results).

Thank you so much!

Florence