Pevious multiplication vs single variables for instrumenting

I think, that this is a more theoretical question, but I can't find a solution in literature.

I am running a 2sls regression, where one variable cause a causality problem. Therefore I have instrumented it. The problem is, that the instrumented value is panel data (value for each country and year) and the instruments are country specific ( constant over time ) and time specific ( constant for all countries) . Does it make a difference between premultiplying all instruments to get a panel "instrument variable " or connecting all linear and run a ols regression ?

kind regards, Noah