Is it reasonable, in panel data, to use past values of explanatory variables as instruments to deal with simultaneous causality?
I suggest looking into System GMM. It is a panel regression method that uses past values as instruments and is exactly what you're looking for, I think. It has a few restrictions that much be met, the most important requires you to have more cross-sections than time periods. Without seeing your model and other details that is all I can provide for help. I hope this works for you.