# Past values of Y correlated with future values of X1 in fixed effects model: use instrumental variable?

I am using panel data, running a fixed effects regression using xtreg Y X1 X2 X3, fe. I suspect, however, that past values of Y are correlated with future values of one of the regressors e.g. X1. This means that the strict exogeneity assumption of fixed effects regression will be violated.

To correct for this, can I use an IV? I have another variable Z1 which is correlated with X1 but uncorrelated with Y once all other regressors are controlled for.

Could I, for example, run ivreg Y X2 X3 ... Xn (X1=Z1)? How would I interpret my results?

$$E[\varepsilon_{it} \vert \alpha_{i},x_{i1},...,x_{it}]=0.$$