I have seen many papers using dynamic panel regressions when the lagged dependent is a regressor and the data has the standard panel format. so, y(t)=constant + beta1*y(t-1)+ beta2*X(t) is often assessed using dynamic panel data regression. My question is that I have a study where I want to use the predicted X in the regression instead of the realized X. So X(t) depends on X(t-1) and X2(t-1). Can I run in this context a 2sls regression where in the first stage: X(t)= constant+ gamma1*X(t-1)+ gamma2*X2(t-1). Then in the 2nd stage: y(t)=constant + beta1*y(t-1)+ beta2*Predicted X(t) from the 1st stage.... is it sound ?