[Sebastian Kripfganz]

As long as you do not change the second equation, my earlier statement about X_it being predetermined still stands.

Once X_it becomes a direct function of Y_it, as in your amended second equation, X_it becomes endogenous.

[Nursena Sagir]

Dear Sebastian,

Is there any reference that I can understand this better and explain why I can treat X_it as predetermined? I had difficulties to explain it in the method section of my paper. Or can you elaborate more on your reasoning?

Best regards,
Nursena

[Sebastian Kripfganz]

Any standard econometrics textbook should cover systems of simultaneous equations and regressor endogeneity.

A variable is predetermined if it is a function of (i.e., determined by) previous periods' shocks to the equation of interest (but not current or future periods' shocks).