I want to know if it is possible to find the global solution of a DSGE model using projection method and then compute the IRFs to some news shocks?
For example, in a simple RBC model without capital, TFP level Z would be the only state variable. Then, using projection method, consumption C is only a function of Z, say C = f(Z), for some function f. So at time t, C_t = f(Z_t). It seems that an expected increase in Z_t+1 would have no impact on C_t, because Z_t does not change at all. Why is this the case?