Projection method and news shock


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?

No, that is not true. The news shock itself becomes an additional state. So the policy function will depend on Z_t and Z_{t+1}.

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