Log-linearized shocks (t) and (t+1)

[binhpham]

Dear Prof Johannes,

I've got a confusing when dealing with the problem in Dynare as below:

Suppose I have an equation: Beta*Rb(t) = Et[(eps_z(t)/eps_z(t+1))*(C(t+1)/C(t))] with eps_z = rhoZ*eps_z(-1) + e_z

Log-linearization gives: Rb(t) = Et[C(t+1)] - Et[eps_z(t+1)] - C + eps_z(t) in term of deviation from SS.
Coding is as:

Code: Select all

model(linear);
...
Rb = C(+1) - C + vareps_z - vareps_z(+1);
...
vareps_z = rhoZ*vareps_z(-1) + e_z;
end;


If I replace Et[eps_z(t+1)] = Et[rhoZ*eps_z(t) + e_z(t+1)] = rhoZ*eps_z(t), with the fact that Et[e_z(t+1)] = 0
then I will have: Rb(t) = Et[C(t+1)] - C + (1-rhoZ)*eps_z(t)
Coding is as:

Code: Select all

model(linear);
...
Rb = C(+1) - C + (1-rhoZ)*vareps_z;
...
vareps_z = rhoZ*vareps_z(-1) + e_z;
end;


Coding two equations as above give me two somewhat different IRFs due to shocks to eps_z. Could you please tell me why is the difference? Because I do think it should be the same things as we know e_z is iid N(0,sig_ez^2).

Thank you very much for your help.
Best,

[jpfeifer]

That should not happen. Please provide the full file.

[binhpham]

Thanks for reply Prof. Johannes.
Indeed, I made some typos so that the inconsistence happened. You're absolutely right! It should not happen.

Best.