Description

Sébastien Villemot
1. Open the file nk3.mod. Observe that it describes a minimal New Keynesian model with 3 equations (Euler equation, Phillips curve, Taylor rule) and three shocks.
2. Run the file. Observe the IRFs. In particular, notice that the zero-lower bound is crossedfor the IRF related to the productivity shock (recall that IRFs are plotted by Dynare in deviation from the steady state for a positive one-standard-deviation shock).
3. Modify the file by enforcing the zero-lower bound in the Taylor rule. You will need themax operator. What do you observe in the IRF? Why?
4. Transform the file into a perfect foresight simulation. You will need to completely rewritethe shocks block, by hard coding a positive productivity shock (in period 1) of the size of one standard deviation of the stochastic version. Display the interest rate with rplot. What do you observe?
5. Now, transform the previous example by adding a negative (i.e. inflationary) onestandard-deviation productivity shock in period 5, in two different ways. In the first version, the shock will be anticipated; in the second one, the shock will be unexpected (for the latter, you will need to run perfect_foresight_solver twice, and manipulate matrices by hand). Verify that the ZLB is never hit with the anticipated shock, and that the ZLB is left at the time of the unexpected shock.
6. Finally, transform the file into an extended path simulation. You will need to revert theshocks block into the form used in the stochastic case. Again, use rplot to display the interest rate. Observe that the ZLB is enforced on the simulation path.
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