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\title{Zero lower bound in a New Keynesian model}
\author{Sébastien Villemot}
\date{June 4, 2019}
\maketitle
\begin{enumerate}
\item Open the file \texttt{nk3.mod}. Observe that it describes a minimal New
Keynesian model with 3 equations (Euler equation, Phillips curve, Taylor rule)
and three shocks.
\item Run the file. Observe the IRFs. In particular, notice that the zero-lower
bound is crossed for 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).
\item Modify the file by enforcing the zero-lower bound in the Taylor rule. You
will need the \texttt{max} operator. What do you observe in the IRF? Why?
\item Transform the file into a perfect foresight simulation. You will need to
completely rewrite the \texttt{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 \texttt{rplot}. What do
you observe?
\item Now, transform the previous example by adding a \emph{negative}
(\texttt{i.e.} inflationary) one-standard-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 \texttt{perfect\_foresight\_solver} twice, and
manipulate matrices by hand). Verify that in the first version the ZLB is
never hit, and in the second version the ZLB is left at the time of the
unexpected shock (and is therefore shorter than in question 4).
\item Finally, transform the file into an extended path simulation. You will need
to revert the \texttt{shocks} block into the form used in the stochastic case.
Again, use \texttt{rplot} to display the interest rate. Observe that the ZLB is
enforced on the simulation path.
\end{enumerate}
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