exercise-zlb.tex 2.08 KB
 Sébastien Villemot committed Nov 08, 2018 1 2 3 4 5 6 7 8 9 10 11 12 \documentclass[11pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amssymb} \usepackage{fullpage} \begin{document} \title{Zero lower bound in a New Keynesian model} \author{Sébastien Villemot}  Sébastien Villemot committed Jun 03, 2019 13 \date{June 4, 2019}  Sébastien Villemot committed Nov 08, 2018 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 \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} \end{document}