Added week 10 material

README.md

@@ -195,7 +195,7 @@ Please feel free to use this for teaching or learning purposes; however, taking
 
 
 <details>
-  <summary>Week 9: First-order perturbation, Identification, Sensitivity</summary>
+  <summary>Week 9: First-order perturbation, Shock transmission channels</summary>
 
 ### Goals
 * understand the concept of a policy function
@@ -215,36 +215,36 @@ Please feel free to use this for teaching or learning purposes; however, taking
 
 </details>
 
-<!---
 
 <details>
-  <summary>Week 10: Log-Linearization; Practicing Stochastic Simulations, Impulse Response Functions, Perturbation. Environmental Policy, Trend Inflation in the New Keynesian model. OccBin, Introduction to Higher-Order Approximation</summary>
+  <summary>Week 10: Identification, Sensitivity, Log-Linearization, Trend Inflation in the New Keynesian model.</summary>
 
 ### Goals
-* 
 * understand and get used to Dynare's *stoch_simul* command
 * understand Dynare's sensitivity toolbox
-* study the modeling approach and effects of different environmental policies in a New Keynesian model
 * study the macroeconomics of trend inflation in a New Keynesian model
 
 ### To Do
-* prepare [week 9's exercise sheet](https://github.com/wmutschl/Computational-Macroeconomics/releases/latest/download/week_9.pdf)
-  * [x] read the case-study papers on environmental policy and trend inflation carefully
+* prepare [week 10's exercise sheet](https://github.com/wmutschl/Computational-Macroeconomics/releases/latest/download/week_10.pdf)
+  * [x] we will work through exercise 1 and 2 together in class, exercise 3 is for you to do on your own in class
+  * [x] read the case-study paper on trend inflation carefully
   * [x] download all files
   * [x] read all the exercises
-  * [x] try to prepare the replications
+  * [x] try to prepare the replication
 
 </details>
 
+<!---
 
 <details>
-  <summary>Week 11: Recursive Preferences and Equity Risk Premium and Stochastic Volatility</summary>
+  <summary>Week 11: ; Practicing Stochastic Simulations, Impulse Response Functions, Perturbation. Environmental Policy,OccBin, Introduction to Higher-Order Approximation Recursive Preferences and Equity Risk Premium and Stochastic Volatility</summary>
 
 ### Goals
-* 
+* study the modeling approach and effects of different environmental policies in a New Keynesian model
 
 ### To Do
 * [ ]
+  * [x] read the case-study paper on environmental policy
 
 </details>
 

exercises/case_study_ascari_sbordone_2014.tex

@@ -12,24 +12,24 @@
 Explain what each file is doing.
 
 \item Replicate figure 14 of the paper.
-Set initially $\varphi = 1$, $\phi_\pi=2$, $\phi_y = 0.5/4$ and $\rho_i=0.8$.
+Set initially \(\varphi = 1\), \(\phi_\pi=2\), \(\phi_y = 0.5/4\) and \(\rho_i=0.8\).
 
 \item Replicate figure 13 of the paper.
-Set initially $\varphi = 0$, $\phi_\pi=1.5$, $\phi_y = 0.5/4$ and $\rho_i=0$.
+Set initially \(\varphi = 0\), \(\phi_\pi=1.5\), \(\phi_y = 0.5/4\) and \(\rho_i=0\).
 
 \item Replicate the business cycle moments reported on page 717.
-Set initially $\varphi = 1$, $\rho_a=0.95$, $\rho_i=0$ $\phi_\pi=1.5$, and $\phi_y = 0.5/4$.
-Note that for the business cycle moments, the technology shock standard error is actually $0.45$.
+Set initially \(\varphi = 1\), \(\rho_a=0.95\), \(\rho_i=0\) \(\phi_\pi=1.5\), and \(\phi_y = 0.5/4\).
+Note that for the business cycle moments, the technology shock standard error is actually \(0.45\).
 
 \item Replicate figure 7 of the paper.
-Set initially $\varphi = 1$, $\phi_\pi=2$, $\phi_y = 0.5/4$ and $\rho_i=0.8$.
+Set initially \(\varphi = 1\), \(\phi_\pi=2\), \(\phi_y = 0.5/4\) and \(\rho_i=0.8\).
 
 \item Replicate figure 8 of the paper.
-Set initially $\varphi = 1$, $\phi_\pi=2$, $\phi_y = 0.5/4$ and $\rho_i=0.8$.
+Set initially \(\varphi = 1\), \(\phi_\pi=2\), \(\phi_y = 0.5/4\) and \(\rho_i=0.8\).
 
 \item Replicate figure 11 of the paper.
-Set initially $\varphi = 1$, $\phi_\pi=2$, $\phi_y = 0.5/4$ and $\rho_i=0.8$.
-Note that as described in footnote 54, the determinacy region in Figure 11 is actually the "determinacy and stability region",
+Set initially \(\varphi = 1\), \(\phi_\pi=2\), \(\phi_y = 0.5/4\) and \(\rho_i=0.8\).
+Note that as described in footnote 54, the determinacy region in Figure 11 is actually the \enquote{determinacy and stability region},
   i.e.\ it does not distinguish whether the Blanchard-Kahn conditions fail because of too many unstable roots (instability, info==3)
   or because of too few unstable roots (indeterminacy, info==4).
 
@@ -50,7 +50,7 @@
 
 
 \begin{solution}\textbf{Solution to \nameref{ex:CaseStudy.Ascari.Sbordone.2014}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/case_study_ascari_sbordone_2014_solution.tex}
 \fi
 \newpage

exercises/log_linearization.tex

@@ -1,4 +1,4 @@
-\section{Log-Linearization vs. first-order perturbation\label{ex:LogLinearization}}
+\section{Log-Linearization vs first-order perturbation\label{ex:LogLinearization}}
 
 \subsection*{Model variants}
 Let us consider the small scale New Keynesian model from \textcite{An.Schorfheide_2007_BayesianAnalysisDSGE},
@@ -21,29 +21,32 @@ \subsection*{Model variants}
 \bar{g} = 1/0.85.
 \end{align*}
 
-\paragraph{Model A: original nonlinear model}
+\paragraph{Model A:\ original nonlinear model}
 \begin{align}
-1 &= \beta \mathbb{E}_t\left[\left(\frac{C_{t+1}/A_{t+1}}{C_t/A_t}\right)^{-\tau} \frac{A_t}{A_{t+1}} \frac{R_t}{\pi_{t+1}}\right]
+1 &= \beta \mathbb{E}_t\left[{\left(\frac{C_{t+1}/A_{t+1}}{C_t/A_t}\right)}^{-\tau} \frac{A_t}{A_{t+1}} \frac{R_t}{\pi_{t+1}}\right]
 \\
-1 &= \phi \left(\pi_t - \pi\right) \left[\left(1-\frac{1}{2\nu}\right)\pi_t + \frac{\pi}{2\nu}\right] - \phi \beta \mathbb{E}_t \left[\left(\frac{C_{t+1}/A_{t+1}}{C_t/A_t}\right)^{-\tau} \frac{Y_{t+1}/A_{t+1}}{Y_t/A_t} \left(\pi_{t+1} - \pi \right) \pi_{t+1}\right] + \frac{1}{\nu}\left[1-\left({\frac{C_t}{A_t}}\right)^{\tau}\right]
+1 &= \phi \left(\pi_t - \pi\right) \left[\left(1-\frac{1}{2\nu}\right)\pi_t + \frac{\pi}{2\nu}\right] \nonumber
+\\&\qquad\qquad\qquad
+- \phi \beta \mathbb{E}_t \left[{\left(\frac{C_{t+1}/A_{t+1}}{C_t/A_t}\right)}^{-\tau} \frac{Y_{t+1}/A_{t+1}}{Y_t/A_t} \left(\pi_{t+1} - \pi \right) \pi_{t+1}\right] + \frac{1}{\nu}\left[1-{\left({\frac{C_t}{A_t}}\right)}^{\tau}\right]
 \\
-Y_t &= C_t + G_t + \frac{\phi}{2} \left({\pi_t - \pi}\right)^2 Y_t
+Y_t &= C_t + G_t + \frac{\phi}{2} {\left({\pi_t - \pi}\right)}^2 Y_t
 \\
 G_t &= \frac{g_t-1}{g_t} Y_t
 \\
 R_t &= {R_t^{*}}^{1-\rho_R} R_{t-1}^{\rho_R} e^{\epsilon_{R,t}}
 \\
-R_t^* & = R \left(\frac{\pi_t}{\bar{\pi}}\right)^{\psi_1} \left(\frac{Y_t}{Y_t^*}\right)^{\psi_2}
+R_t^* & = R {\left(\frac{\pi_t}{\bar{\pi}}\right)}^{\psi_1} {\left(\frac{Y_t}{Y_t^*}\right)}^{\psi_2}
 \\
 \ln(A_t) &= \ln(\gamma) + \ln(A_{t-1}) + \ln(z_t)
 \\
 \ln(z_t) &= \rho_z \ln(z_{t-1}) + \epsilon_{z,t}
 \\
 \ln(g_t) &= (1-\rho_g)\ln(\bar{g}) + \rho_g \ln(g_{t-1}) + \epsilon_{g,t}
 \\
-Y_t^* &= (1-\nu)^{\frac{1}{\tau}} A_t g_t
+Y_t^* &= {(1-\nu)}^{\frac{1}{\tau}} A_t g_t
 \end{align}
-The productivity shock $\varepsilon_{z,t}$, the government spending shock $\varepsilon_{g,t}$ and the monetary policy shock $\varepsilon_{R,t}$ are iid Gaussian:
+The productivity shock \(\varepsilon_{z,t}\), the government spending shock \(\varepsilon_{g,t}\)
+  and the monetary policy shock \(\varepsilon_{R,t}\) are iid Gaussian:
 \begin{align*}
 \begin{pmatrix}
 \varepsilon_{z,t}\\\varepsilon_{g,t}\\\varepsilon_{R,t}
@@ -59,24 +62,25 @@ \subsection*{Model variants}
 \phi=\tau\frac{1-\nu}{\nu\bar{\pi}^2\kappa}
 \end{align*}
 
-\paragraph{Model B: stationary nonlinear model}
-Let's denote: $c_t= C_t/A_t$, $y_t= Y_t/A_t$ and $y_t= Y_t/A_t$, then Model A can be equivalently represented as:
+\paragraph{Model B:\ stationary nonlinear model}
+Let's denote: \(c_t= C_t/A_t\), \(y_t= Y_t/A_t\) and \(y^*_t= Y^*_t/A_t\), then Model A can be equivalently represented as:
 \begin{align}
-1 &= \beta \mathbb{E}_t\left[\left(\frac{c_{t+1}}{c_t}\right)^{-\tau} \frac{1}{\gamma z_{t+1}} \frac{R_t}{\pi_{t+1}}\right] \label{eq:AS_B1}
+1 &= \beta \mathbb{E}_t\left[{\left(\frac{c_{t+1}}{c_t}\right)}^{-\tau} \frac{1}{\gamma z_{t+1}} \frac{R_t}{\pi_{t+1}}\right] \label{eq:AS_B1}
 \\
-1 &= \phi \left(\pi_t - \pi\right) \left[\left(1-\frac{1}{2\nu}\right)\pi_t + \frac{\pi}{2\nu}\right] - \phi \beta \mathbb{E}_t \left[\left(\frac{c_{t+1}}{c_t}\right)^{-\tau} \frac{y_{t+1}}{y_t} \left(\pi_{t+1} - \pi \right) \pi_{t+1}\right] + \frac{1}{\nu}\left[1-c_t^{\tau}\right]
+1 &= \phi \left(\pi_t - \pi\right) \left[\left(1-\frac{1}{2\nu}\right)\pi_t + \frac{\pi}{2\nu}\right]
+- \phi \beta \mathbb{E}_t \left[{\left(\frac{c_{t+1}}{c_t}\right)}^{-\tau} \frac{y_{t+1}}{y_t} \left(\pi_{t+1} - \pi \right) \pi_{t+1}\right] + \frac{1}{\nu}\left[1-c_t^{\tau}\right]
 \\
-y_t &= c_t + \frac{g_t-1}{g_t} y_t + \frac{\phi}{2} \left({\pi_t - \pi}\right)^2 y_t
+y_t &= c_t + \frac{g_t-1}{g_t} y_t + \frac{\phi}{2} {\left({\pi_t - \pi}\right)}^2 y_t
 \\
 R_t &= {R_t^{*}}^{1-\rho_R} R_{t-1}^{\rho_R} e^{\epsilon_{R,t}}
 \\
-R_t^* & = R \left(\frac{\pi_t}{\bar{\pi}}\right)^{\psi_1} \left(\frac{y_t}{y_t^*}\right)^{\psi_2}
+R_t^* & = R {\left(\frac{\pi_t}{\bar{\pi}}\right)}^{\psi_1} {\left(\frac{y_t}{y_t^*}\right)}^{\psi_2}
 \\
 \ln(z_t) &= \rho_z \ln(z_{t-1}) + \epsilon_{z,t}
 \\
 \ln(g_t) &= (1-\rho_g)\ln(\bar{g}) + \rho_g \ln(g_{t-1}) + \epsilon_{g,t}
 \\
-y_t^* &= (1-\nu)^{\frac{1}{\tau}} g_t
+y_t^* &= {(1-\nu)}^{\frac{1}{\tau}} g_t
 \end{align}
 with the following auxiliary parameters:
 \begin{align*}
@@ -87,17 +91,19 @@ \subsection*{Model variants}
 \end{align*}
 The steady-state is given by:
 \begin{align*}
-z=1, \qquad\pi = \bar{\pi}, \qquad g=\bar{g}, \qquad R=\frac{\gamma}{\beta}\pi, \qquad R^* = R, \qquad c = (1-\nu)^{\frac{1}{\tau}}, \qquad y = gc , \qquad y^*=y
+z=1, \qquad\pi = \bar{\pi}, \qquad g=\bar{g}, \qquad R=\frac{\gamma}{\beta}\pi, \qquad R^* = R, \qquad c = {(1-\nu)}^{\frac{1}{\tau}}, \qquad y = gc , \qquad y^*=y
 \end{align*}
 
-\paragraph{Model C: Exponential transform}
-Let's denote hat variables as log deviations from steady-state: $\hat{x}_t = \ln\left(\frac{X_t}{X}\right)$, then Model B can be equivalently represented as:
+\paragraph{Model C:\ Exponential transform}
+Let's denote hat variables as log deviations from steady-state: \(\hat{x}_t = \ln\left(\frac{X_t}{X}\right)\), then Model B can be equivalently represented as:
 \begin{align}
 1 &= \mathbb{E}_t \left[e^{-\tau \hat{c}_{t+1} + \tau \hat{c}_{t} + \hat{R}_{t} - \hat{z}_{t+1} - \hat{\pi}_{t+1} }\right]\label{eq:AS_C1}
 \\
-0 &= \left(e^{\hat{\pi}_{t}}-1\right) \left[\left(1-\frac{1}{2\nu}\right)e^{\hat{\pi}_{t}} + \frac{1}{2\nu}\right] - \beta \mathbb{E}_t \left[\left(e^{\hat{\pi}_{t+1}}-1 \right) e^{-\tau \hat{c}_{t+1} + \tau \hat{c}_{t} + \hat{y}_{t+1} - \hat{y}_{t} + \hat{\pi}_{t+1}}\right] + \frac{1-\nu}{\nu\pi^2\phi}\left(1-e^{\tau\hat{c}_{t}}\right)
+0 &= \left(e^{\hat{\pi}_{t}}-1\right) \left[\left(1-\frac{1}{2\nu}\right)e^{\hat{\pi}_{t}} + \frac{1}{2\nu}\right] \nonumber
+\\&\qquad\qquad\qquad
+- \beta \mathbb{E}_t \left[\left(e^{\hat{\pi}_{t+1}}-1 \right) e^{-\tau \hat{c}_{t+1} + \tau \hat{c}_{t} + \hat{y}_{t+1} - \hat{y}_{t} + \hat{\pi}_{t+1}}\right] + \frac{1-\nu}{\nu\pi^2\phi}\left(1-e^{\tau\hat{c}_{t}}\right)
 \\
-e^{\hat{c}_{t}-\hat{y}_{t}} &= e^{-\hat{g}_{t}} - \frac{\phi \pi^2 g}{2} \left(e^{\hat{\pi}_{t}}-1\right)^2\label{eq:AS_C3}
+e^{\hat{c}_{t}-\hat{y}_{t}} &= e^{-\hat{g}_{t}} - \frac{\phi \pi^2 g}{2} {\left(e^{\hat{\pi}_{t}}-1\right)}^2\label{eq:AS_C3}
 \\
 \hat{R}_{t} &= \rho_R \hat{R}_{t-1} + (1-\rho_R) \psi_1 \hat{\pi}_{t} + (1-\rho_R)\psi_2(\hat{y}_{t}-\hat{g}_{t}) + \epsilon_{R,t}
 \\
@@ -106,8 +112,8 @@ \subsection*{Model variants}
 \hat{g}_{t} &= \rho_g \hat{g}_{t-1} + \epsilon_{g,t}
 \end{align}
 
-\paragraph{Model D: Log-linearization}
-Taking the first-order Taylor approximation in logged variables (aka hat variables) yields:
+\paragraph{Model D:\ Log-linearization}
+Taking the first-order Taylor approximation in logged variables (also known as hat variables) yields:
 \begin{align}
 \hat{y}_{t} &= \mathbb{E}_t \hat{y}_{t+1} + \hat{g}_{t} - E_t\hat{g}_{t+1} - \frac{1}{\tau} \left(\hat{R}_{t}- \mathbb{E}_t \hat{\pi}_{t+1} - \mathbb{E}_t \hat{z}_{t+1}\right) \label{eq:AS_D1}
 \\
@@ -121,16 +127,16 @@ \subsection*{Model variants}
 \\
 \hat{z}_{t} &= \rho_z \hat{z}_{t-1} + \epsilon_{z,t}
 \end{align}
-where $\beta = \frac{1}{1+R^{A}/400}$ and $\kappa=\tau\frac{1-\nu}{\nu\bar{\pi}^2\phi}$.
+where \(\beta = \frac{1}{1+R^{A}/400}\) and \(\kappa=\tau\frac{1-\nu}{\nu\bar{\pi}^2\phi}\).
 
 \paragraph{Measurement Equations}
 The measurement equations are given by:
 \begin{align}
-YGR_t &= \gamma^{(Q)} + 100(\hat{y}_t-\hat{y}_{t-1} + \hat{z}_t)
+{YGR}_t &= \gamma^{(Q)} + 100(\hat{y}_t-\hat{y}_{t-1} + \hat{z}_t)
 \\
-INFL_t &= \pi^{(A)} + 400 \hat{\pi}_t
+{INFL}_t &= \pi^{(A)} + 400 \hat{\pi}_t
 \\
-INT_t &= \pi^{(A)} + r^{(A)} + 4 \gamma^{(Q)} 400 \hat{R}_t
+{INT}_t &= \pi^{(A)} + r^{(A)} + 4 \gamma^{(Q)} 400 \hat{R}_t
 \end{align}
 
 \subsection*{Exercises}
@@ -143,25 +149,25 @@ \subsection*{Exercises}
 
 \item Derive (on paper)
 \begin{itemize}
-    \item equation \eqref{eq:AS_C1} from equation \eqref{eq:AS_B1}
-    \item equation \eqref{eq:AS_D1} by combining the first-order Taylor expansion of equations \eqref{eq:AS_C1} and \eqref{eq:AS_C3}
+    \item equation~\eqref{eq:AS_C1} from equation~\eqref{eq:AS_B1}
+    \item equation~\eqref{eq:AS_D1} by combining the first-order Taylor expansion of equations~\eqref{eq:AS_C1} and~\eqref{eq:AS_C3}
 \end{itemize}
 
 \item Write a mod file for Model B (including the measurement equations) in Dynare
   and solve it using a first-order perturbation approximation of the policy function.
 Make note of the impulse response functions and of the theoretical moments.
 
-\item Write a mod file for Model C (including the measurement equations)in Dynare
+\item Write a mod file for Model C (including the measurement equations) in Dynare
   and solve it using a first-order perturbation approximation of the policy function.
 Make note of the impulse response functions and of the theoretical moments.
 Compare the theoretical moments and explain the differences or equivalences to Model B.
 
-\item Write a mod file for Model D (including the measurement equations)in Dynare,
+\item Write a mod file for Model D (including the measurement equations) in Dynare,
   and solve it using a first-order perturbation approximation of the policy function.
 Make note of the impulse response functions and of the theoretical moments
 Compare the theoretical moments and explain the differences or equivalences with Model C.
 
-\item What are the advantages and disadvantages of (log-)linearizing model equations by hand
+\item What are the advantages and disadvantages of log-linearizing model equations by hand
   or by using first-order perturbation on the nonlinear model equations?
 
 \end{enumerate}
@@ -172,7 +178,7 @@ \subsection*{Exercises}
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:LogLinearization}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/log_linearization_solution.tex}
 \fi
 \newpage

literature/_biblio.bib

@@ -71,6 +71,19 @@ @article{Aruoba.Fernandez-Villaverde_2015_ComparisonProgrammingLanguages
   annotation = {note the Update available at https://www.sas.upenn.edu/{\textasciitilde}jesusfv/Update\_March\_23\_2018.pdf}
 }
 
+@article{Ascari.Sbordone_2014_MacroeconomicsTrendInflation,
+  title = {The {{Macroeconomics}} of {{Trend Inflation}}},
+  author = {Ascari, Guido and Sbordone, Argia M.},
+  year = {2014},
+  month = sep,
+  journal = {Journal of Economic Literature},
+  volume = {52},
+  number = {3},
+  pages = {679--739},
+  doi = {10.1257/jel.52.3.679},
+  abstract = {Most macroeconomic models for monetary policy analysis are approximated around a zero inflation steady state, but most central banks target an inflation rate of about 2 percent. Many economists have recently proposed even higher inflation targets to reduce the incidence of the zero lower bound constraint on monetary policy. In this survey, we show that the conduct of monetary policy should be analyzed by appropriately accounting for the positive trend inflation targeted by policymakers. We first review empirical research on the evolution and dynamics of U.S. trend inflation and some proposed new measures to assess the volatility and persistence of trend-based inflation gaps. We then construct a Generalized New Keynesian model that accounts for a positive trend inflation. In this model, an increase in trend inflation is associated with a more volatile and unstable economy and tends to destabilize inflation expectations. This analysis offers a note of caution regarding recent proposals to address the existing zero lower bound problem by raising the long-run inflation target. (JEL E12, E31, E32, E52, E58)}
+}
+
 @article{Baxter.King_1993_FiscalPolicyGeneral,
   title = {Fiscal {{Policy}} in {{General Equilibrium}}},
   author = {Baxter, Marianne and King, Robert G.},
@@ -230,6 +243,16 @@ @book{Heijdra_2017_FoundationsModernMacroeconomics
   keywords = {Macroeconomics,Problems and exercises,Problems exercises etc}
 }
 
+@book{Herbst.Schorfheide_2016_BayesianEstimationDSGE,
+  title = {Bayesian {{Estimation}} of {{DSGE Models}}},
+  author = {Herbst, Edward and Schorfheide, Frank},
+  year = {2016},
+  series = {The {{Econometric}} and {{Tinbergen Institutes Lectures}}},
+  publisher = {Princeton University Press},
+  abstract = {Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations.},
+  isbn = {978-0-691-16108-2}
+}
+
 @article{Ivashchenko.Mutschler_2020_EffectObservablesFunctional,
   title = {The Effect of Observables, Functional Specifications, Model Features and Shocks on Identification in Linearized {{DSGE}} Models},
   author = {Ivashchenko, Sergey and Mutschler, Willi},

week_10.tex

@@ -0,0 +1,42 @@
+% !TEX root = week_10.tex
+\input{exercises/_common_header.tex}
+\Newassociation{solution}{Solution}{week_10_solution}
+\newif\ifDisplaySolutions%\DisplaySolutionstrue
+
+\begin{document}
+\title{Computational Macroeconomics\\~\\Summer 2024\\~\\Week 10}
+\author{Willi Mutschler\\[email protected]}
+\date{Version: 1.0\\Latest version available on: \href{https://github.com/wmutschl/Computational-Macroeconomics/releases/latest/download/week_10.pdf}{GitHub}}
+\maketitle\thispagestyle{empty}
+
+\newpage
+\Opensolutionfile{week_10_solution}[week_10_solution]
+\tableofcontents\thispagestyle{empty}\newpage
+
+\setcounter{page}{1}
+\input{exercises/an_schorfheide_identif_bk.tex}\newpage
+\input{exercises/log_linearization.tex}\newpage
+\input{exercises/case_study_ascari_sbordone_2014.tex}\newpage
+
+\printbibliography%
+
+\newpage
+
+\appendix
+
+\section{Helper functions for New Keynesian Trend Inflation model}
+
+\subsection{ascari\_sbordone\_2014\_common.mod\label{app:ascari_sbordone_2014_common}}
+\lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily\scriptsize,title=\lstname]{progs/replications/Ascari_Sbordone_2014/ascari_sbordone_2014_common.mod}
+
+\subsection{ascari\_sbordone\_2014\_calib\_common.mod\label{app:ascari_sbordone_2014_calib_common}}
+\lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily\scriptsize,title=\lstname]{progs/replications/Ascari_Sbordone_2014/ascari_sbordone_2014_calib_common.inc}
+
+\Closesolutionfile{week_10_solution}
+\ifDisplaySolutions%
+\newpage
+\appendix
+\section{Solutions}
+\input{week_10_solution}
+\fi
+\end{document}