Added week 9 materials

.github/workflows/dynare-6.2-matlab-r2024b-macos.yml

@@ -106,4 +106,13 @@ jobs:
           command: |
             addpath("Dynare-6.2-arm64/matlab");
             cd("progs/matlab");
-            USOil;
+            USOil;
+
+      - name: Run week 9 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("Dynare-6.2-arm64/matlab");
+            cd("progs/matlab");
+            keatingSR;
+            BlanchardQuahLR;

.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml

@@ -135,4 +135,13 @@ jobs:
           command: |
             addpath("dynare/matlab");
             cd("progs/matlab");
-            USOil;
+            USOil;
+
+      - name: Run week 9 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("dynare/matlab");
+            cd("progs/matlab");
+            keatingSR;
+            BlanchardQuahLR;

.github/workflows/dynare-6.2-matlab-r2024b-windows.yml

@@ -97,4 +97,13 @@ jobs:
           command: |
             addpath("D:\hostedtoolcache\windows\dynare-6.0\matlab");
             cd("progs/matlab");
-            USOil;
+            USOil;
+
+      - name: Run week 9 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("D:\hostedtoolcache\windows\dynare-6.0\matlab");
+            cd("progs/matlab");
+            keatingSR;
+            BlanchardQuahLR;

README.md

@@ -120,7 +120,7 @@ Please feel free to use this for teaching or learning purposes; however, taking
 ### To Do
 
 * [x] review the solutions of [last week's exercises](https://github.com/wmutschl/Quantitative-Macroeconomics/releases/latest/download/week_4.pdf) and write down all your questions
-* [x] re-read Lütkepohl (2004) and quickly go through Kilian and Lütkepohl (2007, Ch. 12.2); make note of all the aspects and concepts that you are still not familiar with or that you find difficult to understand
+* [x] re-read Lütkepohl (2004) and briefly go through Kilian and Lütkepohl (2007, Ch. 2.6, 2.7, 12.2); make note of all the aspects and concepts that you are still not familiar with or that you find difficult to understand
 * [x] Do exercise 1 of the problem set for week 5; we will do exercises 2 and 3 in class
 * [x] participate in the Q&A sessions with all your questions and concerns
 * [x] for immediate help: [schedule a meeting](https://schedule.mutschler.eu)
@@ -152,50 +152,57 @@ Familiarize yourself with
 </details>
 
 
-<!---
-
 <details>
   <summary> Week 7: The identification problem in SVAR models</summary>
 
 ### Goals
 
 * understand the identification problem in SVAR models
+* understand recursive identification, short-run restrictions and the impact matrix
+* implement recursive identification via Cholesky or numerical optimization
+
 
 ### To Do
 
 * [x] Review the solutions of [last week's exercises](https://github.com/wmutschl/Quantitative-Macroeconomics/releases/latest/download/week_6.pdf) and write down all your questions
-* [x] Read Kilian and Lütkepohl (2007, Ch. 2.3 and Ch. 2.6); make note of all the aspects and concepts that you are not familiar with or that you find difficult to understand
-* [x] Do exercises 1 and 2 of problem set 7; we will do exercise 3 in class
+* [x] Read Kilian and Lütkepohl (2007, Ch. 4.1, 7.6, 8, 9); make note of all the aspects and concepts that you are not familiar with or that you find difficult to understand
+* [x] We will do the exercises in class
 * [x] If you have questions, get in touch with me via email or (better) [schedule a meeting](https://schedule.mutschler.eu)
 
 </details>
 
+
 <details>
-  <summary> Week 8: Short-run restrictions in Structural Vector Autoregressive (SVAR) Models</summary>
+  <summary> Week 8: MIDTERM EXAM</summary>
+</details>
+
+
+<details>
+  <summary> Week 9: Short-run and Long-run restrictions in Structural Vector Autoregressive (SVAR) Models</summary>
 
 ### Goals
 
-* understand recursive identification, short-run restrictions and the impact matrix
-* implement recursive identification both via Cholesky or numerical optimization
 * implement short-run restrictions using numerical optimization
+* understand long-run restrictions and the long-run multiplier matrix
+* implement long-run restrictions using Cholesky or numerical optimization
 
 ### To Do
 
 * [x] Review the solutions of [last week's exercises](https://github.com/wmutschl/Quantitative-Macroeconomics/releases/latest/download/week_7.pdf) and write down all your questions
-* [x] Read Kilian and Lütkepohl (2007, Ch. 4.1, Ch. 7.6, Ch.8, Ch.9); make note of all the aspects and concepts that you are not familiar with or that you find difficult to understand
-* [x] Do exercises 1 and 2 from problem set 8; we will do exercise 3 in class
+* [x] Read Kilian and Lütkepohl (2007, Ch. 4.1, Ch. 7.6, Ch.8, Ch.9) and Blanchard and Quah (1989); make note of all the aspects and concepts that you are not familiar with or that you find difficult to understand
+* [x] We will do the exercises in class
 * [x] If you have questions, get in touch with me via email or (better) [schedule a meeting](https://schedule.mutschler.eu)
 
 </details>
 
+<!---
 
 <details>
-  <summary> Week 9: Short-run and Long-run restrictions in Structural Vector Autoregressive (SVAR) Models, Asymptotic and Bootstrap Inference in SVARs Identified By Exclusion Restrictions: Theory</summary>
+  <summary> Week 10: Asymptotic and Bootstrap Inference in SVARs Identified By Exclusion Restrictions: Theory</summary>
 
 ### Goals
 
-* understand long-run restrictions and the long-run multiplier matrix
-* implement short-run and long-run restrictions using numerical optimization
+* implement both short-run and long-run restrictions using numerical optimization
 * understand pros and cons of asymptotic inference for the impulse-response function of SVAR models
 * understand pros and cons of bootstrap inference for the impulse-response function of SVAR models
 

exercises/svar_longrun.tex

@@ -5,55 +5,61 @@
   whereas \(gdp_t\) exhibits a unit root;
   that is, GDP growth, \(\Delta gdp_t = gdp_{t} - gdp_{t-1}\), is covariance-stationary.
 \textcite{Blanchard.Quah_1989_DynamicEffectsAggregate} set up a SVAR model for \(y_t = (\Delta gdp_t, ur_t)'\)
-  and analyze the effects of two structural shocks, an aggregate supply shock \(\varepsilon_t^{AS}\) and an aggregate demand shock \(\varepsilon_t^{AD}\).
+  and analyze the effects of two structural shocks,
+  an aggregate supply shock \(\varepsilon_t^{AS}\)
+  and an aggregate demand shock \(\varepsilon_t^{AD}\).
 
 \begin{enumerate}
 \item Why are short-run restrictions sometimes (or even often) \emph{problematic}?
 What about long-run restrictions?
 
-\item Assume for simplicity a VAR(1) model for \(y_t\).
-Derive the effect of the structural shocks on the behavior of \(ur_{t+h}\), \(\Delta gdp_{t+h}\) and \(gdp_{t+h}\) for \(h=0,1,2\cdots \).
+\item Assume for simplicity a VAR{(1)} model for \(y_t\).
+Derive the effect of the structural shocks on the behavior of
+  \(ur_{t+h}\), \(\Delta gdp_{t+h}\) and \(gdp_{t+h}\) for \(h=0,1,2\cdots \).
 What happens in the long-run, i.e.\ for \(h\rightarrow \infty \)?
 
-\item Discuss the implications on the structural impulse responses of requiring \(gdp_t\) to return to its initial level in the long-run in response to an aggregate demand shock.
+\item Discuss the implications on the structural impulse responses of requiring \(gdp_t\)
+  to return to its initial level in the long-run in response to an aggregate demand shock.
 
 \item Given knowledge of the reduced-form VAR model parameters,
-  show how to recover the short-run impact matrix \(B_0^{-1}\) from the long-run structural impulse response matrix
+  show how to recover the short-run impact matrix \(B_{0}^{-1}\) from the long-run structural impulse response matrix
   \begin{align*}
-  \Theta(1)={(I-A_1-\cdots -A_p)}^{-1}B_0^{-1} = {A(1)}^{-1}B_0^{-1}
+  \Theta(1)={(I-A_{1}-\cdots -A_{p})}^{-1}B_{0}^{-1} = {A(1)}^{-1}B_{0}^{-1}
   \end{align*} 
   where \(A(1)\) denotes the lag polynomial evaluated at \(L=1\).
 
 \item Consider the data given in \texttt{BlanchardQuah1989.csv}.
-Estimate a SVAR(8) model with a constant term.
+Estimate a SVAR{(8)} model with a constant term.
 The structural shocks are identified by imposing that \(\varepsilon_t^{AD}\) has no long-run effect on the level of real GDP\@.
-Estimate the impact matrix \(B_0^{-1}\) using 
+Estimate the impact matrix \(B_{0}^{-1}\) using 
 \begin{enumerate}
-\item the Cholesky decomposition on \({\hat{A}(1)}^{-1} \hat{\Sigma}_u {\hat{A}(1)}^{-1'}= \Theta(1) \Theta(1)'\)
+\item the Cholesky decomposition on \({\hat{A}(1)}^{-1} \hat{\Sigma}_{u} {\hat{A}(1)}^{-1'}= \Theta(1) \Theta(1)'\)
 
 \item a nonlinear equation solver that minimizes
 \begin{align*}
-F(B_0^{-1}) = \begin{bmatrix}
-vech(B_0^{-1}B_0^{-1'}-\hat{\Sigma}_u)\\
+F(B_{0}^{-1}) =
+\begin{bmatrix}
+vech(B_{0}^{-1}B_{0}^{-1'}-\hat{\Sigma}_u)
+\\
 \text{restrictions on } \Theta(1)
 \end{bmatrix}
 \end{align*}
 
 \end{enumerate}
-where \(\Theta(1)={(I-A_1-\cdots -A_p)}^{-1}B_0^{-1} = {A(1)}^{-1}B_0^{-1}\).
-Assume that \(E(\varepsilon_t\varepsilon_t')=I_2\) and the diagonal elements of \(B_0^{-1}\) are positive.
+where \(\Theta(1)={(I-A_{1}-\cdots-A_{p})}^{-1}B_{0}^{-1} = {A(1)}^{-1}B_{0}^{-1}\).
+Assume that \(E(\varepsilon_{t}\varepsilon_{t}')=I_{2}\) and the diagonal elements of \(B_{0}^{-1}\) are positive.
 
 \item Plot the structural impulse response functions using \texttt{irfPlots.m} for the level of GDP and the unemployment rate.
 Interpret your results in economic terms.
 \end{enumerate}
 
 \paragraph{Readings}
 \begin{itemize}
-	\item \textcite[Ch.~10.1, 10.3, 11.1, 11.2]{Kilian.Lutkepohl_2017_StructuralVectorAutoregressive}
+\item \textcite[Ch.~10.1, 10.3, 11.1, 11.2]{Kilian.Lutkepohl_2017_StructuralVectorAutoregressive}
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:BlanchardQuahLongRunRestrictions}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/svar_longrun_solution.tex}
 \fi
 \newpage