Added week 9 material

wmutschl · Jun 10, 2024 · a8afe92 · a8afe92
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diff --git a/README.md b/README.md
@@ -193,11 +193,9 @@ Please feel free to use this for teaching or learning purposes; however, taking
 
 </details>
 
-<!---
-
 
 <details>
-  <summary>Week 9: , Practicing preprocessing and deterministic simulations, Deal with numerical issues, Homotopy, New-Keynesian SIR, First-order perturbation, Identification, Sensitivity, Log-Linearization; Practicing Stochastic Simulations, Impulse Response Functions, Perturbation. Environmental Policy, Trend Inflation in the New Keynesian model.</summary>
+  <summary>Week 9: First-order perturbation, Identification, Sensitivity</summary>
 
 ### Goals
 * understand the concept of a policy function
@@ -206,37 +204,34 @@ Please feel free to use this for teaching or learning purposes; however, taking
 * understand the algorithm to compute the perturbation matrices using the Linear Rational Expectation model framework
 * [optional] understand Dynare's first-order perturbation solver
 
-* 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
-  * [RBC Baseline Model in Dynare: Deterministic vs Stochastic Simulations](https://youtu.be/KHTEZiw9ukU)
-* [x] watch [Solving rational expectation models with first order perturbation: what Dynare does (Part 1 of 2)](https://youtu.be/hmVxasBgbqM) on YouTube
-* [x] [optional] [Solving rational expectation models with first order perturbation: what Dynare does (Part 2 of 2)]() on YouTube
-* [x] read section 2 of An and Schorfheide (2007)
+* [x] watch
+  * [x] [RBC Baseline Model in Dynare: Deterministic vs Stochastic Simulations](https://youtu.be/KHTEZiw9ukU)
+  * [x] [Solving rational expectation models with first order perturbation: what Dynare does (Part 1 of 2)](https://youtu.be/hmVxasBgbqM) on YouTube
 * [x] [optional] read Rupert and Šustek (2019)
-
-* 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
-  * [x] download all files
-  * [x] read all the exercises
-  * [x] try to prepare the replications
 * [x] bring all your questions and concerns to the Q&A sessions
 
 
 </details>
 
+<!---
 
 <details>
-  <summary>Week 10: OccBin, Introduction to Higher-Order Approximation</summary>
+  <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>
 
 ### 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
+  * [x] download all files
+  * [x] read all the exercises
+  * [x] try to prepare the replications
 
 </details>
 

diff --git a/exercises/an_schorfheide_identif_bk.tex b/exercises/an_schorfheide_identif_bk.tex
@@ -96,11 +96,11 @@ \subsection*{Exercises}
 \paragraph{Readings}
 \begin{itemize}
 	\item \textcite{An.Schorfheide_2007_BayesianAnalysisDSGE}
-	\item \textcite{Ivashchenko.Mutschler_2020_EffectObservablesFunctionala}
+	\item \textcite{Ivashchenko.Mutschler_2020_EffectObservablesFunctional}
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:AnScho2007_identif_bk}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/an_schorfheide_identif_bk_solution.tex}
 \fi
 \newpage

diff --git a/literature/_biblio.bib b/literature/_biblio.bib
@@ -22,6 +22,18 @@ @misc{Aguirre.Danielsson_2020_WhichProgrammingLanguage
   abstract = {The most widely used programming languages for economic research are Julia, Matlab, Python and R. This column uses three criteria to compare the languages: the power of available libraries, the speed and possibilities when handling large datasets, and the speed and ease-of-use for a computationally intensive task. While R is still a good choice, Julia is the language the authors now tend to pick for new projects and generally recommend.}
 }
 
+@article{An.Schorfheide_2007_BayesianAnalysisDSGE,
+  title = {Bayesian {{Analysis}} of {{DSGE Models}}},
+  author = {An, Sungbae and Schorfheide, Frank},
+  year = {2007},
+  journal = {Econometric Reviews},
+  volume = {26},
+  number = {2-4},
+  pages = {113--172},
+  doi = {10.1080/07474930701220071},
+  abstract = {This paper reviews Bayesian methods that have been developed in recent years to estimate and evaluate dynamic stochastic general equilibrium (DSGE) models. We consider the estimation of linearized DSGE models, the evaluation of models based on Bayesian model checking, posterior odds comparisons, and comparisons to vector autoregressions, as well as the non-linear estimation based on a second-order accurate model solution. These methods are applied to data generated from correctly specified and misspecified linearized DSGE models and a DSGE model that was solved with a second-order perturbation method.}
+}
+
 @incollection{Anderson.McGrattan.Hansen.EtAl_1996_MechanicsFormingEstimating,
   title = {Mechanics of Forming and Estimating Dynamic Linear Economies},
   booktitle = {Handbook of {{Computational Economics}}},
@@ -83,6 +95,18 @@ @book{Brandimarte_2006_NumericalMethodsFinance
   keywords = {Economics,Finance,Statistical methods}
 }
 
+@article{Brock.Mirman_1972_OptimalEconomicGrowth,
+  title = {Optimal Economic Growth and Uncertainty: {{The}} Discounted Case},
+  author = {Brock, William A and Mirman, Leonard J},
+  year = {1972},
+  month = jun,
+  journal = {Journal of Economic Theory},
+  volume = {4},
+  number = {3},
+  pages = {479--513},
+  doi = {10.1016/0022-0531(72)90135-4}
+}
+
 @article{Calvo_1983_StaggeredPricesUtilitymaximizing,
   title = {Staggered Prices in a Utility-Maximizing Framework},
   author = {Calvo, Guillermo A.},
@@ -171,6 +195,17 @@ @book{Gali_2015_MonetaryPolicyInflation
   keywords = {BUSINESS & ECONOMICS / Economics / Theory,BUSINESS & ECONOMICS / Finance,BUSINESS & ECONOMICS / Money & Monetary Policy,Business cycles,Inflation (Finance),Keynesian economics,Monetary policy}
 }
 
+@book{Hansen.Sargent_2013_RecursiveModelsDynamic,
+  title = {Recursive {{Models}} of {{Dynamic Linear Economies}}},
+  author = {Hansen, Lars Peter and Sargent, Thomas J.},
+  year = {2013},
+  month = dec,
+  publisher = {Princeton University Press},
+  doi = {10.1515/9781400848188},
+  abstract = {A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. In Recursive Models of Dynamic Linear Economies, Lars Peter Hansen and Thomas Sargent use these tools to create a class of econometrically tractable models of prices and quantities. They present examples from microeconomics, macroeconomics, and asset pricing. The models are cast in terms of a representative consumer. While Hansen and Sargent demonstrate the analytical benefits acquired when an analysis with a representative consumer is possible, they also characterize the restrictiveness of assumptions under which a representative household justifies a purely aggregative analysis. Hansen and Sargent unite economic theory with a workable econometrics while going beyond and beneath demand and supply curves for dynamic economies. They construct and apply competitive equilibria for a class of linear-quadratic-Gaussian dynamic economies with complete markets. Their book, based on the 2012 Gorman lectures, stresses heterogeneity, aggregation, and how a common structure unites what superficially appear to be diverse applications. An appendix describes MATLAB programs that apply to the book's calculations.},
+  isbn = {978-1-4008-4818-8}
+}
+
 @book{Heer.Maussner_2024_DynamicGeneralEquilibrium,
   title = {Dynamic {{General Equilibrium Modeling}}: {{Computational Methods}} and {{Applications}}},
   author = {Heer, Burkhard and Mau{\ss}ner, Alfred},
@@ -195,6 +230,18 @@ @book{Heijdra_2017_FoundationsModernMacroeconomics
   keywords = {Macroeconomics,Problems and exercises,Problems exercises etc}
 }
 
+@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},
+  year = {2020},
+  month = jun,
+  journal = {Economic Modelling},
+  volume = {88},
+  pages = {280--292},
+  doi = {10.1016/j.econmod.2019.09.039},
+  abstract = {The decisions a researcher makes at the model building stage are crucial for parameter identification. This paper contains a number of applied tips for solving identifiability problems and improving the strength of DSGE model parameter identification by fine-tuning the (1) choice of observables, (2) functional specifications, (3) model features and (4) choice of structural shocks. We offer a formal approach based on well-established diagnostics and indicators to uncover and address both theoretical (yes/no) identifiability issues and weak identification from a Bayesian perspective. The concepts are illustrated by two exemplary models that demonstrate the identification properties of different investment adjustment cost specifications and output-gap definitions. Our results provide theoretical support for the use of growth adjustment costs, investment-specific technology, and partial inflation indexation.}
+}
+
 @book{Judd_1998_NumericalMethodsEconomics,
   title = {Numerical {{Methods}} in {{Economics}}},
   author = {Judd, Kenneth L.},
@@ -244,6 +291,18 @@ @incollection{King.Rebelo_1999_ResuscitatingRealBusiness
   isbn = {978-0-444-50157-8}
 }
 
+@book{Ljungqvist.Sargent_2018_RecursiveMacroeconomicTheory,
+  title = {Recursive Macroeconomic Theory},
+  author = {Ljungqvist, Lars and Sargent, Thomas J.},
+  year = {2018},
+  edition = {Fourth Edition},
+  publisher = {MIT Press},
+  address = {Cambridge, Massachusetts},
+  abstract = {Recursive methods provide powerful ways to pose and solve problems in dynamic macroeconomics. Recursive Macroeconomic Theory offers both an introduction to recursive methods and more advanced material. Only practice in solving diverse problems fully conveys the advantages of the recursive approach, so the book provides many applications. This fourth edition features two new chapters and substantial revisions to other chapters that demonstrate the power of recursive methods.   One new chapter applies the recursive approach to Ramsey taxation and sharply characterizes the time inconsistency of optimal policies. These insights are used in other chapters to simplify recursive formulations of Ramsey plans and credible government policies. The second new chapter explores the mechanics of matching models and identifies a common channel through which productivity shocks are magnified across a variety of matching models. Other chapters have been extended and refined. For example, there is new material on heterogeneous beliefs in both complete and incomplete markets models; and there is a deeper account of forces that shape aggregate labor supply elasticities in lifecycle models.   The book is suitable for first- and second-year graduate courses in macroeconomics. Most chapters conclude with exercises; many exercises and examples use Matlab or Python computer programming languages.},
+  isbn = {978-0-262-03866-9},
+  keywords = {Macroeconomics,Recursive functions,Statics and dynamics (Social sciences)}
+}
+
 @incollection{Maliar.Maliar_2014_NumericalMethodsLargeScale,
   title = {Numerical {{Methods}} for {{Large-Scale Dynamic Economic Models}}},
   booktitle = {Handbook of {{Computational Economics Volume}} 3},
@@ -296,6 +355,22 @@ @book{Romer_2019_AdvancedMacroeconomics
   keywords = {Macroeconomics}
 }
 
+@article{Rupert.Sustek_2019_MechanicsNewKeynesianModels,
+  title = {On the Mechanics of {{New-Keynesian}} Models},
+  author = {Rupert, Peter and {\v S}ustek, Roman},
+  year = {2019},
+  month = apr,
+  journal = {Journal of Monetary Economics},
+  volume = {102},
+  pages = {53--69},
+  issn = {03043932},
+  doi = {10.1016/j.jmoneco.2019.01.024},
+  url = {https://linkinghub.elsevier.com/retrieve/pii/S0304393219300145},
+  urldate = {2022-05-16},
+  abstract = {The monetary transmission mechanism in New-Keynesian models is put to scrutiny. We show that, contrary to the conventional view, the transmission mechanism does not operate through the real interest rate channel. Instead, equilibrium inflation is approximately determined as in a flexible-price model; output is then pinned down by the New-Keynesian Phillips curve. The real rate only reflects the feasibility to keep consumption smooth when income changes. Contractionary monetary policy shocks reducing output and inflation are consistent with an increase, decline, or no change in the real rate. Consistency with the real rate channel is observational, not structural.},
+  langid = {english}
+}
+
 @article{Taylor_1993_DiscretionPolicyRules,
   title = {Discretion versus Policy Rules in Practice},
   author = {Taylor, John B.},

diff --git a/week_9.tex b/week_9.tex
@@ -0,0 +1,32 @@
+% !TEX root = week_9.tex
+\input{exercises/_common_header.tex}
+\Newassociation{solution}{Solution}{week_9_solution}
+\newif\ifDisplaySolutions%\DisplaySolutionstrue%
+
+\begin{document}
+\title{Computational Macroeconomics\\~\\Summer 2024\\~\\Week 9}
+\author{Willi Mutschler\\[email protected]}
+\date{Version: 1.0\\Latest version available on: \href{https://github.com/wmutschl/Computational-Macroeconomics/releases/latest/download/week_9.pdf}{GitHub}}
+\maketitle\thispagestyle{empty}
+
+\newpage
+\Opensolutionfile{week_9_solution}[week_9_solution]
+\tableofcontents\thispagestyle{empty}\newpage
+
+\setcounter{page}{1}
+\input{exercises/brock_mirman_policy_function.tex}\newpage
+\input{exercises/nk_simulations.tex}\newpage
+\input{exercises/an_schorfheide_identif_bk.tex}\newpage
+
+\printbibliography%
+
+\newpage
+
+\Closesolutionfile{week_9_solution}
+\ifDisplaySolutions%
+\newpage
+\appendix
+\section{Solutions}
+\input{week_9_solution}
+\fi
+\end{document}