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Computational Macroeconomics

These are my course materials for a graduate course on Computational Macroeconomics taught at the University of Tübingen. The compiled materials (such as PDFs) are available under Releases.

Please feel free to use this for teaching or learning purposes; however, taking into account the GPL 3.0 license.

Schedule with To-Do Lists

Week 1: Introductions

Goals

understand the scope and topics of Computational Macroeconomics
decide whether you want to take the course
prepare your computer for the course with MATLAB/Octave and Dynare
do your first steps in MATLAB/Octave and Dynare

To Do

Week 2: RBC Model, Calibration and Steady-State

Goals

understand and get comfortable with the algebra of RBC models
understand the concept of a steady-state
understand the concept of calibration
practice Dynare
start programming with MATLAB

To Do

watch the following videos (on YouTube)
do exercises 1 and 2 of week 2's exercise sheet, we will do the case study together
bring all your questions and concerns to the Q&A sessions

Week 3: Practicing MATLAB, New Keynesian Model

Goals

practice MATLAB: symbolic toolbox, matrix algebra, loops, Kronecker products, functions
understand and get comfortable with the algebra of New Keynesian models
practice Dynare with the New Keynesian model

To Do

watch Algebra of New Keynesian Models with Calvo price rigidities on YouTube
do the MATLAB exercises 1 and 2 of week 3's exercise sheet
work carefully and thoroughly through the very long exercise 3 of week 3's exercise sheet
we will do exercise 4 of week 3's exercise sheet together in class
bring all your questions and concerns to the Q&A sessions

Week 4: Preprocessing and steady-state in MATLAB, numerical optimization

Goals

understand and replicate preprocessing and steady-state computations in MATLAB
understand and start using numerical optimizers

To Do

watch the (very short) videos:
do exercises 1-3 of week 4's exercise sheet
bring all your questions and concerns to the Q&A sessions

Week 5: Deterministic simulations and perfect-foresight algorithm

Goals

understand Dynare's commands to do deterministic simulations
understand the Newton algorithm used by Dynare to solve perfect foresight problems
re-implement deterministic simulations in MATLAB

To Do

watch the videos
do exercise 1 of week 5's exercise sheet
we will do a case study together in class
bring all your questions and concerns to the Q&A sessions

Week 6: Practicing preprocessing and deterministic simulations, Deal with numerical issues, Homotopy, New-Keynesian SIR

Goals

understand the SIR (Susceptible, Infected, Recovered) epidemiology model
understand and get used to Dynare's macro preprocessing directives
understand timing conventions of predetermined variables
understand the difference between sticky-price and flex-price New Keynesian economies
deal with common numerical issues in the perfect foresight solution algorithm
understand homotopy in the context of perfect foresight simulations
simulate a New-Keynesian SIR model

To Do

prepare exercise 1 of week 6's exercise sheet
- read the case-study paper carefully
- download all files
- read all the exercises
- try to prepare the exercises (this will be hard, so we will go through this together in class)
bring all your questions and concerns to the Q&A sessions

Week 7: Midterm Exam: Monopolistic Competition, Irreversible Investment, War Shock

Goals

understand monopolistic competition and the Dixit Stiglitz elasticity parameter
understand irreversible investments as an occasionally binding constraint
understand the modeling of a war in a New Keynesian model
get a good grade

To Do

read the instructions and do both exercises from the summer 2023 midterm exam
read the case-study paper carefully
hand in your solutions via email
for immediate help: contact me via email or schedule a meeting

Week 8: First-order perturbation, Identification, Sensitivity, Log-Linearization

Goals

understand the concept of a policy function
understand the general idea of first-order perturbation approximation
understand certainty equivalence
understand the algorithm to compute the perturbation matrices using the Linear Rational Expectation model framework
[optional] understand Dynare's first-order perturbation solver

To Do

watch Solving rational expectation models with first order perturbation: what Dynare does (Part 1 of 2) on YouTube
[optional] Solving rational expectation models with first order perturbation: what Dynare does (Part 2 of 2) on YouTube
prepare week 8's exercise sheet: exercise 1 and 2 for the first meeting and exercises 3 and 4 for the second meeting
read section 2 of An and Schorfheide (2007)
[optional] read Rupert and Šustek (2019)
bring all your questions and concerns to the Q&A sessions

Week 9: Practicing Stochastic Simulations, Impulse Response Functions, Perturbation. Environmental Policy, Trend Inflation in the New Keynesian model.

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
- read the case-study papers on environmental policy and trend inflation carefully
- download all files
- read all the exercises
- try to prepare the replications
bring all your questions and concerns to the Q&A sessions

Week 10: OccBin, Introduction to Higher-Order Approximation

Goals

To Do

Week 11: Recursive Preferences and Equity Risk Premium and Stochastic Volatility

Goals

To Do

Week 12: Optimal Policy and Welfare assessment

Goals

To Do

Week 13: Projection

Goals

To Do

Week 14: Projection

Goals

To Do

Content

We cover modern theoretical macroeconomics (the study of aggregated variables such as economic growth, unemployment and inflation by means of structural macroeconomic models) and combine it with numerical methods to study abstract macroeconomic concepts such as optimal monetary, fiscal and environmental policy, occasionally binding constraints (zero-lower-bound, irreversible investment), quantitative easing and rare disasters. To this end, we use the Dynamic Stochastic General Equilibrium (DSGE) model paradigm, particularly focusing on different variants of the New-Keynesian model, and develop the numerical procedures and algorithms required to solve and simulate such models. Using several case studies from the literature the theoretical and methodological foundations of computational macroeconomics are taught.

Topics

Algebra of RBC and New-Keynesian models
Steady-state
Preprocessing of DSGE models
Simulation and solution methods
- perfect foresight
- 1st-order perturbation (log-linearization)
- k-order perturbation
- projection
Impulse response analysis
Sensitivity analysis
Large shocks
Rare events
Occasionally binding constraints
Optimal policy

Case Studies and Replications (Preliminary)

Learning target

Students acquire knowledge of advanced numerical methods in the field of computational macroeconomics. This knowledge is relevant for the realization of a wide variety of macroeconomic research projects and is applied in central banks, ministries, research institutes (e.g. DIW, ifo, IfW, IWH, RWI) and research departments of international organizations (e.g. IMF, World Bank). Upon successful completion of this module, students are prepared to work in these areas. At the same time, the module prepares students for the requirements of a methodologically oriented macroeconomic dissertation.

Students get familiar with a variety of algorithms, examples and situations in which computational thinking is useful in approximating and evaluating abstract macroeconomic phenomena. They recognize and appreciate the connections between theory and computational methods and use their training to find possible avenues of research. While constructing abstract algorithms, they identify appropriate computational tools and evaluate their strengths and weaknesses in the context of problem solving. They utilize computers and software effectively as tools for solving and simulating macroeconomic models. In addition, because students work on the problem sets as a team, students' coordination, organization, and communication skills are enhanced.

Requirements

Basic undergraduate knowledge of macroeconomics as well as econometrics are required, programming skills in a scripting language are advantageous, but not necessary.

Software used

MATLAB or Octave
Dynare

Getting Involved

If you spot mistakes, let me know by opening an issue or write me an email to [email protected]. Moreover, solutions to the exercises in other computer languages (e.g. Julia, Python or R) are highly appreciated. Please sent me those either via email or (better) open a pull request.

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