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Quantitative Macroeconomics

Download the course syllabus here

General Information

Lectures: Thursday 2:00-4:15 in room 736

Office Hours: You can always contact me by phone at extension X2-9771 or by email to arrange a meeting.

Homework: In the first ten weeks or so, there will be weekly problem sets that are required for a passing grade. They are due the following week at the beginning of the class. You are allowed to cooperate with other students, but every student has to hand in his/her own uniquely written assignment. At the beginning of each class, one student will present the solution of last week's homework. The presentation must be done with slides and timed to 10 minutes maximum. Weight: 50%

Final assignment: It consists of a replication of the main results from a published paper of your choice (subject to my approval). I can also suggest papers if you're short of ideas. Weight: 50%

Goals and summary of the course

Goals: The primary goal of the course is to equip students with the numerical methods necessary to tackle interesting  questions in quantitative macroeconomics. The course has two main focuses. The first is the study of computational tools and  algorithms useful to solving and analyzing macro models. The second is the study of interesting applications to macroeconomics. This is not a course in computer languages so students are responsible to learn to write their code. Students can choose their favorite language (Matlab, Fortran, C, Julia, Python, etc...). While all the coursework can be completed with Matlab, my recommendation to students who are serious about  computing is to use this course as an opportunity to learn a more advanced and faster language.

Summary: The course is divided into three parts. In the first part I will teach basic numerical methods. In the second, we will apply these methods to solving representative agent and heterogeneous agent models. The third part of the course is devoted to ongoing frontier research in macroeconomics based on heterogeneous-agent  models (i.e., "the field after Krusell-Smith"). 

Textbooks, Reading Material, and Website 

Suggested textbooks
Other useful references

Course website: Check regularly this web-page where announcements, readings, slides, and homework will be regularly posted in PDF form to be downloaded.

Course Outline

In what follows, I will outline the topics that we cover during the course, as we make progress.

September 3: What is Quantitative Macroeconomics?/Micro Data: A Helicopter Tour
I will begin with a methodological discussion about different approaches to quantitative research in macroeconomics. Next, I'll explain the role of micro data in macro research, and give you a brief overview of the available micro data that researchers routinely use in heterogeneous-agent macro models.
Homework 1 (due next Thursday)
Brief description of some datasets (thanks Victor Rios-Rull) and useful list of data sources (thanks Victoria!)

September 10: Income process: Facts, Estimation and Discretization
I presented some facts about individual earnings dynamics, and explained how to estimate the parameters of an income process from an unbalanced panel, like PSID.
I then discussed the Rowenhorst method to discretize a continuous income process and the Extended Tauchen method to discretize processes with skewness and kurtosis.

Slides on Income Process

Homework 2 (due next Thursday) Data are in the Google Drive folder

September 17: Value Function Iteration+Discretization and LQ
I explained how to solve a DP problem with VFI by entirely discretizing the state space. Next, I explained the linear-quadratic approach, our first step towards local solution methods that we will discuss thoroughly next week. [For VFI, read chapter 4 in the HM book. For LQ read chapter 2 by Diaz-Jimenez in the MS book, and sections 2.2-2.3 in the HM book]
Homework 3 (due next Thursday)

September 24: Local Approximations
I gave an overview of linearization methods and explained the method of undetermined coefficients. I then outlined how to write a Dynare code. Read HM chapter 2 and J section IV

Slides on linearization methods

Homework 4 (Victoria will present)

October 1: Perturbation methods
 Today we had a short class because of my lunch talk. I briefly discussed higher order perturbation, pruning, and OCCBIN.
Read HM chapter 2 and J section IV

Slides on Perturbation methods

Homework 5

October 8: Finite-Element methods
We talked about interpolation of known functions, and presented various examples of splines. We discussed how to solve the income fluctuation problem through piece-wise linear approximation and also presented the endogenous grid method. Read MF chapter 6, Judd ch. 6, HM chapter 6

Homework 6

October 15: Spectral Methods
We discussed spectral methods, Chebyshev polynomials and how to apply weighted residual methods with Chebyshev polynomials to the income fluctuation problem (including how to deal with constraints).
Read Judd ch. 6, McGrattan's chapter in the Marimon-Scott book (ch. 6), HM chapter 11
Slides on Global methods (Part 2)

Bonus material from last year (some of which can be useful for the homework):

Slides on Computational basics and differentiation

Slides on Root-finding methods

Slides on Numerical Integration  

Slides on Optimization 

October 22: Envelope methods, accuracy criteria and computation of invariant distribution
I presented the envelope method and discussed the use of accuracy checks. Next, we started thinking about how to compute the invariant distribution
in a model with a continuum of agents.
Read HM chapter 7

Slides on approximating the stationary distribution

October 29: Computing equilibrium in models with idiosyncratic and aggregate shocks (part 1)
I described the Krusell-Smith (1998) economy, outlined the KS algorithm and discussed accuracy tests for the solution. Next week we'll study the case where there is a market to clear at every step of the simulation (slides already in here).
Read HM 8.3-8.5

Homework 8   the last one!

November 5: Liquid-illiquid asset models with application to fiscal policy
I started to present my papers with Kaplan. The slides also contain a section on how to generalize the EGM to models with multiple assets and discrete choices.

Slides on model with two assets

November 12: G and transfer multipliers in heterogeneous-agents models
I talked about fiscal multipliers in neoclassical and New-Keynesian versions of heterogeneous agents models.

Slides on fiscal multipliers

December 3-10: Continuous time tools to solve heterogeneous-agent models and HANK
In these two classes I presented some useful tools to solve continuous time versions of the income-fluctuation problem and of a Huggett economy. Classes were based on the material developed by Ben Moll. Then, I presented my paper with Kaplan and Moll on monetary policy in HANK (the paper is in the Google drive folder).

Thanks for attending!