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Quantitative Macroeconomics

Download the course syllabus here

General Information

Lectures: Tuesday 1:00-3:15 in Tisch UC-07

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: 25%

Referee report: on a paper chosen from a list that I will distribute sometime during the course (in the 6th week or so), based on your specific research interests. Suggestions welcome. Every student has to hand in a report on a different paper. You have until the 11th week to do it. Weight: 25%

Final assignment: In the 11th week (or so), there will be a final assignment that consists of a replication of the main results from a published paper. I will list a number of papers you can choose from. I will also consider your own suggestions.  You will then have until the end of the course, roughly one moth, to hand it in. 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.

January 27: Blizzard, class cancelled, we'll start next week.

February 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 Tuesday) NOTE: You need to email me to get permission to access the folder

February 10: Computational basics/Root-finding methods/Unconstrained optimization
We discussed the homework. Thanks to Jonathan and Igor. I gave an overview of basics concepts in computation such as errors and numerical derivatives. Next, I presented univariate and multivariate rootfinding methods, i.e. methods that allow to solve for x s.t. f(x)=0. Root-finding methods are motivated by the Pissarides' model. Finally, I discussed how these same techniques can be applied to unconstrained optimization problems.
Read MF, chapters 1, 2, 3 and 5. J chapters 1,2,3,5,7.

Slides on Computational basics and differentiation

Slides on Root-finding methods

Slides on Numerical Integration    NEW

Homework 2 (due next Tuesday)

February 17: Constrained optimization/Discretization methods
We have discussed the homework, thanks to Alberto and Peifan. I continued the discussion of constrained optimization methods (incidentally, the proof of convergence of SUM was correct, but unfinished, I added the last step). I explained how to solve a DP problem with discretization and value function/policy function iteration.
Read HM chapter 4

Slides on Optimization 

Slides on Discretization

Homework 3 (due next Tuesday)

February 24: 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.

Slides on Income Process  TYPO CORRECTED

March 3: Discretization of income process/ LQ
I discussed the Rowenhorst method to discretize a continuous income process.
I explained how to stationarize a model where productivity has a deterministic or stochastic trend. I have presented the LQ method, and started discussing perturbation methods. Thanks Spencer for presenting the solution to HW3. 
[For LQ read chapter 2 by Diaz-Jimenez, in MS and sections 2.2-2.3 in HM]
Slides on LQ Methods

Homework 4 (due next Tuesday)  File 1 and 2

March 10: Perturbation methods
I gave an overview of linearization and explained the method of undetermined coefficients. I then explained first and second order perturbation methods and how to write a Dynare code. Thanks Fiona for presenting the solution to HW4.
Read HM chapter 2 and J section IV

Slides on Perturbation methods

Homework 5 (due Tuesday 24)  

Open the spreadsheet "Suggestions" in the folder Instructions for Report and Replication on Google Drive

Have a nice Spring break!

March 24: Global function approximation methods
I described OCCBIN and then we moved to interpolation methods of known functions. We talked about spectral and finite element methods and studied Chebyshev polynomials and splines in some details. I presented three ways of solving the weighted residual problem and discussed how to extend this logic to the case where the function is unknown.
Read MF chapter 6, Judd ch. 6, HM chapter 6

March 31: Endogenous grid and envelope methods/Numerical accuracy/Multidimensional interpolation/Smolyak grids
We discussed how to solve the income fluctuation problem in a number of ways, including the endogenous grid and envelope methods, we talked about EE errors and the den Haan-Marcet statistic. We extended interpolation to many dimensions and introduced Smolyak grids as a way to reduce the curse of dimensionality intrinsic in tensor products.
Read Judd ch. 6.12-6.15, McGrattan's chapter in the Marimon-Scott book (ch. 6), HM 11.2.7 and 12.3
Homework 6

April 7: Calculating the invariant distribution
We discussed four different ways of computing the invariant distribution in a model with a continuum of agents. Thanks Carlos for presenting the homework.
Slides on approximating the stationary distribution

Homework 7  (due in 2 weeks)

April 14: A self-contained algorithm to compute the stationary equilibrium in heterogeneous agents economies
Simon Mongey combined all we learned about global methods and approximations of invariant distributions and put it all nicely together and parallelize the algorithm. He also briefly explained how to run jobs on the NYU HPC. Thanks Simon for presenting this material.

Slides from Simon's class

Notes on using HPC

Matlab code

April 21: Computing equilibrium in models with idiosyncratic and aggregate shocks (part 1)
I described the Krusell-Smith (1998) economy, described the KS algorithm and discussed two alternatives to the simulation step: (i) non-stochastic simulation, and (ii) explicit aggregation.
Read HM 8.3-8.5

April 28: Computing equilibrium in models with idiosyncratic and aggregate shocks (part 2)
We discussed measures of accuracy in this model, as well as how to deal with non-trivial market clearing. I presented an alternative method to solve this model which combines projections and perturbations, and I discussed the parametrized distribution method.

Slides on KS  (final version)

May 5: Liquid-illiquid asset models with application to fiscal policy
I explained how to generalize the EGM to models with multiple assets and discrete choices. I presented my papers with Kaplan and briefly discussed how to embed the model into a GE framework.

Slides on model with two assets