This course is not for everybody. It is important that you have a solid knowledge of macroeconomic models taught at the graduate level. If you don't have the right background yet, then it is better to wait a year.
Recommended prerequisites
Solid knowledge of how to solve linear models
Programming experience (preferably in Matlab)
A strong understanding of recursivity (i.e. Bellman equations, state- vs choice variables etc)
You can find some preparation tips here.
This course runs online only. Therefore, if you are accepted and enroll into the course, you will need:
access to Zoom to participate in lectures and computer sessions.
access to Matlab for computer sessions (with the optimization toolbox).
some elements will require Dynare. If you're new to Dynare, make sure to go through the tutorial and example code here (please make sure you are able to run Dynare code before the course starts).
This graduate-level course focusses on three main topics: 1, Nonlinear solution methods, making use of nonlinear equation solvers (such as Newton's method) and functional approximation, with an emphasis on occassionally binding constraints (eg. borrowing constraints); 2, Heterogenous agents models (the Bewley-Hugget-Aiyagari framework, and its descendants); 3, methods in continuous time. This courses uses Matlab throughout, and is intended for students that have either taken "The Essentials", or students with sufficiently sophisticated background in economics AND numerical methods (ie effectively knowing the material in Essentials).
Monday - Nonlinear solution methods (i)
To solve nonlinear models efficiently, it is common to operate directly on a collection of nonlinear equations. These normally include optimality conditions (first order conditions) alongside with budget constraints, as well as market clearing conditions. To this end, we need to develop an understanding of how to solve nonlinear equations, and how to make use of functional approximations.
Topics
Functional approximations.
Nonlinear equations.
Numerical differentiation and integration.
Exercise
Monday's exercise will involve solving a nonlinear equations with and without a functional approximation.
Tuesday - Nonlinear solution methods (ii)
In this lecture we will focus on how to put the methods explored on Monday into use for economics problems. In particular, we will discuss various methods that operate directly on the optimality conditions (e.g time iteration, projection methods etc), and various improvements (e.g the method of endogenous gridpoints), and how to deal with some common inequality constraints.
Topics
Iterative methods.
Method of endogenous gridpoints.
Inequality constraints.
Exercise
Tuesday's exercise involves solving a stochastic Ramsey growth model with an irreversibility constraint on investment.
Wednesday - Agent heterogeneity
Wednesday's lecture will look at popular algorithms used to solve models with heterogeneous agents. We begin by discussing an algorithm to solve (Bewley-Hugget-Aiyagari-style) heterogeneous agent models without aggregate uncertainty. Next, we discuss how the addition of aggregate uncertainty introduces additional challenges and how we could handle those. In doing so, we touch upon the Krusell-Smith algorithm, simulation methods avoiding sampling uncertainty and algorithms avoiding simulation altogether.
Topics
Bewley-Hugget-Aiyagari model and solution algorithm
Aggregate uncertainty (Krusell and Smith and alternatives)
Simulation methods
Exercise
In Wednesday's assignment you will be asked to solve a heterogeneous firm model with aggregate uncertainty using Dynare.
Thursday - Continuous time (i)
This is the first lecture on continuous time methods and models. To introduce the concept, we will carefully derive the continuous time representation of discrete time models, arriving at the so-called Hamilton-Jacobi-Bellman (HJB) equations. Next, we will discuss some preliminary methods of how to solve these. While these methods are inferior to those presented in the next lecture, they are simple and serve the useful purpose of providing intuition
Topics
Continuous time in representative agent models.
The explicit method.
Search and matching models in continuous time.
Exercise
Thursday's assignment will amount to solving a Mortensen-Pissarides model in continuous time.
Friday - Continuous time (ii)
In the second lecture on continuous time we will start by first introducing a highly efficient method to solving HJB equations, known as the implicit method, and apply this to a standard Ramsey growth model cast in continuous time. Next, we will carefully go through a heterogenous agents model - a la Aiyagari - in continuous time, and illustrate how it can be solved.
Topics
Implicit method
The Aiyagari model in continuous time.
Kolmogorov forward equation.
Exercise
Friday's assignment amounts to solving the Aiagari model in continuous time.