Notes on Computational Methods

This page is an archive of lecture notes and slides that I created mostly when I was teaching at the University of Illinois, Urbana-Champaign (UIUC). Naturally, since the materials are old (most notes were written in 2006-2007), and there are so many textbooks on numerical mathods written since the days I was teaching, I am not sure about the value of these notes. But I still hear nice words about these notes (thanks!), so I leave them here. I am hoping to create my own textbook based on the materials here and other things I learned since my days at UIUC some day.

Numerical Methods

1. Numerical differentiation [DL]

2. Numerical optimization (one-dimensional) [DL]

3. Numerical integration: Gaussian quadrature [DL]

4. Numerical integration: Newton-Coates quadrature [DL]

5. Numerical integration: Applications for quantitative macroeconomics [DL]

6. Function approximation: Finite element methods [DL]

7. Function approximation: Weighted residual methods [DL]

8. Function approximation: Chebyshev regression [DL]

9. Approximating AR(1) process [DL]

Dynamic Programming

1. Practical introduction to dynamic programming [DL]

Neoclassical Growth Model

1. Introduction to solving neoclassical growth model [DL]

2. Solving neoclassical growth model using discretization [DL]

3. Solving neoclassical growth model using finite element method [DL]

4. Solving neoclassical growth model using Chebyshev regression [DL]

Real Business Cycle (RBC) Model

1. Solving RBC model using linear-quadratic (LQ) approximation [DL]

2. Solving RBC model using log-linearization and Blanchard-Kahn method [DL]

3. Solving RBC model using log-linearization and method of undetermined coefficients [DL]

Heterogeneous-Agent Model in Steady State (Aiyagari Model)

1. How to store type distribution [DL]

2. Solving Aiyagari model [DL]

3. Solving Aiyagari model with labor-leisure choice and fiscal policy [DL]

Heterogeneous-Agent Model with Aggregate Shocks (Krusell-Smith Model)

1. Solving the baseline Krusell-Smith model [DL]

2. Solving Krusell-Smith model with labor-leisure choice

3. Solving Krusell-Smith model with portfolio choice

Heterogeneous-Agent Model with Endogenous Debt and Default

1. Solving heterogeneous-agent model with equilibrium default

2. Solving heterogeneous-agent model with endogenous borrowing constriant

3. Solving the baseline model with sovereign default

Parallel Computing

1. Slides on practical introduction for MPI (Message Passing Interface) [DL]