"Introduction to Numerical Methods in Economics"

Course Objectives

This course introduces the students with basic methods for solving and estimating economics models. During the course the students will get familiar with the concept of Bayesian estimation, quadrature methods for solving expectation equations and projection methods for solving macro models. The students will also get familiar with modern software for solving DSGE models.

Main Texts

Judd, K. (1998) Numerical Methods in Economics. MIT Press Books, Cambridge, MA.

Kim, C.-J. and Nelson, C. R. (1999). State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. MIT Press Books, Cambridge, MA.

Bertsekas D. (2005) Dynamic Programming and Optimal Control, Vol. I. Athena Scientific.

Course Outline

The Classical Approach to Estimation

• Maximum Likelihood Estimation
• Markov-Switching Models
• State-Space Models and the Kalman Filter

The Gibbs-Sampling Approach to Estimation

• Introduction to Bayesian Inference and Gibbs-Sampling
• Markov-Switching Models and Gibbs-Sampling
• State-Space Models and Gibbs-Sampling

Introduction to Dynamic Programming

• Discrete-Time Dynamic Programming
• Continuous-Time Dynamic Programming
• Example

Approximation Methods

• Local Approximation Methods
• Orthogonal Polynomial Approximation
• Uniform Approximation
• Interpolation, Splines
• Multidimensional Approximation

Numerical Dierentiation and Integration

• Newton-Cotes Formulas
• Gaussian Formulas
• Multidimensional Quadrature
• Numerical Differentiation

Projection Methods for Solving Functional Equations

• General Projection Method
• Ordinary Dierential Equation Example
• Partial Dierential Equation Example
• Going Back to Economics: Life-Cycle and Growth Models

A Complete Guide to Soving Asset-Pricing Models

• Setting up the model
• Estimation and calibration of the model: What to take from others and what do on
• your own?
• Solving the asset-pricing with dierent preferences
• Interpreting the results: An example of particular model

Software Tutorial

• A short tutorial on R: installation and basic introduction
• A short tutorial on AMPL: installation and basic introduction