Overview

Description

CALENDAR DESCRIPTION:

Computational methods for solving and analyzing economic models. Topics include solving systems of equations, optimization, computing equilibria of economic models, computing dynamic and stochastic models, and data-driven estimation. Students will apply these methods to conduct economic analysis using a general-purpose programming language like Python.

COURSE DETAILS:

The course will focus on computational tools and their applications in economics. The topics will be covered in this course include solving linear and non-linear systems of equations, matrix operations, constrained and unconstrained optimization, iterative methods, and statistical approaches such as Monte Carlo simulations.

 

Students will learn how to apply these computational tools to solve economic problems, including supply-demand analysis, portfolio choices, equilibrium dynamics, and forecasting problems. A general-purpose programming language (e.g. Matlab) will be used throughout the course. For each topic, the course will first lay out a simple theoretical framework, show how to solve theoretical problems computationally in the software, and apply these tools to conduct quantitative economic analysis.

 

The course will cover the following topics (subject to changes):

 

1. Linear Equations and Linear Algebra
   - Vectorization and Matrix Operation
   - Solving system of equations (Computational and Mathematical)
   - Linear solvers
   - Applications: Supply-demand; multi-product model; Least-squares
2. Static Optimization
   - Methods: Newton’s Method;Lagrange
   - Unconstrained and constrained optimization
   - Applications: Portfolio Choice; Finite period consumption; Static consumption-labor;
3. Nonlinear Equations and Fixed Point
   - Methods: Gaussian Jacobi; Iterative methods
   - Nonlinear solvers
   - Applications: Solow Model; Cobweb Model; General Equilibrium.
4. Approximation
   - Method: Local Approximation, Ordinary Regression, Polynomials
   - Application: Prediction Problems and functional fitting.
5. Numerical Differentiation and Integration
   - Applications: Uncertainty, Risks and Evaluation of Expectations, Monte Carlos.
6. Probability and Distributions
   - Basic Reviews of Probability and Distributions
   - LLN and CLT
   - Simple Stochastic Process: Markov Chain; Auto-Regressive Models
   - Numerical Integration: Monte Carlo
   - Applications: Option Values; Expected Utility Evaluations
7. Prediction and Forecasting (Optional)

 

The course will have bi-weekly group assignments that emphasize computation of the solutions to economic models.

Grading

Materials

REQUIRED READING:

RECOMMENDED READING:

REQUIRED READING NOTES: