Intermediate Computational Economics

Course Overview

This course provides students with a computational foundation for solving economic models numerically. The focus is on applying numerical methods to linear algebra, nonlinear analysis, and dynamic systems using Python. By the end of this course, students will be able to implement and analyze numerical algorithms relevant to economic modeling.

Course Outline

Part 1: Foundations of Computational Economics

📌 Objective: Introduce students to numerical methods and Python for economic applications.

1.1 Introduction to Numerical Methods in Economics

• Why numerical methods?

• Overview of numerical approaches in economic modeling

• Key computational tools: Python, NumPy, SciPy, and Matplotlib

1.2 Numerical Precision and Errors

• Floating-point arithmetic and round-off errors

• Conditioning and stability of numerical algorithms

1.3 Programming in Python for Economics

• Basics of Python: data structures, loops, and functions

• Vectorized computations with NumPy

• Symbolic mathematics with SymPy

Part 2: Linear Algebra for Economic Modeling

📌 Objective: Equip students with matrix-based numerical techniques to solve economic models.

2.1 Solving Systems of Linear Equations

• Gaussian elimination, LU decomposition

• Economic applications: General equilibrium models, Leontief input-output models

2.2 Matrix Operations and Their Economic Interpretation

• Matrix inversion, determinants, rank

• Economic applications: Linear regression and least squares estimation

2.3 Eigenvalues and Eigenvectors (Theory & Computational Aspects)

• Spectral decomposition, diagonalization

• Economic Applications:

  • Markov chains and transition matrices

  • Leontief input-output models

  • Preview for Part 4: Eigenvalues in dynamic stability analysis

📌 Connection to Part 4: Eigenvalue analysis will be applied to study stability of economic dynamics in Part 4.

Part 3: Nonlinear Analysis – Root-Finding and Optimization

📌 Objective: Introduce numerical techniques for solving nonlinear equations and optimization problems in economics.

3.1 Root-Finding Methods for Nonlinear Equations

• Bisection method, Newton-Raphson method, fixed-point iteration

• Economic applications: Market equilibrium computation

3.2 Unconstrained Optimization

• Gradient-based methods (steepest descent, Newton’s method)

• Economic applications: Utility maximization, firm profit maximization

3.3 Constrained Optimization

• Lagrange multipliers, Kuhn-Tucker conditions

• Numerical approaches: Penalty and interior-point methods

• Economic applications: Constrained utility maximization, dynamic pricing

Part 4: Dynamics – Numerical Solutions to Difference and Differential Equations

📌 Objective: Develop numerical approaches for solving dynamic economic models.

4.1 Numerical Methods for Solving Difference Equations

• First- and second-order difference equations

• Eigenvalues and stability analysis (linked to Part 2)

• Economic applications: Growth models (Solow, Ramsey), OLG models

4.2 Numerical Solutions for Differential Equations

• Euler method, Runge-Kutta methods

• Phase diagrams and stability analysis using eigenvalues

• Economic applications: Continuous-time dynamic optimization, DSGE models

4.3 Dynamic Programming and Bellman Equations

• Value function iteration and policy function iteration

• Applications in macroeconomics and finance

📌 Connection to Part 2: Eigenvalue analysis from Part 2 helps determine the stability of dynamic models in Part 4.

Reading Materials

Main Textbook:

• Qingkai Kong et al. (2021). Python Programming and Numerical Methods: A Guide for Engineers and Scientists. Online access

Additional References:

Numerical Methods & Computation

• Robert Johansson (2018). Numerical Python. Online notebook

• Svein Linge & Hans Petter Langtangen (2020). Programming for Computations - Python. Open access

Computational Economics

• Kenneth Judd (1998). Numerical Methods in Economics. MIT Press.

• Jeremy Greenwood & Ricardo Marto (2023). Numerical Methods for Macroeconomists with Julia and MATLAB.

• Mario Miranda & Paul Fackler (2004). Applied Computational Economics and Finance.

Online Resources:

• QuantEcon https://quantecon.org/ – Computational methods for economics (Python & Julia).

• Juergen Jung (2024). Computational Economics. https://juejung.github.io/jdocs/Comp/html_new/