Week 4

Week 4 – Matrix Algebra for Economics

Learning Outcomes By the end of this week, students will be able to:

1. Create and manipulate matrices in MATLAB.
2. Understand the difference between element-wise and matrix operations.
3. Solve systems of linear equations relevant to economics.
4. Compute matrix inverses, determinants, and eigenvalues.
5. Apply matrix algebra to a simple macroeconomic model (e.g., IS–LM).

Suggested Readings

• Frain, MATLAB for Economics and Econometrics, Ch. 2.1.1–2.1.13 (Matrix operations).
• Greenwood & Marto, Numerical Methods for Macroeconomists, Appendix A.10 (Eigenvalues & Eigenvectors).
• MatlabCheatSheet.pdf – Matrix operations section.

In-Class Activities

• Construct small matrices and perform:
  • Addition, subtraction, scalar multiplication.
  • Element-wise multiplication (.*) vs. matrix multiplication (*).
• Solve a 2×2 linear system representing goods and money market equilibrium using:
  • The backslash operator (A\b).
  • inv() (and discuss why it’s less efficient).
• Compute determinants and eigenvalues of a transition matrix.
• Demonstrate stability analysis in a 2-equation dynamic system using eigenvalues.

Homework / Practice

• Write a script that:
  • Defines an IS–LM model as a system of equations.
  • Represents it in matrix form.
  • Solves for equilibrium output and interest rate.
• Extend the script to:
  • Change a parameter (e.g., government spending) and re-solve.
  • Plot how equilibrium values change with the parameter.
  • Compute the Cholesky decomposition of a given covariance matrix to simulate correlated shocks to the IS and LM equations and analyze their impact on equilibrium outcomes.

Files

• Slides Week 4 – Slides from lecture.
• week4.m – Example script from lecture.
• codes_week4 on Matlab online
  • week4_micro_exercise1.m – Solution file for micro-exercise 1 in class.
  • week4_micro_exercise2.m – Solution file for micro-exercise 2 in class.
  • week4_micro_exercise3.m – Solution file for micro-exercise 3 in class.
• week4_homework_solution.m – Solution file for homework.

Homework submission

• Submit your homework here
• Please upload your homework as a single zip file. Access it’s now open with any email address! But remember to name your file with your full name and or student ID.
• The submission should include the .m file used to produce the results.
• You can modify you submission until the beginning of week 5.