🌍 Week 4 Homework β€” Feedback

Student: Alessia Canuto
Assignment: Extended IS–LM and Cholesky Decomposition

βœ… Overall Assessment

Result: βœ… More than 50% Correct

The student demonstrates excellent code organization and effort, implementing most components with sophisticated structure and detailed comments. While there is a critical error in the A matrix construction, she completes 6/8 tasks correctly and includes advanced features like confidence ellipses, analytical derivatives, and professional-quality visualizations.

πŸ” Task-by-Task Check

Task Description Status Notes
1 Parameter setup & system definition ❌ Critical Error: A matrix is [1, alpha; -beta/gamma, 1] instead of [1, alpha; -beta, gamma]. Wrong normalization of LM equation. b vector construction is also affected.
2 Equilibrium solution ⚠️ Solves system correctly given the wrong A matrix, but results are economically incorrect due to matrix error. Includes residual check.
3 Comparative statics setup βœ… Correctly creates G grid using linspace(50, 150, 201), loops through values, and stores results in Ygrid and igrid arrays.
4 Plotting comparative statics βœ… Creates sophisticated tiled layout with IS-LM diagram and comparative statics. Professional-quality visualization. No figure saving in code.
5 Cholesky decomposition βœ… Correctly defines Sigma matrix, checks eigenvalues > 0, computes L using chol(Sigma, 'lower'), and verifies reconstruction error.
6 Stochastic simulation setup βœ… Correctly generates u ~ N(0,I) with proper dimensions (2Γ—10000), transforms to eps = L*u, and sets random seed (123).
7 Equilibrium distribution analysis βœ… Correctly computes empirical and theoretical covariances. Includes advanced analytical derivatives and Frobenius norm comparison.
8 Visualization of stochastic results βœ… Creates sophisticated scatter plot with confidence ellipse, histogram distributions, and professional styling. No figure saving in code.

πŸ“ˆ Technical Implementation

  • Critical Matrix Error: A matrix [1, alpha; -beta/gamma, 1] should be [1, alpha; -beta, gamma] (wrong normalization)
  • Code Structure: Excellent organization with clear sections, professional formatting, and detailed comments
  • Advanced Features:
    • Analytical derivatives (dx/dG = A^{-1} * db/dG)
    • Confidence ellipses for scatter plots
    • Histogram distributions
    • Theoretical vs empirical covariance comparison
    • Professional figure styling with tiled layouts
  • Numerical Methods: Uses correct A\b method and efficient computation
  • G Grid: Uses linspace(50, 150, 201) which is economically reasonable
  • Figure Management: Missing saveas() commands in code

πŸ’¬ Style & Clarity

  • Code Quality: Excellent structure with clear section headers and detailed economic explanations
  • Variable Naming: Logical names (Ggrid, Ygrid, igrid, Xsim)
  • Comments: Detailed comments explaining economic theory, matrix operations, and methodology
  • Output: Professional use of fprintf with clear formatting and progress indicators
  • Organization: Clear separation into parts with sophisticated figure management

πŸ“Š Visual Output Assessment

Please remember to save the figures in the Figures folder!

Figure 1: week4_1.png ⚠️

  • Layout: Sophisticated tiled layout with IS-LM diagram and comparative statics
  • Features: Includes IS-LM curves, equilibria points, fiscal expansion analysis
  • Styling: Professional-quality visualization with proper annotations
  • Issue: Wrong relationships due to matrix error

Figure 2: week4_2.png ⚠️

  • Layout: Scatter plot with confidence ellipse
  • Features: Includes deterministic equilibrium point and 1Οƒ confidence ellipse
  • Styling: Professional styling with proper transparency and colors
  • Issue: Results based on incorrect underlying system due to matrix error

Figure 3: week4_3.png ⚠️

  • Layout: Histogram distributions of Y and i
  • Features: Separate histograms with professional styling
  • Styling: Clean appearance with proper colors and formatting
  • Issue: Distributions based on wrong underlying system

βœ… Suggestions for Improvement

  1. Critical: Fix A matrix to [1, alpha; -beta, gamma] instead of [1, alpha; -beta/gamma, 1]
  2. Important: Add saveas() commands to save figures automatically
  3. Style: Consider adding semicolons on assignment lines to reduce command window output
  4. Verification: Check that results are economically reasonable

🎯 Summary

Excellent implementation with critical economic error. The student demonstrates outstanding programming skills, sophisticated code organization, and attention to detail. The submission includes advanced features like confidence ellipses, analytical derivatives, and professional-quality visualizations. However, the wrong matrix normalization prevents correct economic interpretation of the IS-LM system.

Grade Level: βœ… More than 50% Correct (6/8 tasks fully correct, 1/8 partially correct, 1/8 incorrect)