🌍 Week 4 Homework — Feedback

Student: Matteo Pugliese
Assignment: Extended IS–LM and Cholesky Decomposition

✅ Overall Assessment

Result: ✅ More than 50% Correct

The student demonstrates good code organization and effort, implementing most components with clear structure and detailed comments. However, there are critical errors in matrix construction and shock generation that lead to economically incorrect results. The Cholesky decomposition is implemented correctly, but the IS-LM system setup and stochastic simulation contain fundamental mistakes.

🔍 Task-by-Task Check

Task Description Status Notes
1 Parameter setup & system definition ❌ Critical Error: b vector is [MP + theta*G] instead of [MP - theta*G]. A matrix is correct. This error affects all economic results.
2 Equilibrium solution ⚠️ Solves system correctly given the wrong b vector, but results are economically incorrect due to matrix error.
3 Comparative statics setup ✅ Correctly creates G grid using linspace(50, 150, 101), loops through values, and stores results in Y_vals and i_vals arrays.
4 Plotting comparative statics ✅ Creates separate figures for Y vs G and i vs G. Shows relationships correctly given the wrong system. No figure saving in code.
5 Cholesky decomposition ✅ Correctly defines Sigma matrix, checks eigenvalues > 0, computes L using chol(Sigma, 'lower'), and verifies decomposition.
6 Stochastic simulation setup ❌ Critical Error: Uses randn(n_sims, 2) instead of randn(2, n_sims). Wrong dimensions for shock generation.
7 Equilibrium distribution analysis ⚠️ Computes means, standard deviations, and correlations, but based on wrong shock generation and wrong underlying system.
8 Visualization of stochastic results ✅ Creates histogram and scatter plot correctly with proper labels and styling. No figure saving in code.

📈 Technical Implementation

  • Critical Matrix Error: b vector [MP + theta*G] should be [MP - theta*G]
  • Critical Shock Error: Uses randn(n_sims, 2) instead of randn(2, n_sims) for proper 2D shock generation
  • Code Structure: Good organization with clear sections and detailed comments
  • Numerical Methods: Uses correct A\b method and efficient computation
  • G Grid: Uses linspace(50, 150, 101) which is economically reasonable
  • Figure Management: Missing saveas() commands in code
  • Advanced Features: Includes histogram visualization and correlation analysis

💬 Style & Clarity

  • Code Quality: Good structure with clear section headers and detailed comments
  • Variable Naming: Logical names (G_grid, Y_vals, i_vals, solutions)
  • Comments: Detailed comments explaining economic theory and matrix operations
  • Output: Good use of fprintf with clear formatting
  • Organization: Clear separation into three main parts with progress indicators

📊 Visual Output Assessment

Please remember to save the figures in the Figures folder!

Figure 1: week4_1.png ⚠️

  • Layout: Separate figure for Y vs G
  • Relationships: Shows relationship, but based on wrong b vector
  • Labels: Proper axis labels and title
  • Styling: Clean appearance with grid
  • Issue: Wrong relationship due to matrix error

Figure 2: week4_2.png ⚠️

  • Layout: Separate figure for i vs G
  • Relationships: Shows relationship, but based on wrong b vector
  • Labels: Proper axis labels and title
  • Styling: Clean appearance with grid
  • Issue: Wrong relationship due to matrix error

Figure 3: week4_3.png ⚠️

  • Layout: Histogram of simulated Y
  • Distribution: Shows distribution, but based on wrong shock generation
  • Styling: Good use of color and transparency
  • Issue: Wrong underlying shock structure

Figure 4: week4_4.png ⚠️

  • Layout: Scatter plot of (Y, i)
  • Correlation: Shows correlation structure, but based on wrong system
  • Styling: Good use of MarkerFaceAlpha for transparency
  • Issue: Results based on incorrect matrix construction and shock generation

✅ Suggestions for Improvement

  1. Critical: Fix b vector to [MP - theta*G] instead of [MP + theta*G]
  2. Critical: Fix shock generation to use randn(2, n_sims) instead of randn(n_sims, 2)
  3. Important: Add saveas() commands to save figures automatically
  4. Style: Consider creating subplots instead of separate figures for comparative statics
  5. Verification: Check that results are economically reasonable

🎯 Summary

Good implementation with critical economic errors. The student demonstrates solid programming skills, clear code organization, and attention to detail. However, the wrong b vector construction and incorrect shock dimensions prevent correct economic interpretation of the IS-LM system.

Grade Level: ✅ More than 50% Correct (4/8 tasks fully correct, 2/8 partially correct, 2/8 incorrect)