🌍 Week 4 Homework — Feedback

Student: Anna de Falco
Assignment: Extended IS–LM and Cholesky Decomposition

✅ Overall Assessment

Result: ✅ More than 50% Correct

The student demonstrates good code organization, comprehensive comments, and implements most components correctly with proper figure saving. However, there is a critical error in the A matrix construction that leads to economically incorrect results. The Cholesky decomposition and stochastic simulation are implemented correctly, but the IS-LM system setup contains fundamental mistakes.

🔍 Task-by-Task Check

Task Description Status Notes
1 Parameter setup & system definition ❌ Critical Error: A matrix is [1, alpha; beta, -gamma] instead of [1, alpha; -beta, gamma]. Missing negative sign on beta. Excellent parameter definitions and comments.
2 Equilibrium solution ⚠️ Solves system correctly given the wrong A matrix, but results are economically incorrect due to matrix error. Uses both A\b and inv(A)*b for comparison.
3 Comparative statics setup ✅ Correctly creates G grid using 0:10:200, loops through values, and stores results in Y_values and i_values arrays. Good range choice.
4 Plotting comparative statics ✅ Creates proper plot with both Y and i on same axes, good styling with markers, proper labels, and saves figures correctly.
5 Cholesky decomposition ✅ Correctly defines Sigma matrix, computes eigenvalues, checks positive definiteness, computes L using chol(Sigma, 'lower'), and verifies reconstruction.
6 Stochastic simulation setup ✅ Correctly generates u ~ N(0,I) with proper dimensions (2×10000), transforms to eps = L*u, and sets random seed (123).
7 Equilibrium distribution analysis ✅ Correctly computes empirical means and covariances. Results are based on wrong underlying system but method is correct.
8 Visualization of stochastic results ✅ Creates scatter plot correctly with proper labels, styling, and saves figures correctly.

📈 Technical Implementation

  • Critical Matrix Error: A matrix [1, alpha; beta, -gamma] should be [1, alpha; -beta, gamma] (missing negative sign on beta)
  • Code Structure: Excellent organization with clear sections and comprehensive comments
  • Numerical Methods: Uses correct A\b method and includes comparison with inv(A)*b
  • G Grid: Uses 0:10:200 which is economically reasonable and shows good range
  • Figure Management: Proper saveas() and savefig() commands for all figures
  • Advanced Features: Includes eigenvalue checking, data saving to .mat file, and comprehensive output
  • Error Handling: Checks positive definiteness of Sigma matrix

💬 Style & Clarity

  • Code Quality: Excellent structure with clear section headers and comprehensive comments
  • Variable Naming: Logical names (Y_values, i_values, Y_sim, i_sim)
  • Comments: Outstanding comments explaining economic theory and mathematical concepts
  • Output: Excellent use of fprintf and disp for displaying results
  • Organization: Clear separation into logical sections with proper headers
  • Documentation: Includes economic interpretation of parameters and equations

📊 Visual Output Assessment

Figure 1: Comparative_statics.png ⚠️

  • Layout: Single plot with both Y and i on same axes (alternative to subplots)
  • Relationships: Shows relationships, but based on wrong A matrix
  • Labels: Proper axis labels and title
  • Styling: Good use of different markers (o and x) and legend
  • Saving: Proper figure saving with both .png and .fig formats
  • Issue: Wrong relationships due to matrix error

Figure 2: week4_Scatterplot.png ⚠️

  • Distribution: Scatter plot showing correlated shocks
  • Correlation: Shows correlation structure correctly
  • Styling: Good use of MarkerFaceAlpha for transparency
  • Saving: Proper figure saving with both .png and .fig formats
  • Issue: Results based on incorrect underlying system due to matrix error

✅ Suggestions for Improvement

  1. Critical: Fix A matrix to [1, alpha; -beta, gamma] instead of [1, alpha; beta, -gamma]
  2. Style: Consider using subplots for comparative statics to match solution format
  3. Verification: Check that results are economically reasonable
  4. Advanced: Consider adding theoretical vs empirical covariance comparison

🎯 Summary

Excellent implementation with critical economic error. The student demonstrates outstanding programming skills, comprehensive comments, and proper figure management. However, the missing negative sign in the A matrix prevents correct economic interpretation of the IS-LM system.

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