🌍 Week 4 Homework — Feedback

Student: Pablo Romanella
Assignment: Extended IS–LM and Cholesky Decomposition

✅ Overall Assessment

Result: ✅ More than 50% Correct

The student demonstrates reasonable code organization and implements most components correctly. 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, alfa; beta, -gamma] instead of [1, alfa; -beta, gamma]. Missing negative sign on beta. Uses non-standard parameter name (alfa).
2 Equilibrium solution ⚠️ Solves system correctly given the wrong A matrix, but results are economically incorrect due to matrix error.
3 Comparative statics setup ✅ Correctly creates G grid using linspace(100, 150, 51), loops through values, and stores results in Yvar and ivar arrays.
4 Plotting comparative statics ✅ Creates proper subplots 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, computes eigenvalues, 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 means, standard deviations, 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 and styling. No figure saving in code.

📈 Technical Implementation

  • Critical Matrix Error: A matrix [1, alfa; beta, -gamma] should be [1, alfa; -beta, gamma] (missing negative sign on beta)
  • Parameter Naming: Uses non-standard name (alfa) instead of alpha
  • Code Structure: Reasonable organization with clear sections
  • Numerical Methods: Uses correct A\b method and efficient computation
  • G Grid: Uses linspace(100, 150, 51) which is economically reasonable but limited range
  • Figure Management: Missing saveas() commands in code
  • Advanced Features: Includes statistical analysis (means, standard deviations, covariances)

💬 Style & Clarity

  • Code Quality: Reasonable structure with clear section headers
  • Variable Naming: Logical names (Gvar, Yvar, ivar, Ysim, isim)
  • Comments: Minimal comments but clear section separation
  • Output: Good use of disp for displaying results
  • Organization: Clear separation into three main parts

📊 Visual Output Assessment

Please remember to save the figures in the Figures folder!

Figure 1: week4_1.png ⚠️

  • Layout: Two subplots stacked vertically (correct format)
  • Relationships: Shows relationships, but based on wrong A matrix
  • Labels: Proper axis labels and titles
  • Styling: Clean appearance with good line width
  • Saving: No figure saving in code
  • Issue: Wrong relationships due to matrix error

Figure 2: week4_2.png ⚠️

  • Distribution: Scatter plot showing correlated shocks
  • Correlation: Shows correlation structure correctly
  • Styling: Good use of MarkerFaceAlpha for transparency
  • Saving: No figure saving in code
  • 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, alfa; beta, -gamma]
  2. Important: Use standard parameter name (alpha) instead of alfa
  3. Important: Add saveas() commands to save figures automatically
  4. Style: Consider adding more detailed comments explaining the economic theory
  5. Verification: Check that results are economically reasonable

🎯 Summary

Reasonable implementation with critical economic error. The student demonstrates solid programming skills and clear code organization. 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)