🌍 Week 4 Homework — Feedback

Student: Michele Nascia
Assignment: Extended IS–LM and Cholesky Decomposition

✅ Overall Assessment

Result: ✅ More than 50% Correct

The student demonstrates good code organization and implements most components correctly with proper figure saving. However, there are critical errors in the b vector construction that lead 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: b vector is [MP + theta*G] instead of [MP - theta*G]. A matrix is correct. Also inconsistent b vector usage.
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 50:1:200, loops through values, and stores results in Y_values and i_values arrays.
4 Plotting comparative statics ✅ Creates proper subplots for Y vs G and i vs G. Shows relationships correctly given the wrong system. Saves figures properly.
5 Cholesky decomposition ✅ Correctly defines Sigma matrix, checks eigenvalues, computes L using chol(Sigma, 'lower'), and displays results.
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 sample means, covariances, and theoretical covariance. Includes comparison.
8 Visualization of stochastic results ✅ Creates scatter plot and histograms correctly with proper labels and styling. Saves figures properly.

📈 Technical Implementation

  • Critical Matrix Error: b vector [MP + theta*G] should be [MP - theta*G]
  • Inconsistent Implementation: Uses different b vector in initial setup vs loop (line 10 vs line 23)
  • Code Structure: Good organization with clear sections and concise comments
  • Numerical Methods: Uses correct A\b method and efficient computation
  • G Grid: Uses 50:1:200 which is economically reasonable
  • Figure Management: Properly saves figures with both .png and .fig formats
  • Advanced Features: Includes theoretical vs empirical covariance comparison and histograms

💬 Style & Clarity

  • Code Quality: Good structure with clear section headers and concise comments
  • Variable Naming: Logical names (G_values, Y_values, i_values, Y_sim, i_sim)
  • Comments: Minimal but clear comments explaining each section
  • 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: Fig_Yi_vs_G.png ⚠️

  • Layout: Two subplots stacked vertically (correct format)
  • Relationships: Shows relationships, but based on wrong b vector
  • Labels: Proper axis labels and titles
  • Styling: Clean appearance with grid
  • Saving: Correctly saves both .png and .fig files
  • Issue: Wrong relationships due to matrix error

Figure 2: Fig_Scatter_Yi.png ⚠️

  • Distribution: Scatter plot showing correlated shocks
  • Correlation: Shows correlation structure correctly
  • Styling: Clean appearance with proper labels
  • Saving: Correctly saves both .png and .fig files
  • Issue: Results based on incorrect underlying system due to matrix error

Figure 3: Fig_Hist_Yi.png ⚠️

  • Layout: Two histograms stacked vertically
  • Distribution: Shows distributions of Y and i
  • Styling: Clean appearance with proper labels
  • Saving: Correctly saves both .png and .fig files
  • Issue: Distributions based on wrong underlying system

✅ Suggestions for Improvement

  1. Critical: Fix b vector to [MP - theta*G] instead of [MP + theta*G]
  2. Important: Ensure consistent b vector usage throughout the code
  3. Style: Consider adding more detailed comments explaining the economic theory
  4. Verification: Check that results are economically reasonable

🎯 Summary

Good implementation with critical economic error. The student demonstrates solid programming skills, clear code organization, and proper figure management. However, the wrong b vector construction 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)