🌍 Week 4 Homework — Feedback

Student: Giovanni Di Miele
Assignment: Extended IS–LM and Cholesky Decomposition

✅ Overall Assessment

Result: ✅ More than 50% Correct

The student implements most components correctly. The core IS-LM system is implemented correctly with proper matrix construction and completes most tasks successfully. While missing the comparative statics plot (Task 4) and using an economically questionable G range (Task 3), he demonstrates solid understanding of the material with 5/8 tasks completed correctly. The Cholesky decomposition and stochastic simulation are implemented well.

🔍 Task-by-Task Check

Task Description Status Notes
1 Parameter setup & system definition ✅ All parameters correctly defined. A matrix properly constructed as [1, alpha; -beta, gamma]. b vector correctly constructed.
2 Equilibrium solution ✅ Uses A\b method correctly. Extracts Y and i properly. Displays results.
3 Comparative statics setup ⚠️ Creates G grid but uses wrong range (1:0.2:10 instead of reasonable range like 80:2:120). Loops correctly but range is economically meaningless.
4 Plotting comparative statics ❌ Missing: No comparative statics plot created. Only computes values but doesn’t visualize them.
5 Cholesky decomposition ✅ Correctly defines Sigma matrix, checks symmetry, computes eigenvalues, and computes L using chol(Sigma, 'lower').
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 and covariances. Results are economically reasonable.
8 Visualization of stochastic results ✅ Creates scatter plot correctly with proper labels, styling, and includes mean equilibrium point. Saves as ISLM_shocks.png.

📈 Technical Implementation

  • Matrix Construction: Correct A matrix [1, alpha; -beta, gamma] and b vector
  • Code Structure: Poor formatting with missing semicolons causing command window clutter
  • G Grid Issue: Uses 1:0.2:10 instead of economically meaningful range (80:2:120)
  • Missing Visualization: No comparative statics plot despite computing the data
  • Figure Management: Only saves stochastic plot, missing comparative statics figure
  • Numerical Methods: Uses correct A\b method and proper matrix operations

💬 Style & Clarity

  • Code Quality: Poor formatting with missing semicolons on most lines
  • Variable Naming: Reasonable names (G_values, Y_values, i_values)
  • Comments: Minimal comments, relies on Copilot suggestions
  • Output: Excessive command window output due to missing semicolons
  • Organization: Basic structure but lacks clear section separation

📊 Visual Output Assessment

Please remember to save the figures in the Figures folder!

Figure 1: Comparative Statics Plot ❌

  • Status: Missing - No comparative statics plot created
  • Issue: Computes Y_values and i_values but doesn’t plot them
  • Impact: Major task incomplete

Figure 2: ISLM_shocks.png ✅

  • Distribution: Elliptical scatter plot showing correlated shocks
  • Correlation: Correct correlation structure
  • Styling: Good use of MarkerFaceAlpha for transparency
  • Enhancement: Includes mean equilibrium point as red star
  • Saving: Correctly saves figure
  • Labels: Proper axis labels and title

✅ Suggestions for Improvement

  1. Critical: Create comparative statics plot showing Y vs G and i vs G
  2. Important: Use economically meaningful G range (e.g., 80:2:120 instead of 1:0.2:10)
  3. Important: Add semicolons to all assignment lines to reduce command window clutter
  4. Style: Add more comments explaining the economic theory
  5. Organization: Use clear section headers (%% Part 1, %% Part 2, etc.)
  6. Verification: Check that G range produces reasonable economic values

🎯 Summary

Incomplete submission with correct core implementation but missing key visualization. The student demonstrates understanding of the IS-LM system and stochastic simulation, but fails to complete the comparative statics visualization task. Code quality issues (missing semicolons, poor formatting) detract from the overall submission.

Grade Level: ✅ More than 50% Correct (5/8 tasks fully correct, 1/8 partially correct, 1/8 incorrect, 1/8 missing)