🌍 Week 4 Homework — Feedback

Student: Ignazio Nunzi
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. However, there are several critical errors including wrong parameter choice for comparative statics, incorrect Sigma matrix, and missing figure saving. The Cholesky decomposition and stochastic simulation are implemented correctly, but the IS-LM system setup contains some mistakes. Important: The original file name had spaces which prevented it from running properly.

🔍 Task-by-Task Check

Task	Description	Status	Notes
1	Parameter setup & system definition	✅	Correct A matrix: `[1, alpha; -beta, gamma]` is correct! Good parameter definitions and comments.
2	Equilibrium solution	✅	Solves system correctly using `A\B`, extracts Y_eq and i_eq correctly, and displays results properly.
3	Comparative statics setup	❌	Wrong Parameter: Varies bG instead of G. Uses `bG_values = 0.3:0.1:2.0` instead of varying G.
4	Plotting comparative statics	⚠️	Creates proper subplots for Y vs bG and i vs bG, good styling, proper labels. No figure saving in code.
5	Cholesky decomposition	⚠️	Wrong Sigma: Uses `[4, 2; 2, 3]` instead of `[4, 1.2; 1.2, 3]`. Computes L correctly using `chol(Sigma, 'lower')`.
6	Stochastic simulation setup	✅	Correctly generates shocks with proper dimensions (2×1000), transforms to correlated shocks, and sets up simulation loop.
7	Equilibrium distribution analysis	✅	Correctly applies shocks to system and computes simulated equilibria. Results based on wrong Sigma but method is correct.
8	Visualization of stochastic results	⚠️	Creates histograms instead of scatter plot, good styling and labels. No figure saving in code.

📈 Technical Implementation

Correct A Matrix: [1, alpha; -beta, gamma] is actually correct! (One of the few students who got this right)
Wrong Comparative Statics: Varies bG instead of G, which is not what was asked
Wrong Sigma Matrix: Uses [4, 2; 2, 3] instead of [4, 1.2; 1.2, 3]
Code Structure: Good organization with clear sections and comprehensive comments
Numerical Methods: Uses correct A\B method
Figure Management: Missing saveas() commands in code
Advanced Features: Includes detailed comments and economic interpretation
Simulation Size: Uses 1000 simulations instead of 10000 (smaller but acceptable)

💬 Style & Clarity

Code Quality: Good structure with clear section headers and comprehensive comments
Variable Naming: Logical names (Y_eq, i_eq, Y_vals, i_vals, Y_shocks, i_shocks)
Comments: Excellent comments explaining economic theory and mathematical concepts
Output: Good use of disp for displaying results
Organization: Clear separation into logical sections with proper headers
Documentation: Includes economic interpretation of parameters and equations
Honesty: Acknowledges ChatGPT help and expresses uncertainty about results

📊 Visual Output Assessment

Please remember to save the figures in the Figures folder!

Figure 1: Comparative Statics ⚠️

Layout: Two subplots stacked vertically
Relationships: Shows Y vs bG and i vs bG (wrong parameter)
Labels: Proper axis labels and titles
Styling: Good styling with different colors and grid
Saving: No figure saving in code
Issue: Wrong parameter (bG instead of G)

Figure 2: Histograms ⚠️

Distribution: Histograms showing distributions of Y and i
Correlation: Cannot show correlation structure with histograms
Styling: Good use of colors and proper labels
Saving: No figure saving in code
Issue: Should be scatter plot to show correlation, not histograms

✅ Suggestions for Improvement

Critical: Vary G instead of bG for comparative statics
Critical: Use correct Sigma matrix [4, 1.2; 1.2, 3] instead of [4, 2; 2, 3]
Important: Add saveas() commands to save figures automatically
Important: Create scatter plot instead of histograms to show correlation structure
Style: Consider using subplots for comparative statics to match solution format
Verification: Check that results are economically reasonable

🎯 Summary

Good implementation with some critical errors. The student demonstrates solid programming skills and comprehensive comments. However, the wrong parameter choice for comparative statics and incorrect Sigma matrix prevent correct economic interpretation. Notably, this student got the A matrix correct, which many others missed.

Grade Level: ✅ More than 50% Correct (4/8 tasks fully correct, 3/8 partially correct, 1/8 incorrect)