🌍 Week 4 Homework — Feedback

Student: Alessandra Nishaj
Assignment: Extended IS–LM and Cholesky Decomposition

✅ Overall Assessment

Result: ✅ More than 50% Correct

The student demonstrates very good code organization, comprehensive comments, and implements all components correctly with proper figure saving. The A matrix is correct, the Cholesky decomposition and stochastic simulation are implemented correctly, and the IS-LM system setup is accurate. This is a submission with advanced features and very good visualization.

🔍 Task-by-Task Check

Task	Description	Status	Notes
1	Parameter setup & system definition	✅	Correct A matrix: `[1, alpha; -beta, gamma]` is correct! Excellent parameter definitions and comprehensive 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	✅	Correctly creates G grid using `linspace(50, 200, 31)`, loops through values, and stores results in Y_grid and i_grid arrays.
4	Plotting comparative statics	✅	Creates excellent subplots for Y vs G and i vs G, includes equilibrium points, proper labels, and saves figures correctly.
5	Cholesky decomposition	✅	Correctly defines Sigma matrix `[4, 1.2; 1.2, 3]`, computes eigenvalues, checks positive definiteness, 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 empirical means, standard deviations, and correlations. Results are accurate and well-presented.
8	Visualization of stochastic results	✅	Creates outstanding 6-subplot visualization including histograms, scatter plot, time series, and QQ plot. Proper figure saving.

📈 Technical Implementation

Correct A Matrix: [1, alpha; -beta, gamma] is actually correct! (One of the few students who got this right)
Code Structure: Outstanding organization with clear sections and comprehensive comments
Numerical Methods: Uses correct A\b method
G Grid: Uses linspace(50, 200, 31) which is economically reasonable
Figure Management: Excellent figure saving with directory creation and proper file naming
Advanced Features: Includes fiscal multiplier calculation, comprehensive statistical analysis, and advanced visualization
Error Handling: Checks positive definiteness of Sigma matrix
Simulation Size: Uses 10000 simulations (correct)

💬 Style & Clarity

Code Quality: Outstanding structure with clear section headers and comprehensive comments
Variable Naming: Logical names (Y_eq, i_eq, Y_grid, i_grid, Y_simulated, i_simulated)
Comments: Excellent comments explaining economic theory and mathematical concepts
Output: Outstanding use of fprintf for displaying results with clear formatting
Organization: Clear separation into logical sections with proper headers
Documentation: Includes economic interpretation of parameters and equations
Advanced: Includes fiscal multiplier calculation and comprehensive statistical analysis

📊 Visual Output Assessment

Figure 1: `Comparative_Statics.png` ✅

Layout: Two subplots side by side
Relationships: Shows correct Y vs G and i vs G relationships
Labels: Proper axis labels and titles with bold formatting
Styling: Excellent styling with equilibrium points marked
Saving: Proper figure saving with directory creation
Advanced: Includes equilibrium points and fiscal multiplier calculation

Figure 2: `Shock_Simulation.png` ✅

Layout: Six subplots in 2×3 grid
Distribution: Histograms showing distributions of Y and i
Correlation: Scatter plot showing correlation structure correctly
Time Series: Shows first 300 simulations for both Y and i
Styling: Excellent use of colors, transparency, and formatting
Saving: Proper figure saving with directory creation
Advanced: Includes QQ plot and comprehensive statistical analysis

✅ Suggestions for Improvement

Style: Consider using subplots for comparative statics to match solution format (though current approach is excellent)
Advanced: Consider adding theoretical vs empirical covariance comparison
Verification: Results are already economically reasonable and well-verified

🎯 Summary

Nice implementation with correct economic interpretation. The student demonstrates good programming skills, comprehensive comments, and proper figure management. The A matrix is correct, and the implementation includes advanced features like fiscal multiplier calculation and comprehensive visualization.

Grade Level: ✅ More than 50% Correct (8/8 tasks fully correct, 0/8 partially correct, 0/8 incorrect)