🌍 Week 4 Homework — Feedback

Student: Bakytkul Baltabay
Assignment: Extended IS–LM and Cholesky Decomposition

✅ Overall Assessment

Result: ✅ More than 50% Correct

The student implements most components correctly but has critical errors in the matrix construction that lead to economically nonsensical results (negative interest rates). The code structure is good, but fundamental mistakes in the IS-LM system setup prevent correct economic interpretation.

🔍 Task-by-Task Check

Task Description Status Notes
1 Parameter setup & system definition ❌ Critical Error: A matrix is [1, alpha; -beta, 1] instead of [1, alpha; -beta, gamma]. b vector is [-MP + theta*G0] instead of [MP - theta*G0]. These errors cause negative interest rates.
2 Equilibrium solution ⚠️ Solves system correctly given the wrong matrices, but results are economically meaningless (negative interest rates).
3 Comparative statics setup ⚠️ Correctly implements loop and storage, but uses wrong system matrices throughout.
4 Plotting comparative statics ⚠️ Creates plots correctly, but shows wrong economic relationships due to matrix errors. No figure saving in script.
5 Cholesky decomposition ✅ Correctly defines Sigma, checks eigenvalues, computes L, and verifies decomposition.
6 Stochastic simulation setup ✅ Correctly generates shocks and applies Cholesky transformation. Sets random seed properly.
7 Equilibrium distribution analysis ⚠️ Correctly computes statistics, but based on wrong underlying system.
8 Visualization of stochastic results ⚠️ Creates scatter plot correctly, but shows wrong correlation due to matrix errors. No figure saving in script.

📈 Technical Implementation

  • Critical Matrix Errors:
    • A matrix: [1, alpha; -beta, 1] should be [1, alpha; -beta, gamma]
    • b vector: [-MP + theta*G0] should be [MP - theta*G0]
    • These errors cause negative interest rates and wrong economic relationships
  • Code Structure: Good organization with clear sections and comments
  • Numerical Methods: Uses correct A\b method and efficient A^(-1) computation
  • Statistical Analysis: Includes theoretical vs empirical covariance comparison (good addition)
  • Error Handling: Checks positive definiteness of Sigma matrix
  • Figure Saving: Missing saveas() commands in script

💬 Style & Clarity

  • Code Quality: Very well-commented with clear section headers.
  • Variable Naming: Logical names (G_grid, Y_grid, i_grid, EPS, X).
  • Output Formatting: Good use of fprintf with appropriate precision.
  • Visualization: Clean plots with proper legends, labels, and styling.

📊 Visual Output Assessment

Please remember to save the figures in the Figures folder!

Figure 1: week4_IS_LM.png ⚠️

  • Layout: Two subplots stacked vertically (valid format)
  • Relationships: Shows relationships, but interest rates are negative (economically wrong)
  • Labels: Proper axis labels and titles
  • Styling: Clean appearance with grid enabled
  • Issue: Negative interest rates indicate fundamental matrix errors

Figure 2: week4_shocks.png ⚠️

  • Distribution: Elliptical scatter plot showing correlated shocks
  • Correlation: Shows correlation structure, but based on wrong underlying system
  • Centering: Points clustered around wrong deterministic equilibrium
  • Enhancement: Includes deterministic equilibrium point as red dot with legend
  • Issue: Results based on incorrect matrix construction

✅ Suggestions for Improvement

  1. Critical: Fix A matrix to [1, alpha; -beta, gamma] instead of [1, alpha; -beta, 1]
  2. Critical: Fix b vector to [MP - theta*G0] instead of [-MP + theta*G0]
  3. Important: Add saveas() commands to save figures automatically
  4. Style: Consider using semicolons on assignment lines to reduce command window output
  5. Verification: Check that interest rates are positive and economically reasonable

🎯 Summary

Good technical implementation with critical economic errors. The student demonstrates solid programming skills and understanding of matrix operations, but makes fundamental mistakes in the IS-LM system setup that lead to economically nonsensical results (negative interest rates). The Cholesky decomposition and stochastic simulation components are implemented correctly.

Grade Level: ✅ More than 50% Correct (2/8 tasks fully correct, 5/8 partially correct, 1/8 incorrect)