Feedback on Week 9 Homework: Numerical Approximation & Simulation

Student: Alessandra Nishaj Assignment: Week 9 - Monte Carlo OLS & Numerical Integration

Overall Assessment

Grade: ✅ (Pass)

Your submission is excellent. It is very well-structured, thoroughly commented, and technically accurate. You correctly handled the parity issue in Simpson’s rule by adjusting the grid size, and your visual analysis of the results—especially the convergence gap plot—is outstanding.

Task-by-Task Check

Part 1: Monte Carlo OLS

  1. Function Definition: ✅ montecarlo_ols is correctly defined with comprehensive documentation.
  2. DGP Logic: ✅ Correct.
  3. OLS Logic: ✅ Correct.
  4. Execution: ✅ Loops over sample sizes.
  5. Visuals: ✅ High-quality histograms with theoretical overlay.
  6. Statistics: ✅ Empirical moments and bias calculated.
  7. Interpretation: ✅ Detailed answers printed to the command window.

Part 2: Numerical Integration

  1. Utility Function: ✅ CRRA defined using handles.
  2. Trapezoidal Rule: ✅ Correctly implemented.
  3. Simpson’s Rule: ✅ Correctly handled. You identified the requirement for an odd number of grid points. Your solution to increase $N$ by 1 (N_simp = N + 1) when $N$ is even allows you to apply the rule correctly to a re-discretized grid.
  4. Grid Loop: ✅ Correct.
  5. Visuals: ✅ Excellent. The subplot showing the “Convergence Gap” (difference between methods) on a log scale is a perfect way to visualize the relative performance of the two methods.
  6. Interpretation: ✅ Thorough analysis of stability and accuracy.

Technical Implementation

  • Code Structure: The use of struct to store simulation results is excellent. The script is very easy to follow.
  • Documentation: Your function header for montecarlo_ols is a perfect example of how to document code.

Style & Clarity

  • Formatting: The console output is formatted beautifully with borders and clear labels.
  • Visuals: The figures are well-labeled and informative.

Suggestions for Improvement

  • None. This is a high-quality submission.

Summary

You demonstrated a mastery of both the coding implementation and the numerical concepts. The attention to detail in formatting and visualization is commendable.

Tasks Correct: 13/13