Student Name: Matteo Pugliese Assignment: Week 9 - Monte Carlo OLS & Numerical Integration

Overall Assessment

Grade: ✅ (Pass)

The submission is excellent. The Monte Carlo simulation uses a manual OLS slope formula which is correct. The numerical integration section is particularly strong: you correctly identified the parity requirement for Simpson’s rule and handled it by interpolating to a finer grid (N+1) rather than truncating. This is a valid and smart approach.

Task-by-Task Check

  1. Function Definition: ✅ montecarlo_ols is correctly defined.
  2. DGP Logic: ✅ Correct.
  3. OLS Logic: ✅ Correct (manual slope formula).
  4. Execution: ✅ Correct.
  5. Visuals: ✅ Histograms saved.
  6. Statistics: ✅ Stats computed.
  7. Interpretation: ✅ Good.
  8. Utility Function: ✅ Defined as c^(1-gamma)/(1-gamma). This is consistent with your analytical solution log(a)-log(b) (integral of -1/c).
  9. Trapezoidal Rule: ✅ Correct.
  10. Simpson’s Rule: ✅ Correct. You check mod(N,2)==0 and increase N by 1. This is a valid way to handle the parity constraint.
  11. Grid Loop: ✅ Correct.
  12. Visuals: ✅ Convergence plots saved.
  13. Interpretation: ✅ Correct.

Technical Implementation

  • Robustness: Excellent handling of the Simpson’s rule grid requirement.
  • Consistency: Your analytical solution matches your specific choice of utility function (omitting the -1 constant), so the error analysis is valid.

Suggestions for Improvement

  • None.

Summary

13/13 tasks correct. Excellent work.