Feedback on Week 9 Homework: Numerical Approximation & Simulation

Student: Islomjon Shermirzaev Assignment: Week 9 - Monte Carlo OLS & Numerical Integration

Overall Assessment

Grade: ✅ (Pass)

Your submission is outstanding. It is one of the most technically accurate implementations I have seen. Your use of a hybrid Simpson/Trapezoidal approach to handle even grid sizes is mathematically rigorous, and your log-log convergence plot is the professional standard for analyzing numerical errors.

Task-by-Task Check

Part 1: Monte Carlo OLS

  1. Function Definition: ✅ montecarlo_ols is correctly defined as a local function.
  2. DGP Logic: ✅ Correct.
  3. OLS Logic: ✅ Correct.
  4. Execution: ✅ Loops over sample sizes.
  5. Visuals: ✅ Professional-quality histograms using subplot.
  6. Statistics: ✅ Empirical moments calculated.
  7. Interpretation: ✅ Clear presentation of results.

Part 2: Numerical Integration

  1. Utility Function: ✅ CRRA defined using handles.
  2. Trapezoidal Rule: ✅ Manual implementation (valid) or trapz. (You used trapz formula manually).
  3. Simpson’s Rule: ✅ Excellent. You correctly identified that for even $N$, standard Simpson’s rule cannot cover the entire grid. Your solution—applying Simpson’s to the first $N-1$ points and Trapezoidal to the last interval—is a sophisticated and correct way to handle this without changing the grid resolution.
  4. Grid Loop: ✅ Correct.
  5. Visuals: ✅ Outstanding. You plotted the absolute error on a log-log scale. This is the best way to visualize convergence rates (slope of the line corresponds to the order of accuracy).
  6. Interpretation: ✅ The analytical benchmark calculation was a great addition.

Technical Implementation

  • File Structure: You correctly used the modern MATLAB structure of putting local functions at the end of the script.
  • Hybrid Method: Implementing the hybrid Simpson+Trapezoidal method shows deep understanding of numerical integration.

Style & Clarity

  • Formatting: Your use of fprintf to create tables in the command window is excellent.
  • Code: Very clean and readable.

Suggestions for Improvement

  • None. This is a model solution.

Summary

A fantastic submission. You clearly understood both the coding requirements and the underlying numerical theory.

Tasks Correct: 13/13