Week 10 Homework Feedback: Davide Magnini

Overall Assessment

Grade: ✅ (Pass)

Correct submission. You correctly implemented the tasks, solved the model using EGM (hybrid approach), and provided clear results and figures.

Task-by-Task Check

Task 1: Quantifying Precautionary Savings

  1. Parameter & Grid Setup: ✅ Correct.
  2. Solution Method: ✅ EGM logic is correct.
  3. Deterministic Case: ✅ Solved.
  4. Stochastic Case: ✅ Solved.
  5. Simulation: ✅ Simulation logic is correct.
  6. Comparison: ✅ Premium calculated.

Task 2: The Role of Risk Aversion

  1. Sigma Variation: ✅ $\sigma=1$ and $\sigma=5$ implemented.
  2. Solving Sigma Cases: ✅ Solved correctly.
  3. Policy Plot: ✅ Plot generated and saved.
  4. Simulation Comparison: ✅ Means compared.
  5. Interpretation: ✅ Good intuition, though note that $\sigma=1$ is Log Utility (risk averse), not “no risk aversion”. Risk neutrality would be $\sigma=0$ (linear utility).

Technical Implementation

  • Code Structure: Script is organized.
  • Interpolation: The use of unique before interp1 in the EGM step is good practice to handle potential non-monotonicities, though with this production function it shouldn’t be strictly necessary if the grid is fine enough.
  • Comparison: You correctly identified that higher risk aversion leads to higher savings.

Visual Output

  • Figures are saved correctly and are legible.

Suggestions for Improvement

  1. Terminology: In your comments, you mentioned “sigma = 0 instead there is no risk adversion”. Your code uses sigma=1 (Log Utility), which is risk averse (Arrow-Pratt measure = 1). “No risk aversion” corresponds to $\sigma=0$ (Linear Utility).
  2. Efficiency: Similar to other students, using fzero inside the EGM loop works but slows it down. You can often invert the resource constraint using interpolation for speed.

Summary

11/11 tasks correct. Correct work.