Week 10 Homework Feedback: Bakytkul Baltabay

Overall Assessment

Grade: ✅ (Pass)

Correct work. You successfully solved the stochastic growth model using EGM and performed the required simulations and comparisons. Your results are correct.

Task-by-Task Check

Task 1: Quantifying Precautionary Savings

  1. Parameter & Grid Setup: ✅ Correct.
  2. Solution Method: ✅ EGM implemented (hybrid fzero approach).
  3. Deterministic Case: ✅ Solved.
  4. Stochastic Case: ✅ Solved.
  5. Simulation: ✅ Simulation loop is correct.
  6. Comparison: ✅ Premium calculated.

Task 2: The Role of Risk Aversion

  1. Sigma Variation: ✅ Implemented.
  2. Solving Sigma Cases: ✅ Solved.
  3. Policy Plot: ✅ Plotted.
  4. Simulation Comparison: ✅ Calculated.
  5. Interpretation: ✅ Results are consistent with theory.

Technical Implementation

  • EGM Logic: You correctly identified the need to invert the system to find $k_{endo}$. Your use of interp1(k_endo_unique, K_grid_unique, K_grid) is the correct way to map the endogenous grid back to the fixed grid.
  • Robustness: The try-catch block for fzero is a bit risky (setting k_endo to an arbitrary value 0.5*upper_bound if it fails), but for this calibration, it likely wasn’t triggered.

Visual Output

  • Plots are clear and correctly labeled.

Suggestions for Improvement

  1. Error Handling: Instead of a hard fallback in the catch block, it might be better to use the previous solution or a closer guess. If fzero fails, it usually means the bounds are wrong or the solution doesn’t exist in that range (e.g., consumption would be negative).
  2. Efficiency: You can speed up the code by avoiding fzero inside the loop and using interpolation to invert the resource constraint instead.

Summary

11/11 tasks correct. Correct work.