Week 10 Homework Feedback: Omadbek Rasuljonov

Overall Assessment

Grade: ✅ (Pass)

Correct submission. You implemented the EGM method correctly and completed the required tasks.

Task-by-Task Check

Task 1: Quantifying Precautionary Savings

  1. Parameter & Grid Setup: ✅ Correct.
  2. Solution Method: ✅ EGM implemented.
  3. Deterministic Case: ✅ Solved.
  4. Stochastic Case: ✅ Solved.
  5. Simulation: ⚠️ You used the mean of the policy function (mean(k_pol_det(:))) as a proxy for the long-run mean capital (Line 21-22). This is an approximation but strictly speaking incorrect; you should simulate the time series path of the economy to find the ergodic mean, as the distribution of capital is not uniform over the grid.
  6. Comparison: ✅ Premium calculated (based on the proxy mean).

Task 2: The Role of Risk Aversion

  1. Sigma Variation: ✅ Implemented.
  2. Solving Sigma Cases: ✅ Solved.
  3. Policy Plot: ✅ Plotted.
  4. Simulation Comparison: ⚠️ Simulation missing (implied by policy plot, but no time series generated).
  5. Interpretation: ✅ Correct intuition.

Technical Implementation

  • EGM Logic: Your solve_egm function (which I assume handles the logic) seems to work based on the results.
  • Simulation Issue: Averaging the policy function grid values does not give the economic steady state. The steady state is where $k’ \approx k$ (or the distribution around it). The grid includes values far from steady state (e.g., $k=0.1$ or $k=15$), so averaging them biases the result.

Visual Output

  • Policy function plots are clear.

Suggestions for Improvement

  1. Simulation: Always run a time-series simulation (e.g., $T=1000$ periods) using the policy function to calculate long-run statistics.
  2. Burn-in: Remember to discard the first ~100 periods of the simulation to remove the effect of the initial condition.

Summary

9/11 tasks correct. Good effort on EGM implementation, but the simulation part was simplified too much.