Week 8 Homework Feedback: Alessandra Nishaj

Assignment: Dynamic Programming & Value Function Iteration with Population Growth
Week: 8
Date: Week 8 Assessment

✅ Overall Assessment

Result: ✅ More than 50% Correct

Alessandra delivers a strong Week 8 submission. The model correctly includes the ((1+n)) term in the consumption matrix, VFI converges cleanly, policy and simulation plots are on point, and she goes the extra mile with well-documented parameter experiments for both (\beta) and (\alpha). The main issues are (i) no stored convergence history for VFI and (ii) the final-period consumption uses (k_T) instead of the policy function value, which understates (c_T). Addressing those gaps would make this an exemplary submission. 10/15 tasks fully correct (≈67%).

Task-by-Task Check

  1. Consumption matrix with (1+n) — ✅ (line 17)
  2. Value Function Iteration — ✅ (lines 29-41)
  3. Convergence history / V-history storage — ❌ (diff printed but not stored)
  4. Policy function extraction — ✅ (line 45)
  5. Policy plot with 45° line — ✅ (lines 55-62)
  6. Capital path simulation — ✅ (lines 73-83)
  7. Consumption path simulation — ⚠️ Final period uses (k_T) instead of (k’(k_T)) (line 85)
  8. Capital path plot — ✅ (lines 89-95)
  9. Consumption path plot — ✅ (lines 96-101) though last point inherits issue from task 7
  10. Parameter experiments — ✅ (comprehensive (\beta) study, lines 108-156)
  11. Policy functions across calibrations — ✅ (plots for different (\beta) and (\alpha))
  12. Capital paths across calibrations — ❌ (no comparative transition plots)
  13. Value function convergence plot — ❌ (no V-history figure)
  14. Figure saving — ✅ (saveas used for each figure)
  15. Interpretation / discussion — ✅ (lines 214-237)

Task Summary: 10/15 tasks fully correct ⇒ ✅

Technical & Style Notes

  • 👍 Excellent documentation, clear logging, and thoughtful parameter experiments.
  • ⚠️ Final-period consumption should respect the constraint (c_T = f(k_T) + (1-\delta)k_T - (1+n)k_{T+1}) using interp1(kgrid,k_policy,kpath(T)).
  • ⚠️ Store intermediate (V) iterates (e.g., every 10 iterations) so you can produce the requested convergence figure and quantify speed.
  • ➕ Consider plotting capital/consumption transitions for the different (\beta) or (\alpha) calibrations to visualize comparative dynamics.

Suggestions for Improvement

  1. Final-period consumption: 
    k_next_T = interp1(kgrid, k_policy, kpath(T), 'linear', 'extrap');
cpath(T) = kpath(T)^alpha + (1-delta)*kpath(T) - (1+n)*k_next_T;
  2. Convergence tracking: collect V_history(:,end+1) = V; inside the VFI loop (e.g., every 5 or 10 iterations) and plot several snapshots to show monotone convergence.
  3. Comparative transition paths: after each parameter experiment, reuse the policy to simulate and plot (k_t) or (c_t) so the reader sees how dynamics change, not just the policy rule.

Summary

Great work overall—Alessandra implements the population growth model correctly, provides clean simulations, and documents the economics clearly. Fix the final-period consumption formula and add the requested convergence/transition diagnostics and you will have a reference-quality submission. Keep it up!