Week 8 Homework – Common Errors & Feedback Summary

Document date: Week 8 assessment
Purpose: Share recurring strengths and issues to discuss in class.
Scope: 21 submissions reviewed (14 ✅, 6 ⚠️, 1 ❌).

📊 Overall Snapshot

  • Population-growth twist landed: most students updated the Bellman equation correctly.
  • Main blockers: forgetting the ((1+n)) factor, incomplete convergence evidence, and missing transition comparisons for parameter experiments.
  • Wrong assignment count: 2 students solved the Week 7 Solow task; 1 student resubmitted a previously flagged Solow script.

🔴 Critical Error 1 — Missing ((1+n)) in the Resource Constraint

Files affected: week8_homework_murzabulatova.m, week8_homework_romanella.m, plus earlier ❌ resubmission (week8_homework_shermirzaev.m).

  • Symptom: cons = f + (1-delta)*kgrid - kgrid'; (or c_t = ... - k_{t+1}) with no (1+n) multiplier.
  • Impact: Entire exercise reverts to the Week 7 model; all policy, simulation, and comparative-static results are invalid.
  • Fix: Pass n everywhere the resource constraint appears, e.g. 
    cons = f + (1-delta)*kgrid - (1+n)*kgrid';
cpath(t) = kpath(t)^alpha + (1-delta)*kpath(t) - (1+n)*kpath(t+1);
  • Reminder: Parameter experiments may vary any parameters, but the baseline must showcase (n>0).

🔴 Critical Error 2 — Solving / Submitting the Wrong Assignment

  • Who: Same scripts as above (plus previously flagged Solow-only submission).
  • Why it matters: Week 8 explicitly asked for VFI with population growth; a Solow simulation with exogenous (s) scores zero, even if coded well.
  • Action: Re-run the homework with the correct Bellman equation and resubmit for reassessment.

🟠 Common Error — Terminal Consumption Uses (k_T) Instead of (k’(k_T))

Seen in week8_homework_nishaj.m, ..._nascia.m, ..._pugliese.m and several others.

  • Symptom: cpath(T) = kpath(T)^alpha + (1-delta)*kpath(T) - (1+n)*kpath(T);
  • Issue: Re-using (k_T) for both current and next-period capital understates final consumption (and can go negative).
  • Fix: Use the policy function (or steady-state) to estimate (k_{T+1}): 
    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;

🟠 Common Error — Missing VFI Convergence Evidence

  • Observed in: most ✅ submissions except Alice Ciavatta (who plotted value_function_convergence.png).
  • Requirement: store the value function every few iterations and plot snapshots to show monotone convergence.
  • Suggested pattern: 
    if mod(iter,10)==0
    V_history(:,end+1) = V;
end
...
plot(kgrid, V_history(:,j));

🟠 Common Error — Parameter Experiments Without Transition Comparisons

  • Good start: Almost everyone plotted policy functions under alternative (\beta) / (\alpha) / (n).
  • Missing piece: Very few students simulated (k_t) or (c_t) paths for those alternative calibrations.
  • Homework expectation: After plotting the new policy, reuse it to produce transition paths so we can see the dynamic implications, not just the steady state.

🟢 Notable Good Practices

Student Highlight
Alessia Canuto Full checklist hit, including comparative statics with different (n) values and detailed interpretation.
Simone Iudice Complete documentation and population-growth experiments with polished figures saved to Figures/.
Giovanni Rampello Excellent parameter experiments (β, n, δ) plus clear economic narration.
Alice Ciavatta Proper V_history snapshots and professional figure exports.

Common strengths:

  • Consistent use of exportgraphics / saveas into a Figures/ folder.
  • Clean log outputs (fprintf) summarising convergence speed and steady-state outcomes.
  • Thoughtful explanations of how patience/productivity shifts the policy rule.

🎯 Action Items for Class

  1. Resource constraint drill: Re-derive (c_t = f(k_t) + (1-\delta)k_t - (1+n)k_{t+1}) on the board so nobody omits the multiplier.
  2. Terminal consumption demo: Walk through how to use the policy function to compute (c_T).
  3. Convergence plots: Show a template script that stores V_history and produces the expected figure.
  4. Comparative transitions: Illustrate how to reuse a policy to simulate alternative (k_t) paths after changing (\beta) or (\alpha).
  5. Refresher on assignment scope: Remind everyone that re-submitting the Solow calibration (Week 7) yields an automatic ⚠️/❌.

📦 Deliverables

  • This summary is saved at docs/week8/feedbacks homework/WEEK8_COMMON_ERRORS_SUMMARY.md.
  • Linked from docs/Homeworks_submissions.md under the common-errors bullet list (Week 8 entry still TODO once class discussion is scheduled).

Let me know if you’d like slides or snippets prepared for the next session. Happy to draft a short template showing the corrected terminal-consumption calculation and a sample V-history plot if helpful.