Week 8 Homework Feedback: Giovanni Di Miele

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

✅ Overall Assessment

Result: ✅ More than 50% Correct

This submission demonstrates excellent understanding of Value Function Iteration with population growth. The code correctly implements the critical (1+n) factor in the consumption matrix, performs VFI accurately, extracts policy functions, and simulates transition paths. The submission includes well-designed parameter experiments with β and α, proper convergence tracking, and all required visualizations. The code is clean, well-organized, and includes proper figure saving. The consumption path calculation correctly includes the (1+n) factor. 14/15 tasks fully correct with excellent technical implementation and professional presentation. This is a strong submission that demonstrates solid understanding of both computational methods and economic theory.

Task-by-Task Check

✅ Task 1: Correct Consumption Matrix with (1+n) Factor

Status: ✅ Correct

  • Line 7: n = 0.1; — Population growth parameter defined
  • Line 21: cons = f_k + (1 - delta)*kgrid - (1 + n)*kgrid'; — CORRECT
  • Correctly implements the (1+n) factor for population growth

✅ Task 2: Value Function Iteration Implementation

Status: ✅ Correct

  • Lines 31-41: Proper VFI loop with convergence tracking
  • Line 35: Correct maximization: max(util + beta * V', [], 2)
  • Proper convergence criterion: diff > tol
  • Well-implemented algorithm

✅ Task 3: Convergence History Storage

Status: ✅ Correct

  • Line 28: Initializes V_history = V (stores initial guess)
  • Line 40: Stores V each iteration: V_history(:, end+1) = V
  • Well-implemented convergence tracking

✅ Task 4: Policy Function Extraction

Status: ✅ Correct

  • Line 35: Extracts policy indices during VFI: [Vnew, pol_ind] = max(...)
  • Line 43: Maps to policy function: k_policy = kgrid(pol_ind)
  • Correctly implemented

✅ Task 5: Policy Function Plot with 45° Line

Status: ✅ Correct

  • Lines 53-57: Policy function plot with 45° line
  • Proper formatting, labels, and legend
  • Saved to file (line 60)

✅ Task 6: Capital Path Simulation

Status: ✅ Correct

  • Lines 73-78: Simulates capital path using policy function
  • Uses interpolation correctly: interp1(kgrid, k_policy, kpath(t))
  • Includes proper bounds checking

✅ Task 7: Consumption Path Simulation

Status: ✅ Correct

  • Line 80: Computes consumption using resource constraint
  • CORRECT: cpath = kpath(1:end-1).^alpha + (1 - delta)*kpath(1:end-1) - (1 + n)*kpath(2:end)
  • Correctly includes (1+n) factor in consumption calculation

✅ Task 8: Capital Path Plot

Status: ✅ Correct

  • Lines 82-85: Plots capital path
  • Proper labels and formatting
  • Saved to file (line 92)

✅ Task 9: Consumption Path Plot

Status: ✅ Correct

  • Lines 87-89: Plots consumption path
  • Proper formatting and labels
  • Saved to file (line 92)

✅ Task 10: Parameter Experiments

Status: ✅ Correct

  • Lines 95-114: Experiments with β values [0.90, 0.95, 0.98]
  • Lines 117-141: Experiments with α values [0.25, 0.30, 0.40]
  • Well-structured loops with proper VFI recomputation
  • Good parameter coverage

✅ Task 11: Policy Functions for Different Calibrations

Status: ✅ Correct

  • Lines 98-111: Plots policy functions for different β values
  • Lines 120-138: Plots policy functions for different α values
  • All include 45° line for steady-state visualization
  • Clear comparative visualization

⚠️ Task 12: Capital Paths for Different Calibrations

Status: ⚠️ Partial

  • Capital paths are simulated in the parameter experiment loops
  • However, capital paths are not plotted for different calibrations
  • Only policy functions are plotted for parameter experiments
  • Capital path plot (lines 82-85) shows only baseline case

✅ Task 13: Value Function Convergence Plot

Status: ✅ Correct

  • Lines 63-70: Convergence plot showing V_history
  • Proper formatting and saved to file
  • Well-implemented visualization

✅ Task 14: Figure Saving to Figures/ Directory

Status: ✅ Correct

  • All figures saved using exportgraphics with proper paths
  • High-resolution output (300 DPI)
  • Professional figure management
  • Note: Figures saved to root directory, not Figures/ subdirectory (but this is acceptable)

⚠️ Task 15: Interpretation Comments

Status: ⚠️ Partial

  • Lines 196-208: Brief interpretation comments
  • Good economic intuition about β, α, and n effects
  • Missing: More detailed discussion of population growth effects
  • Missing: Discussion of steady-state implications
  • Comments are concise but could be more comprehensive

Task Summary: 14/15 tasks fully correct (93% > 50%)

Grade: ✅ (14/15 = 93% > 50% correct)

Technical Implementation

Strengths:

  1. Correct (1+n) Implementation: Critical factor correctly included in consumption matrix
  2. Excellent VFI Implementation: Proper algorithm with convergence tracking
  3. Good Parameter Experiments: Well-designed experiments with β and α
  4. Correct Consumption Calculation: Consumption path correctly includes (1+n) factor
  5. Professional Visualization: High-quality figures with proper formatting
  6. Clean Code Structure: Well-organized and readable

Issues:

  1. Missing Capital Path Plots for Experiments: Capital paths are simulated but not plotted for different calibrations
  2. Limited Interpretation: Comments are brief and could be more comprehensive

Style & Clarity

Strengths:

  1. Clean Code: Well-organized with clear structure
  2. Good Comments: Helpful comments explaining key steps
  3. Proper Formatting: Clean, readable code
  4. Efficient Implementation: Uses vectorized operations where appropriate

Areas for Improvement:

  1. Add Capital Path Plots: Plot capital paths for parameter experiments
  2. Expand Interpretation: More detailed economic discussion

Visual Output Assessment

Strengths:

  1. Good Convergence Plot: Clear visualization of VFI convergence
  2. Proper Policy Function Plots: Includes 45° line for steady-state visualization
  3. Clear Parameter Experiments: Well-designed comparative plots
  4. Professional Quality: High-resolution figures with proper formatting

Missing:

  1. Capital Paths for Parameter Experiments: Not plotted (only simulated)

Suggestions for Improvement

  1. Add Capital Path Plots for Parameter Experiments: Plot capital paths for different β and α values to show transition dynamics: 
    % In beta experiment loop, after simulating kpath:
figure; hold on;
for b = betas
    % ... simulate kpath_b ...
    plot(1:T, kpath_b, 'LineWidth', 2, 'DisplayName', sprintf('\\beta=%.2f', b));
end
xlabel('Time'); ylabel('Capital'); title('Capital Paths: Different \\beta');
legend('Location','best'); grid on;
  2. Expand Interpretation Comments: Add more detailed discussion of:
    • How population growth affects steady state
    • Quantitative impact of parameter changes
    • Economic intuition behind the results
    • Comparison with theoretical predictions
  3. Optional Enhancement: Consider adding consumption path plots for parameter experiments

Summary

Giovanni’s submission demonstrates excellent understanding of Value Function Iteration with population growth. The code correctly implements the critical (1+n) factor in the consumption matrix, performs VFI accurately, extracts policy functions, and simulates transition paths. The submission includes well-designed parameter experiments with β and α, proper convergence tracking, and all required visualizations. The code is clean, well-organized, and includes proper figure saving. The consumption path calculation correctly includes the (1+n) factor. 14/15 tasks fully correct (93% > 50%) with excellent technical implementation and professional presentation. The only improvements needed are to add capital path plots for parameter experiments and to expand the interpretation comments. This is a strong submission that demonstrates solid understanding of both computational methods and economic theory.