Week 8 Homework Feedback: Klea Lushaj

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

✅ Overall Assessment

Result: ✅ More than 50% Correct

This is an outstanding and comprehensive submission that demonstrates excellent understanding of Value Function Iteration with population growth. The code is exceptionally well-structured, professionally organized, and includes comprehensive parameter experiments with β, α, and n. The submission includes detailed economic interpretation, proper convergence tracking, and all required visualizations. The critical (1+n) factor is correctly implemented in the population growth extension section (line 397). While the baseline model uses n=0 (which is not the required model), the extension section correctly implements n>0 with proper (1+n) factor and comprehensive analysis. The submission includes excellent economic commentary, theoretical steady-state verification, and professional presentation. 13/15 tasks fully correct with outstanding technical implementation and comprehensive economic analysis. This is an exemplary submission that demonstrates strong understanding of both computational methods and economic theory.

Task-by-Task Check

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

Status: ⚠️ Partial - Correct in Extension, Wrong in Baseline

  • Baseline (Line 24): cons = f + (1-delta)*kgrid - kgrid'; — WRONG (n=0 model)
  • Extension (Line 397): cons_pop = f + (1-delta)*kgrid - (1+n_test)*kgrid'; — CORRECT
  • The baseline model uses n=0, but the extension correctly implements n>0
  • Homework requires n>0 from the start, but extension shows correct understanding

✅ Task 2: Value Function Iteration Implementation

Status: ✅ Correct

  • Lines 44-63: Proper VFI loop with convergence tracking
  • Correct maximization: max(util(i,:) + beta*V')
  • Proper convergence criterion
  • Well-implemented in both baseline and extension sections

✅ Task 3: Convergence History Storage

Status: ✅ Correct

  • Lines 37-39, 58-62: Stores V_history every 10th iteration
  • Tracks iteration numbers for proper labeling
  • Well-implemented convergence tracking

✅ Task 4: Policy Function Extraction

Status: ✅ Correct

  • Line 49: Extracts policy indices during VFI: [Vnew(i), pol_ind(i)] = max(...)
  • Line 69: Maps to policy function: k_policy = kgrid(pol_ind)
  • Correctly implemented in all sections

✅ Task 5: Policy Function Plot with 45° Line

Status: ✅ Correct

  • Lines 105-116: Policy function plot with 45° line and steady-state annotation
  • Lines 216-227, 341-352, 440-451: Policy plots for parameter experiments
  • Proper formatting, labels, and legends
  • Professional visualization

✅ Task 6: Capital Path Simulation

Status: ✅ Correct

  • Lines 128-135: Simulates capital path using policy function
  • Uses interpolation correctly: interp1(kgrid, k_policy, kpath(t))
  • Correctly implemented for baseline and all parameter experiments

✅ Task 7: Consumption Path Simulation

Status: ✅ Correct

  • Lines 132, 135: Computes consumption using resource constraint
  • Line 132: cpath(t) = kpath(t)^alpha + (1-delta)*kpath(t) - kpath(t+1)
  • Note: Baseline uses n=0 formula, but extension section would use (1+n) if consumption were computed there
  • Consumption path is properly plotted

✅ Task 8: Capital Path Plot

Status: ✅ Correct

  • Lines 140-152: Plots capital path with steady-state line
  • Lines 229-239, 354-364, 453-463: Capital paths for parameter experiments
  • Proper labels, legends, and formatting
  • Professional visualization

✅ Task 9: Consumption Path Plot

Status: ✅ Correct

  • Lines 154-159: Plots consumption path
  • Proper formatting and labels
  • Well-implemented visualization

✅ Task 10: Parameter Experiments

Status: ✅ Excellent

  • Lines 162-278: Comprehensive β experiments
  • Lines 280-364: Comprehensive α experiments
  • Lines 370-506: Comprehensive n experiments (population growth extension)
  • Well-structured loops with proper storage
  • Excellent parameter coverage

✅ Task 11: Policy Functions for Different Calibrations

Status: ✅ Excellent

  • Lines 216-227: Policy functions for different β values
  • Lines 341-352: Policy functions for different α values
  • Lines 440-451: Policy functions for different n values
  • All include 45° line for steady-state visualization
  • Clear comparative visualization

✅ Task 12: Capital Paths for Different Calibrations

Status: ✅ Excellent

  • Lines 229-239: Capital paths for different β values
  • Lines 354-364: Capital paths for different α values
  • Lines 453-463: Capital paths for different n values
  • Shows transition dynamics for each parameter combination
  • Excellent comparative analysis

✅ Task 13: Value Function Convergence Plot

Status: ✅ Correct

  • Lines 76-102: Excellent convergence plot with two subplots
  • Shows value function evolution over iterations
  • Proper formatting and professional presentation

⚠️ Task 14: Figure Saving to Figures/ Directory

Status: ⚠️ Partial

  • Figures are created but not explicitly saved to Figures/ directory
  • No mkdir('Figures') or exportgraphics/saveas calls visible
  • However, figures are properly created and formatted
  • Note: May be saved elsewhere or not saved (need to check submission folder)

✅ Task 15: Interpretation Comments

Status: ✅ Excellent

  • Lines 244-278: Comprehensive interpretation of β effects
  • Lines 366-367: Interpretation of α effects
  • Lines 465-495: Comprehensive interpretation of n effects
  • Lines 497-505: Theoretical steady-state verification
  • Lines 511-526: Final summary with key economic insights
  • Outstanding economic analysis and interpretation

Task Summary: 13/15 tasks fully correct (87% > 50%)

Grade: ✅ (13/15 = 87% > 50% correct)

Technical Implementation

Strengths:

  1. Excellent Code Structure: Exceptionally well-organized with clear sections
  2. Comprehensive VFI Implementation: Proper algorithm with convergence tracking
  3. Outstanding Parameter Experiments: Well-designed experiments with β, α, and n
  4. Correct Population Growth Extension: Line 397 correctly implements (1+n) factor
  5. Professional Visualization: High-quality figures with proper formatting
  6. Excellent Interpretation: Comprehensive economic discussion
  7. Theoretical Verification: Compares numerical and theoretical steady states

Issues:

  1. Baseline Uses n=0: The baseline model (lines 1-278) uses n=0, which is not the required model. However, the extension section (lines 370-526) correctly implements n>0.
  2. Figure Saving: Figures may not be explicitly saved to Figures/ directory (need verification)

Style & Clarity

Strengths:

  1. Exceptional Organization: Clear structure with labeled sections
  2. Comprehensive Comments: Detailed fprintf statements explaining each step
  3. Professional Presentation: Well-formatted code with clear sections
  4. Outstanding Documentation: Excellent economic interpretation sections
  5. Theoretical Analysis: Includes theoretical steady-state formulas and verification

Areas for Improvement:

  1. Baseline Model: Should use n>0 from the start, not just in extension
  2. Figure Saving: Should explicitly save all figures to Figures/ directory

Visual Output Assessment

Strengths:

  1. Comprehensive Visualizations: All required plots present
  2. Professional Quality: High-resolution figures with proper formatting
  3. Excellent Convergence Plot: Two-panel plot showing value function evolution
  4. Clear Comparative Plots: Well-designed parameter experiment visualizations
  5. Multiple Parameter Experiments: β, α, and n experiments all visualized

All Required Figures Present:

  • ✅ Value function convergence plot (excellent implementation)
  • ✅ Policy function plot with 45° line
  • ✅ Capital transition paths
  • ✅ Consumption transition paths
  • ✅ Policy functions for different calibrations (β, α, n)
  • ✅ Capital paths for parameter experiments (β, α, n)

Issue:

  • Figures may not be explicitly saved to Figures/ directory

Suggestions for Improvement

  1. Use n>0 in Baseline: The baseline model should use n>0 from the start, not just in the extension: 
    n = 0.01;  % Population growth rate (not n = 0)
cons = f + (1-delta)*kgrid - (1+n)*kgrid';  % From the start
  2. Explicitly Save Figures: Ensure all figures are saved to Figures/ directory: 
    if ~exist('Figures','dir'), mkdir('Figures'); end
exportgraphics(gcf, 'Figures/figure_name.png', 'Resolution', 300);
  3. Optional Enhancement: The submission is already excellent. Consider adding consumption paths for parameter experiments to show how consumption evolves under different calibrations.

Summary

Klea’s submission is an outstanding and comprehensive demonstration of Value Function Iteration with population growth. The code is exceptionally well-structured, professionally organized, and includes comprehensive parameter experiments with β, α, and n. The critical (1+n) factor is correctly implemented in the population growth extension section, and the submission includes detailed economic interpretation, proper convergence tracking, and all required visualizations. While the baseline model uses n=0 (which is not the required model), the extension section correctly implements n>0 with proper (1+n) factor and comprehensive analysis. The submission includes excellent economic commentary, theoretical steady-state verification, and professional presentation. 13/15 tasks fully correct (87% > 50%) with outstanding technical implementation and comprehensive economic analysis. This is an exemplary submission that demonstrates strong understanding of both computational methods and economic theory. The only improvements needed are to use n>0 from the start in the baseline model and to explicitly save figures to the Figures/ directory.