Week 8 Homework Feedback: Iusupova Farangizbegim

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

⚠️ Overall Assessment

Result: ⚠️ Partial <50% Correct

This submission demonstrates excellent code structure, comprehensive parameter experiments, and outstanding economic interpretation. The VFI implementation is technically sound, convergence tracking is well-implemented, and the visualization is professional. However, there is a critical error: the consumption matrix is missing the (1+n) factor required for population growth. Line 33 computes cons = f + (1-delta)*kgrid - kgrid', which is the formula for the model without population growth (n=0). Additionally, no population growth parameter (n) is defined anywhere in the code. As a result, the entire VFI computation, policy functions, and simulations are for the wrong model (n=0 instead of n>0). Despite this critical error, the submission shows strong understanding of VFI methodology, excellent parameter experiments with β and α, and comprehensive economic interpretation. The code structure and presentation are exemplary.

Task-by-Task Check

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

Status: ❌ CRITICAL ERROR

  • Line 33: cons = f + (1-delta)*kgrid - kgrid';
  • WRONG: This is the formula for n=0 (no population growth)
  • CORRECT: Should be cons = f + (1-delta)*kgrid - (1+n)*kgrid';
  • Missing: No population growth parameter n is defined in the code
  • This error affects all subsequent computations

✅ Task 2: Value Function Iteration Implementation

Status: ✅ Correct Algorithm (Wrong Model)

  • Lines 27-69: Proper VFI function with convergence tracking
  • Lines 44-60: Correct VFI loop with Bellman update
  • Correct maximization: max(util(i,:) + beta*V')
  • Proper convergence criterion
  • BUT: Solving the wrong model (n=0 instead of n>0)

✅ Task 3: Convergence History Storage

Status: ✅ Correct

  • Lines 42, 57-59, 66-68: Stores V_history at selected iterations
  • Stores every 10th iteration plus early iterations
  • Well-implemented convergence tracking

✅ Task 4: Policy Function Extraction

Status: ✅ Correct (Wrong Model)

  • Line 49: Extracts policy indices during VFI: [Vnew(i), pol_ind(i)] = max(...)
  • Line 63: Maps to policy function: k_policy = kgrid(pol_ind)
  • BUT: Policy function is for n=0 model, not n>0

✅ Task 5: Policy Function Plot with 45° Line

Status: ✅ Correct Visualization (Wrong Model)

  • Lines 129-138: Policy function plot with 45° line
  • Proper formatting, labels, and legend
  • BUT: Shows policy for n=0 model, not n>0

✅ Task 6: Capital Path Simulation

Status: ✅ Correct Algorithm (Wrong Model)

  • Lines 148-159: Simulates capital path using policy function
  • Uses interpolation correctly: interp1(kgrid, k_policy_base, k_path_base(t))
  • BUT: Uses policy function from n=0 model

✅ Task 7: Consumption Path Simulation

Status: ✅ Correct Algorithm (Wrong Model)

  • Lines 156, 159: Computes consumption using resource constraint
  • Line 156: c_path_base(t) = k_path_base(t)^alpha_base + (1-delta)*k_path_base(t) - k_path_base(t+1)
  • BUT: Missing (1+n) factor in consumption calculation
  • Should be: c = f(k) + (1-δ)k - (1+n)k'

✅ Task 8: Capital Path Plot

Status: ✅ Correct (Wrong Model)

  • Lines 161-170: Plots capital path with steady-state line
  • Proper labels, legend, and formatting
  • Saved to Figures/ directory
  • BUT: Path is for n=0 model

✅ Task 9: Consumption Path Plot

Status: ✅ Correct (Wrong Model)

  • Lines 351-372: Plots consumption paths and consumption policy function
  • Proper formatting and labels
  • Saved to Figures/ directory
  • BUT: Consumption is for n=0 model

✅ Task 10: Parameter Experiments

Status: ✅ Correct Structure (Wrong Model)

  • Lines 174-314: Comprehensive parameter experiments
  • Experiments with β ∈ {0.90, 0.95, 0.98} and α ∈ {0.25, 0.40, 0.50}
  • Well-structured loops with proper storage
  • BUT: All experiments are for n=0 model

✅ Task 11: Policy Functions for Different Calibrations

Status: ✅ Correct (Wrong Model)

  • Lines 198-200, 265-267: Plots policy functions for different β and α
  • Includes 45° line for steady-state visualization
  • Clear comparative visualization
  • BUT: All for n=0 model

✅ Task 12: Capital Paths for Different Calibrations

Status: ✅ Correct (Wrong Model)

  • Lines 209-218, 276-285: Simulates and plots capital paths for different calibrations
  • Shows transition dynamics for each parameter combination
  • BUT: All for n=0 model

✅ Task 13: Value Function Convergence Plot

Status: ✅ Correct

  • Lines 77-116: Excellent convergence plot with two subplots
  • Shows value function evolution and convergence metric
  • Proper formatting and saved to Figures/ directory
  • Well-implemented visualization

✅ Task 14: Figure Saving to Figures/ Directory

Status: ✅ Correct

  • Lines 11-13: Creates Figures/ directory
  • All figures saved using exportgraphics with proper paths
  • High-resolution output (300 DPI)
  • Professional figure management

✅ Task 15: Interpretation Comments

Status: ✅ Excellent

  • Lines 316-346: Comprehensive economic interpretation
  • Detailed discussion of β effects (patience → savings)
  • Detailed discussion of α effects (productivity → capital)
  • Excellent economic intuition and explanation
  • Missing: Discussion of n effects (because n is not implemented)

Task Summary: 14/15 tasks have correct structure/implementation, but 1 critical error (missing (1+n) factor) means all results are for wrong model. Effectively 6/15 tasks fully correct for the right model.

Grade: ⚠️ (6/15 = 40% < 50% correct for the right model, but > 0%)

Technical Implementation

Critical Error:

  1. Missing (1+n) Factor: The consumption matrix does not include the (1+n) factor required for population growth. This is the most critical requirement of the homework. The entire submission solves the n=0 model instead of the n>0 model.

  2. Missing Population Growth Parameter: No variable n is defined anywhere in the code. The homework requires n>0 (typically n=0.01).

Strengths:

  1. Excellent Code Structure: Well-organized with helper function for VFI
  2. Comprehensive VFI Implementation: Proper algorithm with convergence tracking
  3. Outstanding Parameter Experiments: Well-designed experiments with β and α
  4. Professional Visualization: High-quality figures with proper formatting
  5. Excellent Interpretation: Comprehensive economic discussion

Issues:

  1. Wrong Economic Model: Entire submission is for n=0 model, not n>0 as required
  2. Missing (1+n) in Consumption: Both in utility matrix and simulation

Style & Clarity

Strengths:

  1. Excellent Organization: Clear structure with helper function
  2. Comprehensive Comments: Detailed fprintf statements explaining each step
  3. Professional Presentation: Well-formatted code with clear sections
  4. Outstanding Documentation: Excellent economic interpretation section

Areas for Improvement:

  1. Missing Population Growth: Need to define n and include (1+n) factor
  2. Consumption Calculation: Should include (1+n) in simulation as well

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 both value function evolution and convergence metric
  4. Clear Comparative Plots: Well-designed parameter experiment visualizations

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
  • ✅ Capital paths for parameter experiments

Issue:

  • All visualizations show results for n=0 model, not n>0 as required

Suggestions for Improvement

  1. Fix Consumption Matrix (CRITICAL): Add population growth parameter and correct the consumption matrix: 
    n = 0.01;  % Population growth rate
% In run_VFI function, line 33:
cons = f + (1-delta)*kgrid - (1+n)*kgrid';  % CORRECT formula
  2. Fix Consumption in Simulation: Update consumption calculation to include (1+n): 
    % Line 156 should be:
c_path_base(t) = k_path_base(t)^alpha_base + (1-delta)*k_path_base(t) - (1+n)*k_path_base(t+1);
  3. Add Population Growth Interpretation: Include discussion of how n affects steady state:
    • Higher n → lower k* (dilution effect)
    • Population growth requires more capital to equip new workers
    • Comparison of policy functions: n>0 vs n=0
  4. Optional Enhancement: Consider also experimenting with different n values to show how population growth affects optimal savings behavior, in addition to the excellent β and α experiments.

Summary

Iusupova’s submission demonstrates excellent technical competence and outstanding economic understanding. The code structure is professional, the VFI implementation is sound, parameter experiments are comprehensive, and the economic interpretation is exemplary. However, there is a critical error: the consumption matrix is missing the (1+n) factor required for population growth, and no population growth parameter (n) is defined. As a result, the entire submission solves the n=0 model instead of the n>0 model as required. 14/15 tasks have correct structure, but the critical error means all results are for the wrong model. Effectively 6/15 tasks fully correct for the right model (40% < 50%). The submission shows strong understanding of VFI methodology and would be outstanding once the (1+n) factor is added. The code structure, parameter experiments, and interpretation demonstrate excellent work - it just needs the population growth correction to fully meet requirements.