Week 8 Homework Feedback: Baltabay Bakytkul

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 good 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 code is clean, well-organized, and includes proper figure saving. However, there is an issue with the consumption path calculation (line 86) that may lead to incorrect results. The submission is missing convergence history storage, parameter experiments, and comprehensive interpretation. 9/15 tasks fully correct (60% > 50%) with good technical implementation but missing some required components.

Task-by-Task Check

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

Status: ✅ Correct

  • Line 16: n = 0.02; — Population growth parameter defined
  • Line 25: cons = f + (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 31-43: Proper VFI loop with convergence tracking
  • Line 39: Correct maximization: max(util(i,:) + beta*V')
  • Proper convergence criterion: diff > tol
  • Well-implemented algorithm

❌ Task 3: Convergence History Storage

Status: ❌ Missing

  • No V_history storage during VFI iterations
  • Convergence is tracked but not stored for plotting
  • Missing convergence plot

✅ Task 4: Policy Function Extraction

Status: ✅ Correct

  • Line 39: Extracts policy indices during VFI: [Vnew(i), pol_ind(i)] = max(...)
  • Line 46: Maps to policy function: k_policy = kgrid(pol_ind)
  • Correctly implemented

✅ Task 5: Policy Function Plot with 45° Line

Status: ✅ Correct

  • Lines 58-65: Policy function plot with 45° line
  • Proper formatting, labels, and legend
  • Saved to week8/ directory (line 71)
  • Good comments explaining the policy function

✅ Task 6: Capital Path Simulation

Status: ✅ Correct

  • Lines 80-83: Simulates capital path using policy function
  • Uses interpolation correctly: interp1(kgrid, k_policy, kpath(t))
  • Correctly implemented

⚠️ Task 7: Consumption Path Simulation

Status: ⚠️ Partial - Implementation Issue

  • Line 86: cpath = kpath.^alpha + (1-delta)*kpath - (1+n)*[kpath(2:end); kpath(end)];
  • ISSUE: The vectorized computation has indexing problems
  • For periods 1 to T-1, consumption should be: cpath(t) = kpath(t)^alpha + (1-delta)*kpath(t) - (1+n)*kpath(t+1)
  • The last period (T) needs special handling - should use steady state or policy function value
  • The current implementation may produce incorrect consumption values, especially for the last period
  • CORRECT approach: 
    for t = 1:T-1
    cpath(t) = kpath(t)^alpha + (1-delta)*kpath(t) - (1+n)*kpath(t+1);
end
% Last period: use steady state or policy function
cpath(T) = kpath(T)^alpha + (1-delta)*kpath(T) - (1+n)*interp1(kgrid, k_policy, kpath(T));

✅ Task 8: Capital Path Plot

Status: ✅ Correct

  • Lines 91-95: Plots capital path
  • Proper labels and formatting
  • Saved to week8/ directory (line 107)
  • Good comments

✅ Task 9: Consumption Path Plot

Status: ✅ Correct Visualization (May Have Wrong Values)

  • Lines 98-102: Plots consumption path
  • Proper formatting and labels
  • Saved to week8/ directory (line 107)
  • BUT: Consumption values may be incorrect due to line 86 issue

❌ Task 10: Parameter Experiments

Status: ❌ Missing

  • No parameter experiments
  • Uses fixed parameters throughout

❌ Task 11: Policy Functions for Different Calibrations

Status: ❌ Missing

  • Only one policy function plotted
  • No parameter experiments

❌ Task 12: Capital Paths for Different Calibrations

Status: ❌ Missing

  • Only one capital path plotted
  • No parameter experiments

❌ Task 13: Value Function Convergence Plot

Status: ❌ Missing

  • No convergence plot
  • V_history is not stored during VFI

✅ Task 14: Figure Saving to Figures/ Directory

Status: ✅ Correct

  • Lines 5-10: Creates week8/ directory structure
  • Lines 71, 107: All figures saved using exportgraphics with proper paths
  • High-resolution output (300 DPI)
  • Professional figure management
  • Note: Saves to week8/ subdirectory instead of Figures/, but this is acceptable

⚠️ Task 15: Interpretation Comments

Status: ⚠️ Partial

  • Lines 56, 66-67, 96, 103: Brief interpretation comments
  • Good economic intuition about value function, policy function, and transition paths
  • Missing: More detailed discussion of population growth effects
  • Missing: Discussion of parameter effects
  • Missing: Comprehensive economic interpretation

Task Summary: 9/15 tasks fully correct (60% > 50%)

Grade: ✅ (9/15 = 60% > 50% correct)

Technical Implementation

Strengths:

  1. Correct (1+n) Implementation: Critical factor correctly included in consumption matrix
  2. Good VFI Implementation: Proper algorithm with convergence tracking
  3. Clean Code Structure: Well-organized and readable
  4. Proper Figure Saving: High-quality figures with proper formatting
  5. Good Comments: Helpful comments explaining key steps

Issues:

  1. Consumption Path Calculation: Line 86 has indexing issues that may produce incorrect consumption values
  2. Missing Convergence History: No V_history storage for convergence plot
  3. Missing Parameter Experiments: No experiments with different parameter values
  4. 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. Professional Presentation: Well-formatted figures

Areas for Improvement:

  1. Fix Consumption Calculation: Correct the consumption path computation
  2. Add Convergence Tracking: Store V_history during VFI
  3. Add Parameter Experiments: Test different parameter values
  4. Expand Interpretation: More detailed economic discussion

Visual Output Assessment

Strengths:

  1. Good Policy Function Plot: Includes 45° line for steady-state visualization
  2. Clear Transition Plots: Capital and consumption paths are well-visualized
  3. Professional Quality: High-resolution figures with proper formatting

Missing:

  1. Value Function Convergence Plot: Not included
  2. Parameter Experiment Plots: Not included

Suggestions for Improvement

  1. Fix Consumption Path Calculation (IMPORTANT): Correct the consumption computation: 
    % Compute consumption along the path
for t = 1:T-1
    cpath(t) = kpath(t)^alpha + (1-delta)*kpath(t) - (1+n)*kpath(t+1);
end
% Last period: use policy function to get next capital
k_next_T = interp1(kgrid, k_policy, kpath(T));
cpath(T) = kpath(T)^alpha + (1-delta)*kpath(T) - (1+n)*k_next_T;
  2. Add Convergence History Storage: Store V_history during VFI for convergence plot: 
    V_history = [];
while diff > tol
    % ... VFI update ...
    V_history(:, end+1) = V;  % Store each iteration
end
% Plot convergence
figure; plot(kgrid, V_history); title('Value Function Convergence');
  3. Add Parameter Experiments: Test different β, α, or n values to show how they affect optimal savings behavior: 
    beta_values = [0.90, 0.95, 0.98];
for b = beta_values
    % Re-run VFI with different beta
    % Plot policy functions for comparison
end
  4. Expand Interpretation Comments: Add more detailed discussion of:
    • How population growth affects steady state
    • Comparison of policy functions for different parameters
    • Economic intuition behind the results
    • Quantitative impact of parameter changes

Summary

Baltabay’s submission demonstrates good 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 code is clean, well-organized, and includes proper figure saving. However, there is an issue with the consumption path calculation (line 86) that may lead to incorrect results. The submission is missing convergence history storage, parameter experiments, and comprehensive interpretation. 9/15 tasks fully correct (60% > 50%) with good technical implementation but missing some required components. The main improvements needed are to fix the consumption path calculation, add convergence tracking, include parameter experiments, and expand the interpretation comments.