Week 8 Homework Feedback: Islomjon Shermirzaev

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

❌ Overall Assessment

Result: ❌ Incorrect Submission

This submission is for the wrong homework assignment. The code implements a Solow model with a constant saving rate (s), which is the topic of Week 7, not Week 8. Week 8 requires implementing Value Function Iteration (VFI) to solve a dynamic optimization problem where agents choose optimal savings endogenously. The submission contains:

  • No Bellman equation
  • No value function iteration
  • No policy function extraction
  • No dynamic programming
  • Just a simple Solow simulation with exogenous saving rate s=0.2

The code itself is well-written and correctly implements a Solow model simulation, but it does not address any of the Week 8 requirements. This appears to be a submission for Week 7 (Solow model with population growth) rather than Week 8 (Dynamic Programming & VFI).

Task-by-Task Check

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

Status: ❌ Wrong Assignment

  • This task is not applicable - submission is for Solow model, not VFI
  • Week 8 requires VFI with Bellman equation, not Solow simulation

❌ Task 2: Value Function Iteration Implementation

Status: ❌ Missing

  • No VFI implementation
  • No Bellman equation
  • No value function computation

❌ Task 3: Convergence History Storage

Status: ❌ Not Applicable

  • No VFI, so no convergence to track

❌ Task 4: Policy Function Extraction

Status: ❌ Missing

  • No policy function
  • Uses constant saving rate s instead of optimal choice

❌ Task 5: Policy Function Plot with 45° Line

Status: ❌ Missing

  • No policy function plot
  • Only plots capital and consumption paths

✅ Task 6: Capital Path Simulation

Status: ✅ Correct (Wrong Model)

  • Lines 24-33: Simulates capital path
  • Uses Solow law of motion correctly
  • BUT: This is for Solow model, not VFI model

✅ Task 7: Consumption Path Simulation

Status: ✅ Correct (Wrong Model)

  • Lines 32, 36-37: Computes consumption
  • Uses Solow consumption rule: c = (1-s)y
  • BUT: This is for Solow model, not VFI model

✅ Task 8: Capital Path Plot

Status: ✅ Correct (Wrong Model)

  • Lines 40-49: Plots capital path with steady-state line
  • Proper formatting
  • BUT: This is for Solow model, not VFI model

❌ Task 9: Consumption Path Plot

Status: ⚠️ Partial (Wrong Model)

  • Lines 51-55: Plots consumption path
  • Missing steady-state reference line
  • BUT: This is for Solow model, not VFI model

❌ Task 10: Parameter Experiments

Status: ❌ Missing

  • No parameter experiments
  • Uses fixed parameters throughout

❌ Task 11: Policy Functions for Different Calibrations

Status: ❌ Missing

  • No policy functions computed

❌ 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 VFI, so no convergence plot

❌ Task 14: Figure Saving to Figures/ Directory

Status: ❌ Missing

  • Figures are created but not saved to disk
  • No mkdir('Figures') or saveas/exportgraphics calls

❌ Task 15: Interpretation Comments

Status: ❌ Missing

  • No interpretation comments
  • No discussion of VFI, policy functions, or parameter effects

Task Summary: 3/15 tasks partially correct (but for wrong assignment), 12 tasks completely missing

Grade: ❌ (3/15 = 20% < 50%, but these 3 tasks are for wrong homework)

Technical Implementation

Critical Issue:

Wrong Homework Assignment: This submission implements a Solow model with constant saving rate, which is Week 7 material. Week 8 requires:

  • Bellman equation formulation
  • Value function iteration
  • Policy function extraction
  • Dynamic optimization

What’s Present (but for wrong assignment):

  1. Solow Model Simulation: Correctly implements Solow model with population growth
  2. Steady-State Calculation: Correct analytical formula for Solow steady state
  3. Transition Dynamics: Properly simulates capital and consumption paths
  4. Visualization: Creates plots with proper formatting

What’s Missing (Week 8 requirements):

  1. No VFI: The core requirement of Week 8 is completely missing
  2. No Bellman Equation: No dynamic programming formulation
  3. No Policy Function: Uses exogenous saving rate instead of optimal choice
  4. No Parameter Experiments: No experiments with β, α, or other parameters
  5. No Convergence Analysis: No VFI convergence tracking

Style & Clarity

Strengths:

  1. Clear Code Structure: Well-organized with comments
  2. Proper Formatting: Clean, readable code
  3. Good Variable Naming: Descriptive variable names

Issues:

  1. Wrong Assignment: Code solves different problem than required
  2. No Documentation: Missing interpretation and economic discussion

Visual Output Assessment

What’s Present:

  • Capital path plot with steady-state line
  • Consumption path plot (missing steady-state line)

What’s Missing (Week 8 requirements):

  • Value function plot
  • Policy function plot with 45° line
  • Value function convergence plot
  • Policy functions for different calibrations
  • Capital paths for parameter experiments
  • All figures saved to Figures/ directory

Suggestions for Improvement

  1. CRITICAL: Submit Correct Assignment: This submission is for Week 7 (Solow model), not Week 8 (VFI). Please review the Week 8 homework instructions and implement:
    • Bellman equation: V(k) = max_{k’} { u(f(k) + (1-δ)k - (1+n)k’) + βV(k’) }
    • Value function iteration algorithm
    • Policy function extraction
    • Parameter experiments
  2. Implement VFI Algorithm: 
    % Create consumption matrix with (1+n) factor
cons = f + (1-delta)*kgrid - (1+n)*kgrid';
util = log(cons); util(cons <= 0) = -inf;
   
% VFI loop
V = zeros(N,1);
while diff > tol
    Vnew = max(util + beta*V', [], 2);
    diff = max(abs(Vnew - V));
    V = Vnew;
end

  3. Extract Policy Function: After VFI converges, extract k’(k) from argmax

  4. Add Parameter Experiments: Test different β, α, or n values

  5. Save Figures: Create Figures/ directory and save all plots

  6. Add Interpretation: Comment on how parameters affect optimal savings behavior

Summary

Islomjon’s submission is for the wrong homework assignment. The code correctly implements a Solow model with constant saving rate (Week 7 material), but Week 8 requires Value Function Iteration to solve a dynamic optimization problem where agents choose optimal savings endogenously. The submission contains no VFI, no Bellman equation, no policy function, and no dynamic programming elements. 3/15 tasks partially correct, but these are for the wrong assignment (Solow model instead of VFI). The submission needs to be completely redone to address Week 8 requirements: implement the Bellman equation, perform value function iteration, extract policy functions, and conduct parameter experiments. Please review the Week 8 homework instructions carefully and resubmit with the correct implementation.