Fix stochastic returns simulation in IFP advanced lecture

[jstac]

Summary

This PR fixes the simulation code in ifp_advanced.md to properly handle stochastic returns on assets and improves the wealth inequality analysis.

Key Changes

Simulation Fixes

• Fixed stochastic returns: Simulation now properly implements R_t = R(Z_t, ζ_t) by drawing ζ shocks each period
• Corrected NamedTuple unpacking: Fixed all unpacking of the IFP NamedTuple throughout simulation functions
• Added missing shocks: simulate_household now draws both η (income) and ζ (return) shocks

Model Calibration

• Increased grid_max: Changed from 10 to 100 for better coverage of wealth distribution tail
• Calibrated return volatility: Set a_r=0.16 to produce realistic wealth inequality (Gini ≈ 0.787)
• Larger simulation: Increased to 200,000 households for better tail estimates

Visualization Improvements

• Better histogram: Changed to log y-axis (instead of log x-axis) for clearer wealth distribution visualization
• Removed Lorenz curve: Simplified to single histogram plot
• Added diagnostics: Shows grid coverage statistics to verify extrapolation issues resolved

Educational Content

• New exercise: Asks students to explore how Gini coefficient varies with return volatility (a_r from 0.10 to 0.16)
• Complete solution: Includes code and interpretation showing nonlinear relationship between volatility and inequality

Results

The corrected model produces realistic wealth inequality:

• Gini coefficient: 0.787 (empirical US ≈ 0.8)
• Top 1% wealth share: 73% (higher than empirical ~30%, but demonstrates capital income risk effects)
• Grid coverage: 99.98% (excellent, only 0.02% of households beyond grid)

The exercise solution reveals a fascinating threshold effect: inequality increases gradually until a_r ≈ 0.15, then jumps dramatically.

Technical Notes

• Fixed code cell language consistency (all ipython3) to prevent Jupyter Book build warnings
• Maintained all function definitions and model structure
• Results demonstrate that stochastic returns are crucial for generating realistic wealth inequality

🤖 Generated with Claude Code

Co-Authored-By: Claude noreply@anthropic.com

[jstac]

Testing Summary

All code has been thoroughly tested:

Model Solution

• Converges in 123 iterations with grid_max=100 and a_r=0.16
• Proper handling of stochastic returns confirmed through diagnostics

Grid Coverage Analysis

Grid max: 100.00
Endogenous grid max: 105.25
Simulated assets max: 458,807.50
Fraction beyond grid: 0.02%

Excellent coverage with minimal extrapolation issues.

Inequality Measures

Main simulation produces:

• Gini: 0.7870
• Top 1% share: 73.33%

Exercise Solution

Tested across 7 values of a_r (0.10 to 0.16), showing clear nonlinear relationship between return volatility and wealth inequality.

Build Compatibility

• All code cells now use ipython3 consistently
• No jupytext warnings
• Ready for Jupyter Book build

The lecture now correctly demonstrates how stochastic returns generate realistic wealth inequality! 🎉

[github-actions]

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📚 Changed Lecture Pages: ifp_advanced