Add labor income volatility analysis to IFP advanced lecture

[jstac]

Summary

This PR adds a new exercise to the IFP advanced lecture that analyzes the relationship between labor income volatility and wealth inequality. This complements the existing exercise on return volatility, allowing students to compare the relative importance of these two sources of risk.

Changes

• New Exercise 2: Added analysis of how the Gini coefficient varies with labor income volatility (a_y)

  • Tests values from 0.125 to 0.20 (similar percentage range as the return volatility exercise)
  • Sets a_r=0.10 to isolate the effect of labor income risk
  • Includes solution with code and interpretation

• Code improvements:

  • Cleaned up wealth distribution histogram (now plots log wealth)
  • Removed diagnostic output from the simulation section
  • Minor formatting improvements to Exercise 1

Key Findings

The new exercise demonstrates a striking difference in how these two types of risk affect inequality:

• Return volatility (a_r: 0.10 → 0.16): Gini coefficient rises from 0.19 to 0.79 (316% increase)
• Labor income volatility (a_y: 0.125 → 0.20): Gini coefficient rises from 0.18 to 0.19 (7% increase)

This shows that capital income risk is a far more powerful driver of wealth inequality than labor income risk, because favorable returns compound over time as wealth is reinvested, while labor income shocks don't have the same multiplicative effect.

Testing

• Converted to Python using jupytext
• Ran all code cells successfully
• Verified both exercises produce expected results and plots

🤖 Generated with Claude Code

[jstac]

Additional Context

This exercise was developed to help students understand the relative importance of different sources of risk in generating wealth inequality. The comparison between capital income risk and labor income risk provides valuable economic intuition:

Why Capital Income Risk Dominates

1. Compounding effect: Returns on assets compound over time. A household that gets lucky with high returns can reinvest those returns, leading to exponential wealth growth.

2. Multiplicative vs additive shocks: Return shocks multiply existing wealth, while labor income shocks add to current income. This makes return shocks increasingly impactful for wealthier households.

3. Path dependence: A sequence of favorable returns creates a persistent advantage that grows over time, whereas labor income shocks have more transient effects.

Pedagogical Value

By explicitly comparing these two channels, students can see why models with only labor income risk (like the basic Aiyagari model) struggle to match empirical wealth inequality, while models with stochastic returns (like Benhabib-Bisin-Zhu 2015) can generate realistic Gini coefficients.

The exercise uses comparable percentage variations in both volatility parameters, making the comparison fair and the results even more striking.

[github-actions]

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📚 Changed Lecture Pages: ifp_advanced