Add new lecture: Aiyagari model with Endogenous Grid Method (#676)

* Add new lecture: Aiyagari model with Endogenous Grid Method

This PR adds a new lecture aiyagari_egm.md that combines the Aiyagari model with the Endogenous Grid Method (EGM).

Key Features:
- Combines concepts from egm_policy_iter.md and aiyagari.md
- Uses EGM to solve the household problem (avoiding costly root-finding)
- Uses simulation to compute aggregate capital (instead of analytical stationary distribution)
- EGM operator for the Aiyagari model - Corrected implementation, converges in ~90 iterations
- Simulation-based aggregation - Simulates 10,000+ households via Monte Carlo
- Equilibrium computation - Uses bisection to find equilibrium capital stock (K* ≈ 8)
- Wealth distribution analysis - Histograms, Lorenz curves, and Gini coefficient
- Educational content - Comparison with standard approach and four exercises

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

* misc

* Rewrite aiyagari_egm as a single fully-JAX implementation

Reworks the lecture so the EGM operator, the household solver and the
cross-section simulation are all JIT-compiled and vectorized in JAX,
matching the conventions in os_egm_jax.

- Remove the broken @jax.jit `K_egm` (data-dependent Python branch) and the
  unusable jitted `simulate_households` (per-household Python loops); keep a
  single vectorized `K_egm` and one `simulate_cross_section`.
- Solver now uses `jax.lax.while_loop`; simulation uses `jax.lax.fori_loop`
  with vmap-ed interpolation and inverse-CDF Markov transitions.
- Drop the unused numba import; use deterministic PRNG keys so bisection sees
  a deterministic excess-demand function.
- Use qe.lorenz_curve / qe.gini_coefficient instead of hand-rolled np.trapz.

Runs end-to-end: K* = 8.15, r* = 0.031, Gini = 0.36, Euler residual 8e-07.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

---------

Co-authored-by: Claude <noreply@anthropic.com>

Author: jstac

lectures/_toc.yml

@@ -129,6 +129,7 @@ parts:
   - file: markov_perf
   - file: uncertainty_traps
   - file: aiyagari
+  - file: aiyagari_egm
   - file: ak2
   - file: ak_aiyagari
   - file: two_computation