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Improve McCall model with separation: Fix function signatures and optimize sampling
This commit makes several improvements to the job search model with separation and Markov wages: **Function signature fixes:** - Modified `simulate_employment_path` to accept policy `σ` as a parameter instead of computing it internally - Updated `update_agent` to use generic parameter name `σ` instead of `σ_star` for better flexibility - This makes the simulation functions more modular and allows policy reuse across multiple simulations **Performance optimization:** - Added `P_cumsum` (precomputed cumulative sum of transition matrix) to the Model class - Eliminated redundant cumsum computations during Markov chain simulation - Replaced `weighted_choice` function with direct `jnp.searchsorted` on precomputed cumulative sums - For n=200 wage states and 100k agents over 200 periods, this eliminates ~20 million O(n) operations **Documentation:** - Added explanation of the inverse transform sampling method - Documented the performance benefits of precomputing cumulative sums - Clarified the role of each model component These changes significantly improve simulation performance while making the code more maintainable and reusable. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude <[email protected]>
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