Add OptimumDebt Bellman stage decomposition notebook#4
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Decomposes the elastic-labor benchmark model from Aiyagari & McGrattan (1998) into the stage/perch/connector architecture from SolvingMicroDSOPs Sections 12-13. The notebook covers: - Section 1: Paper, model, Bellman equation - Section 2: Why multiple stages (timing, modularity, DDSL concepts) - Section 3: Three-stage decomposition (labor-supply, consumption, disc) with connector, explicit FOC derivations, and EGM inversion - Section 4: Comparison with monolithic formulation Made-with: Cursor
Align the stage descriptions more closely with the lecture-note perch format and clarify the labor-supply shock timing wording. Add a brief explanation that the Cobb-Douglas structure keeps the labor-consumption coupling tractable despite the non-separable utility. Made-with: Cursor
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Changes from instructor feedback (already applied before this session):
- Revised stage tables, connector description, and equivalence proof
Changes from AI critique (SolvingMicroDSOPs Section 13 comparison):
- Fix labor-supply arrival: e is inherited from connector, not
"realized between prec and sim" (contradicted V_prec = V_sim)
- Add bracket-notation stage list [labor-supply, consumption, disc]
and control-name form [l, c̃, β̃]
- Add Element | Transition | Action table (matching Section 13 format)
- Add k-type / m-type state annotations at each perch
- Add subscript convention paragraph (period, stage, perch ordering)
- Align disc stage: discounting at decision perch (v_sim = β̃ v_succ),
matching the disc table in the lecture notes
- Show explicit max in consumption decision-perch value function
MyST reference:
- Add {cite}`AiyagariMcGrattan1998` with YAML bibliography front matter
- Create OptimumDebt-references.bib with BibTeX entry
- Add entry to SolvingMicroDSOPs.bib
Made-with: Cursor
Author
|
Revision (Class 08): Updated per instructor feedback and AI critique against SolvingMicroDSOPs Section 13. Changes: (1) fixed labor-supply arrival perch — e inherited from connector, not realized between ≺ and ~; (2) added bracket stage list and transition table; (3) added k-type/m-type annotations; (4) aligned disc stage discounting to decision perch; (5) added MyST citation with .bib file. |
Made-with: Cursor # Conflicts: # .devcontainer/devcontainer.json # .devcontainer/post-create.sh # .github/workflows/ci.yml # .latexmkrc # @resources/bash/@resources-update-from-remote.sh # @resources/bash/split-to-sentences-all-tex-files.py # @resources/bash/split-to-sentences-all-tex-files.sh # @resources/bash/split-to-sentences.py # @resources/bash/split-to-sentences.sh # @resources/bash/symbols-mapping.bash # @resources/econ-ark/PoweredByEconARK.jpg # @resources/econ-ark/PoweredByEconARK.pdf # @resources/econ-ark/PoweredByEconARK.png # @resources/econ-ark/PoweredByEconARK.xbb # @resources/econ-ark/econ-ark-html-theme-get.sh # @resources/emacs/prettify-symbols-tex_add-econark-symbols.el # @resources/texlive/texmf-local/tex/latex/econark-ark-required.sty # @resources/texlive/texmf-local/tex/latex/econark-ifsubfile.sty # @resources/texlive/texmf-local/tex/latex/econark-shortcuts.sty # @resources/texlive/texmf-local/tex/latex/econark-theorems.sty # @resources/texlive/texmf-local/tex/latex/econark.sty # @resources/texlive/texmf-local/tex/latex/llorracc-handouts.sty # @resources/texlive/texmf-local/tex/latex/pdfsuppressruntime.sty # CHANGELOG.md # CITATION.cff # Calibration/EstimationParameters.py # Code/Python/StructEstimation.py # Figures/SMMcontour.pdf # Figures/SMMcontour.png # Figures/Sensitivity.pdf # Figures/Sensitivity.png # README.md # REMARK.md # SolvingMicroDSOPs-clean-clean.tex # SolvingMicroDSOPs-clean.tex # SolvingMicroDSOPs-hypersetup.tex # SolvingMicroDSOPs.bib # SolvingMicroDSOPs.cfg # SolvingMicroDSOPs.ipynb # SolvingMicroDSOPs.pdf # Tables/estimate_results.csv # _sectn-multiple-control-variables-input.tex # _sectn-multiple-control-variables.tex # _sectn-normalization-input.tex # _sectn-normalization.tex # _sectn-notation-input.tex # _sectn-notation.tex # pyproject.toml # reproduce.sh # reproduce/docker/setup.sh # reproduce/reproduce_environment.sh # reproduce/required_latex_packages.txt # uv.lock
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Summary
OptimumDebt_bellman-stages.ipynbfor the elastic-labor benchmark in Aiyagari and McGrattan (1998)labor-supply,consumption, anddiscstages plus an inter-period connectorTest plan
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