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[ge_arrow] Add the rational expectations reading of Arrow's sequential equilibrium - #1084
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…l equilibrium Follows the corresponding RMT5 chapter in drawing out connections to Arrow (1964), Hart (1975), and Kihlstrom (2019) that the lecture had left implicit. - Overview: record that both trading arrangements, and the proof that they support the same allocation, come from the paper Arrow read in 1952, and that his sequential equilibrium is a rational expectations equilibrium in Muth's sense - New section on rational expectations: what a sequential trader must forecast here, why one good per date and history makes the forecasting requirement vacuous, why Arrow's unit of account settles the span before any forecast, Arrow's distinction between beliefs about nature and expectations of prices, and his remark about economizing on markets - Concluding remarks: provenance and the knife edge that Hart exposed - Related lectures: frame the heterogeneous-beliefs entries by Arrow's distinction Two new exercises: - Arrow's two trading arrangements with many goods: compute a contingent claims equilibrium, construct the sequential rational expectations equilibrium from it, verify the equivalence in both directions, and show that a misforecast of relative prices is not an equilibrium - Hart's examples: two rational expectations equilibria that are strictly Pareto ranked because the span of the asset market depends on forecasts, and a variant in which no equilibrium exists Add bib entries hart1975, kihlstrom2019, diamond1967. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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The Part 1 interpretation in ge_arrow_ex5 is reversed relative to the equilibrium the code computes, and a minor year-count ("eight years") is inconsistent with the stated 1952 date.
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What changed in this PR
This PR extends the ge_arrow lecture by drawing out its intellectual connections to Arrow (1964), Hart (1975), and Muth (1961): it frames Arrow's sequential equilibrium as a rational expectations equilibrium, explains why the single-good formulation makes the forecasting requirement vacuous, and adds concluding remarks plus two new worked exercises with executable code. It fits into the broader lecture series on heterogeneous beliefs and complete/incomplete markets, and the numerical code I checked is mathematically consistent with the accompanying derivations.
Changes:
- New "rational expectations equilibrium" section and concluding remarks tying the model to Arrow/Muth/Radner/Hart/Diamond, plus reframed "Related lectures" intro.
- Two new exercises:
ge_arrow_ex4(multi-good Arrow equivalence, contingent-claims ↔ sequential REE) andge_arrow_ex5(Hart's securities-pay-goods examples: Pareto-ranked REE and non-existence). - Three new BibTeX entries (
hart1975,kihlstrom2019,diamond1967).
| File | Description |
|---|---|
| lectures/ge_arrow.md | Adds RE reading, concluding remarks, Related-lectures reframing, and two exercises with solution code; all cross-references and citations resolve. One reversed economic interpretation and one year-arithmetic slip noted. |
| lectures/_static/quant-econ.bib | Adds well-formed hart1975, kihlstrom2019, diamond1967 entries, each cited in the new text. |
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Follow the QuantEcon.manual style guide in the material added for the rational expectations section: - move the scipy.optimize import into the lecture's imports cell - write exponents as a**b without surrounding spaces (PEP8) - replace named lambdas with def functions - split two multi-sentence paragraphs into one-sentence paragraphs No change to results; all solution cells re-run with identical output. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
- Arrow's 1952 talk is nine years before Muth (1961), not eight - Correct the interpretation of the no-securities spot equilibrium in exercise 5: each consumer eats mostly the good it likes more, and the price asymmetry comes from the wealth distribution, not from the aggregate endowment Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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… the 2026-09-20 and 2026-10-09 sync failures) (#292) * Resync ge_arrow and misspecified_recovery to current source translate forward -f at engine v0.29.4, one file at a time, from lecture-python.myst main (35832b12). Both lectures missed the sync of QuantEcon/lecture-python.myst#1059, which errored on them (failure issue QuantEcon/lecture-python.myst#1061); ge_arrow then also missed QuantEcon/lecture-python.myst#1084, whose sync refused to patch the stale target (QuantEcon/lecture-python.myst#1086). Output as written by the CLI. ge_arrow.md carries a model preamble and a duplicate front-matter block, removed in the next commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> * ge_arrow: drop the model preamble and duplicate front matter The resync output opened with a line of model commentary followed by a second copy of the front matter, below the one the CLI writes. The CLI's embedded-front-matter guard did not strip it because the model's copy is not valid YAML (unquoted "Examples::Example 1: ..." heading-map keys). Removes lines 56-113, which is what that guard would have done; the kept front matter and the body are byte-identical to the CLI output. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> * bib: add hart1975, kihlstrom2019 and diamond1967 Cited by the resynced ge_arrow.md. Copied verbatim from the source bib, at the same position (between muth1961 and radner1972). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
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Follows the corresponding RMT5 chapter in drawing out connections to Arrow (1964), Hart (1975), and Kihlstrom (2019) that the lecture had left implicit.
Two new exercises:
Add bib entries hart1975, kihlstrom2019, diamond1967.