[mmcky]

Review and revision of the seven lectures in the Bounded Rationality in Macroeconomics suite, checked against the 1993 book and Marimon, McGrattan and Sargent (1990).

Shared across the suite

• One stochastic-approximation / E-stability thread, introduced in bounded_rationality ("One recursion, many learners") and used by the later lectures, with the history credited accurately (DeCanio, Evans, Marcet-Sargent, Woodford; Evans-Honkapohja as systematizers)
• Consistent verdicts on selection: MMS economy A2 is convergence to a non-equilibrium; the two-currency exchange rate is history-dependent
• Repaired hand-offs and cross-links, the book's four payoffs, the prompting gradient, a notation table, and de-duplicated quotes
• Ten new bibliography entries

By lecture

• bounded_rationality: Bray's learners, E-stability, the bubble linked to olg_adaptive_money, corrected quotes and attributions
• olg_adaptive_money: remove the pi0 = 3 floating-point artifact, explain the stability reversal by E-stability, condense the Phillips section with corrected attributions, three new exercises
• learning_approximation: simulate the same 201-state chain the benchmark is solved on, converge the kernel smoother, correct the recursive kernel formula, ODE comparison of batch and online learning
• exchange_rate_learning: fix the tautological limits figure and a print bug, correct the kappa, election-operator, and time-series claims
• genetic_classifier: common random numbers and a 20-seed sweep for the prisoner's dilemma, matching perceptron code, a bucket-brigade subsection
• marimon_mcgrattan_sargent: correct the Kiyotaki-Wright condition, adopt the paper's encoding and a single paper-style genetic algorithm, report every economy across seeds, derive the bucket brigade's effective discount factor
• prospects_bounded_rationality: correct the history (Bray, E-stability, Chung, SWZ), settle the four payoffs, qualify the identification argument, four new exercises

[Copilot]

🔵 Needs a closer look

Execution and output correctness of the substantial new notebook code across the large multi-file revision couldn't be validated in this environment, so confirmation of a clean CI build is needed before approval.

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What changed in this PR

This PR revises the seven-lecture "Bounded Rationality in Macroeconomics" suite (checked against Sargent 1993 and Marimon–McGrattan–Sargent 1990), of which five files appear here: four lecture files plus the shared bibliography. The changes tighten the economics narrative, repair hand-offs and cross-links between lectures, introduce a single stochastic-approximation / E-stability thread used across the series, correct quotes/attributions and a few numerical artifacts, add many new worked exercises with executable solutions, and register ten new bibliography entries.

Changes:

• Introduce and reuse one E-stability / stochastic-approximation framing (new br_one_recursion, br_payoffs, br_notation sections in bounded_rationality), with consistent cross-lecture {ref}/{doc} links and a notation table.
• Rework code and prose in learning_approximation (single 201-state chain for benchmark and learners, matrix-form T_map, converged kernel smoother, ODE batch-vs-online comparison) and exchange_rate_learning (ridge/κ stabilizer, limits figure fix, genetic-algorithm volatility diagnostics), plus many new exercises in all four files.
• Add 10 new .bib entries (DeCanio1979, Evans1989, denHaanMarcet1990, Giannitsarou2005, MalmendierNagel2016, Arthur1991, BullardDuffy1993, Hopfield1982, Arifovic1994, KuanLiu1995), all referenced and unique.

Verification performed: all 65 {cite*} keys across the four lectures resolve to the bib; all {ref}/{numref}/{eq}/{doc} targets resolve; no duplicate figure names or labels; exercise/solution directives and code fences are balanced; removed symbols (brentq, market_prices, sigma_u) are fully unused; and the refactored helpers (e.g., the lfilter rewrite of smoothing_mse, rule/parameterized_expectations/online_pea, and exercise algebra such as the T-map fixed points and slopes) are internally consistent. Notebook execution could not be run in this environment, so output correctness should be confirmed by the CI build.

File	Description
lectures/​bounded_rationality.md	Adds the quest/payoffs/notation framing and the "One recursion, many learners" E-stability section; corrects quotes, attributions (muth1961, Friedman1957), and bubble/two-currency exposition; adds exercises br_ex4–ex5.
lectures/​prospects_bounded_rationality.md	Rewrites the 1993 "ledger" and postscript (four payoffs, identification argument, constant-gain estimability), corrects history/attributions, adds exercises pbr_ex1–ex4.
lectures/​learning_approximation.md	Unifies benchmark and learners on one 201-state chain, matrix-form T_map/PEA, converged recursive kernel smoother, batch-vs-online ODE/eigenvalue analysis; adds exercises lae_ex4–ex5.
lectures/​exchange_rate_learning.md	Clarifies Newton–Raphson history-dependence, adds the κ ridge stabilizer, fixes the limits figure and spectrum/print bugs, adds genetic-population diagnostics and exercises xr_ex4–ex5.
lectures/​_static/​quant-econ.bib	Adds ten new bibliography entries supporting the new citations across the suite.

_{Review effort: Balanced}

[mmcky]

Review summary

I reviewed all seven lectures:

• Execution: ran every code cell in a fresh kernel at the PR head and on main.
• Corrections: reproduced each bug the description claims on main and confirmed the fix on this branch.
• Maths: re-derived the new mathematics.
• Numbers: checked the numbers quoted in the prose against the executed output, and reran stochastic claims on extra seeds wherever the prose says "every", "always" or quotes a specific value.
• References: checked labels, cross-references and bibliography keys across the lecture set.

Bottom line: the corrections are real and the mathematics holds up. Every error named in the description reproduces on main and is fixed here. Nothing blocks the build.

One substantive error (the bid-fraction claim in marimon_mcgrattan_sargent) and a set of smaller prose issues are fixed in f596e5f, pushed to this branch. One multi-seed claim in marimon_mcgrattan_sargent needs an author decision and is raised with @thomassargent30 in #1102.

Line numbers below refer to 473d382.

Fixed in f596e5f

marimon_mcgrattan_sargent: bid fractions (L463–464, L555–556). The lecture said a larger bid fraction "lowers" a rule's stationary strength, and used that to correct the paper's claim that specificity-linked bids "favor specific rules". But its own rest-point equation gives S_e = E[b₂S_c]/(1+b₁). A larger b₁ therefore pulls S_e toward zero, raising it when downstream payments are negative. Among such rules, higher bids do favor specific rules, as the paper says. The text and the note now state both cases.

Prose that contradicted the output, or claimed more than the seeds support:

Lecture	Where	Change
marimon_mcgrattan_sargent	L1215–1222	Said "the thick arrows are the fundamental triangle". In the seed-0 figure, type 3's payoff-neutral 1→2 trade (0.33 per period) is twice its equilibrium 1→3 trade (0.165), so the extra arrows are not thin.
marimon_mcgrattan_sargent	L1966–1971	Fiat holdings were described as "close to" the paper's run. Its type 1 holds fiat 46% of the time against our 30%. The largest gap from the paper (0.158) is that, not type 2's good 1.
marimon_mcgrattan_sargent	L1148, L1715, L1733, L2520–2529	Economy D uses 10 seeds, not 20. Crossover only wildcards positions where the parents carry different specific bits. A child's birth strength survives its first update through the bid it pays. Ex5's conclusions are now scoped to its six runs: on seeds 6–29 the accepting rule already wins 5 of 24 runs at u₁ = 12,000.
bounded_rationality	L794	"None of this postdates the book" came right after citations from 1999–2019. Now: "The core of the theory predates the book".
bounded_rationality	L1167	"Judges this 'a weak reed'" dropped the book's hedge. It now quotes "may seem a weak reed", as exchange_rate_learning and prospects do.
bounded_rationality	L666	"Bray's feedback coefficient b is our h′": in this lecture b is the slope of demand, so the clash is now spelled out.
olg_adaptive_money	L359	"There the gain was constant", but the Bray section of bounded_rationality uses a 1/t gain. Now contrasts with the relaxation algorithm.
olg_adaptive_money	L1356	Restored the "with positive saving" qualifier that L909 and ex6 carry.
olg_adaptive_money	L1845 (ex5)	The first realized inflation rate from a belief near 6 is exactly 1 (T ≡ 1 at G = 0). The deep deflation is the second.
learning_approximation	L761	"Cuts their error by a factor of about four": 4.1 is the printed asymptotic prediction 500^0.228. The lecture's own θ path gives 6.3 (4.6–6.3 over 8 seeds). Now "would cut".
learning_approximation	L1044 (ex1)	"Stay well above" the population errors: on history 0 the sup error is below the population value (0.0170 vs 0.0176 at degree 3). Now refers to the ergodic RMS, which stays above on every history.
learning_approximation	L1320 (ex4)	The high-inflation equilibrium, with saving about (1.19, 1.63), is also a fixed point of the linear-family map. It is E-unstable (eigenvalue 1.515), which is why the algorithm settles on the low one.
exchange_rate_learning	L473	The zero gap from the λ∞ curve is close to automatic: e_t = (H₁/H₂)(1−λ)/λ at the young class's share holds at every date, transients included, to 3e-16. So it only confirms that the classes merged; the dashed curve carries the content.
exchange_rate_learning	L879, L1180, L1194	The election operator is not the only source of learning. Without it, the spread of saving within the population is 1.31–1.37, against 3.15 for an unselected population, and mean λ moves more than pure averaging would allow. Softened.
genetic_classifier	L1534 (ex3)	"β = 32 is on average an improvement": over 400 seeds the mean share is 0.627 vs 0.599, a paired difference of +0.029 (se 0.024). Now says the gain is not robust.
genetic_classifier	L1422 (ex2), L1666 (ex4)	Scoped to the seeds shown. At the higher mutation rate, seeds 24–35 give crossover +0.029. At b = 0.7, 4 of 60 extra runs are still 0.3–1.25 from p* at t = 299.
genetic_classifier	L1337, L1351	11 of the 33 distinct shallow spurious states have a lower-energy single flip, so they are fixed points, not all local minima.
prospects_bounded_rationality	L1356	"Permanence is necessary for identification" is contradicted by part 2 of the same exercise: at b = 0.7 the penalty grows like T^0.4 without bound. Now "at the usual rate".
prospects_bounded_rationality	L787	"A case in point" followed the paragraph on E-stability's limits. Now introduced as the condition working within those limits.
prospects_bounded_rationality	L1466 (ex3)	The single learner's penalty is bounded, but its expected value tends to about 6.4, above 3.84, so "stays small" became "stays bounded".

These are prose-only changes. A full jb build with execution off gives 133 warnings before and after; none come from these edits, and the only warnings this PR adds are the expected undefined labels for figure names that come from cell outputs.

Raised for the author: #1102

A2.1 lock-in. "So these runs are slow rather than stuck for good" (L1348) and "all of them reach the fundamental pattern by t = 6000" (L1363) hold for seeds 0–19 only. On seeds 20–39, 3 of the 16 runs that are off the pattern at t = 1000 are still off at t = 6000. Seeds 24 and 26 are unchanged at t = 24,000. The cause is a different lock-in from the one described: type 2's general consumption rule ##0 -> 1 eats every good 1 it trades for.

Economy B.1. The overview's "nearly every run" is 31 of 40 on seeds 20–59.

The main A2 verdict is unaffected: type 1 never speculates in any of 60 seeds. The issue sets out three ways to reword the claims.

Left for the author (optional, not changed)

• Gain notation in prospects: pbr_ex1 writes the gain as λ (around L1094) and pbr_ex4 as g (L1492–1530), against the series convention γ (bounded_rationality L274, olg_adaptive_money L1032). g also clashes with the perfect-foresight map g(π) at L1091. pbr_ex1 also writes realized inflation as π_t where olg_adaptive_money calls the same object π_{t−1}; the dynamics are identical.
• Bullard–Duffy: least squares "fails to converge" for n ≥ 4 (olg_adaptive_money L968–970) vs "can fail" (prospects L803–805).
• Economy B as a selection credit: prospects (L576–578, L693, L709) counts it as one. marimon_mcgrattan_sargent (L1577–1580, L1689–1690) attributes B's outcome to the same bucket-brigade impatience that makes A2 a debit. This is interpretive.
• genetic_classifier L120 says the recursion is "shared by every learner in this series", but bounded_rationality L735 says "most learners", and L789 puts population algorithms outside the theory.
• olg_adaptive_money ex7 (L2056–2059), "most of it arrives during escapes" (uncertain): on seeds 1–3, the periods with fast falls in g carry 6–14% of the penalty, about their share of time. Low-inflation periods carry more, 51–63%.
• marimon_mcgrattan_sargent crowding score (L1720, L1800): it adds 1 when the action differs, which reverses the usual similarity measure. Prose and code agree, and main had the same; worth checking against the paper.
• Description: olg_adaptive_money gains four new exercises and drops one (the old Phillips-gain exercise), a net of three, not "three new".

Verified corrections (highlights)

• marimon_mcgrattan_sargent
  • main's Kiyotaki–Wright condition could never fail, contradicting its own A2 verdict. The new π₃(1) − π₂(1) form matches independent value iteration exactly (114.11 / 137.75 at β = .999).
  • The derivation of β_eff checks out, and the lecture's own bucket_brigade reproduces it to four decimals.
  • The one-hot encoding gives the stated rule counts.
• olg_adaptive_money
  • On main, convergence from π₀ = 3 to 2 was a rounding artifact. In exact arithmetic β stays at 3; in floats the 4.4e-16 error grows ×2.41 per period.
  • T′(2) = ½ and T′(3) = 2.
  • The off-by-one in main's β formula is fixed.
• learning_approximation
  • On main, the learners converged to the fixed point of a clipped 21-state simulation, which is 0.20 (sup) from the benchmark. That mismatch, not sampling noise, produced Ex1's errors rising with degree.
  • The kernel smoother now converges (140 passes, against main's silent stop at 40).
  • The recursive kernel formula now carries h^{-d}: 0.3965 against a true density of 0.3989, where main's version decays toward 0.
• exchange_rate_learning
  • main's limits figure was tautological: λ never moved (1.1e-16).
  • The κ = 0 step explodes rather than stalling.
  • φ = 0.874–0.908 over 14 seeds, so the "near unit root" claim on main was wrong.
• genetic_classifier
  • main's perceptron code was the logistic-likelihood gradient, not the displayed NLS recursion.
  • main's PD champion fitness (2.672) exceeded the true ceiling (2.608).
  • The CRN implementation is exact: 60 copies of one gene give fitness sd 9e-16.
  • The 20-seed sweep reproduces exactly and holds over 60 seeds.
• bounded_rationality and prospects_bounded_rationality: the SA/ODE and E-stability statements, Bray's convergence results, and the six new exercises re-derive.
• Suite consistency: the A2 and two-currency verdicts, the four payoffs, and the hand-offs all match the toc. No long quotation is repeated across lectures.

Build and runtime

All seven lectures execute with zero cell errors. Locally, marimon_mcgrattan_sargent drops from 191 s to 89 s, and the suite's total is about the same as on main.

Not verified

Quotations and chapter or footnote locators for Sargent (1993) and Marimon, McGrattan and Sargent (1990), the Arifovic and Bullard–Duffy results as characterised, and the rendered figures.

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[mmcky]

Style-guide pass

I checked the PR against the QuantEcon style guide (rules from action-style-guide at main).

• Scanner: I ran the deterministic scanner from compliance-lecture-style on all seven lectures at main and at the PR head, kept only the issues on lines this PR adds, and checked each by hand.
• Rules the scanner doesn't cover: citation style, heading case, exercise and solution format, and math notation, checked by hand.

The new material is in good shape. Commit f9a095d applies the two changes worth making.

Pushed in f9a095d

Change	Rule	Where
Fold the two-sentence parenthetical about starting at exactly π₀ = 3 into one sentence.	qe-writing-001	olg_adaptive_money
"i.i.d." → "IID". This was the only non-"IID" form in the suite.	qe-writing-009 (proposed)	exchange_rate_learning (xr_ex5)

Both are prose-only. A rescan shows both issues cleared.

Checked and fine

• Citations (qe-ref-001): every citation whose authors are the subject of the sentence already uses {cite:t}. This is the rule that needed 15 fixes in [stats_info] Correct the mathematics and add exercises across the Statistics and Information lectures #1099.
• Headings (qe-writing-006): H1 is in Title Case and every new H2–H4 is in sentence case.
• Exercises (qe-admon-001, -002, -005): all 36 exercises use the gated exercise-start form, and every solution is a dropdown linked to its exercise.
• Math (qe-math-002, -004, -006, -007): no transposes written with ', no bold vectors, no align environments and no manual \tags. The primes are all derivatives.
• Figures: axis labels are lowercase or math (qe-fig-006), and no spines are removed (qe-fig-007). New figsize settings are on multi-panel figures or follow each lecture's own convention (qe-fig-001). The one figure without mystnb metadata is in a solution (qe-fig-005).
• Packages (qe-code-003): installs are at the top of the lecture.
• Scanner false positives:
  • qe-writing-004 flags "Economy A2", "Economy B.1" and similar 30 times, but these are the names of economies. It also flags "Inflation" in The Conquest of American Inflation and "the Great Inflation".
  • qe-math-013 (proposed) flags "the paper's equation (6)" and similar, which refer to the paper's numbering, not the lecture's.

Left for the author (optional)

• Exercise parts with several sentences (qe-writing-001): the scanner flags 39 numbered exercise parts and summary bullets that hold two to four sentences. The rule's examples are about paragraphs, and the scoring spec says the check should leave lists alone. Splitting them would mean restructuring most of the new exercises, so I left them.
• Greek names in marimon_mcgrattan_sargent code (qe-code-002): the new code uses β, β_A, β_eff, π31 and π21, but ASCII eta (16 uses), tau (7) and sigma (5). Renaming them touches the numba functions, the Economy.eta field and the eta=0.5 arguments that the text of two exercises names, so it is a whole-lecture change.
• Caption length (qe-fig-004, at most 5–6 words): three new captions run to 9–10 words, against 6–7 for the suite's existing captions:
  • "Relaxation algorithm paths: the cobweb and three smaller relaxation parameters"
  • "Belief errors in Bray's market under fixed and declining gains" (both bounded_rationality)
  • "Limiting exchange rate against the mean initial portfolio share" (exchange_rate_learning)
• Line width (qe-fig-008): the speculation-threshold figure in marimon_mcgrattan_sargent and the olg_ex7 likelihood plot use the default line width rather than lw=2.
• Panel titles (qe-fig-003): ax.set_title labels the panels of the relaxation figure in bounded_rationality and of one figure in learning_approximation. Both were already on main.
• Probability notation (qe-math-010, proposed): \Pr appears in genetic_classifier (two places) and \operatorname{Prob} in olg_adaptive_money, rather than \mathbb{P}.

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[mmcky]

Follow-up: A2.1 lock-in (#1102)

@thomassargent30 chose option 2 from #1102: describe the second lock-in as a failure mode in its own right. Done in 5a2bf5a, changing marimon_mcgrattan_sargent only.

• First lock-in: a once-lucky refusal rule shuts out an untried trade rule. It is still described as slow rather than permanent, but now only for that mode.
• Second lock-in: a new seed-24 cell shows it. Type 2's general consumption rule ##0 -> 1 is kept strong by eating good 2 (strength 146.86), so it also eats the good 1 it should keep for trade. The specific rule 100 -> 0 was tried 3 times, sits at 0.54, and never wins the argmax auction again. Seeds 24 and 26 are unchanged at t = 24,000.
• Two failure modes compared: the new text calls this lock-in the cost of generality, against optimistic initialization. It also records that type 1 never speculates on seeds 20–59 (0 of 40 runs).
• Overview and summary: in A2, "a few stay stuck for good". Economy B selects the fundamental equilibrium "in most runs and the speculative one in none": 18 of 20 on the lecture's seeds, 31 of 40 on seeds 20–59.

The lecture runs cleanly: 51 cells, 0 errors, 57 s locally.

#1102 stays open as the reminder to return to option 3 (more seeds and longer horizons, reporting frequencies) in about six months, as Tom suggested.

With this, all the review items are addressed. This is ready to merge once the preview build is green.

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Preview URL: https://pr-1101--sunny-cactus-210e3e.netlify.app

Commit: 6c1ab72

📚 Changed Lectures

• bounded_rationality
• exchange_rate_learning
• genetic_classifier
• learning_approximation
• marimon_mcgrattan_sargent
• olg_adaptive_money
• prospects_bounded_rationality

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• Workflow: Build Project [using jupyter-book]

[mmcky]

✅ Translation sync completed (zh-cn)

Target repo: QuantEcon/lecture-python.zh-cn
Translation PR: QuantEcon/lecture-python.zh-cn#311
Files synced (7):

• lectures/bounded_rationality.md
• lectures/exchange_rate_learning.md
• lectures/genetic_classifier.md
• lectures/learning_approximation.md
• lectures/marimon_mcgrattan_sargent.md
• lectures/olg_adaptive_money.md
• lectures/prospects_bounded_rationality.md