chang_credible#

Series: lecture-python-advanced.myst
File: lectures/chang_credible.md
Audit date: 2026-08-26
Corpus snapshot: b83d6da399
Categories audited: writing, math, code, figures, references, links (JAX out of scope)
Overall score: 8.5 / 10
Priority: HIGH

Score breakdown#

Category	Score	One-line note
Writing	3/10	`qe-writing-001` ×5; `qe-writing-005` ×8; `qe-writing-004` ×2, +4 more.
Math	10/10	no mechanical violations detected.
Code	8.5/10	`qe-code-001` ×4.
JAX	out of scope	JAX rules target `lecture-jax`.
Figures	9.5/10	`qe-fig-001` ×1.
References	10/10	no mechanical violations detected.
Links	10/10	no mechanical violations detected.
Admonitions	N/A	no admonitions, exercises or solutions.

Issues#

Critical#

None found.

High severity#

[qe-writing-001] — Use one sentence per paragraph. Count: 5. Lines: 459, 612, 725, 792, 797. Example: 2 sentences in one paragraph.
[qe-writing-005] (reviewer) — Use bold for definitions, italic for emphasis. Count: 8. Lines: 170, 328, 330, 339, 385, 429, 561, 679. Example: the two uses are exactly inverted throughout this lecture. Every term is defined in italic where the rule asks for bold - value of money (170), government policy / price system / allocation (330-332), competitive equilibrium (339), credible (385), sustainable plan (429), outer hyperplane approximation algorithm (679), and earlier Ramsey planner (43), sustainable plan (53), credible public policy (54), sustainable (78-79) - while bold is used for the block labels that should be {prf:definition} / {prf:proposition} directives instead: Definition: (328, 336), A credible government policy with a recursive representation (349), Proposition: (561, 566), Step 1-Step 4 (693, 695, 725, 771).
[qe-writing-008] — Remove excessive whitespace between words. Count: 21. Lines: 38, 41, 43, 60, 69, 91, 93, 103, 134, 215, …. Example: 2 spaces.

Medium severity#

[qe-code-001] (reviewer) — Follow PEP8 unless closer to mathematical notation. Count: 4. Lines: 829, 855, 868, 869. Example: line 829 names a function parameter ChangModel - CapWords for a parameter, and it shadows the class of the same name that the calls at 818 and 868 instantiate; 855’s continuation (R[1]), fontsize=18)) is indented to the xytext line rather than to the open paren it continues (E128); 868 writes h_max=1/0.8 with no spaces around the operator while the same call spaces nothing else ambiguously; and 869 continues that call at a flat 4-space indent instead of aligning under the opening paren.
[qe-writing-002] (reviewer) — Keep writing clear, concise, and valuable. Count: 4. Lines: 319, 403, 423, 725. Example: 319-321 delays its verb for twenty words (“The observation that the one dimensional promised marginal utility of real balances $\theta_{t+1}$ functions in this way is an important step in …”); 403-405 spends 33 words asking the reader to “note the subtle change in arguments” without saying what the change is, which the next paragraph then does; 423-424 is garbled - “For a credible government plan, we the two-dimensional state vector $(w_t, \theta_t)$ encodes history dependence”; and 725-728 packs two sentences and 40 words into one paragraph, the second restating the first.
[qe-writing-003] (reviewer) — Maintain logical flow. Count: 3. Lines: 435, 447, 594. Example: $CE_\pi$ is used at 435 and $CE_\pi^0$ at 477, 509, 528 and 638 without being defined anywhere in this lecture, as are $\Omega$ (459) and $\Theta$ (441 defines $\Theta$ but in terms of the undefined $CE$); each set-builder definition is then split across separate display blocks with prose wedged between the braces - $S$ opens \Bigl\{ at 448 and closes \Bigr\} at 456 with “with value” in between, $\tilde D(Z)$ opens at 508 and closes at 551 across six independently-labelled {math} blocks, and $E(Z)$ opens at 648 and closes at 672 across eight; and because of that fragmentation the sentence at 598, “Chang (1998) provides a method for dealing with the final three constraints”, refers to constraints the reader cannot count.
[qe-writing-004] — Avoid unnecessary capitalization in narrative text. Count: 2. Lines: 726, 765. Example: mid-sentence ‘Step’.
[qe-writing-007] (reviewer) — Use visual elements to enhance understanding. Count: 2. Lines: 242, 768. Example: the lecture improvises a diagram in math mode at 467 - $(h,x) \rightarrow m=q M \rightarrow y = c$ - which is the tell that the within-period timing protocol described at 242-259 wants a real figure; that protocol is the one thing this lecture changes relative to {doc}`chang_ramsey`, and it is the only mechanism here with no picture. Second, 768-769 says the algorithm “constructs a sequence of progressively smaller sets $S_{t+1} \subset S_t \subset S_{t-1} \cdots \subset S_0$” and the reader is shown only the final set at 860 and 879; one plot of two or three successive iterates would show the outer hyperplane approximation actually working.

Low severity#

[qe-fig-001] — Do not set figure size unless necessary. Count: 1. Lines: 833. Example: figsize=.

Strengths#

The lecture states its own delta precisely: 34-51 says it assumes the environment of {doc}`chang_ramsey` and that the only change is the within-period timing protocol, and 554-559 then says exactly what the new operator adds - $\tilde D$ is $D$ plus the deterrence condition {eq}`eqn_chang14`.
The timing protocol is presented as a mechanism rather than a convention: 256-263 explains that the within-period order is what creates the government’s temptation and therefore what the new operator has to price.
Chang’s simplification is motivated before it is used - 604-610 argues that only the best deviation and the harshest punishment matter, which is what makes the scalar $BR(Z)$ enough to replace three constraints.
The punchline is delivered visually and twice with one parameter changed: at $\beta = 0.3$ the Ramsey point $R$ lies outside the blue sustainable set (860, 863) and at $\beta = 0.8$ it lies inside (879, 882), using the same plot_equilibria function both times so the comparison is honest.
The algorithm is given first as a four-step loop (681-691) and then each step is expanded into the linear program that implements it (695-772), so the code that follows can be read against a named step.

Recommended actions#

Reassemble the three set definitions into single display blocks: $S$ (447-457), $\tilde D(Z)$ (504-552) and $E(Z)$ (647-673) each open a \Bigl\{ in one block and close the \Bigr\} in another, with prose and separately-numbered equations in between - which is also why “the final three constraints” at 598 cannot be identified.
Fix the sign error at 625: the constraint reads m(h)(u'(f(x(h))) + v'(m(h))) \leq \beta \theta'(h) where 547 and 666 both have a minus, and the line also carries a stray closing \}.
Replace the bold block labels with {prf:definition} and {prf:proposition} directives (328, 336, 349, 561, 566) and bold the terms they define instead of italicising them (170, 330-332, 339, 385, 429, 679); also drop the stray full stops at 429 (“…sustainable plan (SP) if.”) and 566 (“Proposition:.”).
Define $CE$, $CE_\pi^0$, $\Omega$ and $\Theta$ in this lecture or link them explicitly to where {doc}`chang_ramsey` defines them - they carry the whole of 431-568 and appear here without introduction.
Add a figure for the within-period timing protocol (242-259); the arrow chain improvised in math at 467 is doing a diagram’s job. And plot two or three successive iterates $S_t$ so the shrinking claimed at 768 is visible.
Add mystnb: figure: caption/name metadata to the two figure-producing cells (828, 878) and drop the figsize=(7, 5) at 833, so the two equilibrium-set plots can be captioned and cross-referenced.
Sweep the mechanical items: 21 runs of double spaces, the five two-sentence paragraphs at 459, 612, 725, 792 and 797, the mid-sentence “Step” capitals at 726 and 765, and the four PEP8 items above.