Add Measuring Mobility lecture - #839
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New lecture `lectures/mobility.md`, built on Sections 2 and 3 of the working paper "Mobility" by Daniel Carroll, Nicholas Hoffman and Eric R. Young. Covers mobility as the complement to the inequality snapshot, mobility matrices over wealth quantiles, and four measures applied to toy chains and to PSID wealth transition matrices: * the Shorrocks trace index * Bartholomew's measure * one minus the modulus of the second eigenvalue * normalised mean first passage time All four are presented as ratios to the perfect-mobility (origin independence) benchmark, so that 0 is complete immobility and 1 is origin independence for every measure. This required rescaling Bartholomew's measure by 3/(N+1), since mu_B(M*) = (N+1)/3 rather than 1. Uses markov_chains_I, markov_chains_II and eigen_II, and cross-links to inequality. Placed after `networks` for now. Six exercises, including mean first passage time by simulation checked against the linear solve, and the stationary distribution computed by hand against quantecon. Adds 15 bibtex entries to quant-econ.bib. Supersedes QuantEcon/lecture-python.myst#1031 Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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The `@techreport` entry for carroll2026mobility had no `institution` field, which pybtex flags as "missing institution" — and the CI build runs with `-W`, so the single warning failed the build. The paper has no issuing series or working paper number, so naming an institution would be inventing one. `@unpublished` with a `note` is the accurate entry type and matches how Greenfield_Sargent_1993 is recorded. Verified with pybtex across the alpha, unsrt and plain styles: no warnings for this entry or the other 14 added in the previous commit. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Incorporates review edits, plus:
* Rename the normalised Bartholomew measure from \tilde\mu_B to \mu_{NB},
in the maths, the code and the summary tables.
* Label the simulated paths figure in years (0, 5, ..., 45) rather than in
periods, so the horizontal axis is unambiguous.
* Explain why the uniform matrix is singled out as perfect mobility. Any
matrix with identical rows is origin independent, but quantiles are
constructed to hold equal mass at both dates, which forces the mobility
matrix to be doubly stochastic. A doubly stochastic matrix with identical
rows must be uniform, so within this setting M* is the only
origin-independent matrix.
* Report the column sums of the PSID matrices, which are close to but not
exactly one, and attribute the gap to the published rounding and to panel
attrition. This is the same deviation that makes the stationary
distribution only approximately uniform in the final exercise, now
cross-referenced.
* Note that systematic rank reversal, which is what a measure above one
indicates, is unusual in ordinary market economies, and that every
empirical matrix in the lecture scores well below one.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
The derivation of the mean first passage recursion was too compressed, and it also pointed at markov_chains_I for expected unemployment durations, which that lecture poses as a question but never actually derives. The rewrite makes three hidden steps explicit: * the first step costs one period regardless of where it lands, which is where the leading 1 comes from * the k = j term is present but contributes m_ij * 0, so the sum over k != j omits it because it is zero, not because the case is impossible * writing T_kj for the remaining journey uses the Markov property, since the time from k must not depend on having arrived via i Adds an underbraced display separating the three contributions, a two-state sanity check where the recursion collapses to the geometric waiting time 1/alpha, and the matrix form (I - M_-j) t = 1 that the code actually solves. The diagonal convention now carries its justification: by ergodicity the chain spends a fraction psi*(j) of its time in j, so returns occur once every 1/psi*(j) periods. Verified numerically: T[0,1] = 1/alpha exactly for the two-state chain, diag(T) = 1/psi*, and the recursion residual is zero. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
The lecture said it draws on Sections 2 and 3 of the paper. The authors suggested the vaguer "the first few sections", which will not go stale if they renumber before circulating a revision. Prose only, inside a note directive: no code, math, directives or references touched. Verified with a local single-page build, which produces no non-artefact warnings. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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Adds a new lecture,
lectures/mobility.md("Measuring Mobility"), placed afternetworksfor now — the TOC is due for a rejig.Built on Sections 2 and 3 of the working paper "Mobility" by Daniel Carroll (FRB Cleveland), Nicholas Hoffman (CMU) and Eric R. Young (UVa), which is credited at the top of the lecture and returned to at the end for the model side. The draft still needs to go to the authors for permission and comments before this is merged.
Content
Motivated as the complement to {doc}
inequality: two economies can share a Lorenz curve and a Gini coefficient while offering completely different life prospects.Uses
markov_chains_I,markov_chains_IIandeigen_II; the second-eigenvalue measure is a second application of Perron-Frobenius.Note on normalisation
All four measures are presented as ratios to the perfect-mobility (origin independence) benchmark, so 0 is complete immobility and 1 is origin independence throughout, and values above 1 mean systematic rank reversal.
This required rescaling Bartholomew's measure:$\mu_B(M^*) = (N+1)/3$ , not 1, so the lecture also reports $\tilde\mu_B = 3\mu_B/(N+1)$ . Three points worth raising with the authors are noted in the review thread.
Also
quant-econ.bibquanteconValidation
Notebook executes end to end, 46 code cells, 0 errors. Single-page
jb buildproduces the page and all figures, with only the usual single-page artefacts (unknown sibling documents and the spurious bibtex-key warnings). The fulljb build -n -Wis left to CI.🤖 Generated with Claude Code