Add unemployment dynamics lectures (linear + nonlinear)

[jstac]

Implements #910 as a self-contained pair of lectures in the Data and Empirics section, on Bayesian time-series modeling of US unemployment (NUTS in NumPyro). Per discussion, this drops the original draft's fisheries throughline and sinh cautionary tale, and refocuses on the dynamics of a one-dimensional model plus an honest account of what the data can and cannot support.

Lectures

unemployment_linear.md — A Linear Model of Unemployment

• Random walk (probability mass escapes every bounded interval) → linear AR(1) with mean reversion.
• The "is it a random walk?" question: monthly $\phi$ crowds against 1 (~9-yr half-life), annual $\phi\approx0.81$; stationary spread and half-life made explicit.
• An honest section on what's wrong with the linear model: near-unit-root at high frequency, unbounded restoring force, single reversion speed.
• Exercises tie into ar1_turningpts: plug-in vs. posterior-integrated predictive fan charts (the conditional-vs-extended distinction), and a Wecker-style path statistic (max unemployment over the next 8 years; P(reaches 7%) ≈ 0.32 from the end-2019 low).
• Deliberately distinct from ar1_bayes: real data, and the random-walk question rather than the initial-condition focus.

unemployment_nonlinear.md — A Nonlinear Model of Unemployment

• Motivated by the linear model's weaknesses; a saturating tanh restoring force with a bounded pull: $u_{t+1}=u_t+\beta\tanh(\lambda(u_t-\bar u))+\varepsilon$.
• Dynamics: 45°/cobweb stability, the separate roles of $\beta$ and $\lambda$, an iso-$\beta\lambda$ figure that draws the identification ridge before estimation, and the stationary distribution.
• Identification contrast: monthly ($\lambda\to0$, $\beta$–$\lambda$ ridge, ≈ random walk) vs. annual ($\lambda$ identified, ridge dissolves) — information comes from the large-gap recessions.
• An honest linear-vs-nonlinear verdict: the fitted restoring forces coincide in the data-rich center and diverge only at recession extremes, where the bounded force is more defensible.

Verification

Both lectures convert (jupytext→py) and run end-to-end on a GPU (NUTS, 4 chains, chain_method="vectorized", R̂=1.0, 0 divergences); every figure was inspected. Added to _toc.yml under Data and Empirics.

Notes for reviewers

• The CI preview build is the first full render of the MyST directives, exercise/solution dropdowns, and cross-references ({doc} links among these lectures and to ar1_bayes, bayes_nonconj, ar1_turningpts).
• Data are pulled live from FRED (UNRATE) via pandas_datareader, consistent with existing lectures.
• A constant natural rate $\bar u$ over the full post-war sample is a deliberate simplification, flagged in the text and left to the extensions/literature.

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[github-actions]

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Commit: ade5fc0

📚 Changed Lectures

• unemployment_linear
• unemployment_nonlinear

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Build Info

• Workflow: Build Project [using jupyter-book]