Add Bayesian RD example: politicians' salaries and corruption (BJPS replication)

[daimon-pymclabs]

What

An independent Bayesian regression-discontinuity replication, built entirely with CausalPy, of:

Klašnja, Fazekas & Alshaibani (2026), Revisiting the Link between Politicians' Salaries and Corruption, British Journal of Political Science.

Mayoral salaries across 11 EU countries jump discretely at population thresholds. The sharp RD asks whether the salary raise reduces procurement corruption risk (cri2 ∈ [0,1]). Running variable = % distance to the nearest threshold (cutoff 0); treatment = above threshold. Public data: Harvard Dataverse doi:10.7910/DVN/TESJMM (2.43M contracts).

Added under examples/rd_salaries_corruption/: a runnable notebook, a written findings report (REPORT.md), figures, a compact data extract so it runs without the 896 MB raw file, and the full reproduction pipeline in scripts/.

Why it's a good CausalPy example

It's a real, published, peer-reviewed RD on a large multi-country dataset (most RD examples are toy/single-cutoff), and it exercises CausalPy's RegressionDiscontinuity (bandwidth, donut_hole, effect_summary, discontinuity_at_threshold) while deliberately going beyond a global polynomial:

• Local-linear bandwidth sweep — the modern RD default.
• Polynomial-order instability demo — linear/quadratic/cubic estimates swing −0.04 → −0.10 → −0.18 on a fixed window (Gelman & Imbens 2019: don't do this).
• A hierarchical, triangular-kernel-weighted, Beta-likelihood RD (custom PyMC): respects the bounded [0,1] outcome, adds city random intercepts (cluster analogue) + country fixed effects, separate slopes each side. 0 divergences, R̂ ≈ 1.004.

Findings (see REPORT.md)

• The paper's frequentist headline reproduces exactly: rdrobust, unique-threshold sample, τ = −0.078 (p ≈ 1e-5).
• The Bayesian RD agrees on direction: discontinuity in corruption risk is negative at posterior probability ≈ 1.0 at every bandwidth, and −0.044, 94% HDI [−0.082, −0.005] in the covariate-adjusted hierarchical Beta model. Higher salary ⇒ less corruption.
• Reported honestly: the magnitude is specification-dependent (≈ −0.04 to −0.20 unadjusted), and a donut deletion flips the sign — symptoms of mass points / heaping in a pooled-threshold running variable (rdrobust flags "mass points detected"). The qualitative claim is credible; the point estimate is fragile.

Notes

• Draft. Not wired into the docs toctree (the notebook needs the bundled data and isn't set up to execute in the docs build) — happy to integrate it as a rendered docs page if maintainers want.
• Independent replication, not peer-reviewed.
• Built with CausalPy 0.8.1 / PyMC 5.28.5.

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