Democracy, Crime, and Equity in the U.S. States

A Joint Bayesian Framework for Estimating Racial Disparity in Imprisonment When the Measures Disagree

A reproducible study in R on public state-level data, asking whether stronger state democracy tracks less racial inequality in incarceration, and whether felon re-enfranchisement changes it. The point is mostly methodological: run the same question through four ordinary choices about measurement and design and the answer keeps shifting, so what looks like a finding about race and democracy often comes down to the analyst's choices. The full argument and results are in the paper, linked below.

Author: Miura Meng

Under review at Statistics and Public Policy (submitted July 2026).

Read it

• Read the paper (web)
• The paper as a formatted PDF

A longer, more exploratory data walk-through is also included as a self-contained report:

• Read the report (web)

The matching .qmd files are the Quarto sources.

Reproduce

The analysis needs only R (>= 4.5). Install the packages:

install.packages(c("dplyr", "tidyr", "ggplot2", "lme4", "gbmt", "tidysynth",
                   "brms", "posterior", "ggridges", "ragg", "ggrepel", "knitr"))

Then run the scripts in order to rebuild the merged dataset, every model, and the figures:

Rscript R/01_load_merge.R            # build the merged state-year dataset
Rscript R/02_first_plot.R            # cross-section: democracy vs. the Black/White ratio
Rscript R/03_equity_measures.R       # four ways to measure inequity
Rscript R/04_within_state_models.R   # within/between mixed models
Rscript R/05_gbtm_trajectories.R     # trajectory typology
Rscript R/06_causal_amendment4.R     # Florida synthetic control
Rscript R/07_robustness.R            # synthetic-control robustness checks
Rscript R/08_bayes_expansion.R       # joint Bayesian model of the Black and white rates
Rscript R/09_bayes_robustness.R      # robustness checks for the joint model
Rscript R/10_bayes_ar1.R             # the headline model: joint model with AR(1) errors
Rscript R/11_spec_curve.R            # 16-specification curve
Rscript R/12_national_decomposition.R # decomposing the national ratio decline
Rscript R/13_covariate_signflips.R   # the sign flip beyond democracy: poverty, urbanicity, party
Rscript R/14_hispanic_robustness.R   # Hispanic-misclassification robustness

The Bayesian scripts (08–10, 14) fit models with brms/Stan; each takes a few minutes and caches its fit as an .rds at the repo root, refitting only if the cache is absent.

R/00_theme.R holds the shared figure style and is sourced by the plotting scripts; figures land in figures/.

Rebuilding the paper and report documents is optional and not needed to check the analysis. It also requires Quarto (and, for the PDF, quarto install tinytex plus the Times New Roman / Charter fonts used in the figures). The one-liner bash run_all.sh runs the whole pipeline end to end: the analysis, both figure sets, and the rendered documents.

Repository layout

Path	Contents
R/	analysis scripts 00–14 (run 01–14 in order)
data/raw/	third-party source data (see data/SOURCES.md)
data/	state_dem_incarceration.{rds,csv}, the merged dataset built by R/01
figures/	generated figures for the web (Charter, PNG 300 dpi)
figures_pdf/	the same figure set in Times, for the PDF paper
paper/	the paper: Quarto source + rendered PDF and HTML
report/	the longer data report: Quarto source + rendered HTML

Data sources

All data are public. Each dataset belongs to its providers and is subject to their own terms; cite them as the data source. See data/SOURCES.md.

• State Democracy Index 2.0, by Grumbach & Bitton (UC Berkeley Democracy Policy Lab)
• Incarceration Trends, by the Vera Institute of Justice
• Voter Turnout 1980–2022, by M. McDonald (UF Election Lab)

Methods

Linear mixed models with a within/between (Mundlak) decomposition (lme4); group-based multivariate trajectory modeling (gbmt); synthetic control with placebo inference (tidysynth); a specification curve over 16 measure-and-design combinations; and the paper's central model, a joint Bayesian multilevel model of the Black and white imprisonment rates with correlated state effects and AR(1) errors (brms).

License

Code is released under the MIT License (see LICENSE). The data in data/ are not covered by that license and remain subject to the terms of their original providers.