Bayesian Robustness Values for Modern Causal Panel Estimators via Riesz Representations

Abstract

We develop a sensitivity-analysis workflow for causal panel estimators, covering synthetic difference-in-differences, matrix completion, fixed-effect imputation, and group-time average treatment effects. The workflow combines Riesz-representation omitted-variable-bias bounds with partial-$R^2$ robustness values and separates two reporting routes. Route A gives a direct sensitivity profile for additive or projected confounding summarized by outcome-side and Riesz-side partial $R^2$ values. Route B treats observed-covariate benchmarks as auxiliary data only when benchmark-count, alpha-side alignment, model-check, dependence, and dominance diagnostics are credible; otherwise its main role is demotion. We derive estimator-specific Riesz diagnostics and clarify which are fixed-weight, target-level, or first-stage-conditional rather than full derivatives of regularized training maps. Monte Carlo stress tests distinguish calibrated benchmark settings from dominance failure, coarse alpha-side benchmarks, benchmark dependence, noisy covariates, and concentrated SDID weights. In the California tobacco-control panel, the SDID estimate is $-15.60$ packs per capita; corrected finite-donor placebo inference gives standard error 9.49 and add-one $p=0.051$. A refit-weight finite-difference audit changes the Route A nullification robustness value from 0.054 to 0.045, leaving the low-single-digit conclusion unchanged. A county-level minimum-wage application applies the same profile to a multi-cohort staggered panel.