🤖 AI Summary
This study addresses the lack of a unified and interpretable sensitivity analysis framework for causal panel data methods, which hinders quantification of unobserved confounding. It introduces Riesz representation theory into causal panel sensitivity analysis for the first time, proposing a workflow that balances theoretical rigor with practical usability. The framework offers two complementary routes: Route A provides direct sensitivity profiles via bounds on omitted variable bias and partial-R² robustness values, while Route B establishes auxiliary diagnostic benchmarks based on observed covariates. Compatible with diverse estimators—including synthetic difference-in-differences (SDID), matrix completion, and fixed-effects imputation—the approach supports both corrected inference and finite-difference auditing. Applied to California’s tobacco control policy, SDID yields an estimated effect of −15.60 packs per capita (adjusted SE = 9.49, p = 0.051), with low single-digit robustness values indicating reliable conclusions; the method also extends successfully to county-level staggered minimum wage policy analysis.
📝 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.