Bayesian Sensitivity Analysis for Unmeasured Confounding in Causal Panel Data Models

Despite the recent methodological advancements in causal panel data analysis, concerns remain about unobserved unit-specific time-varying confounders that cannot be addressed by unit or time fixed effects or their interactions. We develop a Bayesian sensitivity analysis (BSA) method to address the concern. Our proposed method is built upon a general framework combining Rubin’s Bayesian framework for model-based causal inference (Rubin [1978], The Annals of Statistics 6(1), 34–58) with parametric BSA (McCandless, Gustafson, and Levy [2007], Statistics in Medicine 26(11), 2331–2347). We assess the sensitivity of the causal effect estimate from a linear factor model to the possible existence of unobserved unit-specific time-varying confounding, using the coefficients of the treatment variable and observed confounders in the model for the unobserved confounding as sensitivity parameters. We utilize priors on these coefficients to constrain the hypothetical severity of unobserved confounding. Our proposed approach allows researchers to benchmark the assumed strength of confounding on observed confounders more systematically than conventional frequentist sensitivity analysis techniques. Moreover, to cope with convergence issues typically encountered in nonidentified Bayesian models, we develop an efficient Markov chain Monte Carlo algorithm exploiting transparent parameterization (Gustafson [2005], Statistical Science 20(2), 111–140). We illustrate our proposed method in a Monte Carlo simulation study as well as an empirical example on the effect of war on inheritance tax rates.