Debiased Bayesian Inference for High-dimensional Regression Models

Applied researchers now routinely work with regression models that feature a large number of covariates. A primary inferential goal in econometrics is to estimate the ceteris paribus effect of a specific variable while controlling for other variables (Belloni et al., 2013a, 2018). The prevailing practice interprets the coefficient on a regressor as a causal effect, conditional on the included controls. As the plausibility of conditional unconfoundedness is often argued using a large set of covariates, practitioners have increasingly embraced high-dimensional regression models. This setting has been extensively studied, predominantly using frequentist methods. Bayesian inference, on the other hand, has long been valued for its coherent framework for handling uncertainty in statistical analysis. As highlighted by Rubin (1984), Bayesian methods provide direct answers to many empirical questions by quantifying uncertainty about unknown parameters conditional on the observed data.