Covariate benchmarking for sensitivity analysis when the confounder is correlated with observed covariates

Covariate benchmarking is an important part of sensitivity analysis about omitted variable bias and can be used to bound the strength of the unobserved confounder using information and judgments about observed covariates. It is common to carry out formal covariate benchmarking under the assumption that the unobserved confounder is orthogonal to the observed covariates. This assumption is restrictive and will be difficult to defended in most empirical analyses. In this paper I show that relaxing the orthogo- nality assumption leads to a breakdown of a recently proposed innovative formal covariate benchmarking methodology.