Causal Inference with Secondary Outcomes

In this paper, we develop new methods for identifying causal effects in the presence of unmeasured confounding with continuous treatment and outcome. Under a set of linear structural equation models, we invent two identification strategies by introducing a secondary outcome. Specifically, we utilize the symmetry and asymmetry properties of distributions of random variables to achieve identification. We develop accompanying estimating procedures and evaluate their finite sample performance through simulations and a data application studying the causal effect of tau protein level on behavioral deficits in Alzheimer's disease.