Many empirical applications estimate causal effects of a continuous endogenous variable (treatment) using a binary instrument. Estimation is typically done through linear 2SLS. This approach requires a mean treatment change and causal interpretation requires the LATE-type monotonicity in the first stage. An alternative approach is to explore distributional changes in the treatment, where the first-stage restriction is treatment rank similarity. We propose causal estimands that are doubly robust in that they are valid under either of these two restrictions. We apply the doubly robust estimation to estimate the impacts of sleep on well-being. Our new estimates corroborate the usual 2SLS estimates.
