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Many empirical applications estimate causal effects of a continuousendogenous variable (treatment) using a binary instrument. Estimation istypically done through linear 2SLS. This approach requires a mean treatmentchange and causal interpretation requires the LATE-type monotonicity in thefirst stage. An alternative approach is to explore distributional changes inthe treatment, where the first-stage restriction is treatment rank similarity.We propose causal estimands that are doubly robust in that they are valid undereither of these two restrictions. We apply the doubly robust estimation toestimate the impacts of sleep on well-being. Our results corroborate the usual2SLS estimates.

Nonparametric Doubly Robust Identification of Causal Effects of a Continuous Treatment using Discrete Instruments