  We propose an instrumental variable framework for identifying and estimating
average and quantile effects of discrete and continuous treatments with binary
instruments. The basis of our approach is a local copula representation of the
joint distribution of the potential outcomes and unobservables determining
treatment assignment. This representation allows us to introduce an identifying
assumption, so-called copula invariance, that restricts the local dependence of
the copula with respect to the treatment propensity. We show that copula
invariance identifies treatment effects for the entire population and other
subpopulations such as the treated. The identification results are constructive
and lead to straightforward semiparametric estimation procedures based on
distribution regression. An application to the effect of sleep on well-being
uncovers interesting patterns of heterogeneity.
