  We study what two-stage least squares (2SLS) identifies in models with
multiple treatments under treatment effect heterogeneity. Two conditions are
shown to be necessary and sufficient for the 2SLS to identify positively
weighted sums of agent-specific effects of each treatment: average conditional
monotonicity and no cross effects. Our identification analysis allows for any
number of treatments, any number of continuous or discrete instruments, and the
inclusion of covariates. We provide testable implications and present
characterizations of choice behavior implied by our identification conditions.
