Dynamic LATEs with a Static Instrument

In many situations, researchers are interested in identifying dynamic effects of an irreversible treatment with a time-invariant binary instrumental variable (IV). For example, in evaluations of dynamic effects of training programs with a single lottery determining eligibility. A common approach in these situations is to report per-period IV estimates. Under a dynamic extension of standard IV assumptions, we show that such IV estimands identify a weighted sum of treatment effects for different latent groups and treatment exposures. However, there is possibility of negative weights. We discuss point and partial identification of dynamic treatment effects in this setting under different sets of assumptions.