Don't (fully) exclude me, it's not necessary! Causal inference with semi-IVs

Abstract

This paper proposes semi-instrumental variables (semi-IVs) as an alternative to instrumental variables (IVs) to identify the causal effect of a binary (or discrete) endogenous treatment. A semi-IV is a less restrictive form of instrument: it affects the selection into treatment but is excluded only from one, not necessarily both, potential outcomes. Having two continuously distributed semi-IVs, one excluded from the potential outcome under treatment and the other from the potential outcome under control, is sufficient to nonparametrically point identify marginal treatment effect (MTE) and local average treatment effect (LATE) parameters. In practice, semi-IVs provide a solution to the challenge of finding valid IVs because they are often easier to find: many selection-specific shocks, policies, prices, costs, or benefits are valid semi-IVs. As an application, I estimate the returns to working in the manufacturing sector on earnings using sector-specific characteristics as semi-IVs.