Point Identification of LATE with Two Imperfect Instruments

Abstract: This paper characterizes point identification results of the local average treatment effect (LATE) using two imperfect instruments. The classical approach (Imbens and Angrist (1994)) establishes the identification of LATE via an instrument that satisfies exclusion, monotonicity, and independence. However, it may be challenging to find a single instrument that satisfies all these assumptions simultaneously. My paper uses two instruments but imposes weaker assumptions on both instruments. The first instrument is allowed to violate the exclusion restriction and the second instrument does not need to satisfy monotonicity. Therefore, the first instrument can affect the outcome via both direct effects and a shift in the treatment status. The direct effects can be identified via exogenous variation in the second instrument and therefore the local average treatment effect is identified. An estimator is proposed, and using Monte Carlo simulations, it is shown to perform more robustly than the instrumental variable estimand.