Local Average and Marginal Treatment Effects with a Misclassified Treatment

Abstract

This paper studies identification of the local average and marginal treatment effects (LATE and MTE) with a misclassified binary treatment variable. We derive bounds on the (generalized) LATE and exploit its relationship with the MTE to further bound the MTE. Indeed, under some standard assumptions, the MTE is a limit of the ratio of the variation in the conditional expectation of the observed outcome given the instrument to the variation in the true propensity score, which is partially identified. We characterize the identified set for the propensity score, and then for the MTE. We show that our LATE bounds are tighter than the existing bounds and that the sign of the MTE is locally identified under some mild regularity conditions. We use our MTE bounds to derive bounds on other commonly used parameters in the literature such as the policy relevant treatment parameter (PRTE) and illustrate the practical relevance of our derived bounds through numerical and empirical results.