Identifying the effect of a mis-classified, binary, endogenous regressor

TL;DR

This paper investigates the identification of effects in models with misclassified binary endogenous regressors using instrumental variables, correcting previous results and deriving new bounds under various independence assumptions.

Contribution

It corrects a prior incorrect point identification result and introduces new conditions that enable point identification of the effect.

Findings

Derived sharp bounds for the effect under mean independence.

Identified conditions under which the effect can be point identified.

Provided novel insights into measurement error and endogeneity in binary regressors.

Abstract

This paper studies identification of the effect of a mis-classified, binary, endogenous regressor when a discrete-valued instrumental variable is available. We begin by showing that the only existing point identification result for this model is incorrect. We go on to derive the sharp identified set under mean independence assumptions for the instrument and measurement error. The resulting bounds are novel and informative, but fail to point identify the effect of interest. This motivates us to consider alternative and slightly stronger assumptions: we show that adding second and third moment independence assumptions suffices to identify the model.