On the Estimation of Treatment Effects with Endogenous Misreporting

Participation in social programs is often misreported in survey data, complicating the estimation of the effects of those programs. In this paper we analyze the case of endogenous misreporting. We simplify the identification of the model by only allowing for one type of misreporting, false negative responses, which is the predominant type of misreporting in surveys. We show that endogenous misreporting, similarly to endogenous participation, can result in the estimates of the treatment effect having opposite signs from the true effect. We present an expression for the bias of both OLS and IV estimators. Most importantly, we develop a consistent estimator which eliminates the misreporting and endogeneity biases when researchers have access to information related to both participation and misreporting. We establish both the asymptotic properties of our estimator and its small sample performance through Monte Carlo simulations. We show that our proposed estimator is root-n consistent and asymptotically normal, and can be estimated using semi-parametric methods. We also discuss how to choose identifying variables for misreporting and participation and suggest that researchers draw these data from different data sources. For example, identifying variable for participation can be drawn from the treatment rules data, which identifying variables for the misreporting equation can be drawn from the features or responses to the survey in general, e.g. proportion of non-response by each survey participant.