We examine instrumental variables estimation in situations where the instrument is only observed for a sub-sample, which is fairly common in empirical research. Typically, researchers simply limit the analysis to the sub-sample where the instrument is non-missing. We show that when the...

Many empirical studies specify outcomes as a linear function of endogenous regressors when conducting instrumental variable (IV) estimation. We show that tests for treatment effects, selection bias, and treatment effect heterogeneity are biased if the true relationship is non-linear. These...

We propose a method for using instrumental variables (IV) to draw inference about causal effects for individuals other than those affected by the instrument at hand. Policy relevance and external validity turns on the ability to do this reliably. Our method exploits the insight that both the IV...

Empirical researchers often combine multiple instrumental variables (IVs) for a single treatment using two-stage least squares (2SLS). When treatment effects are heterogeneous, a common justification for including multiple IVs is that the 2SLS estimand can be given a causal interpretation as a...

This paper uses a rich Norwegian dataset to re-examine the causal relationship between family income and child outcomes. Motivated by theoretical predictions and OLS results that suggest a nonlinear relationship, we depart from previous studies in allowing the marginal effects on children's...

We examine instrumental variables estimation in situations where the instrument is only observed for a sub-sample, which is fairly common in empirical research. Typically, researchers simply limit the analysis to the sub-sample where the instrument is non-missing. We show that when the...

Many empirical studies specify outcomes as a linear function of endogenous regressors when conducting instrumental variable (IV) estimation. We show that tests for treatment effects, selection bias, and treatment effect heterogeneity are biased if the true relationship is non-linear. These...

This chapter synthesizes and critically reviews the modern instrumental variables (IV) literature that allows for unobserved heterogeneity in treatment effects (UHTE). We start by discussing why UHTE is often an essential aspect of IV applications in economics and we explain the conceptual...

We examine instrumental variables estimation in situations where the instrument is only observed for a sub-sample, which is fairly common in empirical research. Typically, researchers simply limit the analysis to the sub-sample where the instrument is non-missing. We show that when the...