This paper outlines a framework for causal inference in settings where random assignment has occurred but compliance is not perfect, i.e., the treatment received is nonignorable. The authors use instrumental variables (IVs), which have long been used in economics for regression models with constant treatment effects, to avoid bias associated with simply comparing subjects by randomized treatment assignment. They show that this technique can be integrated into the Rubin Causal Model and used for causal inference without assuming constant treatment effects. The advantages of embedding this approach in the Rubin Causal Model are that it makes the nature of the identifying assumptions more transparent and allows for straightforward sensitivity analysis to deviations from these assumptions. The paper discusses the importance of selection bias in observational studies and how it can affect causal inferences. It provides examples from clinical trials and other fields where non-compliance can lead to biased results. The authors also discuss the use of IVs in various contexts, including the effect of military service on civilian mortality and the impact of Vietnam-era military service on civilian earnings. The paper presents a formal framework for causal inference using IVs, defining the causal effects of Z on D and Y, and the causal effects of D on Y given the exclusion restriction. It discusses the sensitivity of the IV estimand to violations of critical assumptions, such as the exclusion restriction and monotonicity. The authors show that the IV estimand is the ratio of the average causal effect of Z on Y to the average causal effect of Z on D, and that it can be used to estimate the local average treatment effect. The paper concludes with an application of the framework to the effect of military service on civilian mortality, using data from the Vietnam Era draft lottery. The authors show how the sensitivity of the estimated average treatment effect to violations of Assumption 2 can be explored using the results from the previous section. The paper emphasizes the importance of identifying the correct assumptions and the sensitivity of the IV estimand to violations of these assumptions.This paper outlines a framework for causal inference in settings where random assignment has occurred but compliance is not perfect, i.e., the treatment received is nonignorable. The authors use instrumental variables (IVs), which have long been used in economics for regression models with constant treatment effects, to avoid bias associated with simply comparing subjects by randomized treatment assignment. They show that this technique can be integrated into the Rubin Causal Model and used for causal inference without assuming constant treatment effects. The advantages of embedding this approach in the Rubin Causal Model are that it makes the nature of the identifying assumptions more transparent and allows for straightforward sensitivity analysis to deviations from these assumptions. The paper discusses the importance of selection bias in observational studies and how it can affect causal inferences. It provides examples from clinical trials and other fields where non-compliance can lead to biased results. The authors also discuss the use of IVs in various contexts, including the effect of military service on civilian mortality and the impact of Vietnam-era military service on civilian earnings. The paper presents a formal framework for causal inference using IVs, defining the causal effects of Z on D and Y, and the causal effects of D on Y given the exclusion restriction. It discusses the sensitivity of the IV estimand to violations of critical assumptions, such as the exclusion restriction and monotonicity. The authors show that the IV estimand is the ratio of the average causal effect of Z on Y to the average causal effect of Z on D, and that it can be used to estimate the local average treatment effect. The paper concludes with an application of the framework to the effect of military service on civilian mortality, using data from the Vietnam Era draft lottery. The authors show how the sensitivity of the estimated average treatment effect to violations of Assumption 2 can be explored using the results from the previous section. The paper emphasizes the importance of identifying the correct assumptions and the sensitivity of the IV estimand to violations of these assumptions.