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 propose using instrumental variables (IV) to address the bias associated with simply comparing subjects based on their randomized treatment assignment, known as "intention to treat analysis." They show that this technique can be incorporated into the Rubin Causal Model and used for causal inference without assuming constant treatment effects. The advantages of this approach include making the nature of identifying assumptions more transparent and allowing for a straightforward assessment of the sensitivity of results to deviations from these assumptions. The paper begins by discussing the importance of addressing selection bias in observational studies and clinical trials, using examples such as the impact of military service on health and earnings. It then introduces the concept of potential outcomes and the Rubin Causal Model, which defines causality as the difference between the value of the outcome if the unit is treated and if it is not treated. The authors define the causal effect of treatment on an individual or unit as the difference between these potential outcomes. The paper proceeds to describe the principles of causal inference using instrumental variables, including the assumptions required for identification of causal effects. These assumptions include the Stable Unit Treatment Value Assumption (SUTVA), the exclusion restriction, monotonicity, and the non-zero average causal effect of the instrument on the treatment. The authors derive the IV estimand, which is the ratio of the average causal effect of the instrument on the outcome to the average causal effect of the instrument on the treatment. The paper also discusses the sensitivity of the IV estimand to violations of key assumptions, such as the exclusion restriction and monotonicity. It shows that the IV estimand can be biased if these assumptions are violated, but the bias depends on the strength of the instrument and the correlation between the instrument and the treatment status. Finally, the paper applies the framework to an example of the effect of military service on civilian mortality, using draft lottery numbers as instruments. The authors illustrate how to apply the IV approach to this example, including the identification of the causal effect and the sensitivity analysis to violations of key 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 propose using instrumental variables (IV) to address the bias associated with simply comparing subjects based on their randomized treatment assignment, known as "intention to treat analysis." They show that this technique can be incorporated into the Rubin Causal Model and used for causal inference without assuming constant treatment effects. The advantages of this approach include making the nature of identifying assumptions more transparent and allowing for a straightforward assessment of the sensitivity of results to deviations from these assumptions. The paper begins by discussing the importance of addressing selection bias in observational studies and clinical trials, using examples such as the impact of military service on health and earnings. It then introduces the concept of potential outcomes and the Rubin Causal Model, which defines causality as the difference between the value of the outcome if the unit is treated and if it is not treated. The authors define the causal effect of treatment on an individual or unit as the difference between these potential outcomes. The paper proceeds to describe the principles of causal inference using instrumental variables, including the assumptions required for identification of causal effects. These assumptions include the Stable Unit Treatment Value Assumption (SUTVA), the exclusion restriction, monotonicity, and the non-zero average causal effect of the instrument on the treatment. The authors derive the IV estimand, which is the ratio of the average causal effect of the instrument on the outcome to the average causal effect of the instrument on the treatment. The paper also discusses the sensitivity of the IV estimand to violations of key assumptions, such as the exclusion restriction and monotonicity. It shows that the IV estimand can be biased if these assumptions are violated, but the bias depends on the strength of the instrument and the correlation between the instrument and the treatment status. Finally, the paper applies the framework to an example of the effect of military service on civilian mortality, using draft lottery numbers as instruments. The authors illustrate how to apply the IV approach to this example, including the identification of the causal effect and the sensitivity analysis to violations of key assumptions.