ABSTRACT
In this chapter, we discuss methods for the estimation of causal effects using instrumental variables (IVs) with both continuous and binary outcomes. We focus attention on the case of a single continuous exposure variable, as this is the usual situation in Mendelian randomization studies; although the same methods could be used in the case of a single binary exposure. We explain for each method how to estimate a causal effect, and describe specific properties of the estimator. In turn, we consider the ratio of coefficients method, twostage methods, likelihood-based methods, and semi-parametric methods. This order corresponds roughly to the complexity of the methods, with the simplest ones first. These methods are contrasted in terms of bias, coverage, efficiency, power, robustness to misspecification, and existence of finite moments. We have included a simple explanation of each method at first, and then further details for more technical readers. Also discussed are implementations of the methods using standard statistical software packages.
