Three Ways of Thinking About Instrumental Variables

In this post we’ll examine a very simple instrumental variables model from three different perspectives: two familiar and one a bit more exotic. While all three yield the same solution in this particular model, they lead in different directions in more complicated examples. Crucially, each gives us a different way of thinking about the problem of endogeneity and how to solve it. The Setup Consider a simple linear causal model of the form \(Y \leftarrow \alpha + \beta X + U\) where \(X\) is endog