Instrumental variables estimation

• https://en.wikipedia.org/wiki/Instrumental_variables_estimation

A Causal inference method that allows the usage of incomplete random assignments or naturally-occurring “assignments”.

Imagine that we want to infer a causal relationship $X \rightarrow Y$, just showing the relationship $Y = \beta X + \epsilon$ cannot eliminate alternative explanations including hidden Confounding factors or Reverse causality. However, if we identify a variable $Z$ that can affect $Y$ only through its impact on $X$ ($Z \rightarrow X \rightarrow Y$), and if some of the variance in $Y$ can be explained by $Z$, then we can argue the $X$ has a causal effect on $Y$.

More formally, the effect $Z \rightarrow Y$ can be broken down into the product of $Z \rightarrow X$ and $X\rightarrow Y$. To estimate $X\rightarrow Y$, we can divide the $Z \rightarrow Y$ by $Z \rightarrow X$.

It relies on three assumptions. First, substantial first stage assumption states that $Z$ should have a substantial impact on $X$. Second, we assume the independence, which means that $Z$ should be as random as possible. The groups shouldn’t be too different from each other. Finally, the exclusion restriction argues that there shouldn’t be any causal path from $Z$ to $Y$. All causal path must go throgh $X$.

Some variables may be over-used as IV although it is difficult to ensure the exclusion restriction. For instance, it was argued that using weather as IV may be problematic due to so many related variables (Mellon2023rain).

Video tutorials

• A quick explanatory video by Ashley Hodgson: Identification, Part 3: Instrumental Variables
• Introduction to Instrumental Variables (IV) by Joshua Angrist at Marginal Revolution University

Papers to learn IV

- Instrumental variables estimation: Assumptions, pitfalls, and guidelines

History

• Who Invented Instrumental Variable Regression?
  • The History of IV Regression
  • Historical Econometrics: Instrumental Variables and Regression Discontinuity Designs