# Instrumental variables estimation

A Causal inference method.

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 $Y$.

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 (Mellon2022rain).