Instrumental Variables

#Math
Variables that may be used to draw a causal relationship between two things that correlate.
Say smoking (S) correlates with poor health (H) and we suspect smoking to cause poor health (S->H). However, there could be a confounding variable that affects both S and H such as depression. Maybe depression increases the likelihood of smoking and also leads to poor health. We may use a third variable that should only correlate with S but hardly affects anything else (so doesn't cause depression for example). An example would be tax rate on cigarettes (T), which should correlate with lower cigarette usage but not with anything related to depression or other confounding variables. If T correlates with H, we suspect it must be through S, and so we can infer S->H or H->S. Instrumental variables should have high relevance and exogeneity