6.1 Causality

• Descriptions

  • “correlated”, “are related”, “tend to occur together”
  • Better: \(X\) is linked to \(Y\), \(X\) has ramifications for \(Y\)
  • Even better: \(X\) causes \(Y\), \(X\) improves \(Y\), etc.
  • Causality has direction

Draft definition

We say that \(X\) causes \(Y\) if, were we to intervene and change the value of \(X\), then the distribution of \(Y\) would also change as a result.

• But still allows

  • change in \(Y\) without change in \(X\)
  • far off variables

Revised definition

We say that \(X\) causes \(Y\) if, were we to intervene and change the value of \(X\), then

• The distribution of \(Y\) would also change as a result

  • even if changing \(X\) doesn’t always change \(Y\)
  • changes the probability that \(Y\) occurs

• If \(X\) causes \(Y\), then \(X\) must be a part of the DGP (data generating process) that generates our observations of \(Y\).