April 1, 2021

Correlation to Causation

Solutions to Confounding

  1. Recap
  2. Conditioning

Recap

Solutions to Confounding

Solutions to Confounding

Every way of using correlation as evidence for causality makes assumptions

  • FPCI cannot be solved without assumptions
  • With assumptions, can say confounding/bias is not a problem

Internal vs External Validity

Every way of using correlation as evidence for causality makes trade-off between:

  • internal validity: how plausible are assumptions that set aside confounding?
  • external validity: how much does this causal relationship speak to the causal claim/question of interest?

Solution How Bias
Solved
Which Bias
Removed
Assumes Internal
Validity
External
Validity
Experiment Randomization
Breaks \(W \rightarrow X\) link
All confounding variables \(X\) is random
Change only \(X\)
High Low
Conditioning Hold confounders
constant
? ? Low High

Conditioning

conditioning

when we observe \(X\) and \(Y\) for multiple cases, we examine the correlation of \(X\) and \(Y\) within groups of cases that are the same on confounding variables \(W, etc. \ldots\)

How does conditioning solve confounding?

  • Cases compared have same values on confounding variable \(W\)
  • In these groups, \(W\) cannot affect \(X\) or \(Y\)
  • “Backdoor” path from \(X\) to \(Y\) is “blocked”

Conditioning: Example

A few weeks back we asked:

Did Trump rallies increase hate crimes?

  • inflammatory rhetoric \(\xrightarrow{?}\) violence
  • many argue there is a link
  • but is there empirical evidence of causality?

Conditioning: Example

Conditioning: Example

Correlation between Trump Rallies and Hate Crimes might suffer from confounding

  • Places that Trump visits might be different than places he does not.
  • These differences might be related to Hate Crimes.

Example: Conditioning:

Feinberg, Branton, and Martinez-Ebers compare hate crimes in counties with and without Trump rallies, but condition on (hold constant):

  • percent Jewish
  • number of hate groups
  • crime rate
  • 2012 Republican vote share
  • percent university educated
  • region

Example: Conditioning

Example: Conditioning