April 13, 2021

Wrapping Up

Overview

  1. Recap: Solutions to Confounding
  2. Last Examples
  3. End of Term Plan

Recap

Solution How Bias
Solved
Which Bias
Removed
Assumes Internal
Validity
External
Validity
Experiment Randomization
Breaks \(W \rightarrow X\) link
All confounding variables 1. \(X\) is random
2. Change only \(X\)
Highest Lowest
Conditioning Hold confounders
constant
Only variables
conditioned on
1. Condition on all confounders
2. Low measurement error
Lowest Highest
Before and After Hold confounders
constant
variables
unchanging
over time
No confounders
change w/ \(X\)
Lower Higher
Diff in Diff Hold confounders
constant
unchanging and
similarly changing
Parallel trends /
no differently
changing
Higher Lower

Example: Gun Laws

Example: Gun Laws

Expectation is you can answer:

  • What kind of solution to confounding?
  • What kinds of confounding does it eliminate?
  • What do we have to assume in order to believe it is evidence of causality?

Last Examples:

Trump’s Twitter and Hate Crimes

Trump’s Twitter and Hate Crimes

We can’t observe the US in the absence of Trump tweeting against Muslims, so authors use correlation…

Trump’s Twitter and Hate Crimes

Trump’s Twitter gained attention as he ran for President.

Trump made nearly 300 negative tweets about Muslims.

Trump’s Twitter and Hate Crimes

When Trump gained prominence, anti-Muslim hate crimes increased

Trump’s Twitter and Hate Crimes

Trump’s Twitter and Hate Crimes

Even comparing US to itself over time…

  • could be that something other than Trump’s Twitter changed
  • Days with more Trump Tweets could be different in other ways

Trump’s Twitter and Hate Crimes

Counties with more SXSW Twitter Joiners (treated) see larger increase in hate crimes following rise of Trump’s Twitter

Trump’s Twitter and Hate Crimes

Days with Trump golfing followed by more hate crimes

Trump’s Twitter and Hate Crimes

  • Can’t be confounding due to unchanging differences b/t places with more/fewer Twitter users (same counties over time)
  • Can’t be confounding due to changing events (compare high/low twitter use counties on the same dates)
  • Can’t be confounding due to different trends in high/low Twitter counties (use SXSW Twitter joiners)

With reasonable assumptions (no different trends in places with more SXSW 2007 attendees on days when Trump golfs), social media rhetoric causes hate crimes.

Mask Mandates

Karaivanov et al (2020), economists at SFU, investigate:

Have indoor mask mandates reduced COVID cases, on average?

Mask Mandates

Mask Mandates

Could be that mask mandates…

  • happen in places with different socio-economic conditions
  • imposed in places with upward trends

Mask Mandates

Karaivanov et al use a variation on Difference in Difference…

  • Difference in Difference assumes nothing is changing differently between places adopting mask mandate vs not
  • But if mask mandate places

    • adopt other policy changes
    • have more upward trending caseloads \(\to\) people start changing behavior
    • Then no “parallel trends”

Mask Mandates

Karaivanov et al address confounding by variables that change over time differently…

  • difference-in-difference to Ontario PHU that are similar in their trends in COVID cases, stay-at-home behavior, and other public health policies.

Mask Mandates

Estimate counterfactual world…