19.10 Way past LATE

• A local average treatment effect is what 2SLS gives us by default

IV with different values

• Heckman and Vytlacil (1999)
• you can identify a bunch of effects by comparing different values
• what’s the treatment effect among those pushed from the very lowest value of the instrument to just above that?
• assumption: probability of treatment is zero for some values of the instrument, and one for others
• average whole distribution

Correlated random effects and 2SLS

• treatment interacts with some individual variation we can’t observe
• Correlated random effects try to model unobserved individual variation
• treatment \(\times\) control variables, then estimate model with correlated random effects
• give average treatment effect
• this method tends to work better the more continuous the treatment variable is
• Woolridge (2008)