19.12 Validity violation

• a little is okay
• can still get useful inferences out of the analysis
• 2 approaches
  • mostly-valid instrument
  • make up for invalidity by using many instruments

Mostly-valid instrument

• partial identification
  • Conley, Hansen, and Rossi (2012)
  • think about how bad that validity violation is
  • range of plausible estimates based on plausible range of violations
• replace validity assumption
  • Nevo and Rosen (2012): correlation between instrument and 2nd-stage error term is the same sign as the correlation between the treatment variable and the error term, but is smaller
  • Flores and Flores-Lagunes (2013): monotonicity

Many instruments

• instrument has many subcomponents that can each be measured separately and treated as own instrument
• Chernozhukov, Hansen, and Spindler (2015): use LASSO to select most important predictors (controls & instruments)
• Windmeijer et al. (2019)
  • put in all instruments, including invalid ones, in 2nd stage
  • only valid ones have no predictive power
• Kolesár et al. (2015)
  • just use all instruments
  • if not too many are invalid: works