19.2 Assumptions

  1. instrument is relevant
  2. instrument is valid

Relevance

  • Z needs to explain X
  • if correlation is small: weak instrument
    • estimate likely to jump around from sample to sample
    • if small, variation matters
  • We can actually check for relevance: look at relationship b/w X and Z

Validity

  • Instrument has no back doors

  • Any paths b/w Z and Y need to pass through instrument, or be closed

  • here: need to close Z –> B –> Y and Z –>A –> Y

  • validity very hard to argue, e.g. with rain: correlated to many things

  • choosing good instruments:

    • as-good-as-random: truly comes from outside the system, applied almost completely randomly (real randomization / Mendelian randomization)

    • you wouldn’t ever think to include it in your regression

    • randomness is more believable (e.g. RCT with imperfect compliance, RDD)

Monotonicity