19.7 Checking IV assumptions

Relevance

• and Z are strongly enough related to each other that Z is not a weak instrument
• first-stage F-statistic test (comes with fixest)
  1. estimate 1st stage
  2. do a joint F test on instruments
  3. get F statistic from joint F test
• no real cut-off; the bigger, the less bias (b/c of random correlation between Z and error term)
• if weak: use alternative approach (like Anderson-Rubin confidence intervals)

Validity

• test for open back doors between Z and Y, or second-stage error term

  • if they’re related, validity is violated

  • but: if we have a bias, the residual isn’t going to represent the error term very well

• instead: second stage and include instrument as control

  • if coefficient for instrument =/= 0: violation of validity

  • shows there’s another pathway than through X

• Durbin-Wu-Hausman test

  • compare OLS to IV: if different, X does have open back doors

  • compare 2 IVs (overidentification): if different, additional instruments likely invalid

• Overidentification

  • Sargan test (2SLS)

  • Hansen test (GMM)

  • combining two instruments –> different LATE, but doesn’t mean that instruments are invalid; just don’t produce same results

Failing to find evidence of violation doesn’t mean it’s not violated.