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How should we think of compliance in a phase-in RCT design? What are the assumptions recovering the LATE by instrumental variables in this case?

Details: In a traditional (simultaneous) RCT, in case of non-compliance, the LATE (local average treatment effect) can be recovered by using the random assignment as an instrumental variable if two assumptions hold:

  • monotonicity: random assignment weakly increases (or decreases) program participation
  • exogeneity: random assignment itself has no direct effect on Y, except via participation in the program

What are the assumptions required to recover the IV in case of a phase-in design? Is this covered in any paper or textbook?

The reason I ask is because participants may have a preference for receiving the program in a specific time period.

For example:

Setting of the RCT:

  • 3 periods: t={1,2,3}

  • N=100 participants randomized into receiving the RCT in either:

    • Treatment: 50 receive program in t=1
    • Control: : 50 receive program in t=3
  • Outcome Y compared between treatment and control at the end of period 2

  • Non-COmpliance (assumed I know this, which in fact can not be observed):

    • 20 subjects only accept treatment in t=1
    • 10 subjects only accept treatment in t=3
    • 70 subjects are compilers (accept treatment when offered)
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