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I'm designing pretty much a textbook instrumental variable study. Paraphrasing the actually set-up, we're planning to offer in-store discount coupons and trying to assess whether providing coupons is a good idea.

Given there will be a clear self selection involved (more loyal customers will opt in to more discounts) we're sending a mailer with discount to a random subset of customers and a mailer with no discount to the control. Assuming that we have a strong first stage, I'll estimate the true effect size of incremental discount via a 2SLS.

However, in this scenario, how can I decide how many people to send the mailers to so that I have a sufficiently powered experiment?

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  • $\begingroup$ Have you run mailer campaigns before to get a sense of take-up? $\endgroup$
    – dimitriy
    Apr 26, 2021 at 13:40
  • $\begingroup$ If you mean to ask what's the response rate, then yes. It's like 70%+ $\endgroup$
    – user319791
    Apr 26, 2021 at 13:58

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There is a paper by Walker et al (2017) that discusses this power calculation here.

They also have a web calculator, as well as Stata and R code.


Walker, V. M., Davies, N. M., Windmeijer, F., Burgess, S., & Martin, R. M. (2017). Power calculator for instrumental variable analysis in pharmacoepidemiology. International journal of epidemiology, 46(5), 1627–1632. https://doi.org/10.1093/ije/dyx090

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  • $\begingroup$ @user319791 Does this make sense? $\endgroup$
    – dimitriy
    Apr 27, 2021 at 18:11

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