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  • IV estimation with dynamic DID as first stage

    Dear all,

    I am working on a project that examines the effect of receiving a particular treatment on future surgeries. As such treatment is available only in recent years and each general practice picks up this treatment in varying periods, we therefore use 'whether general practice picks up such treatment ' as an instrument variable. So our first stage is D=bZ+e, where D is number of treatments at general practice level at time t, and Z is IV indicating whether general practice picks up this treatment at time t.

    I currently use 'xtivreg' in Stata to do the estimation. However, in our case, the first stage using this command is based on two-way fixed effects assuming all general practice picking up treatment at the same time. Given that pick-up timing for each general practice is varying, our first stage should be similar to difference-in-differences (DID) with multiple time periods proposed by Callaway and Sant’Anna (https://bcallaway11.github.io/did/ar...eriod-did.html).

    My question is how to implement DID method with multiple periods into the second stage of IV estimation? Do I need to manually calculate first stage and second stage and manually correct standard deviation? If you know any references solve such issue, please share with me.

    Many thanks,

    Connie

  • #2
    Maybe use a control function within JWDID. I have no idea whether that's legit, but you'd need to bootstrap both regressions for the SE.

    DID does not require strict exogeneity. So if you got parallel trends, then I suspect the result is legit.

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    • #3
      Many thanks, George!

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