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ebenmichael / augsynth

Augmented Synthetic Control Method
MIT License
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Jackknife+ #40

Closed azev77 closed 3 years ago

azev77 commented 3 years ago

I'm having a little trouble understanding appendix B of your paper.

For Jackknife+: LOO residuals: image Estimated post-treatment outcome (w/o period "t"): image

PI: image I'm confused b/c the following quantity varies w/ dropped-period "t": image Which dropped period "t" is used? Or is this quantity averaged across all t in 1:T0?

Update: for each t in 1:T0, compute x_t = image Then use this to compute the order-stat for x_1 to x_T0: image Then is this a typo?:image

ebenmichael commented 3 years ago

You're right that the quantity varies with the dropped time period. For each time period that we drop, we compute the LOO residual for that time period and the post-treatment outcome, dropping out that time period. We then take the alpha and 1-alpha quantiles as defined.

The intuition for why we want to re-compute the post-treatment estimate is spelled out in Fig 1 of the paper we cite.