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synth-inference / synthdid

Synthetic difference in differences
https://synth-inference.github.io/synthdid
BSD 3-Clause "New" or "Revised" License
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typo in jackknife V.hat computation? #7

Closed bmoallemi closed 4 years ago

bmoallemi commented 5 years ago

You have: V.hat <- (N - 1) * mean((est_jk - est)^2).

Shouldn't we be doing something like: V.hat <- (N / (N - 1)) * mean((est_jk - est)^2),

or: V.hat <- (1 / (N - 1)) * sum((est_jk - est)^2)?

davidahirshberg commented 4 years ago

No. See wikipedia.

bmoallemi commented 4 years ago

Ah thanks for clarifying!

bmoallemi commented 4 years ago

Following the wiki (and the references cited therein), shouldn't we replace est in the formula above with the average of the jackknife estimates, i.e., mean(est_jk)?

bmoallemi commented 4 years ago

Also, do you have any thoughts on applying the jackknife bias reduction?

davidahirshberg commented 4 years ago

Following the wiki (and the references cited therein), shouldn't we replace est in the formula above with the average of the jackknife estimates, i.e., mean(est_jk)?

Our theoretical results don't justify one over the other. Use of the jackknife estimate of variance is justified by asymptotic linearity (Equation 4.8 in the paper). And asymptotic linearity also implies the asymptotic equivalence of using est and mean(est_jk) --- if the op(1) term in Equation 4.8 were not there, they would be identical.

Also, do you have any thoughts on applying the jackknife bias reduction?

I haven't had a chance to look into jackknife bias reduction. If you're interested in the topic, it might be worth doing some simulation. I'd be happy to meet and talk about it. Send me email if you'd like to set something up.