Thread by @arindube

🚨 Difference-in-differences working paper alert 🚨

Our Local-Projections DiD offers a unified approach that encompasses many popular alternatives as specific instances; allows for extensions; and does it all using an OLS regression.

nber.org/papers/w31184

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Why yet another DiD estimator?
* Simple, fast, easy to code (single regression command with an "if" statement)
* Flexible (eg, recurring treatments)
* Easily allows matching on pre-treatment outcomes and covariates
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Baseline version of LP-DiD: estimate a LP regression limiting to "clean controls"
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Baseline, unweighted, approach identifies a VW ATT.

Identical to the "stacked approach" of Cengiz Dube Lindner Zipperer ('19). But can do it without stacking!

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But that's just the beginning...LP-DiD can do many things!

Example: we derive the VWATT weights, so can easily re-weight & estimate an equal weighted ATT. We show the re-weighetd LP-DiD is numerically identical to Callaway and Sant'Anna ('20) but very easy/fast to compute.

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And if you reweight + use a broader pre-treatment period for differencing the outcome, the LP-DiD estimate is shown to be very close to the Borusyak, Jaravel, Spiess imputation estimator.

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You want more? We got more.

LP-DiD easily takes covariates (of course it does, it's an OLS regression!), including pre-treatment outcomes. The latter can be useful for constructing a counterfactual that guards against certain types of violations of parallel trends.

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Give us even more, you say? OK, you got it!

Easily incorporates continuous treatment (with additional assumptions needed for interpretation) or non-absorbing treatments (like minimum wages) where truly never-treated units rarely exist.

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For more, including performance in terms of MSE, bias, as well as computational speed, check out the paper!

Joint with @DanieleGirardi_, O Jorda, and A Taylor.

Also see Daniele's Slide Deck: danielegirardi.github.io/posts/document…

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Finally, for STATA example code on implementing the LP-DiD, check out the Github repository here:

github.com/danielegirardi…

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11/ Tagging a few individuals who may be interested: @pedrohcgs @borusyak @XJaravel @jmwooldridge @CdeChaisemartin @agoodmanbacon @instrumenthull @paulgp