Bruno Ferman
@bruno_ferman
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Professor at Sao Paulo School of Economics (@EconFGVSP/@EconomiaGV)/Econometrics/Applied Micro/affiliate @JPAL
Sao Paulo, Brazil
Joined March 2020
I’ll keep as my pinned Tweet links to the threads my co-authors and I wrote on our papers:. 1) Ferman and Pinto: Inference in DID with few treated. @cristinepinto16.
💡 Inference in difference-in-differences with few treated clusters 💡. Ferman and Pinto (2019) was published a couple of years ago, when I was not on Twitter. But I think it’s not too late to write a thread on it. 1/12
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RT @PossebomVitor: 💡New Working Paper💡Nonlinear Treatment Effects in Shift-Share Designs.with @luigieras. Link: S….
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RT @RevEconStudies: "This study estimates the carbon-efficient forest cover in the Brazilian Amazon. A $10/ton carbon tax could preserve 95….
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RT @PossebomVitor: Are you unsure about how to conduct inference when you only have a few treated units?. @lafalvarez, @bruno_ferman, and W….
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RT @bruno_ferman: 🧵New survey paper: "Inference with Few Treated Units" .Alvarez (@lafalvarez), Ferman (@bruno_ferman) and Wüthrich. Tired….
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@Lycia_Lima @friva_ 8) Alvarez, Ferman and Wüthrich: Inference with Few Treated Units. @lafalvarez .Kaspar is no longer with us on #EconTwitter. .
🧵New survey paper: "Inference with Few Treated Units" .Alvarez (@lafalvarez), Ferman (@bruno_ferman) and Wüthrich. Tired of referees saying your standard errors are wrong?. This survey will help you understand if you really have a problem — and, if so, how to fix it!
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That's a quick overview!. For more details, check out the full survey 📚👇. Link: Hope you find it helpful!.Feedback welcome. 🧠✍️.
arxiv.org
In many causal inference applications, only one or a few units (or clusters of units) are treated. An important challenge in such settings is that standard inference methods that rely on...
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15/.Applied folks: we hope this serves as a warning that standard inference may fail with few treated units + guidance on choosing alternatives. Econometricians: we wanted to provide a state-of-the-art overview — and a call for new methods based on alternative assumptions!.
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14/.And show some equivalences:. e.g., wild-bootstrap (with null imposed) asymptotically equivalent to sign-changes when N₁ is fixed and N₀ → ∞. ⇒ theoretical justification for wild-bootstrap in these settings.
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13/.We also provide finite-N₀ improvements for some methods, such as Conley-Taber and sign-changes. Free lunch: gains with finite N₀ & asymptotic equivalent when N₀ → ∞ (with N₁ fixed).
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12/.What if we have >1 treated (but still few)?. More info on treated ⇒ alternatives: sign-changes, Behrens-Fisher solutions, etc. Relax some assumptions relative to previous methods (but need new ones!). ⚡Power may be an issue when N₁ is very small. Many relevant trade-offs!.
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11/.In this extreme case (1 treated unit & 1 treated period): need strong restrictions on treatment effect heterogeneity!. If interested, see Section 4.1.3 on inference on sharp nulls, inference on realized treatment effects, prediction intervals, and sensitivity analysis.
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10/.📌Extrapolate from time series. Learn about treated error using pre-treatment residuals. ⚡Flip assumptions.Need time series restrictions (stationarity) but relax assumptions on cross-section. Challenges arise when counterfactuals are estimated via high-dimensional approaches.
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9/.Ferman and Pinto (2019): allow for heteroskedasticity that can be estimated based on observables. Example: when units have different variances due to variation in population sizes. See this old thread:
💡 Inference in difference-in-differences with few treated clusters 💡. Ferman and Pinto (2019) was published a couple of years ago, when I was not on Twitter. But I think it’s not too late to write a thread on it. 1/12
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8/ .📌Extrapolate (learn) from control units . Learn the distribution of the treated error using controls' residuals (à la Conley and Taber). ⚡Key assumption: Errors of treated and control units must have the same distribution (homoskedasticity). No restriction on time series!.
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7/.Survey is organized based on data availability. 📌Extreme case.1 treated unit & 1 treated period. Enough info from treated to construct an estimator - but not enough info from treated to learn about its distribution!. ⚡Solution. We need to *extrapolate*⇒stronger assumptions!.
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6/.We focus on model-based approaches, more common in metrics. 📚 Nice citation from Haavelmo to justify this framework + marvel movies to help make the point 🕷️: ). We also discuss design-based approaches at the end
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5/ .Important:.📌Problems arise when the *number* of treated units is small. ✅Standard methods are usually fine with 40 or 50 treated units, even when the *share* of treated is small. Feel free to cite our survey to justify sticking to standard methods when that's your case!😉.
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4/.Extreme case: you have only 1 treated and N₀ controls. The true variance is σ₁² + σ₀²/N₀. But with only one treated, you just don’t have enough info to estimate σ₁² using only 1 treated!. Robust SEs simply set σ̂₁² = 0! 😵💫. σ₁²: var of treated.σ₀²: var of control.
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