Method library WORKFLOW / 030

Research workflow/4 steps

Synthetic difference-in-differences (synthdid)

@synthdid ✓ D · Jun 29, 2026 · 897 views

Source synthdid — Arkhangelsky, Athey, Hirshberg, Imbens & Wager

@misc{synthdid,
  title        = {synthdid},
  author       = {Arkhangelsky and Athey and Hirshberg and Imbens and Wager},
  howpublished = {\url{https://github.com/synth-inference/synthdid}},
  note         = {Software / documentation}
}

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The method workspace

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Method mapInput → 4 steps → output

START WITHInput data

ARRIVE ATResults

Read step 01

Inside the methodReasoning, equations & implementation

Data prep

Balanced panel + treated block

Step notesField note & discussion1

Data preparation — shapes the raw inputs into what the estimator expects.

What happens here

Reshape to a (unit × time) outcome matrix with the treated cells marked.

Formula

\hat\tau^{\mathrm{sdid}}=\arg\min_{\tau,\mu,\alpha,\beta}\textstyle\sum_{i,t}\hat\omega_i\hat\lambda_t\big(Y_{it}-\mu-\alpha_i-\beta_t-W_{it}\tau\big)^2

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Key code

library(synthdid)
setup <- panel.matrices(panel)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

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Estimation

Solve for unit & time weights

Step notesField note & discussion1

The core estimate — where the causal quantity itself is computed.

What happens here

Unit weights match pre-trends; time weights downweight uninformative periods.

Formula

\hat\omega=\arg\min_{\omega}\ \lVert Y_{\text{pre}}^{\text{ctrl}}\omega - Y_{\text{pre}}^{\text{treat}}\rVert^2 + \zeta\lVert\omega\rVert^2

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Key code

tau.hat <- synthdid_estimate(setup$Y, setup$N0, setup$T0)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Inference

Placebo / jackknife standard errors

Step notesField note & discussion1

Uncertainty quantification — standard errors, intervals, and aggregation.

What happens here

Variance from placebo reassignments or a jackknife over control units.

Formula

\widehat{\mathrm{se}}^2=\tfrac{N_0-1}{N_0}\textstyle\sum_j(\hat\tau_{(-j)}-\bar{\hat\tau})^2

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Key code

se <- sqrt(vcov(tau.hat, method = 'placebo'))

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Reporting

Plot trajectories & the gap

Step notesField note & discussion1

Reporting — turn the numbers into a figure or table a reader can act on.

What happens here

Treated vs synthetic path, with the estimated effect shaded.

Reads fromNot specified Feeds intoNot specified

Key code

plot(tau.hat)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Data contract

Inputs & data

A balanced panel (unit × time), with one or a few treated units that switch on at a known time.

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Format — a unit × time outcome matrix; treatment turns on for some units after T0.

 unit  2010 2011 2012* 2013*
   A    8.1  8.4   9.0   9.3   # treated after 2011
   B    7.9  8.0   8.1   8.2

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Results & interpretation

Workflow discussion 0

Context & interpretation

⚠️ Unofficial community showcase of synthdid. Not affiliated with the authors; all credit to them.

Reweight both control units and pre-periods to build a synthetic control, then apply a DiD correction — robust where plain SC or TWFE struggle.

Follow the analysis.

Inputs & data

Results & interpretation

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