git:20261009.b655a26 to git:20261009.0fd7961

---

name: did

description: Design, estimate, validate, and write up a difference-in-differences analysis, using the post-2018 heterogeneity-robust toolkit with an explicit statement of which parallel-trends assumption is imposed. TRIGGER on "difference-in-differences", "DiD", "TWFE", "event study", "staggered adoption", "staggered rollout", "parallel trends", "pre-trends", "Callaway-Sant'Anna", "Sun-Abraham", "imputation estimator", "Goodman-Bacon", "stacked DiD", "not-yet-treated", "repeated cross-section", "HonestDiD", "triple differences", "Poisson DiD", "nonlinear DiD", or any panel or repeated-cross-section setting where units become treated over time (policy rollout, staggered feature launch, state law changes). One or a few treated aggregate units: synthetic-control. No design chosen yet: causal-design.

---

# Difference-in-differences

code, and a methods paragraph. The skill stops at the four stop points in

../causal-design/references/shared-rules.md (section "Stop points") and puts each choice to the user.

Where the literature is unsettled the skill names a default and the condition that moves you off

it, and where the canon genuinely disagrees it says so instead of faking consensus.

## Exemplar designs

Seven shapes worth recognizing on sight. Find the one your data looks like before writing a

| Design shape | Canonical case | Marketing analogue | What kills it |

|---|---|---|---|

| Never-treated comparison with the full evidence battery | Miller, Johnson, and Wherry (2021) | a feature launched in some markets and withheld in others, with take-up data | a control group quietly exposed to the treatment |

| Staggered rollout across institutions, adoption dates rebuilt from an archive | Braghieri, Levy, and Makarin (2022) | a platform reaching accounts, regions, or partners on its own schedule | adoption dates that are wrong, or dated to enforcement when behavior moved at announcement |

| Forward engineering from estimand to estimator | Baker et al. (2026) Medicaid | any panel whose units differ enormously in size | reporting the weighted and the unweighted ATT as a robustness pair |

| Estimand first on a heavy-tailed outcome | Winkler et al. (2026) UMG-TikTok | streams, revenue, views, sessions | a log taken for convenience |

| Compositional change in repeated cross-sections | Hong (2013) Napster | brand trackers and refreshed survey panels | who is sampled moves with treatment timing |

| Triple differences | Gruber (1994) | an ineligible segment inside the same treated markets | reading the placebo DiD as a test that has to return zero |

| The idea, not the inference | Card and Krueger (1994) | a two-region holdout test | G = 2 with one treated cluster |

## Triage: three questions before anything else

From Roth, Sant'Anna, Bilinski, and Poe (2023), the most condensed decision object in the

literature:

1. **Is everyone treated at the same time?** Yes: TWFE is fine, static or dynamic, without

covariates; with covariates see Covariates below. For two groups and two periods the

estimator is interaction OLS or the long difference, clustered at the level of assignment.

The identity of interaction OLS, TWFE, and the long difference holds exactly only in that

2x2 with no covariates, and it is what makes people reach for TWFE-with-controls, where it

no longer holds. Everything else in this skill still applies to a 2x2. No (staggered):

default to a heterogeneity-robust estimator; TWFE only if you will defend effect

homogeneity.

2. **Are you sure about parallel trends, and on which scale?** Justify levels vs logs (PT is

functional-form dependent and generally cannot hold in both) and name the estimand the

scale targets (Functional form below). If PT is plausible only conditional on

covariates, use regression adjustment, IPW, or doubly robust, never bare TWFE-with-controls.

Always pair the event study with a Rambachan-Roth sensitivity analysis, a universal mandate

this skill family hardens beyond the canon's best-practice advice because the analysis is

cheap and the pretest is low-powered.

3. **Do you have many treated and untreated clusters?** Yes: cluster at the level at which

treatment is independently assigned. No: pick a few-clusters method by which homogeneity

assumption you believe (references/details.md has the map), or fall back to a cluster-level

Fisher randomization test. Before picking, run the MacKinnon, Nielsen, and Webb (2023)

battery (CV1, CV3 jackknife, and a restricted wild cluster bootstrap side by side):

agreement means stop, disagreement means escalate to the map.

Two exits from DiD entirely, both routed to the synthetic-control skill: only one or a handful

of treated units, or selection on lagged outcomes with autocorrelated errors, where DiD is

inconsistent even as pre-periods grow while SC is consistent (Arkhangelsky and Hirshberg 2023,

Refusal list. In five cases the skill declines the design and routes back to causal-design. A

failed gate is a verdict.

1. Always-treated units carry the estimand and cannot be dropped.

2. No period has an untreated or not-yet-treated comparison unit.

3. Institutional detail documents selection on realized gains: units took the treatment because

they correctly expected it to help them. Clean pre-trends are no defense (see "Why these

units were treated"). causal-design checks whether an instrument for take-up exists (iv).

4. One treated cluster, and none of synthetic-control, Fallback B, or the two rescues on the

map is feasible.

5. Parallel trends fails on every candidate scale (levels, logs, the nonlinear index), and the

synthetic-control exit is infeasible (no credible donors, short pre-period).

## Assumptions and treatment dating

Parallel trends is the assumption this skill argues about. Two others get stated and forgotten,

and both fail silently.

No anticipation: the treated group's outcome is Y(0) until treatment happens. An already-treated

SUTVA: no interference between units, and the treatment is the same thing for every treated

unit. Panel threats are spillover to adjacent control markets, substitution across one firm's

own units, and the announcement-versus-enforcement gap, which makes "announced" and "announced

and enforced" two treatments. Interference contaminates the control group's Y(0), so the

comparison understates the effect or reverses its sign. Buffer or drop adjacent controls, or

model exposure and make the exposure the treatment.

## Estimand before estimator

Weights define the target parameter, not the specification (Baker et al. 2026). An unweighted

ATT answers "effect on the average treated county"; a population-weighted ATT answers "effect on

the average treated person." In the Baker et al. Medicaid 2x2 these are +0.1 and -2.6 deaths per

100,000: different questions, not a robustness check of each other. In marketing panels where

units differ enormously in size (DMAs, stores, channels), decide by the business or policy

question and, if you report both, report them as different estimands.

Write the target in potential-outcomes notation before touching code: which ATT(g,t) cells, and

which aggregation (event-time, calendar-time, overall; cohort-share or population weights).

Callaway-Sant'Anna aggregates the same building blocks four ways: simple, one average over all

feasible group-times; group, ATT(g), the effect on each cohort; calendar, ATT(t), the effect in

each period, which is the target when the question is about a season, a platform change, or a

macro shock; and dynamic, ATT(l), the event study. Those are four parameters, not four

robustness checks, and the feasible (g,t) set shrinks at long horizons, so each covers a

different slice of the data.

Name the aggregation weights too, since they define the reported number. Deb, Norton,

Wooldridge, and Zabel (2025, NBER 34331, `deb2025aggregating`) show that the standard

Callaway-Sant'Anna software weights cells by counts that include observations in the reference

pre-period. The weights are therefore not the counts of treated observations in treated periods

alone. They discuss when this choice moves the aggregate. When the target is the average over

treated unit-periods, aggregate the ATT(g,t) cells yourself with treated-period counts and

report both aggregates (this skill's judgment).

Functional form and weights are estimand choices too (Winkler, Hotz-Behofsits, Wlömert, Papies,

and Liaukonytė 2026). Three parameters get reported as if they were one: the typical-unit

proportional effect ΔΔE[log Y] (log OLS), the population-total proportional effect ΔΔ log E[Y]

(PPML), and the level effect ΔΔE[Y] (levels OLS). Under heavy-tailed outcomes they differ in

magnitude and can differ in sign with no staggered-timing problem anywhere: in the UMG-TikTok

withdrawal, a clean two-group single-date design with 53,753 matched song pairs, unweighted log

OLS gives +0.0063 and PPML gives -0.0310 on the same panel, and reweighting the log OLS toward

the head gives -0.0286 without touching the transformation. Pick the estimand from the question

("did per-user usage rise 5%?" is typical-unit, "did total revenue rise 5%?" is

population-total, "did this add $2M?" is level), then the estimator. Levels-vs-logs is never a

robustness check: an appendix that reports both without naming the estimand each targets is

reporting two parameters as one. The heterogeneity-robust estimator question and the

estimand-scale question are orthogonal, and both get answered.

## The parallel-trends menu and the estimator it implies

State explicitly which PT assumption you impose (Baker et al. 2026 make this a requirement).

Three variants under staggered adoption, with the estimator crosswalk:

| PT variant | Comparison group | Pre-trends restricted? | Estimators | R |

|---|---|---|---|---|

| PT-Nev | never-treated | no | Callaway-Sant'Anna (never), Sun-Abraham | `did::att_gt(control_group="nevertreated")`, `fixest::sunab()` |

| PT-NYT | not-yet-treated | no | Callaway-Sant'Anna (NYT), dCDH instantaneous | `did::att_gt(control_group="notyettreated")` |

| PT-all | all groups, all periods | yes (testable, and baked in) | BJS/Gardner imputation, Liu-Wang-Xu (2024, `liu2024practical`) FEct imputation, Wooldridge ETWFE | `didimputation`, `did2s`, `fect`, `etwfe` |

Sun-Abraham sits under PT-Nev for a reason worth naming at the point of use: its cohort 2x2s use

the last-treated cohort or the never-treated, never the not-yet-treated. Against a CS-NYT default

the `sunab` cross-check in the template therefore compares two assumptions, and neither agreement

nor divergence is a robustness result.

Default: **Callaway-Sant'Anna with not-yet-treated controls**, Baker et al.'s own choice for

their application. That default is licensed by no anticipation among the not-yet-treated: if

their behavior already responds to the treatment they are about to get, they are not clean

controls. Move to never-treated when the not-yet-treateds' timing plausibly responded

to recent outcomes; move to imputation (PT-all) when you will defend parallel pre-trends over

the whole panel and errors are near-serially-uncorrelated, where it buys real efficiency

(Roth et al. 2023). Each move has a price. The never-treated are a subset of the not-yet-treated

pool, so the comparison group shrinks and the bands widen. A never-treated group can also

differ from the treated in levels and in why it never adopted, which makes PT harder to

argue. Imputation buys its efficiency by

assuming PT in every pre-period. A long covariate list is a further reason to move to Wooldridge

ETWFE with covariate interactions, since the CS propensity score is estimated per cohort and with

fifty covariates common support gets hard to assess and harder to defend. Imputation is no route

for covariates: BJS takes them only in levels and does not implement conditional PT

(references/details.md, RA / IPW / DR mechanics). A further price of imputation is that its

event-study plots are not comparable to CS or TWFE plots, because fitting the counterfactual on

the whole pre-period puts a mechanical kink at t = -1, so do not overlay them. If Y(0) is close

to a random walk, the CS last-pre-period baseline is the

efficient choice and imputation's pre-period averaging buys nothing (Harmon's caveat: averaging

is not guaranteed more precise). If PT is implausible for one specific cohort, drop that cohort

rather than average over it.

"Never-treated" operationally means "not treated by the end of the sample." If all units are

eventually treated, drop periods from when the last cohort adopts and use that cohort as the

comparison, and drop units treated in the first period.

## The TWFE question, stated honestly

The same regression is two designs. With an adoption date and units that are never or not-yet

treated, `y ~ treat | unit + period` is a DiD and the assumption is parallel trends. With a

treatment that varies within unit over time and no comparison group at all, the identical

regression is the within estimator and the assumption is strict exogeneity conditional on the

unit effect, non-nested with parallel trends and failing differently (feedback from past

Default here: estimate the robust estimator as the headline number and report TWFE alongside it.

Agreement is affirmative evidence the simple model suffices (AAFP); divergence means

## Event-study mechanics

Hard rules, mostly from Abadie, Angrist, Frandsen, and Pischke (2025):

- Feasible horizons: with panel end T and cohorts c(s), longest lag q = T - min c(s), longest

lead m = max c(s) - 1. Here s indexes units (states in AAFP) and c(s) is unit s's adoption

period, its cohort. The formulas assume periods renumbered 1..T, so calendar years must be

reindexed first.

- Always omit event time -1. The Mixtape gives the reason, that no anticipation requires an

untreated baseline, and stops there (Cunningham, The Mixtape, online ch. 9 sec. 9.5, Eq.

9.25). With never-treated units that single normalization identifies everything. Without them

a second lead or lag must also be omitted, because the linear component of the effect path is

unidentified (Borusyak, Jaravel, and Spiess 2024, `borusyak2024revisiting`, relayed by AAFP).

Different second choices rotate the whole path around -1. Choose deliberately, never let

the software's default drop decide, and show the path under at least two normalizations

before interpreting dynamics.

- Short gaps versus long differences, a hard rule. OLS event studies mechanically use a

universal baseline, so every coefficient is a long difference against t = -1.

Callaway-Sant'Anna and dCDH can produce either, and a rolling baseline gives short gaps, which

estimate a different quantity (Roth 2026). Stata's `csdid` 2.0.0 defaults to

`base_period(universal)`, which gives long differences; on csdid 1.8x pass `long2`, a name

2.0.0 keeps only for compatibility. csdid 2.0.0 also made not-yet-treated units the default

comparison group, where 1.82 used never-treated, so state the group you pass. The `csdid2`

default is unverified. R's `did` needs

`base_period = "universal"`.

Reader-side tell in someone else's paper: a confidence interval at t = -1 means a rolling

baseline, since t = -1 cannot be its own baseline, and the leads top out one period earlier.

- Reading the coefficients out loud. A lead of +1.5 means the treated group's change from that

period to the omitted baseline ran 1.5 outcome units above the control group's. A lag is the

ATT for that period, valid only under PT from the baseline to it, no anticipation, and an

untreated comparison group. Plot disconnected points with whiskers: connecting the bands makes

the intervals appear to narrow toward the omitted period, where nothing was estimated.

- Bin leads and lags beyond the horizon where only a few units identify the coefficient (AAFP

use +/-15 with 41 periods). Clustered SEs fail at long horizons through leverage: a lone late

adopter can identify the longest leads, and coverage collapses.

- Report simultaneous sup-t uniform bands, computed separately for leads and lags, not only

pointwise bands (recipe in references/details.md; the did package produces them by multiplier

bootstrap). Avoid a clustered joint F over many leads. The clustered variance is biased

downward, and the resulting over-rejection grows with the number of restrictions (AAFP, citing

Pustejovsky and Tipton 2018,

`pustejovsky2018small`, and MacKinnon, Nielsen, and Webb 2023). AAFP use individual t tests

with sup-t bands instead.

- Under staggered timing, build the event study from a robust estimator, never from dynamic

TWFE: cross-lag contamination means TWFE lead coefficients can be nonzero under valid PT and

zero under violations (Sun-Abraham, via Roth et al. 2023).

- Check composition: cohorts entering and leaving event times can manufacture dynamics. Use the

balanced-in-event-time aggregation or a fixed cohort set when in doubt.

## Pre-trends and honest sensitivity

## Why these units were treated

## Covariates

Never bare TWFE-with-controls: even in the 2x2 it identifies the ATT only under constant effects

across covariate strata, weights strata non-convexly, and adds three misspecification bias terms

(Caetano-Callaway, via Baker et al. 2026). Choose covariates from theory (determinants of

untreated trends or of selection), and ask domain experts what ordinarily drives untreated

trends in this outcome, since that is the arm of the DAG nobody guesses well. If you select

covariates from the data, run the selection on untreated units only, so only Y(0) informs it

(Borgschulte and Vogler 2020). State the covariate list before you see results: the choice can

swing the estimate and a DAG does not protect against specification search. Check the covariates

are unaffected by treatment (a time-varying covariate is fine only if its whole path is

unaffected). When PT needs a covariate that treatment moves, dropping it is often ill-advised

(Caetano, Callaway, Payne, and Sant'Anna 2026, arXiv 2608.03881, `caetano2026bad`). They give

conditions under which CS with the covariate's pre-treatment values is valid. Under covariate

unconfoundedness they add imputation and double machine learning estimators, extended to

staggered adoption with pretests (R package badcontrols, CRAN 1.0.1). Otherwise use:

- **Doubly robust (default)**: `did::att_gt(est_method="dr")`, Sant'Anna-Zhao. Consistent if

either the outcome-change model or the propensity model is right.

- Regression adjustment when overlap is weak (extrapolates the outcome model; say so).

- IPW when you understand selection better than outcome dynamics; noisy as control propensity

scores approach 1. Histograms and kernel densities do not reveal explosive weights, so count

the control units with a propensity score near 1 directly. In the Mixtape's CAPS data

(Cunningham, The Mixtape, online ch. 10 sec. 10.14) one control municipality scores

0.999971, which is a weight of p/(1-p) = 34,481. Eleven control units sit above 0.995.

Trim at 0.995 and keep the trim. R's did trims automatically

and not every package does, so check what yours does before trusting the estimate.

Conditioning on lagged outcomes changes the identifying assumption from PT to unconfoundedness.

The two are non-nested; matching on lagged outcomes can create mean-reversion bias when groups

differ in levels but genuinely trend in parallel (Daw and Hatfield 2018, `daw2018matching`).

When they disagree, the two estimates bracket the truth. With the treated group above the

controls before treatment, TWFE is too low if unconfoundedness holds. Lagged-outcome adjustment

is too high if PT holds (Arkhangelsky-Imbens 2024, Section 5.6). Ding and Li (2019,

`ding2019bracketing`) prove the bracketing nonparametrically and extend it to inverse

probability weighting. Their abstract states the mirror case for a positive effect. Assuming PT

overestimates if ignorability holds, and assuming ignorability underestimates if PT holds. That

sign matches a treated group below the controls before treatment, the Angrist-Pischke case

(this skill's reading of the abstract; the theorem's sign condition is unconfirmed here).

Report both estimates and say which selection story you believe.

## Triple differences

## Functional form and nonlinear outcomes

## Inference

Cluster at the level at which treatment is independently assigned (state policies: state), the

design-based rule (`rambachan2025design`, the DiD instance of `abadie2023clustering`), and group

fixed effects do not get you out of it. With few treated clusters no method is assumption-free:

the map in references/details.md lists each option with the homogeneity assumption it needs,

which is the selection criterion (Roth et al. 2023). The honest fallbacks are folding the

cluster shock into the HonestDiD violation bound, or a cluster-level Fisher randomization test,

exact under the sharp null when timing is as good as random.

Full argument: ../causal-design/references/shared-rules.md.

counting clusters.

## Beyond the absorbing binary treatment

- Treatments that turn on and off (promotions, price changes): dCDH estimators require

no-carryover; for advertising and pricing that assumption is usually wrong, so check it and

prefer the intertemporal extension (`DIDmultiplegtDYN` in R, `did_multiplegt_dyn` in Stata).

- Continuous treatment intensity: ATT(d|d) is identified under standard PT, but causal-response

parameters need strong PT across doses (Callaway, Goodman-Bacon, Sant'Anna).

- Exposure designs (baseline exposure share times a national change): the linear-interaction

coefficient is an average marginal effect, roughly kappa + 2 phi E[M], not E[tau_s]; add the

squared-exposure interaction when heterogeneity is plausible and report both (AAFP 2025).

- Repeated cross-sections (brand trackers, surveys, transaction data with one row per unit):

## Diagnostics battery

Report with every DiD analysis, in roughly this order. Items 1 to 10 ask whether the estimator

is doing what it claims; 11 to 13 ask whether something other than the treatment produced the

pattern, and 11 runs before any of the rest:

1. Raw group-mean time-series plot (the anatomy plot; it contains every number the estimator

uses) and the ATT(g,t) matrix in calendar and event time.

2. Event study from the robust estimator with sup-t bands, binned horizons, deliberate

normalization.

3. Sup-t joint pretest of the leads, plus its power against a relevant violation (pretrends).

4. HonestDiD identified set, robust CI, breakdown M-bar, economic reading.

5. Covariate balance as normalized differences, levels and pre-period changes; flag |nd| > 0.25

(0.1 if the covariate is known to matter). A change-imbalance reads as a PT violation only if

the covariate is strictly exogenous.

6. Propensity overlap plot when covariates enter.

7. TWFE alongside the robust estimator; if they diverge, Goodman-Bacon decomposition

(bacondecomp) and dCDH negative-weight diagnostics (TwoWayFEWeights) to show why. Run the

weight diagnostics to explain a divergence, never as a standing robustness table, and do not

read all-positive Bacon weights as a licence for TWFE.

8. Building-block heterogeneity scan by cohort, gap, and time since adoption.

9. Composition checks: balanced event time, fixed cohort set.

10. Outcome concentration (Lorenz, Gini, top-decile share) and the estimand each reported

specification targets; the Ciani-Fisher variance-shift regression whenever a log outcome

is reported; the Roth-Sant'Anna functional-form check when the transformation is

contestable; for nonlinear models, the event study on the index scale.

11. Bite: evidence that the treatment changed the thing it was supposed to change.

13. Mechanism: why the effect happened, and evidence consistent with that story.

## R implementation

The complete runnable pipeline is scripts/did_template.R: estimation, both HonestDiD

restrictions with the official adapter included verbatim, pretest power, TWFE and Sun-Abraham

cross-checks, divergence diagnostics, imputation, the efficient random-timing estimator, and

balance. Call signatures were verified on 2026-07-28, and sections 8b and 8c on 2026-10-08

(the template header records that run).

The core, with the two settings that are easy to get wrong:

```r

library(did)

atts <- att_gt(yname = "y", tname = "period", idname = "unit",

gname = "first_treated", # 0 = never-treated (did's convention)

xformla = NULL, # or ~ x1 + x2 for conditional PT

control_group = "notyettreated", # states the PT variant you impose

est_method = "dr", clustervars = "cluster",

base_period = "universal", # long differences, not short gaps (Roth 2026);

# the honest_did chain also requires it

data = df)

es <- aggte(atts, type = "dynamic", min_e = -15, max_e = 15, cband = TRUE)

```

Cross-package traps the script handles explicitly: never-treated is coded 0 in did and

didimputation, Inf in staggered, and any out-of-range value in fixest::sunab, so one recycled

cohort variable silently misclassifies units; aggte's default type is "group", so event studies

need type = "dynamic"; pretrends installs from GitHub only. Package links live in

references/details.md.

Nonlinear outcomes and repeated cross sections (template section 11; etwfe 0.6.2, signatures

verified against the reference pages and source on 2026-08-26):

```r

library(etwfe)

nl <- etwfe(fml = y ~ 0, tvar = period, gvar = first_treated, data = df,

cgroup = "notyet", family = "poisson", # or "logit"; lags-only version

vcov = ~cluster) # no ivar: a nonlinear family forces ivar = NULL,

# cohort and period enter as explicit dummies, and

# nothing unit-level is used, so repeated cross

# sections run unchanged

emfx(nl, type = "event") # ATT by exposure time, response scale (APEs)

ll <- etwfe(fml = y ~ 0, tvar = period, gvar = first_treated, data = df,

cgroup = "never", family = "poisson", vcov = ~cluster)

emfx(ll, type = "event", predict = "link") # leads and lags on the index scale

```

Stata equivalents on request: csdid, did_imputation, eventstudyinteract, jwdid, honestdid, boottest

for wild bootstrap, ppmlhdfe for PPML, and jwdid with `method(poisson|logit)` for the nonlinear

recipe (no `ivar` means repeated cross-section; covariates are demeaned by default). The Baker et

al. AEA replication package (aeaweb.org/articles/materials/25430, 25431) is a full R and Stata

template.

Python route: `moderndid` (PyPI 0.2.0) and `diff-diff` (PyPI 3.12.0) both implement

Callaway-Sant'Anna and HonestDiD (PyPI pages checked 2026-10-09). Neither has been run against

this template, so reproduce one headline number in R before relying on either.

## Methods paragraph template

Report each effect with the results sentence in ../causal-design/references/shared-rules.md

(section "Results sentence"): magnitude, direction, a benchmark, and the calibration vocabulary.

Adapt, keeping the first-person limitation at the point of the choice:

> Treatment is staggered and effects are plausibly heterogeneous, so static and dynamic two-way

> fixed effects estimands can place negative weights on some group-time effects (de

> Chaisemartin and D'Haultfoeuille 2020; Sun and Abraham 2021 for the dynamic case; Roth,

> Sant'Anna, Bilinski, and Poe 2023). Following the forward-engineering

> approach of Baker, Callaway, Cunningham, Goodman-Bacon, and Sant'Anna (2026), I define the

> target as [unit/person-weighted] group-time ATTs and their event-study aggregation on the

> [level / log-mean / mean-log] scale, which is the [level / population-total proportional /

> typical-unit proportional] effect the research question asks for (Winkler, Hotz-Behofsits,

> Wlömert, Papies, and Liaukonytė 2026) [or, for a binary outcome, on the log-odds index

> (Wooldridge 2023, 2026)], impose parallel trends with respect to [not-yet-treated] units

> [conditional on X] on that scale, and estimate with [the doubly robust procedure of

> Callaway and Sant'Anna (2021) / pooled Poisson or logit quasi-maximum likelihood with

> cohort-by-period treatment effects (Wooldridge 2023, 2026)], reporting uniform confidence

> bands. I assess sensitivity to parallel-trends violations following Rambachan and Roth (2023):

> bounding post-treatment violations by the largest pre-treatment trend difference ([value])

> gives an identified set of [set] and a robust confidence interval of [CI]; the conclusion

> survives violations up to M-bar = [breakdown]. A limitation of this design is [the specific

> PT variant imposed / the few treated clusters / the transformation choice], which costs

> [what it costs]; I address it by [sensitivity/fallback]. Standard errors are clustered at the

> [level], the level at which treatment is independently assigned (Abadie, Athey, Imbens, and

> Wooldridge 2023), with G = [n] clusters, [G1] of them treated, and cluster sizes from [min] to

> [max] (median [m]).

Every claim in the paragraph must trace to a canon entry; references/canon.md maps claims to

papers and BibTeX keys in the shared ../causal-design/references/causal.bib. Verify any primary

paper cited beyond the canon with bibcheck before submission.

## Handoffs

- causal-design: design triage before this skill; shared inference material.

- synthetic-control: few treated units, long pre-period, selection on lagged outcomes, failed

pretests ("sidesteps collinearity concerns while allowing for divergent nonlinear trends",

AAFP citing Abadie 2021). Synthetic DiD is that skill's bridge topic, not this one's. A

levels SDID inherits the baseline-gap sensitivity of levels DiD (Winkler et al. 2026), so the

scale question travels with the handoff.

- field-experiment: owns randomized staggered rollouts (stepped wedge), where the adoption

dates were randomized and inference is design-based. This skill documents the estimator

for randomized timing (R package staggered, Roth and Sant'Anna 2023, `roth2023efficient`).

- Machine-coded variables: an outcome or treatment coded by an LLM or a classifier (sentiment of

reviews, topics of posts, labels on images). The DiD design stays here, and the measurement

correction is added to it: prediction-powered inference on a gold-standard subsample for

a coded outcome, DSL or Battaglia et al. 2025 for a coded treatment

(../causal-design/references/shared-rules.md).

- iv: share-balance pre-trend scrutiny for shift-share exposure designs lands here; the

parallel-trends toolkit applies to share balance.

- rdd: policy-date designs masquerading as RD in time arrive here when many units switch at a

date; treat the date as an event study, not a cutoff.

- Preregistration: the user writes it themselves; this skill supplies the DiD field list for a known upcoming natural experiment.