Sensitivity to parallel trends — Rambachan & Roth (2023)

Parallel trends is an assumption, not a fact. Rambachan & Roth (2023) answer the practical question: how wrong could parallel trends be before my post-treatment conclusion flips? StatsPAI wires their tooling directly into every event-study object in the library.

Functions

Function	Purpose
sp.honest_did(result, e, m_grid=None, method='smoothness')	Robust CI at event time e across a grid of violation magnitudes M
sp.breakdown_m(result, e, method='smoothness')	Largest M* at which the effect remains significant

Both functions are polymorphic: they accept

• a callaway_santanna() result (event study in model_info),
• a sun_abraham() result,
• or an aggte(type='dynamic') result (event study in detail with Mammen uniform bands).

Typical pipeline

cs  = sp.callaway_santanna(df, y='y', g='g', t='t', i='id')
es  = sp.aggte(cs, type='dynamic', n_boot=500, random_state=0)
s   = sp.honest_did(es, e=1)          # robust CI table across M grid
mst = sp.breakdown_m(es, e=1)         # scalar breakdown value

Restriction types

• method='smoothness' — bounds \(|\Delta \delta_t| \le M\) for every consecutive pair of periods (Δ^SD(M)). The M parameter has units of the outcome per period.
• method='relative_magnitude' — post-period violation bounded as M̄ × max|δ_pre|. Useful when you want to express the sensitivity relative to the magnitude of the observed pre-trend violations.

One-shot via cs_report()

The cs_report report card already runs breakdown_m at every post-treatment event time and stores the results in rpt.breakdown. Column robust_at_1_SE flags whether the effect survives a violation equal to one pointwise standard error.

For Agents

Pre-conditions - data is panel or repeated cross-section with a time column - treat column is binary (0/1) for 2x2, or first-treatment-period (int) for staggered - at least one pre-treatment period (≥ 2 periods for 2x2; ≥ 3 recommended for event study) - for staggered designs: id column identifying units across time

Identifying assumptions - Parallel trends: treated and control groups would have followed the same trajectory absent treatment - No anticipation: outcomes in pre-treatment periods are unaffected by future treatment - SUTVA: no spillovers between units - For staggered / heterogeneous effects: use CS or SA — TWFE can produce negative weights (Goodman-Bacon)

Failure modes → recovery

Symptom	Exception	Remedy	Try next
Pre-trend joint test p < 0.05 (or underpowered at 0.10)	AssumptionViolation	Use sp.sensitivity_rr (Rambachan & Roth honest CI) or switch to sp.callaway_santanna.	sp.sensitivity_rr
Staggered treatment timing with TWFE method	AssumptionWarning	TWFE can give negative weights; use Callaway-Sant'Anna, Sun-Abraham, or BJS imputation.	sp.callaway_santanna
Pre-trend test underpowered (Roth 2022)	AssumptionWarning	Check sp.pretrends_power — if low, report honest CI via sp.sensitivity_rr.	sp.sensitivity_rr
Few clusters at unit level	AssumptionWarning	Use wild cluster bootstrap (sp.wild_cluster_bootstrap).	sp.wild_cluster_bootstrap

Alternatives (ranked) - sp.callaway_santanna - sp.sun_abraham - sp.did_imputation - sp.sdid - sp.synth

Typical minimum N: 50