NonlinearDiD

Staggered Difference-in-Differences with Nonlinear Outcomes

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The Problem

The Callaway & Sant'Anna (2021) framework for staggered DiD is hugely influential — but it assumes continuous outcomes with linear parallel trends.

For binary outcomes (employed/not, hospitalized/not, defaulted/not), this creates fundamental problems:

Problem	Why it matters
Scale sensitivity	Parallel trends in P(Y=1) ≠ parallel trends in log-odds. Pre-trends can appear flat or steep depending on the scale.
Jensen's inequality	Treatment effects on probability scale mix the "real" effect with curvature of the CDF.
Heterogeneous baseline rates	Units with different baseline probabilities will show "spurious" violations of parallel trends even under no treatment effect.

NonlinearDiD solves all three by extending the CS2021 framework to properly handle logit, probit, Poisson, and negative binomial outcome models.

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Installation

# CRAN
install.packages("NonlinearDiD")

# GitHub (development version)
remotes::install_github("causalfragility-lab/NonlinearDiD")

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Quick Start

library(NonlinearDiD)

# 1. Simulate staggered binary panel data
dat <- sim_binary_panel(n = 500, nperiods = 8, n_cohorts = 3,
                        prop_treated = 0.5, true_att = 0.25, seed = 42)

# 2. Estimate ATT(g,t) with logistic outcome model
res <- nonlinear_attgt(
  data          = dat,
  yname         = "y",
  tname         = "period",
  idname        = "id",
  gname         = "g",
  xformla       = ~ x1 + x2,      # covariates
  outcome_model = "logit",         # logit / probit / poisson / negbin
  estimand      = "att",           # att / odds_ratio / ape
  control_group = "nevertreated",  # nevertreated / notyetreated
  doubly_robust = TRUE             # doubly-robust estimator
)

# 3. Aggregate into event-study
agg <- nonlinear_aggte(res, type = "dynamic")
plot(agg)

# 4. Pre-treatment parallel trends test
nonlinear_pretest(res)

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Key Functions

Function	Description
nonlinear_attgt()	Main engine: estimates ATT(g,t) for all cohort × time cells
nonlinear_aggte()	Aggregates ATT(g,t) into event-study, group, calendar, or overall ATT
nonlinear_pretest()	Tests pre-treatment parallel trends (joint + individual + HonestDiD)
binary_did_logit()	Simple 2×2 DiD with logistic outcome
binary_did_probit()	Simple 2×2 DiD with probit outcome
binary_did_dr()	Doubly-robust binary DiD
count_did_poisson()	Poisson QMLE DiD for count outcomes (Wooldridge 2023)
odds_ratio_did()	Odds-ratio DiD estimator
nonlinear_bounds()	Nonparametric Manski/PT bounds
sim_binary_panel()	Simulate binary panel data for testing
sim_count_panel()	Simulate count panel data for testing

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Estimands

• ATT (estimand = "att"): Average treatment effect on the treated, on the linear probability / log-odds / log-count scale depending on outcome_model.
• APE (estimand = "ape"): Average partial effect on the probability scale (for logit/probit) — what practitioners usually want.
• Odds-ratio (estimand = "odds_ratio"): Multiplicative odds ratio DiD; invariant to group labeling; natural for 2×2 tables.

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Methods Reference

Outcome Models

outcome_model	Parallel Trends Assumption	Outcome Type
"logit"	Parallel in log-odds	Binary (0/1)
"probit"	Parallel in probit index	Binary (0/1)
"poisson"	Parallel in log-count	Count (≥ 0)
"negbin"	Parallel in log-count	Overdispersed count
"linear"	Parallel in mean (LPM)	Continuous / binary

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References

• Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-differences with multiple time periods. Journal of Econometrics, 225(2), 200–230.

• Roth, J., & Sant'Anna, P. H. C. (2023). When is parallel trends sensitive to functional form? Econometrica, 91(2), 737–747.

• Wooldridge, J. M. (2023). Simple approaches to nonlinear difference-in-differences with panel data. The Econometrics Journal, 26(3), 31–66.

• Sant'Anna, P. H. C., & Zhao, J. (2020). Doubly robust difference-in-differences estimators. Journal of Econometrics, 219(1), 101–122.

• Manski, C. F. (1990). Nonparametric bounds on treatment effects. American Economic Review, 80(2), 319–323.

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Contributing

This package addresses an active research frontier. Contributions, bug reports, and methodological suggestions are welcome — please open an issue or pull request on GitHub.

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License

MIT © 2026 Subir Hait