NonlinearDiD

Staggered Difference-in-Differences with Nonlinear Outcomes

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.

Installation

# CRAN
install.packages("NonlinearDiD")

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

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)

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

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.

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

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.

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.