README.md

In NonlinearDiD: Staggered Difference-in-Differences with Nonlinear Outcomes

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.

License

MIT © 2026 Subir Hait

NonlinearDiD documentation built on May 6, 2026, 1:06 a.m.