diddesign

Double Difference-in-Differences for Python

Overview

diddesign implements the Double Difference-in-Differences estimator proposed by Egami and Yamauchi (2023, Political Analysis). The method addresses a practical question in observational panel studies: when multiple pre-treatment periods are available, how should an analyst exploit them to strengthen causal inference?

The standard DID estimator requires parallel trends between the last pre-treatment period and the post-treatment period. The sequential DID (sDID) estimator requires the weaker parallel trends-in-trends assumption but uses an additional pre-treatment period. These two assumptions are logically distinct—neither implies the other. The Double DID formulates a GMM problem that combines both estimators with variance-minimizing weights. When both identification conditions hold, the combined estimate achieves lower variance than either component alone; when only one holds, the framework remains consistent under that condition.

The package extends to K-DID (Appendix E of the paper): given K ≥ 3 pre-treatment periods, higher-order transformed-outcome estimators provide additional moment conditions that permit up to (K−1)-degree polynomial time-varying confounding, combined via the same GMM weighting. A J-test moment-selection step adaptively discards misspecified components.

For staggered-adoption designs, the package computes lead-specific SA-DID, SA-sDID, and SA-Double-DID (or SA-K-DID) estimates and aggregates them into a time-weighted average treatment effect.

Identification Assumptions

The Double DID framework rests on two assumptions about the counterfactual trend structure:

Assumption	Formal Name	Permitted Bias
A1	Parallel Trends	Constant between groups
A2	Parallel Trends-in-Trends	Linear change between groups

Standard DID requires A1. Sequential DID requires A2. The Double DID requires only that at least one of A1 or A2 holds—a strictly weaker condition than either assumption alone. With K ≥ 3 pre-treatment periods, K-DID adds higher-order assumptions that accommodate polynomial confounding.

The identifying relationship is:

Extended Parallel Trends
        ↓ implies both
   ┌────┴────┐
   ↓         ↓
Standard    Parallel
Parallel    Trends-in-
Trends      Trends

Installation

pip install diddesign

Visualization support (matplotlib):

pip install "diddesign[plot]"

Requirements: Python ≥ 3.12, NumPy ≥ 1.26, pandas ≥ 2.2.

Usage

The package provides three entry points:

• did() fits a DID or staggered-adoption design and returns a DidResult.
• did_check() computes pre-treatment diagnostics and returns a DidCheckResult.
• DidResult provides table-ready accessors (to_dataframe(), to_weights_frame(), to_gmm_frame(), to_latex()).

The Double DID workflow proceeds in two steps: first assess the plausibility of identification assumptions via pre-treatment diagnostics, then estimate treatment effects conditional on those diagnostics.

Step 1: Assess Pre-treatment Assumptions

from diddesign.data import data
from diddesign import did_check

df = data("malesky2014")

check = did_check(
    data=df, outcome="pro4", treatment="treatment",
    time="year", post="post_treat", data_type="rcs",
    id_cluster="id_district", lag=[1], n_boot=50, random_seed=1234,
)
print(check.to_summary_frame())

Output:

   lag  estimate_raw  std_error_raw  eqci95_lb_std  eqci95_ub_std
0    1      -0.00337       0.041026      -0.163403       0.163403

The placebo estimates test whether the DID and sDID estimators yield approximately zero effects in pre-treatment periods where no effect should exist. The equivalence confidence interval (reported in units of baseline control-group standard deviations) provides positive evidence for approximate parallel trends when it excludes substantively large deviations. No universal cutoff exists; researchers must apply domain knowledge.

Step 2: Estimate Treatment Effects

from diddesign import did

result = did(
    df, outcome="pro4", treatment="treatment",
    time="year", post="post_treat", data_type="rcs",
    id_cluster="id_district", n_boot=200, random_seed=1234,
)
print(result.to_dataframe())
print(result.to_latex(caption="Recentralization Effect on Pro4"))

Output:

    estimator  lead  estimate  std_error     ci_lo     ci_hi    weight
0  Double-DID     0  0.076596   0.046146 -0.013849  0.167041       NaN
1         DID     0  0.079314   0.057338 -0.033066  0.191694  1.806658
2        sDID     0  0.082684   0.089100 -0.091949  0.257317 -0.806658

\begin{table}[htbp]
\centering
\caption{Recentralization Effect on Pro4}
\begin{tabular}{llrrrr}
\hline\hline
Estimator & Lead & Estimate & Std. Error & CI Low & CI High \\
\hline
Double-DID & 0 & 0.0766$^{*}$ & 0.0461 & -0.0138 & 0.1670 \\
DID & 0 & 0.0793 & 0.0573 & -0.0331 & 0.1917 \\
sDID & 0 & 0.0827 & 0.0891 & -0.0919 & 0.2573 \\
\hline\hline
\multicolumn{6}{l}{\footnotesize Note: $^{*}$p$<$0.10, $^{**}$p$<$0.05, $^{***}$p$<$0.01} \\
\end{tabular}
\end{table}

The output reports three rows: Double-DID (the GMM-optimal combination), DID, and sDID. The GMM weights indicate which component the data favor—when w_DID ≈ 1, standard DID dominates; when w_sDID ≈ 1, the sequential component dominates.

Staggered Adoption

import numpy as np
from diddesign.data import data
from diddesign import did, did_check

df = data("paglayan2019")
df["log_expenditure"] = np.log(df["pupil_expenditure"] + 1.0)

# Diagnose pre-trends across multiple lags
check = did_check(
    data=df, outcome="log_expenditure", treatment="treatment",
    time="year", unit_id="state", design="sa",
    lag=[1, 2, 3], thres=1, n_boot=50, random_seed=1234,
)
print(check.to_summary_frame())

# SA-Double-DID estimation
result = did(
    df, outcome="log_expenditure", treatment="treatment",
    time="year", unit_id="state", design="sa",
    thres=1, n_boot=200, random_seed=1234,
)
print(result.to_dataframe())

Output:

   lag  estimate_raw  std_error_raw  eqci95_lb_std  eqci95_ub_std
0    1     -0.002669       0.009736      -0.117499       0.117499
1    2     -0.012447       0.007841      -0.151357       0.151357
2    3      0.002269       0.011331      -0.121691       0.121691

       estimator  lead  estimate  std_error     ci_lo     ci_hi    weight
0  SA-Double-DID     0  0.011401   0.012157 -0.011430  0.033800       NaN
1         SA-DID     0  0.010984   0.012247 -0.011420  0.034097  0.843723
2        SA-sDID     0  0.013653   0.014537 -0.014634  0.042717  0.156277

K-DID with J-test Moment Selection

When three or more pre-treatment periods are available, K-DID exploits higher-order moment conditions. The J-test adaptively removes components whose identifying assumptions appear violated.

result = did(
    df, outcome="log_expenditure", treatment="treatment",
    time="year", unit_id="state", design="sa",
    kmax=3, jtest=True, thres=1,
    n_boot=200, random_seed=1234,
)
print(result.to_dataframe())

Output:

   estimator  lead  estimate  std_error     ci_lo     ci_hi weight
0   SA-K-DID     0  0.011685   0.012156 -0.011180  0.034105   None
1     SA-DID     0  0.010984   0.012247 -0.011420  0.034097   None
2    SA-sDID     0  0.013653   0.014537 -0.014634  0.042717   None
3  SA-kDID-3     0  0.003875   0.023613 -0.040192  0.052995   None

Covariates and Interactions

The package supports continuous covariates, factor() categorical encoding, and x1:x2 interaction terms (or x1*x2 for main effects plus interaction):

result = did(
    data, outcome="y", treatment="treat", time="time",
    unit_id="unit", covariates=["x1*x2", "factor(region)"],
    n_boot=50, random_seed=55,
)

Visualization

from diddesign import plot_estimates, plot_diagnostics

plot_estimates(result, check_fit=check,
              title="Double DID Estimates", save="estimates.png", show=False)

plot_diagnostics(check, result=result,
                 title="Pre-treatment Diagnostics", save="diagnostics.png",
                 show=False)

Methodology

The Double DID estimator combines DID (τ̂_DID) and sequential DID (τ̂_sDID) using efficient GMM weights:

$$ \hat{\tau}{DDID} = w{DID} \cdot \hat{\tau}{DID} + w{sDID} \cdot \hat{\tau}_{sDID} $$

where the weights minimize asymptotic variance:

$$ w = \frac{\Sigma^{-1} \mathbf{1}}{\mathbf{1}' \Sigma^{-1} \mathbf{1}} $$

and Σ is the bootstrap covariance matrix of (τ̂_DID, τ̂_sDID)'. Under the extended parallel trends assumption:

$$ \text{Var}(\hat{\tau}{DDID}) \leq \min{\text{Var}(\hat{\tau}{DID}),; \text{Var}(\hat{\tau}_{sDID})} $$

Standard errors and confidence intervals are obtained via a nonparametric bootstrap (cluster bootstrap when id_cluster is specified). The bootstrap covariance matrix Σ̂ determines the GMM-optimal weights, and percentile or normal-approximation intervals are reported depending on the design.

For K-DID, the K-dimensional generalization combines all K component estimators via the K×K bootstrap covariance, with the J-test providing a model-selection step that excludes moments whose overidentification statistic rejects.

API Reference

Core Functions

Function	Purpose
did()	Fit DID or staggered-adoption design →DidResult
did_check()	Pre-treatment diagnostics →DidCheckResult
summary()	Formatted summary of fitted result
fit(..., as_frame=True)	Event-time plotting rows
check(..., as_frame=True)	Diagnostic plotting rows

did() Parameters

did(data, *, formula=None, outcome=None, treatment=None, time,
    unit_id=None, post=None, design="did", data_type="panel",
    covariates=None, lead=0, thres=None, n_boot=30, se_boot=None,
    level=95, id_cluster=None, random_seed=None, parallel=False,
    n_cores=None, parallel_backend="thread", worker_timeout=None,
    verbose=1, kmax=2, jtest=False)

Parameter	Type	Default	Description
data	DataFrame	—	Input data (panel or repeated cross-section)
formula	str| None	None	R-style formula, e.g."y ~ treat"
outcome	str| None	None	Outcome column name (alternative to formula)
treatment	str| None	None	Treatment indicator column
time	str	—	Time period column (required)
unit_id	str| None	None	Unit identifier column (required for panel)
post	str| None	None	Post-treatment indicator (required for RCS)
design	str	"did"	"did" for standard or "sa" for staggered adoption
data_type	str	"panel"	"panel" or "rcs" (repeated cross-section)
covariates	list[str]| None	None	Covariate terms:"x1", "factor(x2)", "x1:x2", "x1*x2"
lead	int| list[int]	0	Lead(s) for staggered adoption
thres	int| None	None	Minimum observations threshold
n_boot	int	30	Number of bootstrap replications
se_boot	bool| None	None	Use bootstrap percentile CI
level	int	95	Confidence level (50–99)
id_cluster	str| None	None	Cluster variable for clustered bootstrap
random_seed	int| None	None	Seed for reproducibility
parallel	bool	False	Enable parallel bootstrap computation
n_cores	int| None	None	Number of cores (default: all available)
kmax	int	2	Maximum DID order: 2 = Double DID, ≥ 3 = K-DID
jtest	bool	False	Apply J-test moment selection for K-DID

Returns: DidResult

did_check() Parameters

did_check(*, data=None, formula=None, outcome=None, treatment=None,
          time=None, unit_id=None, post=None, design="did",
          covariates=None, data_type="panel", id_cluster=None,
          lag=1, thres=None, n_boot=30, random_seed=None,
          verbose=1)

All parameters are keyword-only. Parameters shared with did() have identical semantics. The lag parameter specifies which pre-treatment lag(s) to test.

Returns: DidCheckResult

Result Objects

DidResult is an immutable object returned by did(). It provides frame accessors for downstream analysis:

result.to_dataframe()           # Estimates as DataFrame
result.to_estimates_frame()     # Alias
result.to_bootstrap_frame()     # Bootstrap draws (iterations × components)
result.to_weights_frame()       # GMM weight rows by lead
result.to_gmm_frame()          # Full GMM calculation rows
result.to_k_weights_frame()    # K-dimensional GMM weights (K-DID)
result.to_latex()              # LaTeX table string
result.to_serialized_result()  # Serializable dict for export

DidCheckResult is an immutable object returned by did_check():

check.to_summary_frame()   # Placebo test summary
check.to_placebo_frame()   # Placebo plotting rows
check.to_trends_frame()    # Trend comparison rows
check.to_pattern_frame()   # SA pattern rows
check.named_plot_rows()    # Named plotting records

Each row in the GMM frame is a DidGmmRow containing the covariance entries, weights, and GMM variance for a single lead. The diagnostic result provides DidCheckResult.named_plot_rows() for downstream figure production.

For scripts that need a detached serialized record, DidResult and DidCheckResult provide to_serialized_result(). New reporting code should usually start from the frame accessors above because those preserve the table rows used in the manuscript.

Data Loading

from diddesign.data import data

df = data("malesky2014")    # Vietnam RCS (Malesky et al. 2014)
df = data("paglayan2019")   # US states panel (Paglayan 2019)

Visualization Functions

All plotting functions require diddesign[plot] (matplotlib).

Function	Input	Description
plot_estimates(result, ...)	DidResult	Event-study plot with optional placebo overlay
plot_trends(check_result, ...)	DidCheckResult	Pre-treatment trend comparison
plot_placebo(check_result, ...)	DidCheckResult	Placebo estimate plot
plot_pattern(check_result, ...)	DidCheckResult	Staggered-adoption pattern diagnostic
plot_diagnostics(check_result, ...)	DidCheckResult	Multi-panel diagnostic figure

Errors

diddesign provides structured exceptions with machine-readable error codes (E001–E020) and diagnostic context dictionaries:

from diddesign.errors import DidValueError, ErrorCode

try:
    result = did(data=df, outcome="y", treatment="bad_col", time="t", unit_id="id")
except DidValueError as e:
    print(e.code)     # ErrorCode.E001
    print(e.context)  # {'field_name': 'treatment', ...}

Full parameter documentation is available in the Sphinx API reference. To build docs locally: cd Docs && sphinx-build -b html . _build/html.

Citation

If you use this package in your research, please cite both the software and the methodology paper:

APA Format:

Cai, X. & Xu, W. (2026). diddesign: Python package for Double Difference-in-Differences estimation (Version 0.1.4) [Computer software]. GitHub. https://github.com/gorgeousfish/diddesign-py

Egami, N., & Yamauchi, S. (2023). Using Multiple Pretreatment Periods to Improve Difference-in-Differences and Staggered Adoption Designs. Political Analysis, 31(2), 195-212. https://doi.org/10.1017/pan.2022.8

Authors:

• Xuanyu Cai, University of Macau, xuanyuCAI@outlook.com
• Wenli Xu, City University of Macau, wlxu@cityu.edu.mo

BibTeX:

@software{diddesign2026python,
  title={diddesign: Python package for Double Difference-in-Differences estimation},
  author={Cai, Xuanyu and Xu, Wenli},
  year={2026},
  version={0.1.4},
  url={https://github.com/gorgeousfish/diddesign-py}
}

@article{egami2023using,
  title={Using Multiple Pretreatment Periods to Improve Difference-in-Differences and Staggered Adoption Designs},
  author={Egami, Naoki and Yamauchi, Soichiro},
  journal={Political Analysis},
  volume={31},
  number={2},
  pages={195--212},
  year={2023},
  doi={10.1017/pan.2022.8}
}

Authors

Python Implementation:

• Xuanyu Cai, University of Macau Email: xuanyuCAI@outlook.com
• Wenli Xu, City University of Macau Email: wlxu@cityu.edu.mo

Methodology:

• Naoki Egami, Columbia University
• Soichiro Yamauchi, Harvard University

See Also

• R package by Egami & Yamauchi: DIDdesign
• Stata package: diddesign
• Paper: 10.1017/pan.2022.8

License

GPL-2.0. See LICENSE for details.