hddid

High-Dimensional Doubly Robust Difference-in-Differences

Overview

hddid implements the high-dimensional doubly robust difference-in-differences estimator of Ning, Peng, and Tao (2020). One call to fit_hddid(...) runs cross-fitted nuisance estimation, constructs the doubly robust score, solves the partially-linear sieve regression, and returns an HDDIDFit object containing all intermediate payloads and the user-facing result. Parametric debiased inference (Eq. 4.1–4.2) and nonparametric uniform bands (Eq. 4.3) attach to the same object as explicit follow-up calls.

Requirements

Requirement	Description
Python 3.10+	NumPy, SciPy, and PyYAML are required at runtime.
NumPy ≥ 1.24	Core array computation.
SciPy ≥ 1.10	Optimization and linear algebra backends.
PyYAML ≥ 6.0	Configuration parsing.
scikit-learn	Optional; enables the solver="sklearn" Lasso backend.
pandas	Optional; enables HDDIDFit.from_dataframe(...).
Data format	NumPy arrays: outcomes y0/y1 (shape n), treatment treat (0/1), covariates x (shape n × p), scalar variable z (shape n).

Installation

From PyPI

pip install hddid

Development install

git clone https://github.com/gorgeousfish/hddid-py.git
cd hddid-py
pip install -e ".[dev]"

Quick Start

import numpy as np
from hddid import fit_hddid

rng = np.random.default_rng(42)
n_obs = 30
x = rng.normal(size=(n_obs, 2))
z = rng.normal(size=n_obs)
treat = np.array([0, 1] * 15, dtype=int)
rng.shuffle(treat)
y0 = rng.normal(scale=0.1, size=n_obs)
y1 = (
    y0
    + 0.2
    + 0.4 * x[:, 0]
    - 0.2 * x[:, 1]
    + 0.3 * z
    + rng.normal(scale=0.05, size=n_obs)
)

fit = fit_hddid(
    y0=y0,
    y1=y1,
    treat=treat,
    x=x,
    z=z,
    z0=np.array([-0.5, 0.0, 0.5]),
    basis_family='polynomial',
    basis_degree=1,
    n_folds=3,
    random_state=1,
    trim_lower=0.0,
    trim_upper=1.0,
    penalty_lambda=0.01,
)

print(fit.to_markdown())

Output:

| Section | Name | Index | Estimate | Std. Error | Interval |
|---|---|---:|---:|---:|---|
| **Parametric** | β̂ | 0 | 0.0347 | — | — |
|  | β̂ | 1 | 0.0341 | — | — |
| **Nonparametric** | γ̂ | 0 | 0.0018 | — | — |
|  | γ̂ | 1 | 0.0064 | — | — |
|  | f̂(z₀) | 0 | -0.0014 | — | — |
|  | f̂(z₀) | 1 | 0.0018 | — | — |
|  | f̂(z₀) | 2 | 0.0050 | — | — |

Diagnostics
  Basis: polynomial(1)
  Oracle lane: r-parity-polynomial
  Sample: holdout=30, trimmed=0, valid=30
  Trim: [0.0000, 1.0000]
  Folds: 3

API Reference

fit_hddid

from hddid import fit_hddid

fit = fit_hddid(
    *,
    y0,
    y1,
    treat,
    x,
    z,
    z0,
    basis_family="polynomial",
    basis_degree=1,
    alpha=0.1,
    n_folds=2,
    random_state=0,
    trim_lower=0.01,
    trim_upper=0.99,
    penalty_lambda=0.0,
    max_iter=10_000,
    tol=1e-10,
    n_jobs=1,
    solver="sklearn",
)

Required Parameters

Parameter	Type	Description
y0	array-like (n,)	Pre-treatment outcome vector.
y1	array-like (n,)	Post-treatment outcome vector.
treat	array-like (n,)	Binary treatment indicator (1 = treated, 0 = control).
x	array-like (n, p)	High-dimensional covariate matrix.
z	array-like (n,)	Scalar nonparametric variable entering the sieve component.
z0	float or array-like	Evaluation grid point(s) at which f(z₀) is estimated.

Optional Parameters

Parameter	Default	Description
basis_family	"polynomial"	Sieve basis family. One of "polynomial", "trigonometric", or "bspline".
basis_degree	1	Degree (order) of the sieve basis expansion.
alpha	0.1	Significance level for confidence intervals.
n_folds	2	Number of cross-fitting folds.
random_state	0	Seed for fold assignment. Use None for non-deterministic splits.
trim_lower	0.01	Lower propensity score trimming threshold.
trim_upper	0.99	Upper propensity score trimming threshold.
nuisance_payload	None	Pre-computed nuisance estimates; skips cross-fitting when provided.
oracle_lane	None	Computational lane identifier for R-parity verification.
nuisance_estimator	None	Custom nuisance estimator implementing .fit() / .predict().
penalty_lambda	0.0	L1 penalty on parametric coefficients. Set to "auto" for rate-optimal choice.
max_iter	10_000	Maximum coordinate-descent iterations for the Lasso solver.
tol	1e-10	Convergence tolerance for coordinate descent.
n_jobs	1	Number of parallel jobs for cross-fit fold processing.
solver	"sklearn"	Solver backend: "sklearn" (scikit-learn Lasso) or "builtin" (pure-NumPy).

Return Object: HDDIDFit

Attribute	Type	Description
data	ValidatedHDDIDData	Validated inputs and basis configuration.
crossfit_plan	`CrossfitPlan	None`
nuisance_payload	NuisancePayload	Cross-fitted propensity scores and outcome predictions.
score_payload	ScorePayload	Doubly robust score (Eq. 2.5) and valid-sample masks.
estimation_payload	EstimationPayload	Eq. (3.1) beta, sieve coefficients, residuals, and projection objects.
result	HDDIDResult	User-facing estimates, standard errors, intervals, and diagnostics.

HDDIDResult exposes to_markdown(...) for readable table output and to_summary(...) for structured data extraction.

Inference

Parametric and nonparametric inference are explicit follow-up calls that attach Eq. (4.1)–(4.2) and Eq. (4.3) objects to an existing fit:

from hddid import (
    estimate_parametric_inference,
    estimate_nonparametric_inference,
)

parametric, result = estimate_parametric_inference(
    fit.score_payload,
    fit.estimation_payload,
    result=fit.result,
    xi=np.eye(fit.estimation_payload.beta_hat.size),
    alpha=0.1,
    lambda_prime=0.0,
)

nonparametric, result = estimate_nonparametric_inference(
    fit.score_payload,
    fit.estimation_payload,
    result=result,
    alpha=0.1,
    lambda_double_prime=0.0,
    n_boot=256,
    random_state=123,
)

print(result.to_markdown())

Output:

| Section | Name | Index | Estimate | Std. Error | Interval |
|---|---|---:|---:|---:|---|
| **Parametric** | β̂ | 0 | 0.0347 | — | — |
|  | β̂ | 1 | 0.0341 | — | — |
|  | τ̂ | 0 | 0.0412 | 0.0336 | [-0.0141, 0.0965] (90.0%) |
|  | τ̂ | 1 | 0.0422 | 0.0335 | [-0.0130, 0.0973] (90.0%) |
| **Nonparametric** | γ̂ | 0 | 0.0018 | — | — |
|  | γ̂ | 1 | 0.0064 | — | — |
|  | γ̄ | 0 | 0.0029 | — | — |
|  | γ̄ | 1 | 0.0088 | — | — |
|  | f̂(z₀) | 0 | -0.0014 | — | — |
|  | f̂(z₀) | 1 | 0.0018 | — | — |
|  | f̂(z₀) | 2 | 0.0050 | — | — |
|  | f̄(z₀) | 0 | -0.0015 | 0.0341 | [-0.0577, 0.0546] (90.0%) |
|  | f̄(z₀) | 1 | 0.0029 | 0.0298 | [-0.0461, 0.0519] (90.0%) |
|  | f̄(z₀) | 2 | 0.0072 | 0.0426 | [-0.0628, 0.0773] (90.0%) |

Diagnostics
  Basis: polynomial(1)
  Oracle lane: r-parity-polynomial
  Sample: holdout=30, trimmed=0, valid=30
  Trim: [0.0000, 1.0000]
  Folds: 3

Infeasible directions, missing evaluation grids, and nonpositive variance objects raise typed errors instead of silently producing generic standard-error rows.

Key Formulas

Doubly Robust Score (Eq. 2.5)

The cross-fitted doubly robust score assembles the treatment-weighted residual from cross-fitted nuisance estimates:

Ŝ = ρ̂ × (ΔY − (1 − π̂) φ̂₁ − π̂ φ̂₀)

where π̂ = P̂(D = 1 | X) is the propensity score, φ̂₀ and φ̂₁ are conditional mean estimates, and the propensity weight is:

ρ̂ = (D − π̂) / [π̂(1 − π̂)]

Second-Stage Estimator (Eq. 3.1)

The score is decomposed into a high-dimensional linear part and a nonparametric sieve component:

Ŝ = X'β̂ + f̂(Z) + ε̂

where f̂(Z) = ψ(Z)'γ̂ is a sieve approximation using a polynomial, trigonometric, or B-spline basis. The parametric coefficients β̂ are obtained via penalized (Lasso) regression on the Frisch–Waugh residualized design.

Parametric Inference (Eq. 4.2)

Debiased inference on linear functionals ξ' β uses a sparse direction ŵ solved from:

ŵ = arg min w' Σ̃_X w − 2 w' σ̂_X,ψ + λ' ‖w‖₁

The debiased estimator and its confidence interval are:

t̂ = ξ' β̂ − ŵ' Ŝ_moment

CI = t̂ ± z_1−α/2 × √(ŵ' Ω̂_β ŵ)

Nonparametric Inference (Eq. 4.3)

Debiased inference on f(z) orthogonalizes the sieve basis against the high-dimensional covariates via a projection matrix M̂:

ψ̃ = ψ − M̂ X

The debiased sieve estimator and its uniform band are:

f̄(z₀) = f̂(z₀) − (ψ̃₀)' Σ̂_f⁻¹ M̂ Ŝ_moment

CI_uniform = f̄(z₀) ± ĉ × √(diag(V̂_f))

where ĉ is a bootstrap critical value and V̂_f is the sandwich variance Σ̂_f⁻¹ Ω̂_f Σ̂_f⁻¹.

Plot Output

hddid.plotting.build_nonparametric_effect_plot_data(...) extracts a NonparametricEffectPlotData object from an inference result, containing the evaluation grid, point estimates, pointwise confidence intervals, and the uniform band. The object provides .to_svg(...) for dependency-free SVG output and .to_csv(...) for tabular export.

from hddid.plotting import build_nonparametric_effect_plot_data

plot_data = build_nonparametric_effect_plot_data(
    result=result,
    z0=fit.data.z0,
)

svg_string = plot_data.to_svg()

References

Ning, Y., Peng, S., & Tao, J. (2020). Doubly robust semiparametric difference-in-differences estimators with high-dimensional data. arXiv preprint arXiv:2009.03151. https://arxiv.org/abs/2009.03151

Authors

Python Implementation:

• Xuanyu Cai, City University of Macau
• Wenli Xu, City University of Macau

Methodology:

• Yang Ning, Cornell University
• Shuang Peng, Cornell University
• Jin Tao, Cornell University

License

AGPL-3.0. See LICENSE for details.

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). hddid: High-dimensional doubly robust difference-in-differences (Version 0.1.0) [Computer software]. GitHub. https://github.com/gorgeousfish/hddid-py

Ning, Y., Peng, S., & Tao, J. (2020). Doubly robust semiparametric difference-in-differences estimators with high-dimensional data. arXiv preprint arXiv:2009.03151. https://arxiv.org/abs/2009.03151

BibTeX:

@software{hddid2026python,
      title={hddid: High-dimensional doubly robust difference-in-differences},
      author={Xuanyu Cai and Wenli Xu},
      year={2026},
      version={0.1.0},
      url={https://github.com/gorgeousfish/hddid-py}
}

@misc{ning2020doublyrobust,
      title={Doubly Robust Semiparametric Difference-in-Differences Estimators
             with High Dimensional Data},
      author={Yang Ning and Shuang Peng and Jin Tao},
      year={2020},
      eprint={2009.03151},
      archivePrefix={arXiv},
      primaryClass={stat.ME},
      url={https://arxiv.org/abs/2009.03151}
}