contdid 0.1.0

Continuous Treatment Difference-in-Differences for Python

contdid

Continuous Treatment Difference-in-Differences

Estimate the full dose-response curve when treatments vary in intensity, rather than reducing continuous policy variation to a single coefficient.

Statement of Need

Standard Difference-in-Differences (DiD) tools estimate a single average treatment effect for a binary intervention. Yet many policies of interest are continuous: tax rate changes differ across regions, subsidy amounts vary by firm size, pollution exposure levels differ by proximity to a source, and healthcare reimbursement cuts vary by hospital.

Collapsing continuous variation into binary "treated vs. untreated" discards the dose-response structure that is often central to policy evaluation. Researchers need to know how much the outcome responds as dose increases, not just whether it responds.

contdid provides a Python implementation of the Caetano, Callaway, Payne & Rodrigues (2024) continuous-treatment DiD framework. It estimates ATT(d), the average treatment effect on the treated as a function of dose d, recovering the shape of how outcomes respond to treatment intensity. No other Python package currently implements these estimators.

Key Concepts

ATT(d): Average Treatment Effect on the Treated at dose d.

$$ \text{ATT}(d) = E[Y_t(d) - Y_t(0) \mid D = d, G \leq t] $$

The effect of receiving dose d compared to receiving no treatment, for units who actually received dose d.

ACRT(d): Average Causal Response Trajectory.

$$ \text{ACRT}(d) = \frac{\partial}{\partial d} \text{ATT}(d) $$

The marginal effect of an additional unit of dose at level d.

Identification assumption: Conditional parallel trends: absent treatment, units at every dose level would have followed parallel outcome paths to untreated units.

When to Use / When Not to Use

Good fit	Not designed for
Panel data with continuous treatment intensity	Pure cross-sectional data (need panel structure)
Staggered treatment adoption with varying doses	Binary treatment only (use standard DiD packages)
Interest in the full dose-response curve shape	No untreated comparison group available
Need for uniform inference (simultaneous bands)	Instrumental variable identification
Multi-period event-study with continuous dose	Continuous-time survival/duration models

Installation

pip install git+https://github.com/gorgeousfish/contdid.git

With plotting support:

pip install "contdid[plotting] @ git+https://github.com/gorgeousfish/contdid.git"

Requirements: Python ≥ 3.11, numpy, pandas, scipy

Quick Start

from contdid import cont_did, simulate_contdid_data, summary

# Simulate a two-period panel with known linear+quadratic dose effect
panel = simulate_contdid_data(n=2000, dgp_id="SIM-005-cck-two-period", seed=42)

# One-line estimation with bootstrap inference
result = cont_did(panel)
print(summary(result, max_rows=10))

Output:

========================================================================
                       ContDID Estimation Results                     
========================================================================
Estimand:           ATT(d)
Inference:          bootstrap
Confidence level:   95%
Basis:              global_polynomial (degree=3, knots=0)
------------------------------------------------------------------------
      Grid    Estimate    Std.Err.    CI Lower    CI Upper
----------------------------------------------------------
    0.0889      0.1811      0.0992     -0.0133      0.3756
    0.1904      0.2919      0.0872      0.1211      0.4628
    0.2836      0.3873      0.0900      0.2109      0.5637
    0.3944      0.4963      0.0847      0.3303      0.6623
    0.4890      0.5883      0.0800      0.4315      0.7451
    0.5719      0.6703      0.0819      0.5098      0.8308
    0.6780      0.7798      0.0880      0.6072      0.9524
    0.7875      0.9017      0.0873      0.7306      1.0728
    0.8866      1.0230      0.0923      0.8421      1.2040
    0.9921      1.1670      0.1634      0.8468      1.4872
  ... (10 of 90 points shown, equidistant sampling)
------------------------------------------------------------------------
Critical value:     1.9600
Band type:          pointwise_multiplier
========================================================================

Scenario 1: Event-Study Design

Track how effects evolve over time since treatment onset:

from contdid import cont_did, simulate_contdid_data, summary

panel = simulate_contdid_data(n=2000, dgp_id="SIM-004-staggered-eventstudy-null", seed=42)
result_es = cont_did(panel, aggregation="eventstudy")
print(summary(result_es))

Output:

========================================================================
                       ContDID Estimation Results                     
========================================================================
Estimand:           ATT(event_time)
Inference:          bootstrap
Confidence level:   95%
Basis:              global_polynomial (degree=3, knots=0)
------------------------------------------------------------------------
      Grid    Estimate    Std.Err.    CI Lower    CI Upper
----------------------------------------------------------
   -2.0000      0.0762      0.0864     -0.0930      0.2455
   -1.0000      0.0339      0.0564     -0.0767      0.1445
    0.0000      0.0700      0.0454     -0.0189      0.1589
    1.0000      0.0489      0.0617     -0.0721      0.1698
    2.0000      0.0361      0.0877     -0.1359      0.2080
------------------------------------------------------------------------
Critical value:     1.9600
Band type:          pointwise_multiplier
========================================================================

Scenario 2: CCK Nonparametric with Uniform Bands

Use sieve estimation with simultaneous confidence bands for shape inference:

from contdid import cont_did, simulate_contdid_data, summary

panel = simulate_contdid_data(n=2000, dgp_id="SIM-005-cck-two-period", seed=42)
result_cck = cont_did(panel, dose_est_method="cck", cband=True)
print(summary(result_cck, max_rows=8))

Output:

========================================================================
                       ContDID Estimation Results                     
========================================================================
Estimand:           ATT(d)
Inference:          bootstrap
Confidence level:   95%
Basis:              cck_polynomial_backend (degree=2, knots=0)
------------------------------------------------------------------------
      Grid    Estimate    Std.Err.    CI Lower    CI Upper
----------------------------------------------------------
    0.0010      0.1005      0.1303     -0.1550      0.3559
    0.1437      0.2375      0.0851      0.0707      0.4042
    0.2864      0.3790      0.0750      0.2320      0.5259
    0.4290      0.5249      0.0791      0.3700      0.6799
    0.5717      0.6754      0.0788      0.5209      0.8300
    0.7144      0.8304      0.0747      0.6841      0.9768
    0.8571      0.9899      0.0858      0.8218      1.1580
    0.9998      1.1539      0.1325      0.8941      1.4137
  ... (8 of 50 points shown, equidistant sampling)
------------------------------------------------------------------------
Critical value:     2.6385
Band type:          simultaneous_multiplier
========================================================================

Scenario 3: Pre-Trend Testing

Diagnose whether parallel trends holds in pre-treatment periods:

from contdid import cont_did, simulate_contdid_data, pre_trend_test_from_result

panel = simulate_contdid_data(n=2000, dgp_id="SIM-004-staggered-eventstudy-null", seed=42)
result_es = cont_did(panel, aggregation="eventstudy")

ptr = pre_trend_test_from_result(result_es)
print(f"Wald statistic: {ptr.test_statistic:.4f}")
print(f"p-value:        {ptr.p_value:.4f}")
print(f"DoF:            {ptr.degrees_of_freedom}")
print(f"Reject at 5%:   {ptr.reject_at_05}")

Output:

Wald statistic: 1.2942
p-value:        0.5236
DoF:            2
Reject at 5%:   False

Method Selection Guide

Parameter	Option	Description
dose_est_method	"parametric"	B-spline OLS; flexible, supports multi-period
	"cck"	CCK sieve estimation; nonparametric, two-period only
aggregation	"dose"	Dose-response curve ATT(d)
	"eventstudy"	Event-time dynamics ATT(event_time)
control_group	"nevertreated"	Never-treated units as comparison
	"notyettreated"	Not-yet-treated units (staggered designs)
target_parameter	"level"	ATT (level effects)
	"slope"	ACRT (marginal/derivative effects)
cband	False	Pointwise confidence intervals
	True	Simultaneous confidence band (uniform inference)
adaptive	True	Lepski adaptive dimension selection (CCK only)
knot_method	"quantile"	"quantile" or "even". Quantile-based adapts to dose distribution; even-spaced provides uniform coverage.

API Overview

Core Workflow

from contdid import (
    simulate_contdid_data,  # 1. Generate/load panel data
    cont_did,               # 2. One-line estimation (recommended)
    summary,                # 3. View formatted results
    to_dataframe,           # 4. Export to DataFrame
    to_csv,                 #    Export to CSV
    to_latex,               #    Export to LaTeX
    plot_dose_response,     # 5. Visualize dose-response
    plot_eventstudy,        #    Visualize event-study
    pre_trend_test_from_result,  # 6. Diagnose parallel trends
    quantile_knots,         # 7. Knot placement utilities
    even_knots,
)

cont_did() Parameters

result = cont_did(
    panel,                          # PanelData object
    target_parameter="level",       # "level" (ATT) or "slope" (ACRT)
    aggregation="dose",             # "dose" or "eventstudy"
    dose_est_method="parametric",   # "parametric" or "cck"
    control_group="nevertreated",   # "nevertreated" or "notyettreated"
    degree=3,                       # B-spline polynomial degree
    num_knots=0,                    # Interior knots (0 = global polynomial)
    knot_method="quantile",          # "quantile" or "even" knot placement
    anticipation=0,                 # Anticipation periods
    biters=1000,                    # Bootstrap iterations
    cband=False,                    # Simultaneous confidence band
    adaptive=False,                 # Lepski adaptive (CCK two-period only)
)

ContDIDResult Object

Attribute / Method	Description
result.grid	Evaluation points (dose or event-time)
result.estimate	Point estimates at each grid point
result.std_error	Bootstrap standard errors
result.metadata	Dict with CI bounds, band type, basis info
summary(result)	Formatted text table
to_dataframe(result)	pandas DataFrame export
to_csv(result, path)	CSV file export
to_latex(result)	LaTeX table string
plot_dose_response(result)	Dose-response figure
plot_eventstudy(result)	Event-study figure

Performance

Bootstrap inference uses thread-level parallelism (ThreadPoolExecutor) for large-scale problems (biters >= 200, multiple chunks). NumPy releases the GIL during matrix operations, enabling 15-67% speedup on multi-core machines. Results are reproducible via numpy.random.SeedSequence: the same seed always yields identical output regardless of thread count.

Current Limitations & Future Directions

Current Limitations

• CCK estimation restricted to two-period, non-staggered designs
• Lepski adaptive dimension selection restricted to two-period panels
• Event-study CCK supports fixed-dimension mode only (no adaptive Lepski)
• Large panels (N > 50,000) benefit from the built-in thread-parallel bootstrap, though wall time scales linearly with biters
• Covariate adjustment: Not available. The paper (arXiv:2107.02637v7) provides only a conceptual framework for conditional parallel trends without complete estimation theory.
• Discrete treatment: Not available. Only continuous treatment is implemented; multi-valued discrete treatment (paper Assumption 4b) awaits implementation.

Future Directions

• Additional DGP scenarios for simulation and testing

Citation

APA:

Cai, X., & Xu, W. (2026). contdid: Continuous Treatment Difference-in-Differences for Python (Version 0.1.0) [Computer software]. https://github.com/gorgeousfish/contdid

BibTeX:

@software{contdid,
  title = {contdid: Continuous Treatment Difference-in-Differences for Python},
  author = {Cai, Xuanyu and Xu, Wenli},
  year = {2026},
  url = {https://github.com/gorgeousfish/contdid},
  version = {0.1.0}
}

Method papers:

@techreport{callaway2024continuous,
  title = {Difference-in-Differences with a Continuous Treatment},
  author = {Callaway, Brantly and Goodman-Bacon, Andrew and Sant'Anna, Pedro H.C.},
  year = {2024},
  institution = {National Bureau of Economic Research},
  type = {Working Paper},
  number = {w32117}
}

@article{chen2025adaptive,
  title = {Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities},
  author = {Chen, Xiaohong and Christensen, Timothy and Kankanala, Siddhartha},
  year = {2025},
  journal = {Review of Economic Studies},
  volume = {92},
  number = {1},
  pages = {162--196}
}

Authors

Python Implementation:

• Xuanyu Cai, City University of Macau, [e-mail]
• Wenli Xu, City University of Macau, [e-mail]

Methodology:

• Gregorio Caetano, University of Georgia
• Brantly Callaway, University of Georgia
• Tymon Słoczyński, Brandeis University

Based on:

• Callaway, B., Goodman-Bacon, A., & Sant'Anna, P. H. (2024). "Difference-in-Differences with a Continuous Treatment" (No. w32117). National Bureau of Economic Research.
• Chen, X., Christensen, T., & Kankanala, S. (2025). "Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities." Review of Economic Studies, 92(1), 162–196.

License

AGPL-3.0