[Lecture Idea] Difference-in-Differences with a Continuous Treatment (Callaway, Goodman-Bacon & Sant'Anna)

[mmcky]

Summary

Proposal for a new applied econometrics lecture covering modern difference-in-differences with a continuous treatment (dose), based on:

Callaway, B., Goodman-Bacon, A., & Sant'Anna, P. H. C. (2025). Difference-in-Differences with a Continuous Treatment. American Economic Review (forthcoming). [AEA page](https://www.aeaweb.org/articles?id=10.1257/aer.20240137) · [arXiv:2107.02637](https://arxiv.org/abs/2107.02637)

This is arguably the definitive treatment of continuous-dose DiD and slots naturally into a "modern econometrics" sequence alongside existing causal inference material.

Why this lecture?

• Empirical relevance for trade/macro applications. Most real-world "treatments" in international trade are continuous: tariff changes, import-competition exposure (the ADH China shock), trade-cost reductions, exchange-rate pass-through. The workhorse approach — TWFE regression of an outcome on a continuous exposure measure — is exactly what this paper shows can be misleading.
• Pedagogically rich. The paper cleanly separates (i) identification (ATT-type parameters under parallel trends), (ii) the selection-bias problem when comparing effects across doses (ACRT parameters need stronger assumptions), and (iii) estimation (B-splines, nonparametric sieve methods, multiplier bootstrap for uniform confidence bands). Each piece is implementable from scratch in NumPy/SciPy at lecture scale.
• Fills a gap. QuantEcon has limited coverage of the post-2018 DiD literature (staggered adoption, negative TWFE weights, heterogeneity-robust estimators). This lecture could anchor that area.

Proposed outline

1. Motivation — a trade example: regions exposed to a tariff cut at varying intensity. Why "run TWFE on the dose" is the default and why it's fragile.
2. Setup and notation — potential outcomes indexed by dose Y_t(d); timing groups g; building blocks ATT(g, t, d).
3. Identification — parallel trends identifies ATT(d); comparing across d (slopes / ACRT) requires "strong" parallel trends. Simulation demonstrating the selection-bias wedge.
4. What TWFE actually estimates — decompose the TWFE estimand; show negative-weighting pathologies with simulated heterogeneous dose effects.
5. Estimation — implement the ATT(d) / ACRT(d) estimators with B-splines (scipy.interpolate); event-study and dose aggregations; multiplier bootstrap for uniform confidence bands.
6. Application — replicate (or adapt) the paper's empirical application, or a trade-flavoured alternative (e.g., regional tariff exposure).
7. Exercises — vary the dose-effect functional form; compare TWFE vs. the robust estimator; coverage experiments for pointwise vs. uniform bands.

Implementation notes

• Reference implementation is the authors' R package [contdid](https://bcallaway11.github.io/contdid/) (alpha, GPL-3).
• Python ecosystem: the [diff-diff](https://diff-diff.readthedocs.io/) package (Gerber, 2026) now includes a ContinuousDiD estimator implementing CGS — B-spline dose-response curves (ATT(d) / ACRT(d)), overall ATT/ACRT aggregation, multiplier bootstrap (rademacher/mammen/webb weights) plus analytical SEs, and correct handling of the PT vs. strong-PT identification distinction. It sits within a unified scikit-learn-style API covering 13+ DiD estimators validated against R counterparts.
  • Role in the lecture: build the estimator from first principles (the pedagogical core), then close by cross-checking results against diff-diff and pointing students to it (and contdid in R) for production use. This mirrors the QuantEcon pattern of "implement it yourself, then use the library."
  • Audit task before adoption: verify diff-diff's continuous module against contdid output on fixed simulated data, and confirm coverage of staggered adoption for continuous doses (docs emphasize the dose-response core; staggered support unclear) and whether the CCK data-driven estimator is included. Findings feed the companion project issue.
• Scope for a lecture-scale implementation: simulated panel data + B-spline dose-response estimation + multiplier bootstrap is very tractable (a few hundred lines). The data-driven sieve method (Chen, Christensen & Kankanala 2025, npiv) is harder and could be mentioned rather than implemented, or deferred to a follow-up.
• License note: contdid is GPL-3. The lecture should reimplement from the paper's equations rather than translating package source, to keep our standard BSD-3/CC licensing clean. (Check diff-diff's license before recommending it in lecture text — likely permissive, but confirm.)
• Possible synergy: the estimators here build on the did / ptetools ecosystem; if we later cover Callaway & Sant'Anna (2021) staggered DiD, diff-diff also covers that estimator, so the two lectures could share both from-scratch infrastructure and the same production-library endpoint.

Open questions

• Which repo/series does this belong in?
• Simulated data only, or include an empirical replication (data availability/licensing to check)?
• Implement CCK nonparametric estimator, or B-spline parametric only?
• JAX or NumPy for the bootstrap? (multiplier bootstrap vectorises nicely in either)
• Use diff-diff as the lecture's validation cross-check and "production use" recommendation, pending the audit above?

References

• Callaway, Goodman-Bacon & Sant'Anna (2025), DiD with a Continuous Treatment, AER forthcoming.
• Chen, Christensen & Kankanala (2025), "Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities", REStud 92(1).
• Callaway & Sant'Anna (2021), "Difference-in-Differences with Multiple Time Periods", J. Econometrics.
• Goodman-Bacon (2021), "Difference-in-Differences with Variation in Treatment Timing", J. Econometrics.
• contdid (R, reference implementation): https://bcallaway11.github.io/contdid/
• diff-diff (Python): https://diff-diff.readthedocs.io/ — ContinuousDiD module: https://diff-diff.readthedocs.io/en/stable/api/continuous_did.html

[mmcky]

@jstac collecting new lecture ideas in the future monorepo for lectures now. FYI.

[jstac]

Perfect, thanks @mmcky