Jonas Skjold Raaschou-Pedersen
arXiv 5 May 2026 · Econometrics
arXiv:2605.03699 · PDF · DOI · OpenAlex · Extracted main text
We study estimation of the local average treatment effect on the treated ($LATT$) in instrumented difference-in-differences (IDiD) designs with covariates and staggered instrument exposure. We derive the efficient influence function (EIF) of the target parameter in both panel and repeated cross-sections settings, allowing for two classes of control groups: never-exposed and not-yet-exposed. Building on the EIF, we construct doubly robust estimands and corresponding estimators from first principles. The resulting procedures are the IDiD analogues of the difference-in-differences (DiD) procedures in Callaway and Sant'Anna (2021), targeting $LATT$ rather than $ATT$. We further establish a Bloom-type result under one-sided compliance and absorbing treatment, linking $LATT$ to a convex combination of exposure-cohort-specific $ATT(g, t)$ parameters, making the connection between IDiD and DiD explicit. Asymptotic properties are established under conditions on the remainder term and either Donsker conditions or via cross-fitting. We also construct double machine learning (DML) estimators for the $LATT$ in both data settings and show their equivalence to cross-fitted estimators. Simulations assess the double robustness and finite-sample performance of the proposed methods. An implementation is available in the Python package idid.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Miyaji, Sho Instrumented Difference-in-Differences with Heterogeneous Treatment Effects | 1.000 | 13 | 3 | 100% |
| 2 | Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Du… Double/Debiased Machine Learning for Treatment and Structural Parameters | 1.000 | 5 | 3 | 100% |
| 3 | Kennedy, Edward H Semiparametric Doubly Robust Targeted Double Machine Learning: A Review | 0.961 | 18 | 5 | 89% |
| 4 | Callaway, Brantly and Sant'Anna, Pedro H. C Difference-in-Differences with Multiple Time Periods | 0.956 | 32 | 8 | 88% |
| 5 | Sant'Anna, Pedro H.C. and Zhao, Jun Doubly Robust Difference-in-Differences Estimators | 0.819 | 31 | 7 | 55% |
| 6 | Chen, Xiaohong and Sant'Anna, Pedro H. C. and Xie, Haitian Efficient Difference-in-Differences and Event Study Estimators | 0.737 | 3 | 2 | 100% |
| 7 | Słoczyński, Tymon and Uysal, S Derya and Wooldridge, Jeffrey M Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment | 0.737 | 3 | 2 | 100% |
| 8 | Mogstad, Magne and Torgovitsky, Alexander (2024) Instrumental variables with unobserved heterogeneity in treatment effects | 0.644 | 2 | 2 | 100% |
| 9 | Angrist, Joshua D. and Pischke, Jörn-Steffen Mostly Harmless Econometrics: An Empiricist's Companion | 0.585 | 3 | 1 | 100% |
| 10 | Newey, Whitney K Semiparametric Efficiency Bounds | 0.511 | 2 | 2 | 50% |
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