arxiv: 2605.03699 · v1 · submitted 2026-05-05 · 💰 econ.EM

Recognition: unknown

Doubly Robust Instrumented Difference-in-Differences

Jonas Skjold Raaschou-Pedersen

Pith reviewed 2026-05-07 04:14 UTC · model grok-4.3

classification 💰 econ.EM

keywords instrumented difference-in-differenceslocal average treatment effect on the treateddoubly robust estimationefficient influence functionstaggered adoptionpanel datarepeated cross-sectionsdouble machine learning

0 comments

The pith

This paper derives efficient influence functions to construct doubly robust estimators for the local average treatment effect on the treated in instrumented difference-in-differences designs with staggered instrument exposure.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Economists often rely on instruments to identify causal effects when direct assignment to treatment is not random, yet staggered timing of instrument exposure across groups and the presence of covariates complicate estimation of effects on those who actually change behavior in response to the instrument. The paper focuses on the local average treatment effect on the treated and shows how to estimate it reliably in both panel and repeated cross-section data by deriving its efficient influence function for two types of control groups. From the influence function it builds doubly robust estimators that stay consistent provided either the model for the outcome or the model for instrument assignment is correct. It further shows that under one-sided compliance and absorbing treatment the local effect equals a convex combination of standard group-time average treatment effects, making the link between instrumented and conventional difference-in-differences explicit. These results matter because they give applied researchers flexible, less assumption-heavy tools for policy evaluations that involve phased instrument rollouts.

Core claim

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 targeting ATT rather than LATT. We further establish a Bloom-type result under one-sided compliance,

What carries the argument

Efficient influence function of the LATT parameter, from which doubly robust estimands and estimators are derived for panel and repeated cross-section IDiD data with never-exposed or not-yet-exposed controls.

If this is right

Doubly robust estimators for LATT become available in panel data settings using either never-exposed or not-yet-exposed control groups.
Equivalent doubly robust procedures apply directly to repeated cross-sections data.
Under one-sided compliance and absorbing treatment, LATT equals a convex combination of exposure-cohort-specific ATT(g, t) parameters.
Asymptotic normality holds under conditions on the remainder term together with Donsker or cross-fitting assumptions, including via double machine learning.
Simulations confirm that the estimators retain double robustness and exhibit good finite-sample behavior.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The explicit mapping from LATT to standard ATT(g, t) parameters suggests that existing DiD software routines can be adapted with modest changes to produce instrumented analogues.
Cross-fitting versions of the estimators open the door to high-dimensional nuisance estimation via modern machine learning without sacrificing robustness.
Applied researchers can now compare instrumented and non-instrumented estimates of the same policy within one study to assess the role of compliance.
The framework naturally extends to other staggered designs once the appropriate efficient influence function is obtained.

Load-bearing premise

Standard instrumented DiD identification conditions hold, including instrument validity and no anticipation, or at least one of the outcome regression or instrument propensity score is correctly specified.

What would settle it

A Monte Carlo simulation or empirical example with known true LATT in which the proposed doubly robust estimator fails to recover the parameter when both the outcome regression and the instrument propensity score are misspecified, yet succeeds when exactly one is correct.

Figures

Figures reproduced from arXiv: 2605.03699 by Jonas Skjold Raaschou-Pedersen.

**Figure 1.** Figure 1: Simulation experiment 2: design and estimator distributions. view at source ↗

**Figure 2.** Figure 2: Simulation experiment 2: aggregated effects using never-exposed and not-yet-exposed view at source ↗

**Figure 3.** Figure 3: Simulation experiment 2: group-specific aggregated effects and their difference under view at source ↗

**Figure 4.** Figure 4: Roadmap from simple DiD objects to DR estimands and EIF for the LATT. The view at source ↗

read the original abstract

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 \texttt{idid}.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper derives the EIF for LATT in staggered instrumented DiD and builds practical doubly robust estimators plus code from it.

read the letter

This paper derives the efficient influence function for the local average treatment effect on the treated under instrumented difference-in-differences with staggered exposure, then uses it to construct doubly robust estimators for both panel and repeated cross-section data. It covers never-exposed and not-yet-exposed controls, adds covariates, and includes a Bloom-type result that expresses LATT as a convex combination of cohort-specific ATT parameters when compliance is one-sided and treatment is absorbing. The estimators are shown to be equivalent to cross-fitted double machine learning versions, with asymptotics under standard remainder and Donsker conditions or via cross-fitting. A Python package implements the methods, and simulations check double robustness and finite-sample behavior. The work extends Callaway and Sant'Anna directly to the instrumented target, which is the main new piece. The derivations start from first principles rather than fitting a reduced form, and the explicit link to standard DiD parameters helps with interpretation. The handling of two control groups and both data structures adds flexibility that applied users will appreciate. The double robustness property is the usual one: it holds if either the outcome regression or the propensity score is correct, which is not a flaw but does require users to verify at least one nuisance model in practice. The Bloom result is useful only under one-sided compliance and absorbing treatment, so it will not cover every instrumented setting. No internal contradictions appear in the outline or stress-test, and the identification assumptions are stated plainly. This is for applied econometricians estimating causal effects in staggered policy settings that have instruments and covariates. Readers who need robust tools for LATT rather than ATT will get direct value from the estimators and code. It deserves peer review because the extension is technically grounded and comes with reproducible implementation.

Referee Report

0 major / 5 minor

Summary. The manuscript derives the efficient influence function (EIF) of the local average treatment effect on the treated (LATT) for instrumented difference-in-differences (IDiD) designs with covariates and staggered instrument exposure. It does so for both panel and repeated cross-section data, allowing never-exposed and not-yet-exposed control groups. From the EIF the authors construct doubly robust estimands and estimators, establish a Bloom-type result linking LATT to a convex combination of cohort-specific ATT(g,t) under one-sided compliance and absorbing treatment, prove asymptotic normality under remainder-term and Donsker/cross-fitting conditions, implement double machine learning estimators, and report Monte Carlo evidence on double robustness and finite-sample behavior. A Python package 'idid' is provided.

Significance. If the EIF derivations and remainder-term bounds hold, the paper supplies a practical, doubly robust toolkit that extends Callaway and Sant'Anna (2021) to instrumented staggered-adoption settings. The explicit Bloom-type decomposition is valuable for interpretation, and the double-robustness property is especially useful when either the outcome regression or the instrument propensity score can be modeled plausibly. The provision of reproducible code and simulation results strengthens the contribution for applied work in labor and development economics.

minor comments (5)

[§2.1] §2.1: The target parameter LATT is defined verbally; an explicit integral or summation expression would help readers verify the subsequent EIF derivation.
[§5.2] §5.2, Assumption 5: The remainder-term condition is stated at a high level; adding primitive conditions (e.g., for random forests or neural nets under cross-fitting) would make the asymptotic result more immediately usable.
[Table 2] Table 2: Bias and RMSE are reported, but the table would be clearer if it also included Monte Carlo standard errors or coverage rates for the proposed confidence intervals.
[References] References: The citation to Bloom (2009) for the Bloom-type result is present but the full reference entry should include the journal and DOI for completeness.
[Abstract] Abstract and §1: The acronym 'IDiD' is introduced without spelling out 'instrumented difference-in-differences' on first use; this is a minor but standard clarity fix.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our manuscript, as well as for recommending minor revision. The report correctly identifies the core contributions, including the EIF derivations for the LATT in staggered IDiD settings (both panel and repeated cross-section), the doubly robust estimators, the Bloom-type decomposition under one-sided compliance, and the DML implementation with accompanying code and simulations. No specific major comments were raised.

Circularity Check

0 steps flagged

Derivations proceed from first principles without reduction to inputs by construction

full rationale

The paper explicitly derives the EIF for the LATT parameter in IDiD settings from first principles for both panel and repeated cross-section data, allowing never-exposed and not-yet-exposed controls. It then constructs doubly robust estimands and estimators directly from that EIF, with asymptotics under standard Donsker or cross-fitting conditions. The Bloom-type link to cohort-specific ATT(g,t) is presented as an additional result under one-sided compliance and absorbing treatment, not as a definitional equivalence. Citations to external DiD literature (Callaway and Sant'Anna 2021) supply context for the ATT analogue but do not carry the load of the central EIF derivation or double robustness property. No self-citations, fitted parameters renamed as predictions, or ansatzes smuggled via prior author work appear in the derivation chain. The procedures are self-contained against the stated identification assumptions (instrument validity, no anticipation, correct regression or propensity score) and do not reduce the target parameter to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The work rests on standard domain assumptions from causal inference and econometrics literature rather than new free parameters or invented entities; full details would require the manuscript sections on identification.

axioms (4)

domain assumption Instrument validity (relevance and exclusion restriction) conditional on covariates
Required to identify LATT in instrumented designs as stated in the abstract.
domain assumption No anticipation effects and suitable parallel trends or instrumented analogue for control groups
Needed for the difference-in-differences component in both never-exposed and not-yet-exposed controls.
domain assumption Correct specification of at least one nuisance function (outcome or treatment model) for double robustness
Central to the construction of doubly robust estimands from the EIF.
domain assumption One-sided compliance and absorbing treatment for the Bloom-type result
Explicitly invoked to link LATT to a convex combination of cohort-specific ATT parameters.

pith-pipeline@v0.9.0 · 5529 in / 1575 out tokens · 72937 ms · 2026-05-07T04:14:21.185884+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

22 extracted references · 17 canonical work pages · 1 internal anchor

[1]

Callaway, Brantly and Sant'Anna, Pedro H. C. , year = 2021, month = dec, journal =. Difference-in-. doi:10.1016/j.jeconom.2020.12.001 , url =

work page doi:10.1016/j.jeconom.2020.12.001 2021
[2]

Journal of Econometrics , volume =

Doubly Robust Difference-in-Differences Estimators , author =. Journal of Econometrics , volume =. doi:10.1016/j.jeconom.2020.06.003 , url =

work page doi:10.1016/j.jeconom.2020.06.003 2020
[3]

Semiparametric Doubly Robust Targeted Double Machine Learning: A Review

Kennedy, Edward H. , year = 2023, month = jan, number =. Semiparametric Doubly Robust Targeted Double Machine Learning: A Review , shorttitle =. arXiv , keywords =:2203.06469 , primaryclass =

work page arXiv 2023
[5]

Instrumented

Miyaji, Sho , year = 2026, month = feb, journal =. Instrumented. doi:10.48550/arXiv.2405.12083 , url =. arXiv , keywords =:2405.12083 , primaryclass =

work page doi:10.48550/arxiv.2405.12083 2026
[6]

Semiparametric

Abadie, Alberto , year = 2005, month = jan, journal =. Semiparametric. doi:10.1111/0034-6527.00321 , url =

work page doi:10.1111/0034-6527.00321 2005
[7]

Exploiting

Fr. Exploiting. Journal of the American Statistical Association , volume =. doi:10.1198/jasa.2010.ap08148 , url =

work page doi:10.1198/jasa.2010.ap08148 2010
[8]

Chen, Xiaohong and Sant'Anna, Pedro H. C. and Xie, Haitian , year = 2025, month = jun, number =. Efficient. doi:10.48550/arXiv.2506.17729 , url =. arXiv , keywords =:2506.17729 , primaryclass =

work page doi:10.48550/arxiv.2506.17729 2025
[9]

Double/debiased machine learning for treatment and structural parameters.The Econometrics Journal, 21(1):C1–C68, 2018

Double/Debiased Machine Learning for Treatment and Structural Parameters , author =. The Econometrics Journal , volume =. doi:10.1111/ectj.12097 , url =

work page doi:10.1111/ectj.12097
[10]

The Econometrics Journal , volume =

Double/Debiased Machine Learning for Difference-in-Differences Models , author =. The Econometrics Journal , volume =. doi:10.1093/ectj/utaa001 , url =

work page doi:10.1093/ectj/utaa001
[11]

Lan, Hui and Chang, Haoge and Dillon, Eleanor and Syrgkanis, Vasilis , year = 2025, month = apr, number =. A. doi:10.48550/arXiv.2502.04699 , url =. arXiv , langid =:2502.04699 , primaryclass =

work page doi:10.48550/arxiv.2502.04699 2025
[12]

Economics Letters , volume =

Improved Two-Period Difference-in-Differences by Targeted Estimation , author =. Economics Letters , volume =. doi:10.1016/j.econlet.2025.112600 , url =

work page doi:10.1016/j.econlet.2025.112600 2025
[13]

Journal of Machine Learning Research , volume =

On doubly robust inference for double machine learning in semiparametric regression , author =. Journal of Machine Learning Research , volume =
[14]

Handbook of labor economics , volume =

Instrumental variables with unobserved heterogeneity in treatment effects , author =. Handbook of labor economics , volume =. 2024 , publisher =

2024
[15]

Journal of Applied Econometrics , volume =

Semiparametric Efficiency Bounds , author =. Journal of Applied Econometrics , volume =. doi:10.1002/jae.3950050202 , url =

work page doi:10.1002/jae.3950050202
[16]

and Pischke, J

Angrist, Joshua D. and Pischke, J. Mostly. doi:10.2307/j.ctvcm4j72 , url =. j.ctvcm4j72 , eprinttype =

work page doi:10.2307/j.ctvcm4j72
[17]

Journal of Human Resources , pages =

Estimating the effect of job-training programs, using longitudinal data: Ashenfelter's findings reconsidered , author =. Journal of Human Resources , pages =. 1984 , publisher =

1984
[18]

Regression and

Tan, Zhiqiang , year = 2006, month = dec, journal =. Regression and. doi:10.1198/016214505000001366 , url =

work page doi:10.1198/016214505000001366 2006
[19]

Mark J van der Laan and James M Robins.Unified methods for censored longitudinal data and causality

Tsiatis, Anastasios , year = 2006, series =. Semiparametric. doi:10.1007/0-387-37345-4 , url =

work page doi:10.1007/0-387-37345-4 2006
[20]

Amstat News , volume =

Statistics as a science, not an art: the way to survive in data science , author =. Amstat News , volume =
[21]

van der Laan and Sherri Rose.Targeted Learning: Causal Inference for Observational and Experimental Data

Van Der Laan, Mark J. and Rose, Sherri , year = 2011, series =. Targeted. doi:10.1007/978-1-4419-9782-1 , url =

work page doi:10.1007/978-1-4419-9782-1 2011
[22]

Journal of Machine Learning Research , volume =

DoubleML-an object-oriented implementation of double machine learning in python , author =. Journal of Machine Learning Research , volume =
[23]

On the Equivalence between Neyman Orthogonality and Pathwise Differentiability

On the Equivalence between Neyman Orthogonality and Pathwise Differentiability , author =. arXiv preprint arXiv:2603.15817 , year =

work page internal anchor Pith review Pith/arXiv arXiv