Identification of dynamic treatment effects when treatment histories are partially observed

Akanksha Negi; Didier Nibbering

REVIEW 2 major objections 5 minor 64 references

Identification of dynamic treatment effects when treatment histories are partially observed

T0 review · 2 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper proves that a new robust difference-in-differences estimator identifies path-dependent treatment effects from panel data with partially missing treatment histories whenever any two of three working models are correctly specified.

desk verdict The triple-robust DID estimator is a real contribution, but the efficiency-bound theorem is wrong as written and the paper overclaims it. read the letter →

arxiv 2501.04853 v2 pith:H5VWHE2L submitted 2025-01-08 econ.EM

Akanksha Negi , Didier Nibbering This is my paper · ORCID

classification econ.EM MSC 62D1062P20

keywords partiallyobservedtreatmentsmissingatrandomdifference-in-differencespath-dependenttreatmenteffectsrobustestimationsemiparametricefficiencypaneldatahistories

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tackles a gap in difference-in-differences: estimating how the full history of a binary treatment, such as being treated in both periods versus only the second, affects final outcomes when the first-period treatment is missing for part of the sample. It proposes a new estimator that combines three working models — the outcome regression, the propensity score, and the probability that the treatment history is observed — and proves that the target causal parameter is identified as long as any two of the three are correctly specified. Under the same missing-at-random and parallel-trends assumptions, conventional complete-case and doubly robust estimators require the missing-data model to be correct, while the new estimator remains unbiased when that model fails. The paper also derives the semiparametric efficiency bound for the parameter and shows its estimator attains it when all three models are correct. This matters because missing treatment histories are routine in surveys, rotating panels, and administrative data, and because existing estimators can be biased whether missingness is ignored or modeled.

What carries the argument

The load-bearing object is the augmented inverse-probability-weighted estimand $\tau^R_{dd'}$ in equation (4), constructed from three working models: $\mu_d(X)$ for the outcome mean, $\pi_d(X)$ for the propensity score, and $\phi_{d_2}(X)$ for the probability of observing $D_1$ given $D_2$ and $X$. Its four Hajek-type weights $w_1, w_2, w_3, w_4$ re-weight the observed treated and comparison groups, the $D_2$-only groups, and differences in outcome-model predictions. The mechanism is cancellation: when any two models are correct, the differences between pairs of weight-adjusted expectation terms vanish in expectation, leaving only the term that identifies the PDATT. This same structure nests the OR, IPW, and DR estimands as special cases, which is why those alternatives all require a correct missing-data model whereas the robust estimator does not.

What would settle it

Generate data in which the missingness indicator $S$ depends on $D_1$ or on the individual treatment effect even after conditioning on $D_2$ and $X$, while keeping the outcome regression and propensity score correctly specified; under the paper's Assumption 2.1 the robust estimator should be unbiased, so any bias growing with that dependence would refute the identification claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that the causal parameter $\tau_{dd'} = E[Y_2(d) - Y_2(0,0) \mid D = d]$ — the average effect of treatment path $d$ on the final outcome for individuals who followed that path — can be identified even when $D_1$ is unobserved for some units. Identification is achieved by the robust estimand in equation (4), which re-weights observed outcomes and outcome-model differences using four Hajek-normalized weights built from the missingness probability $q_{d_2}(X)$, the propensity score $p_d(X)$, and the outcome regression $m_d(X)$. Theorem 1 proves this estimand equals $\tau_{dd'}$ whenever any two of the three models are correctly specified: outcome plus propensity score, missingness plus propensity score, or missingness plus outcome. The proof shows that, under each pair of correct models, the spurious adjustment terms in the estimand vanish in expectation and the surviving term equals the path-dependent treatment effect. When all three models are correct, Corollary 3 shows the estimator's asymptotic variance equals the semiparametric efficiency bound for $\tau_{dd'}$, so it is efficient within the class of missingness-adjusted estimators.

Load-bearing premise

The missing-at-random condition $S \perp (D_1, \Delta Y) \mid D_2, X$ must hold, meaning that whether the first treatment is observed is independent of the first treatment and of the outcome change once the second treatment and covariates are controlled; if missingness is driven by unobserved factors tied to treatment-effect heterogeneity, the robust estimator is biased even with perfectly specified models.

Editorial extensions

If this is right

Applied DID studies with partially missing treatment histories can report a causally interpretable PDATT rather than a non-convex mixture of effects from ignoring $D_1$ or a selection-biased complete-case estimate.
Researchers need not correctly model the missingness mechanism: as long as the outcome regression and propensity score are correct, the robust estimator identifies the target parameter even when missingness depends on covariates in unknown ways.
The OR, IPW, and DR estimators are formally nested in the robust estimand, so the paper's inference machinery provides valid standard errors for those alternatives as well.
With all three models correct, the estimator attains the semiparametric efficiency bound, so the efficiency loss from guarding against misspecification of the missing-data model disappears.
The framework extends to multiple periods and arbitrary missing patterns in the treatment history, so the result applies beyond the three-period, $D_1$-missing case.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's robustness claim is conditional on Assumption 2.1 being true; if missingness is driven by unobserved factors correlated with treatment-effect heterogeneity, the robust estimator inherits the same bias as any MAR-based method even with perfectly specified models.
An extension the paper leaves implicit is a practical diagnostic: comparing robust and DR estimates, a large divergence that shrinks when the missingness model is respecified would point to the missingness model as the fragile component rather than the causal parameter itself.
The paper notes that a weaker assumption allowing missingness to depend on the outcome change requires a different inverse-probability-weighted estimand; the main robust estimator is not designed for that case, so its triple-robustness should not be read as covering outcome-dependent missingness.
The Monte Carlo design, which misspecifies each model by using nonlinear transformations of the covariates, suggests that in real applications the triple-robust property is most valuable when the missingness model is the hardest to justify, which is often the case with survey nonresponse and attrition.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The useful core of this paper is Theorem 1: the triple-robust estimand for path-dependent ATTs with partially observed treatment histories, where any two of outcome, propensity, and missingness models being correct identifies the target. I checked the algebra in the appendix and it works. The Monte Carlo evidence backs it up, and the application to COVID-era turnout with 51% missing histories is a good illustration of why this matters. The paper is honestly written and engages the right literature. Credit where due: this is a practical extension that DID practitioners will want.

The soft spot is real, though. The stress-test note about Theorem 2 is right. The paper applies Tsiatis's missing-data influence-function formula with a conditioning set W = (ΔY, S, S·D1, D2, X) that contains the full data whenever S=1, so the augmentation term collapses to zero. The correct conditioning set for the always-observed variables is V = (D2, ΔY, X), giving F_obs = (S/q)F_full - (S/q - 1)E[F_full|V]. The proof drops the second piece. This is not a cosmetic slip: equation (C.3) omits the (ΔY - m_d' - τ) contributions to the projected score, and Table SE.3 shows R variances below the claimed semiparametric bound (for example 49.4 vs 51.1 in the 'None' row for τ_(11)(00)). That is impossible if the bound is correct. Corollary 3's efficiency claim is unsupported, and the paper's advertised efficiency contribution should be withdrawn or correctly derived before publication.

This does not sink Theorem 1 or the simulation-based inference results, which do not rely on the bound. But it does mean the paper's central selling point—efficiency among missingness-adjusted estimators—is currently overstated. The MAR assumption is also genuinely strong (missingness independent of the first treatment and outcome change given D2 and X), and the authors acknowledge it; the alternative in SA.2 is for a different estimand. That is a limitation, not a fatal flaw.

Who should read this? Applied researchers working with short panels where treatment histories are incomplete. It deserves a serious referee: the identification result is substantial, the proofs are detailed enough to check, and the flaw is local and fixable. I would send it out, but with a specific request that the efficiency theorem be corrected or removed, and with the replication code supplied so the numerical claims can be verified.

Referee Report

2 major / 5 minor

Summary. The paper considers a two-period panel with a binary treatment whose first-period value D1 may be missing, and studies path-dependent average treatment effects (PDATTs) such as τ_(11)(00), τ_(10)(00), and τ_(01)(00). It shows that a standard DID estimand that ignores D1 identifies a non-convex weighted average of PDATTs and that complete-case DID is subject to selection bias. It then proposes an augmented inverse-probability-weighted estimand with three working models: an outcome regression, a propensity score, and a missing-treatment probability. Theorem 1 claims that this estimand identifies the PDATT whenever any two of the three models are correctly specified. The paper derives asymptotic normality for the two-step plug-in estimator (Theorem 3), claims semiparametric efficiency when all three models are correct (Theorem 2 and Corollary 3), and supports the results with Monte Carlo experiments and two empirical applications.

Significance. If the identification and inference results are correct, the paper makes a useful contribution to DID estimation with partially observed treatment histories: it relaxes the common requirement that the missingness model be correctly specified, and it nests several existing estimators as special cases. The Monte Carlo design is careful and extensive, covering misspecification of each model individually, multiple misspecifications, varying missingness rates, and varying degrees of misspecification, and the reported finite-sample behavior is consistent with the identification claims. The authors are also transparent about the strong missing-at-random assumption and provide an alternative IPW estimand under a weaker missingness assumption in SA.2. However, the efficiency claim is not supported by the derivation as written, and one of the robustness claims in Section 3.1 overstates what the assumptions deliver. These issues are substantive and need correction.

major comments (2)

[Appendix C, Theorem 2] The derivation of the semiparametric efficiency bound is not correct. In equations (C.2)-(C.3), the observed-data influence function is built by conditioning on W=(∆Y,S,SD1,D2,X), and E[F_full|W] is asserted to equal p_{d1|d2}(X)1[D2=d2]P(D=d)^{-1}(m_d-m_d'-τ). For the missing-data projection theorem, the augmentation must condition on the variables observed for all units, V=(∆Y,D2,X), not on SD1. When S=1, E[F_full|W]=F_full, so the formula collapses to F_obs=F_full and the required augmentation term is dropped; when S=0 the expression in (C.3) also omits the (∆Y-m_d'-τ) components that remain in E[F_full|V]. Hence the F_τ in Theorem 2 is not an efficient influence function. Table SE.3 corroborates this: in the 'None' row the R variance lies below the claimed SEB for τ_(11)(00) (49.404 < 51.099) and for τ_(01)(00) (63.900 < 66.058), which is impossible if the reported bound were a valid lower bound. Corollary 3 and the abstract's efficiency claim therefore need to be corrected or withdrawn.
[Section 3.1] The third illustrative claim after Corollary 2 states that identification still holds when 'missingness is driven by unobserved factors' and 'Assumption 2 depends on unobservables.' This is not supported: every case in the proof of Theorem 1 (Appendix B.2, equations (B.4)-(B.7), (B.13), (B.14)) invokes Assumption 2.1, which requires S to be independent of (D1,∆Y) given (D2,X). If missingness depends on unobserved factors correlated with treatment-effect heterogeneity, the robust estimand is generally biased because the missing-at-random condition fails. Assumption SA.2 only relaxes missingness to depend on ∆Y and supports a different IPW estimand, not the main robust estimand. The sentence should be removed or sharply qualified.

minor comments (5)

[Appendix C, eq. (C.2)] The conditioning set in (C.2) is written inconsistently: W is defined as (∆Y,S,SD1,D2,X), but the conditional expectations condition only on (∆Y,SD1,D2,X). This notation should be aligned.
[Section 2.5] The sentence 'we extend our framework to 1 < T << n' appears to confuse the time dimension with the sample size; it should state that T is an integer number of time periods with 1 < T.
[Section 6.2] There is a typo: 'standardized before before being used' should read 'standardized before being used.'
[Supplementary Appendix SA.2] The proof of Lemma SA.1 refers to 'Lemma 2.2,' but no Lemma 2.2 exists in the manuscript; the cross-reference should be corrected.
[Corollary 3] The proof is said to be in 'Supplementary Appendix D,' but Appendix D appears to be part of the main text; this cross-reference should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the robust identification result is derived algebraically from explicit assumptions with no fitted target parameter entering the proof.

full rationale

The paper's central identification claim (Theorem 1) is self-contained in the sense required by the circularity pass: the robust estimand in equation (4) is built from the outcome, propensity score, and missingness working models, and the proof in Appendix B.2 verifies by iterated expectations and the stated Assumptions 1 and 2 that, under any two correctly specified models, the estimand collapses algebraically to E[p_d(X)]^{-1} E[(m_d(X)-m_{d'}(X))p_d(X)], which is then shown to equal the PDATT in equations (B.17)-(B.18). No estimated or fitted value of tau_{dd'} appears in the identification argument, and the Monte Carlo data generating process in Section 5.1 is independent of the proposed formulas, so the numerical support is not manufactured by the estimand itself. The self-citations to Sant'Anna and Zhao and Callaway and Sant'Anna are used only to position the estimator as nesting existing doubly robust DID estimators in special cases, not to justify the novel robustness property. The efficiency claim in Corollary 3 rests on a derivation involving Tsiatis's Theorem 7.2; to the extent the conditioning set in the observed-data influence function in equations (C.2)-(C.3) may be incorrect, that is a mathematical correctness concern (and is flagged as such by the reported variance falling below the claimed bound in Table SE.3), not circularity, because the claim does not presuppose its own conclusion. Consequently, the derivation chain is not circular and merits a score of 0.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

The central identification results rest on the stated DID and MAR assumptions and on the working-model framework standard for AIPW estimators. No new physical or causal entities are postulated, and no free parameters are fitted to make the derivation work. The Monte Carlo DGP includes parameter values, but these are simulation inputs, not free parameters in the method itself.

assumptions (7)

domain assumption Assumption 1.1 No anticipation: E[Y0(d)|D=d,X] = E[Y0(0)|D=d,X].
Standard DID assumption ruling out anticipatory responses before treatment; invoked in Proposition 1 and Theorem 1.
domain assumption Assumption 1.2 Conditional parallel trends: E[Y2(0)-Y0(0)|D=d,X] = E[Y2(0)-Y0(0)|X].
Core identifying assumption for DID; needed to equate outcome differences with causal path effects.
domain assumption Assumption 1.3 Overlap: P(D=d|X) bounded away from 1.
Ensures comparison groups exist for each treatment path; standard in causal inference.
domain assumption Assumption 2.1 Missing at random: S is independent of (D1, DeltaY) given D2 and X.
Key missingness assumption; permits reweighting by q_d2(X) and identification of outcome and propensity models from complete cases.
domain assumption Assumption 2.2 Partial observability: 0 < P(S=1|D2=d2,X) <= 1.
Guarantees the missingness weights are well-defined.
standard math Assumption 3 Random sampling: observed units are i.i.d. draws.
Provides the stochastic framework for root-n inference.
standard math Appendix D Conditions 1-5: compact parameter spaces, dominance, twice differentiability, and asymptotic linear representation of first-step estimators.
Technical regularity conditions for Theorem 3; not needed for the identification result.

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Pith. "Pith review of Identification of dynamic treatment effects when treatment histories are partially observed." pith.science (2026). https://pith.science/paper/H5VWHE2L

@misc{pith2026250104853,
  author       = {Pith},
  title        = {Pith review of: Identification of dynamic treatment effects when treatment histories are partially observed},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H5VWHE2L}},
  note         = {Machine review of arXiv:2501.04853}
}

read the original abstract

This paper presents a general difference-in-differences framework for identifying path-dependent treatment effects when treatment histories are partially observed. We introduce a novel robust estimator that adjusts for missing histories using a combination of outcome, propensity score, and missing treatment models. We show that this approach identifies the target parameter as long as \textit{any two} of the three models are correctly specified. The method delivers improved robustness against competing alternatives under the same set of identifying assumptions. Theoretical results and numerical experiments demonstrate how the proposed method yields more accurate inference compared to conventional and doubly robust estimators, particularly under nontrivial missingness and misspecification scenarios. Two applications demonstrate that the robust method can produce substantively different estimates of path-dependent treatment effects relative to conventional approaches.

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Works this paper leans on

64 extracted references · 60 canonical work pages

[1]

Abrevaya, J. and S. G. Donald (2017): A GMM approach for dealing with missing data on regressors, Review of Economics and Statistics, 99, 657--662

work page 2017
[2]

Arkhangelsky, D. and G. W. Imbens (2022): Doubly robust identification for causal panel data models, The Econometrics Journal, 25, 649--674

work page 2022
[3]

Arkhangelsky, D., G. W. Imbens, L. Lei, and X. Luo (2021): Double-robust two-way-fixed-effects regression for panel data, arXiv preprint arXiv:2107.13737

work page Pith review arXiv 2021
[4]

o f, T. Lundgren, T. Abzhandadze, and M. Jansson-Fr \

Badinlou, F., F. Rahimian, M. Hedman-Lagerl \"o f, T. Lundgren, T. Abzhandadze, and M. Jansson-Fr \"o jmark (2024): Trajectories of mental health outcomes following COVID-19 infection: a prospective longitudinal study, BMC Public Health, 24, 452

work page 2024
[5]

Bang, H. and J. M. Robins (2005): Doubly robust estimation in missing data and causal inference models, Biometrics, 61, 962--973

work page 2005
[6]

Benatia, and V

Bell \'e go, C., D. Benatia, and V. Dortet-Bernadet (2024): The chained difference-in-differences, Journal of Econometrics, 105783

work page 2024
[7]

Botosaru, I. and F. H. Gutierrez (2018): Difference-in-differences when the treatment status is observed in only one period, Journal of Applied Econometrics, 33, 73--90

work page 2018
[8]

Callaway, B. and T. Li (2019): Quantile treatment effects in difference in differences models with panel data, Quantitative Economics, 10, 1579--1618

work page 2019

Show all 64 references

[9]

--- -.1pt --- -.1pt --- (2023 a ): Evaluating policies early in a pandemic: bounding policy effects with nonrandomly missing data, Review of Economics and Statistics, 1--45

2023
[10]

--- -.1pt --- -.1pt --- (2023 b ): Policy evaluation during a pandemic, Journal of Econometrics, 236, 105454

2023
[11]

Callaway, B. and P. H. Sant’Anna (2021): Difference-in-differences with multiple time periods, Journal of Econometrics, 225, 200--230

2021
[12]

Chernozhukov, V., J. C. Escanciano, H. Ichimura, W. K. Newey, and J. M. Robins (2022): Locally robust semiparametric estimation, Econometrica, 90, 1501--1535

2022
[13]

Coe, J. E. (2019): Estimation of Panel Data Models with Missing Covariate Values, The University of Texas at Austin

2019
[14]

De Chaisemartin, C. and X. D'Haultfoeuille (2020): Two-way fixed effects estimators with heterogeneous treatment effects, American Economic Review, 110, 2964--96

2020
[15]

rep., National Bureau of Economic Research

--- -.1pt --- -.1pt --- (2022): Two-way fixed effects and differences-in-differences estimators with several treatments, Tech. rep., National Bureau of Economic Research

2022
[16]

--- -.1pt --- -.1pt --- (2024): Difference-in-differences estimators of intertemporal treatment effects, Review of Economics and Statistics, 1--45

2024
[17]

De Chaisemartin, C. and X. D’haultf uille (2023): Two-way fixed effects and differences-in-differences estimators with several treatments, Journal of Econometrics, 236, 105480

2023
[18]

Farrell, M. H. (2015): Robust inference on average treatment effects with possibly more covariates than observations, Journal of Econometrics, 189, 1--23

2015
[19]

Hirshleifer, D

Ghanem, D., S. Hirshleifer, D. K \'e dagni, and K. Ortiz-Becerra (2024): Correcting attrition bias using changes-in-changes, Journal of Econometrics, 241, 105737

2024
[20]

(2021): Difference-in-differences with variation in treatment timing, Journal of Econometrics, 225, 254--277

Goodman-Bacon, A. (2021): Difference-in-differences with variation in treatment timing, Journal of Econometrics, 225, 254--277

2021
[21]

Graham, B. S., C. C. de Xavier Pinto, and D. Egel (2012): Inverse probability tilting for moment condition models with missing data, The Review of Economic Studies, 79, 1053--1079

2012
[22]

(1998): On the role of the propensity score in efficient semiparametric estimation of average treatment effects, Econometrica, 315--331

Hahn, J. (1998): On the role of the propensity score in efficient semiparametric estimation of average treatment effects, Econometrica, 315--331

1998
[23]

(1971): Discussion of ‘An essay on the logical foundations of survey sampling, Part I’, by D

H \'a jek, J. (1971): Discussion of ‘An essay on the logical foundations of survey sampling, Part I’, by D. Basu, Foundations of statistical inference, 326

1971
[24]

(2014): Multiply robust estimation in regression analysis with missing data, Journal of the American Statistical Association, 109, 1159--1173

Han, P. (2014): Multiply robust estimation in regression analysis with missing data, Journal of the American Statistical Association, 109, 1159--1173

2014
[25]

Han, P. and L. Wang (2013): Estimation with missing data: beyond double robustness, Biometrika, 100, 417--430

2013
[26]

Herrnson, P. and C. Stewart III (2023): The impact of COVID-19 surges on voter behavior in the 2020 US general election, Available at SSRN 4314257

2023
[27]

(2018): Estimating treatment effects in mover designs, arXiv preprint arXiv:1804.06721

Hull, P. (2018): Estimating treatment effects in mover designs, arXiv preprint arXiv:1804.06721

2018 arXiv
[28]

Imai, K. and I. S. Kim (2021): On the use of two-way fixed effects regression models for causal inference with panel data, Political Analysis, 29, 405--415

2021
[29]

(2021): What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence, arXiv preprint arXiv:2103.12374

Ishimaru, S. (2021): What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence, arXiv preprint arXiv:2103.12374

2021 arXiv
[30]

Yang, and P

Jiang, Z., S. Yang, and P. Ding (2022): Multiply robust estimation of causal effects under principal ignorability, Journal of the Royal Statistical Society Series B: Statistical Methodology, 84, 1423--1445

2022
[31]

Kang, J. D. Y. and J. L. Schafer (2007): Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data, Statistical Science, 22, 523--539

2007
[32]

Katz, L. F., J. Roth, R. Hendra, and K. Schaberg (2022): Why do sectoral employment programs work? Lessons from WorkAdvance, Journal of Labor Economics, 40, S249--S291

2022
[33]

and M.-P

Kim, J. and M.-P. Kwan (2021): The impact of the COVID-19 pandemic on people's mobility: A longitudinal study of the US from March to September of 2020, Journal of transport geography, 93, 103039

2021
[34]

Lewbel, A., J. Y. Choi, and Z. Zhou (2023): Over-identified Doubly Robust identification and estimation, Journal of Econometrics, 235, 25--42

2023
[35]

(2010): Missing treatments, Journal of Business & Economic Statistics, 28, 82--95

Molinari, F. (2010): Missing treatments, Journal of Business & Economic Statistics, 28, 82--95

2010
[36]

Morgenstern, C., D. J. Laydon, C. Whittaker, S. Mishra, D. Haw, S. Bhatt, and N. M. Ferguson (2022): The interaction of transmission intensity, mortality, and the economy: a retrospective analysis of the COVID-19 pandemic, arXiv preprint arXiv:2211.00054

2022 arXiv
[37]

(2020): Efficient GMM estimation with incomplete data, Review of Economics and Statistics, 102, 518--530

Muris, C. (2020): Efficient GMM estimation with incomplete data, Review of Economics and Statistics, 102, 518--530

2020
[38]

(2024): Doubly weighted M-estimation for nonrandom assignment and missing outcomes, Journal of Causal Inference, 12, 20230016

Negi, A. (2024): Doubly weighted M-estimation for nonrandom assignment and missing outcomes, Journal of Causal Inference, 12, 20230016

2024
[39]

Nibbering, D. and M. Oosterveen (2024): Instrument-based estimation of full treatment effects with partial compliers, Review of Economics and Statistics, 1--46

2024
[40]

Pepper, J. V. (2001): How do response problems affect survey measurement of trends in drug use? Tech. rep., National Academy Press, Washington, DC

2001
[41]

Houston, and P

Reuschke, D., D. Houston, and P. Sissons (2024): Impacts of Long COVID on workers: A longitudinal study of employment exit, work hours and mental health in the UK, Plos one, 19

2024
[42]

Robins, J. M., A. Rotnitzky, and L. P. Zhao (1994): Estimation of regression coefficients when some regressors are not always observed, Journal of the American statistical Association, 89, 846--866

1994
[43]

Roth, J., P. H. Sant'Anna, A. Bilinski, and J. Poe (2022): What's trending in difference-in-differences? A synthesis of the recent econometrics literature, arXiv preprint arXiv:2201.01194

2022 arXiv
[44]

Sant’Anna, P. H. and J. Zhao (2020): Doubly robust difference-in-differences estimators, Journal of Econometrics, 219, 101--122

2020
[45]

Scharfstein, D. O., A. Rotnitzky, and J. M. Robins (1999): Adjusting for nonignorable drop-out using semiparametric nonresponse models, Journal of the American Statistical Association, 94, 1096--1120

1999
[46]

Shi, X., W. Miao, J. C. Nelson, and E. J. Tchetgen Tchetgen (2020): Multiply robust causal inference with double-negative control adjustment for categorical unmeasured confounding, Journal of the Royal Statistical Society Series B: Statistical Methodology, 82, 521--540

2020
[47]

(2024): Difference-in-differences design with outcomes missing not at random, arXiv preprint arXiv:2411.18772

Shin, S. (2024): Difference-in-differences design with outcomes missing not at random, arXiv preprint arXiv:2411.18772

2024 arXiv
[48]

Silliman, M. and H. Virtanen (2022): Labor market returns to vocational secondary education, American Economic Journal: Applied Economics, 14, 197--224

2022
[49]

S oczy \'n ski, T. and J. M. Wooldridge (2018): A general double robustness result for estimating average treatment effects, Econometric Theory, 34, 112--133

2018
[50]

(2018): Semiparametric weighting estimators for multi-period difference-in-differences designs, in Annual Conference of the American Political Science Association, August, vol

Strezhnev, A. (2018): Semiparametric weighting estimators for multi-period difference-in-differences designs, in Annual Conference of the American Political Science Association, August, vol. 30

2018
[51]

Sun, L. and S. Abraham (2021): Estimating dynamic treatment effects in event studies with heterogeneous treatment effects, Journal of Econometrics, 225, 175--199

2021
[52]

Tchetgen Tchetgen, E. J. and I. Shpitser (2014): Estimation of a semiparametric natural direct effect model incorporating baseline covariates, Biometrika, 101, 849--864

2014
[53]

Tsiatis, A. A. (2006): Semiparametric theory and missing data, vol. 4, Springer

2006
[54]

Vermeulen, K. and S. Vansteelandt (2015): Bias-reduced doubly robust estimation, Journal of the American Statistical Association, 110, 1024--1036

2015
[55]

Viviano, D. and J. Bradic (2021): Dynamic covariate balancing: estimating treatment effects over time with potential local projections, arXiv preprint arXiv:2103.01280

2021
[56]

Wang, L. and E. Tchetgen Tchetgen (2018): Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables, Journal of the Royal Statistical Society Series B: Statistical Methodology, 80, 531--550

2018
[57]

Wei, K., G. Qin, J. Zhang, and X. Sui (2023): Multiply robust estimation of the average treatment effect with missing outcomes, Journal of Statistical Computation and Simulation, 93, 1479--1495

2023
[58]

Xia, F. and K. C. G. Chan (2023): Identification, semiparametric efficiency, and quadruply robust estimation in mediation analysis with treatment-induced confounding, Journal of the American Statistical Association, 118, 1272--1281

2023
[59]

(2022): Doubly Robust Difference-in-Differences with General Treatment Patterns, arXiv preprint arXiv:2212.13226

Yanagi, T. (2022): Doubly Robust Difference-in-Differences with General Treatment Patterns, arXiv preprint arXiv:2212.13226

2022 arXiv
[60]

Zhang, Z., W. Liu, B. Zhang, L. Tang, and J. Zhang (2016): Causal inference with missing exposure information: Methods and applications to an obstetric study, Statistical methods in medical research, 25, 2053--2066

2016
[61]

Zimmerman, S. D. (2014): The returns to college admission for academically marginal students, Journal of Labor Economics, 32, 711--754

2014
[62]

Bollinger, C. R. and B. T. Hirsch (2006): Match bias from earnings imputation in the Current Population Survey: The case of imperfect matching, Journal of Labor Economics, 24, 483--519

2006
[63]

Burkhauser, R. V., S. Feng, S. P. Jenkins, and J. Larrimore (2012): Recent trends in top income shares in the United States: reconciling estimates from March CPS and IRS tax return data, Review of Economics and Statistics, 94, 371--388

2012
[64]

Greenlees, J. S., W. S. Reece, and K. D. Zieschang (1982): Imputation of missing values when the probability of response depends on the variable being imputed, Journal of the American Statistical Association, 77, 251--261

1982

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Abrevaya, J. and S. G. Donald (2017): A GMM approach for dealing with missing data on regressors, Review of Economics and Statistics, 99, 657--662

work page 2017

[2] [2]

Arkhangelsky, D. and G. W. Imbens (2022): Doubly robust identification for causal panel data models, The Econometrics Journal, 25, 649--674

work page 2022

[3] [3]

Arkhangelsky, D., G. W. Imbens, L. Lei, and X. Luo (2021): Double-robust two-way-fixed-effects regression for panel data, arXiv preprint arXiv:2107.13737

work page Pith review arXiv 2021

[4] [4]

o f, T. Lundgren, T. Abzhandadze, and M. Jansson-Fr \

Badinlou, F., F. Rahimian, M. Hedman-Lagerl \"o f, T. Lundgren, T. Abzhandadze, and M. Jansson-Fr \"o jmark (2024): Trajectories of mental health outcomes following COVID-19 infection: a prospective longitudinal study, BMC Public Health, 24, 452

work page 2024

[5] [5]

Bang, H. and J. M. Robins (2005): Doubly robust estimation in missing data and causal inference models, Biometrics, 61, 962--973

work page 2005

[6] [6]

Benatia, and V

Bell \'e go, C., D. Benatia, and V. Dortet-Bernadet (2024): The chained difference-in-differences, Journal of Econometrics, 105783

work page 2024

[7] [7]

Botosaru, I. and F. H. Gutierrez (2018): Difference-in-differences when the treatment status is observed in only one period, Journal of Applied Econometrics, 33, 73--90

work page 2018

[8] [8]

Callaway, B. and T. Li (2019): Quantile treatment effects in difference in differences models with panel data, Quantitative Economics, 10, 1579--1618

work page 2019