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Difference-in-Differences with Compositional Changes

Pedro H. C. Sant'Anna, Qi Xu

arXiv 27 Apr 2023 · Econometrics · publishedJournal of Econometrics (2025) · 4 citations (OpenAlex)

arXiv:2304.13925 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies difference-in-differences (DiD) setups with repeated cross-sectional data and potential compositional changes across time periods. We begin our analysis by deriving the efficient influence function and the semiparametric efficiency bound for the average treatment effect on the treated (ATT). We introduce nonparametric estimators that attain the semiparametric efficiency bound under mild rate conditions on the estimators of the nuisance functions, exhibiting a type of rate doubly robust (DR) property. Additionally, we document a trade-off related to compositional changes: We derive the asymptotic bias of DR DiD estimators that erroneously exclude compositional changes and the efficiency loss when one fails to correctly rule out compositional changes. We propose a nonparametric Hausman-type test for compositional changes based on these trade-offs. The finite sample performance of the proposed DiD tools is evaluated through Monte Carlo experiments and an empirical application. We consider extensions of our framework that accommodate double machine learning procedures with cross-fitting, and setups when some units are observed in both pre- and post-treatment periods. As a by-product of our analysis, we present a new uniform stochastic expansion of the local polynomial multinomial logit estimator, which may be of independent interest.

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Sant’Anna and Zhao (2020) Doubly robust difference-in-differences estimators1.000356100%
2Abadie (2005) Semiparametric Difference-in-Difference Estimators0.92843100%
3Sequeira (2016) Corruption, trade costs, and gains from tariff liberalization: Evidence from Southern Africa0.874162100%
4Hong (2013) Measuring the effect of Napster on recorded music sales: difference-in-differences estimates under compositional changes0.87452100%
5Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, Newey and Robins (2017) Double/debiased machine learning for treatment and structural parameters0.73732100%
6Kennedy (2023) Semiparametric Doubly Robust Targeted Double Machine Learning: A Review0.73732100%
7Rothe and Firpo (2019) Properties of doubly robust estimators when nuisance functions are estimated nonparametrically0.73732100%
8Heckman, Ichimura and Todd (1997) Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme0.64422100%
9Newey (1994) The asymptotic variance of semiparametric estimators0.64422100%
10Smucler, Rotnitzky and Robins (2019) A unifying approach for doubly-robust $_1$ regularized estimation of causal contrasts0.64422100%

Showing the top 10 of 58 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Synthetic Parallel Trends0.73732
2Difference-in-Differences Designs: A Practitioner's Guide0.69381
3Semiparametric Triple Difference Estimators0.58531
4Conditional Triple Difference-in-Differences0.40511
5Difference-in-Differences Meets Synthetic Control: Doubly Robust Identification and Estimation0.40511
6Better Understanding Triple Differences Estimators0.40511