Semiparametric Inference for Functional Difference-in-Differences
Abstract
We study the functional average treatment effect on the treated in a two-period difference-in-differences design. Under conditional functional parallel trends, we derive the full-curve efficient influence function and efficiency bound and construct a cross-fitted, doubly robust estimator. Under ultra-dense observation, bounds on curve-estimation error and learner stability preserve its full-data first-order behavior. Nuisance-rate and moment conditions yield asymptotic linearity in L2; additional Sobolev regularity gives uniform Gaussian limits and valid continuous-domain bands computed on a refining grid. In simulations, estimation errors decrease with sample size under single-model misspecification, and bands accounting for nuisance estimation have near-nominal or conservative coverage. Further experiments examine basis-truncation bias and nuisance-estimation uncertainty. An application to electricity load profiles from 4389 eligible households estimates a modest reduction concentrated in evening consumption among dynamic-tariff participants.
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BibTeX
@misc{nie2026semiparametric,
title = {{Semiparametric Inference for Functional Difference-in-Differences}},
author = {Junzhu Nie and Chengxiu Ling and Mengfei Ran},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.26964},
eprint = {2605.26964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.26964},
}
RIS
TY - UNPB
TI - Semiparametric Inference for Functional Difference-in-Differences
AU - Junzhu Nie
AU - Chengxiu Ling
AU - Mengfei Ran
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2605.26964
UR - https://arxiv.org/abs/2605.26964
AB - We study the functional average treatment effect on the treated in a two-period difference-in-differences design. Under conditional functional parallel trends, we derive the full-curve efficient influence function and efficiency bound and construct a cross-fitted, doubly robust estimator. Under ultra-dense observation, bounds on curve-estimation error and learner stability preserve its full-data first-order behavior. Nuisance-rate and moment conditions yield asymptotic linearity in L^2; additional Sobolev regularity gives uniform Gaussian limits and valid continuous-domain bands computed on a refining grid. In simulations, estimation errors decrease with sample size under single-model misspecification, and bands accounting for nuisance estimation have near-nominal or conservative coverage. Further experiments examine basis-truncation bias and nuisance-estimation uncertainty. An application to electricity load profiles from 4389 eligible households estimates a modest reduction concentrated in evening consumption among dynamic-tariff participants.
ER -