Entrywise Inference for Causal Panel Data: A Simple and Instance-Optimal Approach
arxiv(2024)
摘要
In causal inference with panel data under staggered adoption, the goal is to
estimate and derive confidence intervals for potential outcomes and treatment
effects. We propose a computationally efficient procedure, involving only
simple matrix algebra and singular value decomposition. We derive
non-asymptotic bounds on the entrywise error, establishing its proximity to a
suitably scaled Gaussian variable. Despite its simplicity, our procedure turns
out to be instance-optimal, in that our theoretical scaling matches a local
instance-wise lower bound derived via a Bayesian Cramér-Rao argument. Using
our insights, we develop a data-driven procedure for constructing entrywise
confidence intervals with pre-specified coverage guarantees. Our analysis is
based on a general inferential toolbox for the SVD algorithm applied to the
matrix denoising model, which might be of independent interest.
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