Bootstrap inference for confidence intervals in the factor-augmented potential outcomes model

Develop a bootstrap technique for constructing confidence intervals for the estimators defined in the factor-augmented potential outcomes model y_it(d) = lambda_{*i}(d)^T f_t + u_{it}(d), where the common factors f_t are estimated from the auxiliary panel X via principal components analysis and the loadings lambda_{*i}(d) are estimated by regressing y_{it} on interactions of the estimated factors with functions of d_{it}. The bootstrap should deliver valid inference for unit-specific, time-specific, and overall average marginal effects (Δ_i, Δ_t, and Δ) and related estimators under the asymptotic regimes considered (T,L→∞, and when applicable N→∞).

Background

The paper introduces a factor-augmented model for potential outcomes with a possibly continuous treatment, linking y_it(d) through common factors f_t that are learned from an auxiliary high-dimensional panel X via principal components analysis. Loadings lambda_{*i}(d) are estimated by regressing observed outcomes on interactions of the estimated factors with functions of the treatment, enabling estimation of unit-specific, time-specific, and overall average marginal effects.

While the authors derive large-sample normal approximations and propose variance estimators (including HAC options) for key estimators, they point out that a bootstrap-based approach could simplify inference and provide a unified method for constructing confidence intervals across a broader set of estimators within their framework. They explicitly note that this remains open for future research.