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Non-parametric Inference for GSC (Xu 2017)

Source: R/gsc.R
gsc_inference.Rd

Estimates SE and confidence intervals for the ATT by re-estimating the fit on resampled units: a bootstrap of the treated and the control units, drawn separately, or a jackknife that drops one unit at a time. Works for both sharp and staggered GSC fits.

Usage

gsc_inference(
  fit,
  method = c("bootstrap", "jackknife", "jackknife_global"),
  n_boot = 499L,
  level = 0.95,
  alternative = c("two.sided", "greater", "less"),
  seed = NULL
)

Arguments

fit

A coresynth object from scm_fit() with method = "gsc".

method

"bootstrap" (default), "jackknife", or "jackknife_global" (staggered fits only).

n_boot

Number of bootstrap replications (default 499L; ignored for jackknife).

level

Confidence level (default 0.95).

alternative

"two.sided" (default), "greater", or "less".

seed

RNG seed for reproducibility (default NULL).

Value

A list of class coresynth_inference.

Details

Xu (2017, S.3.2) notes that resampling units is valid when many units are treated and proposes the parametric bootstrap of gsc_boot() for when few are: the treated units' own noise varies across replicates only through which treated units are drawn. With a single treated unit there is no such variation, so this function stops and points to gsc_boot() and conformal_inference().

On a staggered fit the bootstrap draws the treated units from all cohorts together, so cohort sizes vary across replicates, and draws the controls once per replicate for every cohort; cohorts are rebuilt from the draw and combined with their N_treated * T_post weights. "jackknife" drops each cohort's own donors and treated units and combines the per-cohort variances by the delta method, which ignores the covariance that shared donors induce between cohorts; "jackknife_global" drops every unit from the whole panel in turn and keeps it. Both jackknives drop treated units, so every cohort needs at least two (Clarke et al. 2024, Algorithm 3).

Note: gsc_boot() performs a parametric bootstrap under H0 (hypothesis testing). gsc_inference() provides non-parametric SE and CIs suitable for inference about the ATT magnitude.