Per-(cohort, time) average treatment effects

Extracts the fully disaggregated treatment-effect estimates from a fitted FETWFE / ETWFE / BETWFE object: one row for every (cohort, time) cell, with no averaging over cohorts or over event time. This is the finest-grained view of the estimated effects — the num_treats underlying parameters themselves — complementing cohortStudy() (which averages each cohort's cells over time) and eventStudy() (which averages over cohorts at each event time).

Like eventStudy(), this accessor is not available for twfeCovs() objects: that estimator has a single treatment-effect parameter per cohort (no per-time disaggregation), so its finest granularity is already cohortStudy().

Standard errors are the per-cell regression standard errors \(\sqrt{\sigma_\varepsilon^2 \, \psi' G^{-1} \psi / (NT)}\), recomputed at call time from the fit's stored design (the same Gram-matrix machinery eventStudy() uses; nothing is added to the fitted object). Because each cell is a single cohort-time parameter, the cohort-probability sampling variance that contributes to the aggregated cohortStudy() / eventStudy() standard errors is identically zero here, so a cell's SE is a single coefficient's regression SE.

Confidence intervals and p-values are pointwise \(1 - \alpha\) Wald quantities (estimate +/- z * se). For simultaneous (family-wise) bands over the cell family, use simultaneousCIs(result, family = "all_post_treatment").

Usage

cohortTimeATTs(result, alpha = NULL)

Arguments

result: A fitted object from fetwfe(), etwfe(), or betwfe() (or their *WithSimulatedData() wrapper analogs, which return the same classes). twfeCovs() objects are not supported (see Description).
alpha: Numeric in (0, 1); the pointwise confidence level is 1 - alpha. Defaults to the alpha stored on the fit.

Value

A data frame with class c("cohortTimeATTs", "data.frame") containing one row per (cohort, time) treatment-effect cell, sorted by cohort then time, with columns:

cohort: Character; the cohort label (the calendar time at which the cohort first received treatment), matching cohortStudy().
time: Numeric; the calendar time of the cell, equal to the cohort's adoption time plus the event time (0, 1, ...). Real panels carry their actual calendar times. For synthetic genCoefs() / simulateData() fixtures (whose panel runs 1, ..., T, so the stored first year is 1) this coincides with the 1-based panel-time index. (Only a hand-built or legacy fit with no stored first year falls back to that panel-time index directly.)
estimate: Numeric; the cell's ATT estimate.
se: Numeric; the pointwise standard error. 0 for a cell zeroed out by the fusion/bridge penalty while other cells survive (fetwfe() / betwfe()); NA when standard errors are unavailable — the fit was computed with q >= 1, the Gram matrix on the selected support is singular, or the penalty zeroed the entire treatment block (no cells selected, so there is no support to recompute the Gram from; this matches eventStudy()).
ci_low, ci_high: Numeric; the pointwise 1 - alpha Wald bounds estimate -/+ qnorm(1 - alpha/2) * se. (0, 0) for a fused-away cell; NA when se is NA.
p_value: Numeric; the two-sided pointwise Wald p-value 2 * pnorm(-|estimate / se|). NA when se is 0 or NA.
selected: (fetwfe() / betwfe() only.) Logical; TRUE when the bridge penalty left the cell's estimate nonzero. Absent for etwfe(), which does not perform selection.

Use tidy(cohortTimeATTs(result)) (with the broom package loaded) to reshape to broom convention; see tidy.cohortTimeATTs().

Details

The cell standard error is computed from psi, the cell's row of the (selected) treatment-effect design — for fetwfe() the relevant row of the inverse fusion transform \(D^{-1}\) in the transformed (theta) coordinate space, for betwfe() / etwfe() a unit selector in the original (beta) coordinate space restricted to the selected support. It is never gated on the point estimate: a cell whose estimate is exactly zero because the penalty fused it away has an all-zero psi and therefore se = 0 (the correct degenerate value), while a cell whose estimate happens to be near zero for other reasons still receives its proper nonzero SE.

Examples

if (FALSE) { # \dontrun{
  coefs <- genCoefs(G = 3, T = 6, d = 2, density = 0.5, eff_size = 2)
  dat <- simulateData(coefs, N = 120, sig_eps_sq = 1, sig_eps_c_sq = 0.5, seed = 123)
  res <- fetwfeWithSimulatedData(dat)
  cta <- cohortTimeATTs(res)
  cta
  # Broom-shape translation:
  if (requireNamespace("broom", quietly = TRUE)) {
    broom::tidy(cta)
  }
} # }