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Debiased overall-ATT with a uniformly-valid standard error

Source: R/debiased_att.R
debiasedATT.Rd

Computes a debiased estimate of the overall average treatment effect on the treated (ATT) from a fitted fetwfe() object, together with a uniformly-valid standard error. This is a complement to the fused plug-in interval reported on the fit (fit$att_hat / fit$att_se): the fused SE is the within-selection variance and tends to under-cover the aggregated overall ATT (it omits the between-selection term), whereas debiasedATT() returns an interval with asymptotically nominal coverage at roughly the efficiency of unrestricted ETWFE.

The debiased point estimate differs from the fused fit$att_hat: when p < NT, by the OLS identity (paper eq. debiased.ols.identity) it equals the unrestricted ETWFE/OLS estimate in the ATT direction. You therefore get a dual offering — fit$att_hat / fit$att_se (fused, efficient, pointwise) and debiasedATT(fit) (debiased, ETWFE-efficient, uniformly valid). It is exposed as a separate accessor (rather than a se_type option) precisely because the debiased SE accompanies a different point estimate than the fused one.

When p >= NT the unrestricted ETWFE is infeasible, so the OLS identity no longer applies; the accessor instead builds the debiasing direction by a nodewise (desparsified-lasso) relaxed inverse (Theorem debiased.highdim.thm of Faletto (2025)). The point estimate, SE formula, and return value are otherwise identical — "one estimator, two regimes." The high-dimensional overall-ATT interval is uniformly valid under that theorem, and its coverage is validated near-nominally in simulation (0.94 at the p >= NT anchor of Faletto (2025), robust across the nodewise penalty scales studied); see Assumptions.

Usage

debiasedATT(
  fit,
  alpha = NULL,
  method = c("analytic", "bootstrap"),
  B = 1000L,
  seed = NULL,
  multiplier = c("webb", "rademacher", "mammen"),
  lambda_c = 1,
  riesz_max_iter = 5000L,
  riesz_tol = 1e-09,
  cv_time_budget = Inf
)

Arguments

fit

A fitted object from fetwfe(). In the fixed-p (p < NT) regime the SE needs either bridge selection (q < 1, gls = TRUE) or an un-whitened fit (gls = FALSE, any q, the Omega-free cluster-robust path; #312); a GLS-whitened q >= 1 fit is rejected. The high-dimensional (p >= NT) path accepts any fit. etwfe() / betwfe() / twfeCovs() are not supported (the construction is specific to the FETWFE transformed-coefficient space).

alpha

Numeric in (0, 1); the confidence level is 1 - alpha. Defaults to the alpha stored on the fit.

method

How to form the confidence interval. "analytic" (default) uses the two-channel unit-clustered sandwich SE with a Gaussian critical value. "bootstrap" replaces the Gaussian critical value with a studentized score / influence-function wild cluster bootstrap (#360), floored at the Gaussian quantile so the interval is never narrower than the analytic Wald interval. The point estimate and the reported se are unchanged; only the critical value changes.

This is not a few-clusters remedy. As an unrestricted, no-refit score bootstrap it does not reproduce the tail inflation of the restricted wild-cluster bootstrap-t, and under heterogeneous cluster influence its critical value (before the floor) falls below the Gaussian — so under the floor it reduces to the analytic interval exactly in the small-N regime; it only ever widens the interval when cluster influence is near-homogeneous. For a genuine few-clusters correction the restricted bootstrap-t or a CR2-type analytic adjustment is required (tracked as future work, #361). Supported for both single-sample and indep_counts (two-sample) fits: for a two-sample fit the cohort-weight channel is perturbed on its own independent multiplier stream over the N count-sample units (sum(indep_counts) == N is enforced), yielding the two-sample propensity variance.

B

Integer; the number of wild-bootstrap replicates (default 1000). Ignored unless method = "bootstrap".

seed

NULL (draw from the ambient RNG, the default) or a single integer for a reproducible bootstrap (the RNG state is saved and restored). Ignored unless method = "bootstrap".

multiplier

The wild-bootstrap weight distribution: "webb" (default), "rademacher", or "mammen". "rademacher" (±1) gives a constant studentization denominator (a percentile bootstrap); "webb" and "mammen" vary it (a studentized statistic). Because the critical value is floored at the Gaussian quantile, the multiplier only affects the near-homogeneous case where the bootstrap widens above the floor; in the small-N / heterogeneous regime the interval is the analytic one regardless of the weight. Ignored unless method = "bootstrap".

lambda_c

The leading constant of the high-dimensional (p >= NT) nodewise penalty lambda_node = lambda_c * max(|a|) * sqrt(log(p) / N) (N = number of units). Either a single positive number (a fixed constant; default 1.0 = the theory scale) or the string "cv", which selects the constant per fit by cross-validating the unit-level Riesz loss 0.5 v'Sigma v - a'v over the KKT-feasible region (the desparsified-lasso / auto-DML standard; van de Geer; Chernozhukov-Newey-Singh), falling back to the theory scale 1.0 when no grid penalty is feasible (#295). Larger values shrink the debiasing direction more. Ignored when p < NT. The default stays the fixed 1.0 (the theory scale); the high-dimensional coverage validated in Faletto (2025) is robust across the penalty values studied — a cross-validated selector below the theory scale and a fixed constant above it, which bracket the default 1.0 — so it needs no tuning for valid inference.

riesz_max_iter, riesz_tol

Integer / numeric; coordinate-descent controls for the high-dimensional nodewise solver. Ignored when p < NT.

cv_time_budget

Numeric; a wall-clock backstop (in seconds) for the lambda_c = "cv" cross-validation. Inf (the default) leaves selection fully deterministic / reproducible; a finite value stops the CV early and falls back to the theory scale (lambda_c = 1.0) with a warning, so an adversarial high-dimensional draw cannot spin indefinitely (#384). Whether a finite budget fires depends on machine speed, so the result can too. Ignored unless lambda_c = "cv".

Value

An object of S3 class "debiased_att" (a named list, with a print and a tidy method) with elements:

att

Numeric scalar; the debiased overall-ATT point estimate.

se

Numeric scalar; the uniformly-valid standard error, sqrt(var_reg + var_weight).

ci_low, ci_high

Numeric; the 1 - alpha interval. With method = "analytic" (default) this is the Wald interval att +/- qnorm(1 - alpha/2) * se; with method = "bootstrap" the critical value is the bootstrap crit_value (floored at qnorm(1 - alpha/2), so never narrower than the Wald interval) in place of qnorm(1 - alpha/2).

var_reg

Numeric; the regression (outcome) channel's contribution to se^2, per-unit-clustered.

var_weight

Numeric; the cohort-weight channel's contribution to se^2 — the fit's plug-in propensity variance (att_var_2), which carries the correct single- or two-sample (indep_counts) formula.

var_reg and var_weight are the two se^2-scale (unit-scale) components, so se = sqrt(var_reg + var_weight). They are not the paper's CLT-scale variances V_1^full / V_2 from Theorem debiased.att.thm, which are larger by a factor on the order of NT.

For high-dimensional (p >= NT) fits the list additionally contains feasibility (= ||Sigma v - a||_inf, the nodewise KKT certificate, which should be <= lambda_node), converged (the coordinate-descent flag), lambda_node (the penalty used), lambda_c (the leading constant used), and lambda_c_selection ("fixed" or "cv"). When lambda_c = "cv" it also contains lambda_cv, the cross-validation diagnostics (the grid, the per-grid feasibility flags and CV losses, and whether the theory-scale fallback fired). These are absent for p < NT fits.

With method = "bootstrap" the list additionally contains method, crit_value (the studentized wild-bootstrap critical value, floored at qnorm(1 - alpha/2)), B, multiplier, and alpha. The analytic default adds none of these, so its names() are unchanged.

Details

The standard error has two channels that add under marginal cohort assignment / Assumption (Psi-IF): a regression (outcome) channel, per-unit-clustered, and a cohort-weight channel for the sampling noise in the estimated cohort weights. See Assumptions below.

The cohort-weight channel is the fit's own plug-in propensity variance (att_var_2), the same quantity fit$att_se uses — so it automatically carries the correct single-sample formula and, for indep_counts fits, the two-sample formula (the weight channel concerns the estimated cohort weights, not the selection, so it is shared by the fused and debiased estimators). The fit's se_type does not affect the regression channel — debiasedATT() always computes its own per-unit-clustered version. Fits made with add_ridge = TRUE are not supported (the ridge-augmented design and post-fit un-shrink are outside the validated construction); the accessor errors on them.

Assumptions

The uniformly-valid SE relies on the hypotheses of paper Theorem debiased.att.thm:

  • Marginal cohort assignment / (Psi-IF). Cohort membership is independent of the outcome noise, so the regression and cohort-weight variance channels are uncorrelated and add. The package's default cohort weight estimator (sample proportions) satisfies this. Under confounded assignment (cohort membership correlated with treatment-effect heterogeneity) the two channels correlate and the additive SE can mis-state uncertainty; a combined per-unit score is then required (not yet implemented).

  • Correctly specified conditional mean of the outcome. Neyman-orthogonality removes first-order sensitivity to the selected nuisance coefficients, but not to mean-misspecification. The regression channel is the unit-clustered sandwich, valid as the number of units N -> infinity with no model for within-unit dependence (so a gls = FALSE fit, which skips GLS whitening, yields a valid cluster-robust SE; #307, paper Decision D1). GLS whitening (gls = TRUE) buys efficiency (an asymptotically smaller var_reg), not validity.

  • (Low-dimensional p < NT only) Asymptotically negligible ridge, lambda = o((NT)^(-1/2)) (the theoretical condition; the leading case is the exact inverse lambda = 0). The implementation does not use a vanishing schedule — it adds a fixed numerical stabilizer 1e-6 * mean(diag(Sigma)) to the Gram before solving, which is negligible and cancels in the OLS-identity case.

  • Growing number of clusters, N -> infinity. The CLT is over the N independent units, not the NT rows. With few treated units the cluster approximation is poor and the interval can under-cover; a genuine few-clusters correction (a restricted wild-cluster bootstrap-t or a CR2-type analytic adjustment, #361) is future work. The method = "bootstrap" option does not remedy this (see its documentation).

  • Regularity / two regimes. When p < NT (Theorem debiased.att.thm) the full design Gram is nonsingular and the debiasing direction is the exact inverse; the accessor reduces to debiased ETWFE. When p >= NT (the high-dimensional FETWFE theory) the Gram is singular and the direction is the nodewise (desparsified-lasso) relaxed inverse of equation debiased.highdim.v (the same estimate and SE, only v differs — "one estimator, two regimes"); it requires sparsity (s_N log(p_N) / sqrt(N) -> 0), a restricted-eigenvalue condition over sparse cones, ||v*||_1 = O(1), and a bounded limiting variance a' Sigma_theta^(-1) a. The high-dimensional branch realizes Theorem debiased.highdim.thm (Faletto 2025) with the theory-scaled penalty; its overall-ATT interval is uniformly valid, with coverage validated near-nominally in simulation (0.94 at the p >= NT anchor, robust across the nodewise penalty scales studied). Inspect the returned feasibility / converged diagnostics to confirm the per-fit nodewise directions are well-behaved.

The two regimes use different nuisances. The fixed-p branch uses the fit's bridge (q < 1) theta_hat: Theorem debiased.att.thm needs only consistency of the nuisance, and with the exact inverse this is the OLS identity. The high-dimensional branch instead fits an internal q = 1 fused lasso (grpreg::cv.grpreg(penalty = "gBridge", gamma = 1), CV-selected lambda) as the nuisance, because the high-dimensional FETWFE theory controls the orthogonalization remainder through the nuisance's l1 rate (||theta_hat - theta*||_1 = O_p(s_N lambda_theta)) — the rate the q = 1 fused lasso enjoys under a restricted-eigenvalue condition (the standard desparsified-lasso rate; cf. Negahban et al. 2012), the p >= NT extension the paper points to; the q < 1 bridge is super-efficient / non-uniform — the wrong nuisance for a uniformly-valid CI (#303). The input fit must still be q < 1 (it supplies the cohort-weight variance channel att_var_2); only the high-dimensional debiasing nuisance is q = 1. That nuisance's cross-validation uses a fixed, data-derived seed, so it is deterministic across calls (debiasedATT() and the high-dimensional simultaneousCIs() band center agree exactly) — but it is not tunable via the fit's cv_seed.

References

Faletto, G (2025). Fused Extended Two-Way Fixed Effects for Difference-in-Differences with Staggered Adoptions. arXiv preprint arXiv:2312.05985. https://arxiv.org/abs/2312.05985.

See also

fetwfe() for the fused fit; cohortTimeATTs() / eventStudy() / cohortStudy() for the disaggregated fused effects.

Examples

if (FALSE) { # \dontrun{
  coefs <- genCoefs(G = 3, T = 6, d = 2, density = 0.5, eff_size = 2, seed = 1)
  dat <- simulateData(coefs, N = 200, sig_eps_sq = 1, sig_eps_c_sq = 0.5, seed = 1)
  fit <- fetwfeWithSimulatedData(dat, q = 0.5)
  fit$att_hat # fused (pointwise)
  debiasedATT(fit) # debiased (uniformly valid)
} # }