lou_qtt: Lagged Outcome Unconfoundedness QTT

In qte: Quantile Treatment Effects

Lagged Outcome Unconfoundedness QTT

Description

Estimates the Quantile Treatment Effect on the Treated (QTT) and Average Treatment Effect on the Treated (ATT) under a lagged-outcome unconfoundedness assumption with staggered treatment adoption. The key identifying assumption is Y_{g,t}(0) \perp D \mid X, Y_{\text{pre}}, i.e., conditional on observed covariates and the pre-treatment outcome, treatment is as good as randomly assigned within each cohort-period cell.

Estimation operates at the (g,t) level: for each cohort g and post-treatment period t, a cross-sectional comparison is made between the treated group and a not-yet-treated (or never-treated) comparison group, adjusting for covariates and (optionally) the pre-treatment outcome. Group-time estimates are then aggregated to overall, dynamic, and group-specific summaries.

Three estimation methods are available:

"ipw"

Propensity-score reweighting. Control units are reweighted by \hat p(X,Y_{\text{pre}})/(1-\hat p(X,Y_{\text{pre}})) to approximate the covariate distribution of the treated group.

"or"

Outcome regression. A quantile regression model is fit on control units' post-period outcomes as a function of (X, Y_{\text{pre}}), then predicted at treated units to construct the counterfactual distribution (Melly 2006; Chernozhukov, Fernandez-Val, and Melly 2013).

"aipw"

Doubly-robust augmented IPW. Combines the propensity score and outcome models. Consistent if either model is correctly specified.

When lagged_outcome_cov = FALSE and xformula = ~1, all three methods reduce to a simple distribution comparison within each (g,t) cell, which is consistent under unconditional unconfoundedness.

The ATT analogue (without the QTT) for staggered adoption under lagged-outcome unconfoundedness is developed in Callaway (2023).

Usage

lou_qtt(
  yname,
  gname,
  tname,
  idname = NULL,
  data,
  xformula = ~1,
  lagged_outcome_cov = TRUE,
  est_method = c("ipw", "or", "aipw"),
  panel = TRUE,
  weightsname = NULL,
  control_group = "notyettreated",
  anticipation = 0,
  alp = 0.05,
  cband = TRUE,
  biters = 100,
  cl = 1,
  gt_type = c("att", "qtt"),
  probs = NULL
)

Arguments

yname	Name of the outcome variable in data.
gname	Name of the treatment group variable (first treatment period; 0 for never-treated units).
tname	Name of the time period variable.
idname	Name of the unit id variable. Required when panel = TRUE.
data	A data frame.
xformula	One-sided formula for additional covariates used in the propensity score and/or outcome model. Default ~1 uses no additional covariates beyond the lagged outcome (when lagged_outcome_cov = TRUE).
lagged_outcome_cov	Logical; if TRUE (default), the pre-treatment outcome is added as a covariate in both the propensity score and outcome models. Requires panel = TRUE.
est_method	Estimation method: "ipw" (default), "or", or "aipw". See Details.
panel	Logical; TRUE (default) for panel data, FALSE for repeated cross sections. lagged_outcome_cov = TRUE requires panel = TRUE.
weightsname	Name of the column in data containing sampling weights. Default NULL uses equal weights.
control_group	Which units to use as the comparison group: "notyettreated" (default) or "nevertreated".
anticipation	Number of periods of anticipation. Default 0.
alp	Significance level for confidence intervals. Default 0.05.
cband	Logical; if TRUE (default), report a simultaneous confidence band (uniform over all quantiles in probs) in addition to pointwise intervals.
biters	Number of bootstrap iterations. Default 100.
cl	Number of clusters for parallel bootstrap. Default 1.
gt_type	Type of group-time effect to compute. "att" (default) returns the ATT curve aggregated over (g,t) cells. "qtt" returns the full QTT curve over probs using mixture-CDF aggregation.
probs	For gt_type = "qtt", the quantile grid at which to evaluate the QTT. Default seq(0.05, 0.95, 0.05).

Value

For gt_type = "att", a pte_emp_boot object. For gt_type = "qtt", a pte_qtt object with overall, group-specific, and dynamic QTT curves, bootstrap standard errors, and pointwise and uniform confidence bands.

References

Callaway, Brantly. “Policy Evaluation during a Pandemic.” Journal of Econometrics 236(2), 2023.

Melly, Blaise. “Estimation of Counterfactual Distributions Using Quantile Regression.” Working paper, University of St. Gallen, 2006.

Chernozhukov, Victor, Ivan Fernandez-Val, and Blaise Melly. “Inference on Counterfactual Distributions.” Econometrica 81(6), pp. 2205–2268, 2013.

See Also

unc_qte for the cross-sectional (non-staggered) version. cic, qdid, mdid for alternative identification strategies with staggered adoption.

Examples

data(mpdta, package = "did")

## ATT under lagged-outcome unconfoundedness (IPW with pre-period outcome)
res_att <- lou_qtt(
  yname = "lemp", gname = "first.treat", tname = "year",
  idname = "countyreal", data = mpdta,
  lagged_outcome_cov = TRUE, est_method = "ipw",
  gt_type = "att", biters = 20
)
summary(res_att)

## QTT with doubly-robust estimation
res_qtt <- lou_qtt(
  yname = "lemp", gname = "first.treat", tname = "year",
  idname = "countyreal", data = mpdta,
  lagged_outcome_cov = TRUE, est_method = "aipw",
  gt_type = "qtt", probs = seq(0.1, 0.9, 0.1), biters = 20
)
summary(res_qtt)

qte documentation built on July 23, 2026, 5:13 p.m.