lou_qtt: 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
)

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.

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).

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.

Examples

Run this code

# \donttest{
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)
# }