Computes the distributional DiD ATT and counterfactual outcome
distribution for a single 2x2 (pre/post x treated/control) data subset.
Serves directly as the attgt_fun argument to ptetools::pte.
Identification. Under distributional parallel trends and a copula restriction (Callaway, Li, and Oka 2018), the counterfactual outcome for each control unit \(j\) is $$kcf_j = \Delta Y_{\text{ctrl},j} + Q_{1,\text{pre}}(u_j)$$ where \(\Delta Y_{\text{ctrl},j} = Y_{\text{post},j} - Y_{\text{pre},j}\) is the observed change for control unit \(j\), \(u_j = F_{0,\text{pre}}(Y_{\text{pre},j})\) is that unit's rank in the control pre-period distribution, and \(Q_{1,\text{pre}}\) is the quantile function of the treated pre-period distribution. The unconditional counterfactual distribution \(F_{Y(0),\text{post}|D=1}\) is then the (weighted) empirical CDF of \(\{kcf_j\}\).
Unlike CiC, QDiD, and MDiD, the counterfactual is indexed over
control units, not treated units. Consequently F0 and the
ATT counterfactual term are weighted by w_pre_ctrl, and no
individual treatment effect distribution (Fte) is returned.
Panel data required. The estimator needs the actual change \(\Delta Y_{\text{ctrl},j}\) for each control unit, which requires observing the same units in both periods.
Arguments
- gt_data
A data frame (typically a
gt_data_framefromptetools) with columnsname("pre"or"post"),D(treatment dummy),Y(outcome),id(unit identifier),.w(sampling weights), and any covariate columns referenced byxformula. Control units must be observed in both periods.- xformula
One-sided formula for covariates. Default
~1uses no covariates. With covariates, the unconditional rank \(u_j\) is replaced by a conditional rank estimated via quantile regression on the control pre-period (QR0tmin1), and the treated pre-period quantile is replaced by a conditional quantile (QR1tmin1) evaluated at that rank and the control unit's own covariate values.- ...
Additional arguments passed through by
ptetools; not used directly.
Value
A ptetools::attgt_noif object with the ATT estimate and, in
extra_gt_returns, F0 (weighted ECDF of counterfactual
outcomes indexed over control units), F1 (weighted ECDF of observed
treated post-period outcomes), and Fte = NULL (individual treatment
effect distribution is not identified for this estimator).