Computes the panel QTT and counterfactual outcome distribution
for a single (g,t) cell using the three-period copula-stability estimator
of Callaway and Li (2019). Serves directly as the attgt_fun
argument to ptetools::pte.
Identification. Under copula stability $$C(F_{Y^{\text{pre2}}|D=1},\, F_{\Delta Y^{\text{pre}}|D=1}) = C(F_{Y^{\text{pre1}}(0)|D=1},\, F_{\Delta Y^{\text{post}}(0)|D=1})$$ and distributional parallel trends on changes $$F_{\Delta Y^{\text{post}}(0)|D=1} = F_{\Delta Y^{\text{ctrl}}}$$ the counterfactual outcome for each treated unit \(i\) is \(kcf_i = L_i + C_i,\) where \(L_i = Q_{Y^{\text{pre1}}|D=1}(u_i)\) is the treated pre1 quantile at rank \(u_i = F_{Y^{\text{pre2}}|D=1}(Y^{\text{pre2}}_i)\) (the Rosenblatt transform), and \(C_i = Q_{\Delta Y^{\text{ctrl}}}(v_i)\) is the control change at rank \(v_i = F_{\Delta Y^{\text{pre}}|D=1}(\Delta Y^{\text{pre}}_i)\). The goal is distributional: \(\{kcf_i\}\) is a sample from \(F_{Y(0)^{\text{post}}|D=1}\), not individual counterfactuals.
Panel data required for both groups. Three periods for treated (pre2, pre1, post) and two for control (pre1, post).
Value
A ptetools::attgt_noif object with att and, in
extra_gt_returns, F0 (counterfactual ECDF), F1
(observed post ECDF), and Fte (individual-effect ECDF).