Computes the MDiD 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. Panel
vs. repeated cross sections is detected automatically from whether the
same unit ids appear in both periods.
Identification. MDiD assumes that the counterfactual distribution of untreated potential outcomes for the treated group in the post period is a location shift of the treated group's pre-period distribution: $$F_{Y(0),\text{post}|D=1}(y) = F_{Y,\text{pre}|D=1}(y - \Delta)$$ where \(\Delta = E[Y_{\text{post}}|D=0] - E[Y_{\text{pre}}|D=0]\) is the mean DiD (the change in mean outcomes for the untreated group). The counterfactual quantile function is therefore \(Q_{Y(0),\text{post}|D=1}(\tau) = Q_{Y,\text{pre}|D=1}(\tau) + \Delta\).
Covariate adjustment. With covariates, the scalar shift \(\Delta\) is replaced by a unit-specific conditional mean shift \(\Delta(X_i) = E[Y_{\text{post}}|D=0, X_i] - E[Y_{\text{pre}}|D=0, X_i]\), estimated by weighted OLS on the control group in each period. The counterfactual for treated pre-period unit \(i\) is \(Y_{\text{pre},i} + \Delta(X_i)\). The unconditional counterfactual distribution is the empirical CDF of these shifted values, which by the law of iterated expectations consistently estimates \(F_{Y(0),\text{post}|D=1}(y) = \int F_{Y,\text{pre}|D=1,X=x}(y - \Delta(x))\,dF_{X|D=1}(x)\).
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.- xformula
One-sided formula for covariates. Default
~1uses no covariates. With covariates, separate weighted OLS regressions are fit on the control group in each period; see Details above.- ...
Additional arguments passed through by
ptetools; not used directly.
Value
A ptetools::attgt_noif object with the ATT estimate and, in
extra_gt_returns, three objects: F1 (weighted ECDF of
observed treated outcomes in the post period), F0 (weighted ECDF
of counterfactual untreated outcomes for the treated group), and Fte
(weighted ECDF of individual treatment effects; NULL for repeated
cross sections).