mdid_gt: Mean Difference-in-Differences: group-time estimator

In qte: Quantile Treatment Effects

Mean Difference-in-Differences: group-time estimator

Description

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).

Usage

mdid_gt(gt_data, xformula = ~1, ...)

Arguments

gt_data	A data frame (typically a gt_data_frame from ptetools) with columns name ("pre" or "post"), D (treatment dummy), Y (outcome), id (unit identifier), .w (sampling weights), and any covariate columns referenced by xformula.
xformula	One-sided formula for covariates. Default ~1 uses 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).

References

Athey, Susan and Guido Imbens. “Identification and Inference in Nonlinear Difference-in-Differences Models.” Econometrica 74(2), pp. 431-497, 2006.

Thuysbaert, Bram. “Distributional Comparisons in Difference in Differences Models.” Working Paper, 2007.

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