Naive gross bound on the average treatment effect

The treated mean is taken at face value as E[y(1)] and nothing at all is assumed about E[y(0)] beyond the observed support, so the counterfactual mean is placed at each end of that support in turn. The width of the interval is exactly the range of y, whatever the data look like, which is the point: the bound shows how little the data alone deliver.

Usage

Bndnvg(y, D)

Arguments

y

Observed outcome.

D

Binary treatment indicator, coded 0/1.

Value

List with lower, upper, width, estimate, p_treated, n.

Details

Formula: [E(y | D = 1) - y_1, E(y | D = 1) - y_0] with y_0 = min y and y_1 = max y.

References

Manski, C. F. (1990). Nonparametric bounds on treatment effects. American Economic Review Papers and Proceedings 80(2), 319-323. Restated as equation (2.11) of Molinari, F. (2021), Microeconometrics with partial identification, Handbook of Econometrics 7A, 355-486 (arXiv:2004.11751 p. 17).

Examples

set.seed(1)
r <- Bndnvg(y = rnorm(10), D = rbinom(10, 1, 0.5)); TRUE
#> [1] TRUE