Intersection bounds on the ATE under an exclusion restriction

If the excluded variable X shifts who gets treated but not the counterfactual means, then each value of X yields its own worst-case interval for the same E[y(t)], and the parameter must lie in all of them at once. Intersecting is what makes the assumption bite; it is also what makes it refutable, since an empty intersection contradicts mean independence.

Usage

Bnstvr(y, D, X)

Arguments

y

Observed outcome.

D

Binary treatment indicator, coded 0/1.

X

Discrete excluded variable, one value per unit.

Value

List with lower, upper, width, estimate, n_cells, refuted, n.

Details

Formula: E[y(t)] in [max_x lower(x), min_x upper(x)], then the ATE interval formed from the two intersected arms.

References

Manski, C. F. (1995). Identification Problems in the Social Sciences. Harvard University Press. Intersection-bound form as equation (2.15) of Molinari, F. (2021), Handbook of Econometrics 7A (arXiv:2004.11751 p. 19).

Examples

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