Intersection of the instrument bound and the shape bound

The two assumptions restrict different things – the instrument restricts selection, monotone response restricts the outcome – so their identified sets intersect rather than nest, and the joint bound can be strictly tighter than either. Reporting the two components alongside the intersection shows which assumption is doing the work, and an empty intersection means the two are jointly refuted.

Usage

Bnsipv(y, D, Z)

Arguments

y

Observed outcome.

D

Binary treatment, coded 0/1.

Z

Discrete instrument, one value per unit.

Value

List with lower, upper, width, estimate, iv_lower, iv_upper, mtr_lower, mtr_upper, refuted, n. mtr_upper, refuted, n.

Details

Formula: instrument bound from Molinari (2021) equation (2.15), shape bound [0, upper] from equation (2.13), intersected.

References

Mogstad, M., Santos, A. and Torgovitsky, A. (2018). Using instrumental variables for inference about policy relevant treatment parameters. Econometrica 86(5), 1589-1619. doi:10.3982/ECTA15463 ; their general linear-programming machinery ships as morie_bnd_lp. The component bounds are equations (2.15) and (2.13) of Molinari, F. (2021), Handbook of Econometrics 7A (arXiv:2004.11751 pp. 18-19).

Examples

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