Negative-only treatment bound (decreasing monotone treatment response)

The mirror image of Bndpos. Assuming treatment never helps, y(1) <= y(0) for every unit, pins the upper bound at exactly zero; only the lower bound is estimated, and it uses every (y, D) pair.

Usage

Bndngt(y, D, y_min)

Arguments

y

Observed outcome.

D

Binary treatment indicator, coded 0/1.

y_min

Lower end of the logically possible support; at most min(y).

Value

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

Details

Formula: \(lower = [E(y | D = 1) P(D = 1) + y_min P(D = 0)] - [E(y | D = 0) P(D = 0) + y_max P(D = 1)]\), upper = 0, with y_max = max(y).

References

Manski, C. F. (1997). Monotone treatment response. Econometrica 65(6), 1311-1334. doi:10.2307/2171738 . Equation (2.13) of Molinari, F. (2021), Handbook of Econometrics 7A (arXiv:2004.11751 pp. 18-19), read with the treatment order reversed.

Examples

set.seed(1)
Bndngt(y = rnorm(40), D = rbinom(40, 1, 0.5), y_min = -3)
#> $lower
#> [1] -2.371214
#> 
#> $upper
#> [1] 0
#> 
#> $width
#> [1] 2.371214
#> 
#> $estimate
#> [1] -1.185607
#> 
#> $p_treated
#> [1] 0.45
#> 
#> $n
#> [1] 40
#> 
#> $method
#> [1] "Negative-only treatment bound"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"