Monotone treatment selection bounds

E[Y(d)] <= P(Z<=d) E[Y|Z=d] + P(Z>d) ymax and E[Y(d)] >= P(Z<d) ymin + P(Z>=d) E[Y|Z=d].

Usage

Mtsbound(y, z, d, ymin, ymax)

Arguments

y

Observed outcomes.

z

Observed treatment levels.

d

Level whose mean counterfactual is bounded.

ymin, ymax

A priori support of the outcome.

Value

List with lower, upper, width, condmean, pbelow, pat, pabove, n, d.

References

Manski and Pepper (2000), Econometrica 68(4), 997-1010; the bound in its standard published form.

Examples

set.seed(1)
Mtsbound(y = rnorm(50), z = rbinom(50, 1, 0.5), d = rbinom(50, 1, 0.5),
         ymin = -3, ymax = 3)
#> $lower
#> [1] -0.7528243
#> 
#> $upper
#> [1] 0.6886446
#> 
#> $width
#> [1] 1.441469
#> 
#> $condmean
#> [1] 0.03672386
#> 
#> $pbelow
#> [1] 0.26
#> 
#> $pat
#> [1] 0.52
#> 
#> $pabove
#> [1] 0.22
#> 
#> $n
#> [1] 50
#> 
#> $d
#>  [1] 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1
#> [39] 1 1 1 0 0 1 0 1 0 1 0 1
#> 
#> $method
#> [1] "Monotone treatment selection bounds (Manski-Pepper 2000)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"