Monotone treatment response bounds

L_i = y_i if z_i <= d else ymin; U_i = y_i if z_i >= d else ymax; and E[Y(d)] lies in [mean(L), mean(U)].

Usage

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

Arguments

y

Observed outcomes.

z

Observed treatment levels.

d

Treatment level whose mean counterfactual is bounded.

ymin, ymax

A priori support of the outcome.

Value

List with lower, upper, width, nfixed, n, d.

References

Manski (1997), Econometrica 65(6), 1311-1334; Manski and Pepper (2000), Econometrica 68(4), 997-1010. Standard published form; neither article is in the local corpus and neither could be downloaded, so neither was read.

Examples

set.seed(1)
Mtrbound(y = rnorm(50), z = rbinom(50, 1, 0.5), d = rbinom(50, 1, 0.5),
         ymin = -3, ymax = 3)
#> $lower
#> [1] -0.6510829
#> 
#> $upper
#> [1] 0.8906276
#> 
#> $width
#> [1] 1.54171
#> 
#> $nfixed
#> [1] 26
#> 
#> $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 response bounds (Manski 1997)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"