Monotone treatment selection bounds (alias of Mtsbound)

This module is an ALIAS. The bound is implemented once, in Mtsbound (module bdmnsl); this entry point only supplies the argument spelling used by the selection-bounds literature and the direction switch, then delegates.

Usage

Mtsbnd(Y, X, monotone = TRUE, d = NULL, ymin = NULL, ymax = NULL)

Arguments

Y

Observed outcomes.

X

Observed (selected) treatment levels.

monotone

TRUE if higher selection implies weakly higher outcomes.

d

Level whose mean counterfactual is bounded; defaults to max(X).

ymin, ymax

A priori outcome support; default to the observed range.

Value

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

Details

Under monotone treatment selection, E[Y(d)] <= P(X<=d) E[Y|X=d] + P(X>d) ymax and E[Y(d)] >= P(X<d) ymin + P(X>=d) E[Y|X=d]. monotone = FALSE reverses the selection inequality, which is the same bound on -Y over the reflected support with the sides swapped back.

References

Manski and Pepper (2000), Econometrica 68(4), 997-1010. Standard published form; see bdmnsl for the availability note.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Mtsbnd(V, V)
#> $lower
#> [1] 1.875
#> 
#> $upper
#> [1] 8
#> 
#> $width
#> [1] 6.125
#> 
#> $condmean
#> [1] 8
#> 
#> $pbelow
#> [1] 0.875
#> 
#> $pat
#> [1] 0.125
#> 
#> $pabove
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $d
#> [1] 8
#> 
#> $method
#> [1] "Monotone treatment selection bounds (Manski-Pepper 2000)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"