Manski-Pepper monotone treatment response bounds, either direction

This module is an ALIAS. The increasing-response bound is implemented once, in Mtrbound (module bdmnto); this entry point adds the direction switch and delegates.

Usage

Mtrbnd(y, D, direction = "increasing", d = NULL, y_min = NULL, y_max = NULL)

Arguments

y

Observed outcomes.

D

Observed treatment levels on an ordered scale.

direction

Either "increasing" or "decreasing".

d

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

y_min, y_max

A priori outcome support; default the observed range.

Value

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

Details

Under monotone treatment response Y_i(d) >= y_i when d >= z_i and Y_i(d) <= y_i when d <= z_i, giving L_i = y_i if z_i <= d else ymin, \(U_i = y_i if z_i >= d else ymax\) and E[Y(d)] in [mean(L), mean(U)].

direction = "decreasing" asserts the reverse monotonicity, which is the same statement about the level scale run backwards and is obtained by negating the treatment levels before delegating.

References

Manski (1997), Econometrica 65(6), 1311-1334; Manski and Pepper (2000), Econometrica 68(4), 997-1010. Standard published form; see bdmnto for the availability note.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Mtrbnd(V, V)
#> $lower
#> [1] 4.5
#> 
#> $upper
#> [1] 8
#> 
#> $width
#> [1] 3.5
#> 
#> $nfixed
#> [1] 1
#> 
#> $n
#> [1] 8
#> 
#> $d
#> [1] 8
#> 
#> $method
#> [1] "Monotone treatment response bounds (Manski 1997)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"