Monotone treatment selection and monotone treatment response are
separate assumptions, each of which alone identifies an interval
containing E[Y(d)]. Maintaining both means the truth lies in
both intervals, so the joint bound is their intersection:
lower = max(lower_MTS, lower_MTR) and
upper = min(upper_MTS, upper_MTR).
Usage
Mtsmtv(y, D, y_min, y_max, d = NULL)
Arguments
- y
Observed outcomes.
- D
Observed treatment levels on an ordered scale.
- y_min, y_max
A priori outcome support.
- d
Level whose mean counterfactual is bounded; defaults to
max(D).
Value
List with lower, upper, width, mts_lower, mts_upper, mtr_lower,
mtr_upper, empty, n, d.
Details
Because both components are valid under their own assumption, the
intersection is non-empty whenever the two assumptions are jointly
consistent with the data; an empty result is evidence against the pair
and is flagged rather than returned as a negative width.
The components are not recomputed here: MTS is Mtsbound and MTR
is Mtrbound.
References
Manski and Pepper (2000), Econometrica 68(4), 997-1010.
Standard published form; see bdmnsl for the availability note.
Examples
set.seed(2)
D <- sample(0:2, 300, TRUE)
y <- pmin(pmax(0.2 + 0.2 * D + rnorm(300, sd = 0.1), 0), 1)
Mtsmtv(y, D, y_min = 0, y_max = 1, d = 2)[c("lower", "upper", "empty")]
#> $lower
#> [1] 0.3891324
#>
#> $upper
#> [1] 0.5924826
#>
#> $empty
#> [1] 0
#>
