Manski and morie_bnd_manski are the same method: the
worst-case decomposition of each counterfactual mean over the outcome
support, differenced for the ATE. This function forwards to
morie_bnd_manski with its own argument layout.
The ATE interval always has width exactly \(y_{max} - y_{min}\)
and therefore always contains zero.
Usage
Manski(y, D, y_min, y_max)
Arguments
- y
Observed outcome.
- D
Treatment indicator, coded 0/1.
- y_min
Lower endpoint of the outcome support.
- y_max
Upper endpoint of the outcome support.
Value
Whatever morie_bnd_manski returns for the ATE
case: ate_lower, ate_upper, ate_width,
y1_bounds, y0_bounds, p_treated,
contains_zero, n.
References
Manski, C. F. (1990), Nonparametric Bounds on Treatment
Effects, American Economic Review Papers and Proceedings
80(2):319-323. Molinari, F. (2021), Microeconometrics with Partial
Identification, Handbook of Econometrics 7A, eq. (2.11) and p. 18
(arXiv:2004.11751).
Examples
set.seed(16)
y <- runif(80); D <- rbinom(80, 1, 0.5)
Manski(y, D, y_min = 0, y_max = 1)[c("ate_lower", "ate_upper", "ate_width")] # width 1
#> $ate_lower
#> [1] -0.5682547
#>
#> $ate_upper
#> [1] 0.4317453
#>
#> $ate_width
#> [1] 1
#>
