Manski-Pepper MTR-MTS bounds — morie

Sharp bounds on each mean potential outcome \(E[y(t)]\) under the combined assumptions of monotone treatment response and monotone treatment selection, plus the implied bound on an average treatment effect (Manski and Pepper 2000; Manski 2007, eqs. 9.18-9.19).

Usage

morie_bndapp(y, z, t1 = NULL, t0 = NULL)

Arguments

y: Outcomes.
z: Realised treatment level per observation; its sorted unique values are the levels.
t1: Upper treatment level, default the largest level.
t0: Lower treatment level, default the smallest level.

Value

A list with levels, lower, upper, ate_lower (always 0), ate_upper, t1, t0, n, method.

References

Manski, C. F. and Pepper, J. V. (2000). Monotone instrumental variables. Econometrica, 68(4), 997-1010.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_bndapp(V, V)
#> $levels
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $lower
#> [1] 1.000 1.875 2.625 3.250 3.750 4.125 4.375 4.500
#> 
#> $upper
#> [1] 4.500 4.625 4.875 5.250 5.750 6.375 7.125 8.000
#> 
#> $ate_lower
#> [1] 0
#> 
#> $ate_upper
#> [1] 7
#> 
#> $t1
#> [1] 8
#> 
#> $t0
#> [1] 1
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Manski-Pepper (2000) MTR-MTS bounds (Manski 2007 eqs. 9.18-9.19)"
#>