Monotone instrumental variable bounds

LB(t|v) = max_{u <= v} LB(t|u), UB(t|v) = min_{u >= v} UB(t|u), then average over P(V = v).

Usage

Mivbound(lower, upper, prob)

Arguments

lower, upper

Per-value bounds in increasing order of v.

prob

P(V = v), same order; normalised internally.

Value

List with lower, upper, width, lowerv, upperv, prob, k.

References

Manski and Pepper (2000), Econometrica 68(4), 997-1010; the bound in its standard published form.

Examples

Mivbound(lower = 5L, upper = 5L, prob = 0.5)
#> $lower
#> [1] 5
#> 
#> $upper
#> [1] 5
#> 
#> $width
#> [1] 0
#> 
#> $lowerv
#> [1] 5
#> 
#> $upperv
#> [1] 5
#> 
#> $prob
#> [1] 1
#> 
#> $k
#> [1] 1
#> 
#> $method
#> [1] "Monotone instrumental variable bounds (Manski-Pepper 2000)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"