Confidence set for a partially identified parameter (alias)

"Confidence set for partial ID" and "inference for partially identified parameters" name the same test inversion: the set of parameter values a moment-inequality test fails to reject. This name forwards to Bndinf rather than repeating the construction.

Usage

Bnscnf(theta_grid, moments, alpha = 0.05)

Arguments

theta_grid: Candidate parameter values to test.
moments: Interval data, an (n, 2) matrix.
alpha: Miss probability, default 0.05.

Value

The payload of Bndinf.

References

Imbens, G. W. and Manski, C. F. (2004). Confidence intervals for partially identified parameters. Econometrica 72(6), 1845-1857. The set reported is the criterion level set of Chernozhukov, Hong and Tamer (2007) as given in equation (4.10) of Molinari, F. (2021), Handbook of Econometrics 7A (arXiv:2004.11751 p. 97).

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
D <- data.frame(x = c(1, 2, 3, 4), y = c(2, 4, 5, 9))
Bnscnf(V, D)
#> $lower
#> [1] 1.438252
#> 
#> $upper
#> [1] 7.421159
#> 
#> $width
#> [1] 5.982907
#> 
#> $grid_lower
#> [1] 2
#> 
#> $grid_upper
#> [1] 7
#> 
#> $n_in_set
#> [1] 6
#> 
#> $cutoff
#> [1] 2.705543
#> 
#> $criterion_min
#> [1] 0
#> 
#> $n
#> [1] 4
#> 
#> $method
#> [1] "Confidence set for partial ID"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"