Validity check for a collection of bound assumptions

Each maintained assumption delivers its own interval for the same scalar parameter, so all of them together deliver the intersection. An empty intersection refutes the assumptions jointly, which is the only sense in which a partial-identification analysis can be falsified: a non-empty region is consistent with the data by construction. A non-empty intersection that excludes theta_0 rejects the null.

Usage

Bndvld(lower, upper, theta_0, H0 = 1)

Arguments

lower, upper

Lower and upper end of each maintained bound, same length.

theta_0

Parameter value under test.

H0

Non-zero to test coverage of theta_0 (the default); zero to report the intersection only, leaving reject at 0.

Value

List with lower, upper, width, refuted, covers, reject, n.

Details

Formula: L = max_i lower_i, U = min_i upper_i; refuted iff L > U; covers iff L <= theta_0 <= U.

References

Manski, C. F. (2003). Partial Identification of Probability Distributions. Springer. The refutation reading of an empty identification region is stated in Molinari, F. (2021), Handbook of Econometrics 7A (arXiv:2004.11751 p. 20).

Examples

Bndvld(lower = c(1, 2, 3, 4, 5, 6, 7, 8), upper = c(1, 2, 3, 4, 5, 6, 7, 8),
  theta_0 = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $lower
#> [1] 8
#> 
#> $upper
#> [1] 1
#> 
#> $width
#> [1] -7
#> 
#> $refuted
#> [1] 1
#> 
#> $covers
#> [1] 0
#> 
#> $reject
#> [1] 1
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Validity check for bound assumptions"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"