Monotone-treatment-response bounds for a binary outcome under two sentences

If a harsher sentence never lowers the outcome for any one person (monotone treatment response, Manski 1997), the contrast \(E[y(b)] - E[y(a)]\) is non-negative (Research.P11.Pop.mtr_lower) and at most \(P(y=1, z=b) + P(y=0, z=a)\), the share of people whose observed outcome leaves room for the counterfactual to differ; the upper end is attained (mtr_upper, mtr_upper_attained). Against the assumption-free interval of morie_sentence_effect_bounds (width one, contains zero) MTR buys a sign at the price of a monotonicity assumption; reversing the direction gives the bounds for a "never criminogenic" assumption.

Usage

morie_sentence_effect_mtr(
  y,
  z,
  weights = NULL,
  contrast = NULL,
  direction = c("non-decreasing", "non-increasing")
)

Arguments

y

Binary outcome per person (0/1, e.g. reconviction within two years).

z

Sentence per person, a vector with exactly two distinct values.

weights

Optional non-negative weights.

contrast

Which of the two sentence values is the treatment (default the second in sorted order); the other is the comparison.

direction

"non-decreasing" (harsher sentence never lowers the outcome) or "non-increasing".

Value

A list with levels, bounds (lower and upper on the treatment-minus-comparison contrast), width, naive_difference and theorems.

Examples

set.seed(1)
z <- sample(c("community", "custody"), 500, replace = TRUE)
y <- rbinom(500, 1, ifelse(z == "custody", 0.55, 0.35))
morie_sentence_effect_mtr(y, z)$bounds
#> lower upper 
#>   0.0   0.6