Judge-leniency instrument on observed data: Wald ratio, compliers and the defier sensitivity

From an instrument z (0 lenient, 1 harsh), the treatment d it moved and the outcome y, reports the first stage, the intention-to-treat contrast and the Wald ratio. Under monotonicity the Wald ratio is the mean effect among compliers and the type shares are identified: always-takers \(P(d=1 \mid z=0)\), never-takers \(P(d=0 \mid z=1)\), compliers the rest (Research.P14.late_identification). The defier sensitivity reports, for assumed defier shares and defier effects, the compliers' effect the same Wald ratio would imply (wald_with_defiers): the estimand depends on an assumption the data cannot check.

Usage

morie_judge_iv(
  z,
  d,
  y,
  weights = NULL,
  defier_share = c(0, 0.05, 0.1),
  defier_effect = 0
)

Arguments

z

Instrument (0/1), e.g. a harsh-judge indicator or leniency above the median.

d

Treatment (0/1), e.g. pretrial detention.

y

Outcome.

weights

Optional non-negative weights.

defier_share, defier_effect

Assumed defier shares and effects for the sensitivity table.

Value

A list with first_stage, itt, wald, shares_if_monotone, sensitivity (a data frame of implied complier effects) and theorems.

Examples

set.seed(2)
n <- 2000; z <- rbinom(n, 1, 0.5)
d0 <- rbinom(n, 1, 0.2); d1 <- pmax(d0, rbinom(n, 1, 0.5))     # monotone
d <- ifelse(z == 1, d1, d0); y <- 0.3 * d + rnorm(n)
morie_judge_iv(z, d, y)[c("first_stage", "wald")]
#> $first_stage
#> [1] 0.4176417
#> 
#> $wald
#> [1] 0.2047033
#>