Judge-leniency instrument on a known population: the exact decomposition

With every person's potential treatment under a lenient (d0) and a harsh (d1) judge and potential outcomes under release (y0) and detention (y1), the intention-to-treat contrast splits exactly into the compliers' effect mass minus the defiers' effect mass (Research.P14.itt_decomposition), the first stage into \(P(c) - P(d)\) (first_stage_decomposition), and with no defiers the Wald ratio is the compliers' mean effect (late_identification); with defiers it is \((P(c)\tau_c - P(d)\tau_d)/(P(c)-P(d))\) (wald_with_defiers), whose sign can be wrong when every individual effect is positive (defiers_can_flip). Use it on a simulated or fully specified population to see what a design can and cannot recover; morie_judge_iv is the observational counterpart.

Usage

morie_judge_iv_population(d0, d1, y0, y1, weights = NULL)

Arguments

d0, d1: Potential treatment (0/1) under instrument 0 and 1.
y0, y1: Potential outcomes under treatment 0 and 1.
weights: Optional non-negative weights.

Value

A list with shares (complier, defier, always, never), effects (mean effect by type, NA for an empty type), itt, first_stage, wald, late (the compliers' effect), monotone, ate (the population mean effect, for comparison) and theorems.

Examples

d0 <- c(0, 0, 1, 0, 1); d1 <- c(1, 1, 1, 0, 0)       # two compliers, an always-taker, a never-taker, a defier
y0 <- c(0, 0, 1, 0, 0); y1 <- c(1, 0, 1, 1, 1)
morie_judge_iv_population(d0, d1, y0, y1)[c("shares", "wald", "late")]
#> $shares
#> complier   defier   always    never 
#>      0.4      0.2      0.2      0.2 
#> 
#> $wald
#> [1] 0
#> 
#> $late
#> [1] 0.5
#>