Local average treatment effect

LATE = (E[Y|Z=1] - E[Y|Z=0]) / (E[D|Z=1] - E[D|Z=0]).

Usage

morie_caus_iv_late(y, D, Z)

Arguments

y

outcome.

D

binary treatment taken.

Z

binary instrument.

Value

list: late, se, first_stage, reduced_form, complier_share, n_z1, n_z0, weak_first_stage, estimand, n, method.

Details

Arithmetically the Wald ratio. What Imbens and Angrist established is what it ESTIMATES, and that is the content: under instrument independence, exclusion, a non-zero first stage and MONOTONICITY – no defiers – the ratio is the average effect among COMPLIERS alone. That is a different estimand from the average treatment effect, and the compliers are defined by their response to this particular instrument, so a different instrument gives a different subpopulation and a different number.

complier_share is the denominator and says what fraction of the sample the estimate describes. A LATE from a 4% complier share is a statement about 4% of the sample, however tight its interval.

References

Imbens and Angrist (1994), Econometrica 62:467-475; Angrist, Imbens and Rubin (1996), JASA 91:444-455.

Examples

set.seed(1)
Z <- stats::rbinom(500, 1, 0.5)
D <- Z * stats::rbinom(500, 1, 0.6)
morie_caus_iv_late(3 * D + stats::rnorm(500), D, Z)$late
#> [1] 3.127644