late.aipw {RCAL}

Augmented inverse probability weighted estimation of local average treatment effects

Description

This function implements augmented inverse probability weighted (IPW) estimation of local average treatment effects (LATEs) as proposed in Tan (2006), provided the fitted instrument propensity scores and fitted values from both treatment and outcome regressions.

Usage

late.aipw(y, tr, iv, mfp, mft, mfo, off = NULL)

Arguments

y

An n x 1 vector of observed outcomes.

tr

An n x 1 vector of treatment indicators (=1 if treated or 0 if untreated).

iv

An n x 1 vector of instruments (0 or 1).

mfp

An n x 2 matrix of fitted instrument propensity scores for iv=0 (first column) and iv=1 (second column).

mft

An n x 2 matrix of fitted values from treatment regression, for iv=0 (first column) and iv=1 (second column).

mfo

An n x 4 matrix of fitted values from outcome regression, for iv=0, tr=0 (first column), iv=0, tr=1 (second column), iv=1, tr=0 (third column) and iv=1, tr=1 (fourth column).

off

A 2 x 1 vector of offset values (e.g., the true values in simulations) used to calculate the z-statistics.

Details

The individual expectations \theta_d=E(Y(d)|D(1)>D(0)) are estimated separately for d\in\{0,1\} using inverse probability weighting ("ipw"), treatment and outcome regressions ("or") and augmented IPW methods as proposed in Tan (2006). The population LATE is defined as \theta_1-\theta_0.

Value

ipw

A 2 x 1 vector of IPW estimates of \theta_1 and \theta_0; see Details.

or

A 2 x 1 vector of regression estimates of \theta_1 and \theta_0; see Details.

est

A 2 x 1 vector of augmented IPW estimates of \theta_1 and \theta_0; see Details.

var

The estimated variances associated with the augmented IPW estimates of \theta_1 and \theta_0.

ze

The z-statistics for the augmented IPW estimates of \theta_1 and \theta_0, compared to off.

late.est

The augmented IPW estimate of LATE.

late.var

The estimated variance associated with the augmented IPW estimate of LATE.

late.ze

The z-statistic for the augmented IPW estimate of LATE, compared to off.

References

Tan, Z. (2006) Regression and weighting methods for causal inference using instrumental variables, Journal of the American Statistical Association, 101, 1607–1618.