estimate {GK2011}

estimate

Description

Estimators for Hybrid Experiments

Usage

estimate(rand, tr, y, iterations = 5000L)

Arguments

rand

An integer or logical vector specifying whether each observation is from the random (1) or self-selection (0) arm of the experiment.

tr

An integer or logical vector specifying whether each observation was treated (1) or control (0), regardless of the arm of the experiment.

y

A numeric vector specifying outcome values.

iterations

An integer specifying the number of bootstrap iterations used to estimate standard errors.

Details

The package provides R implementations of the treatment effect estimators for hybrid (self-selection) experiments, as developed by Gaines and Kuklinski (2011). These functions estimate local average treatment effects for unobserved population subgroups inclined and disinclined to be treated, as revealed by a three-condition (two-arm) experimental design. In the design, participants are randomly assigned to one of three conditions: 1) treatment (T), 2) control (C), or 3) self-selection (S) of treatment or control. The design enables the estimation of three treatment effects:

1. First, the sample average treatment effect is estimated from conditions (1) and (2) as:\ \hat{t} = \bar{Y}_{T} - \bar{Y}_{C}

2. The effect for those inclined to choose treatment is given by:\ \hat{t}_s = \frac{\bar{Y}_{S} - \bar{Y}_{C}}{\hat{\alpha}} where \hat{\alpha} is the observed proportion of individuals in group S that choose T (rather than C).

3. The effect for those disinclined to choose treatment (or, equivalently, inclined to choose control) is given by:\ \hat{t}_n = \frac{\bar{Y}_{T} - \bar{Y}_{S}}{1-\hat{\alpha}}

By definition, the sample average treatment effect is an average of the other two effects.

Value

A data.frame containing the following variables:

• Effect, a character vector of effect names (“t”, “t_s”, “t_n”, “naive”)

• Estimate, a numeric vector of effect estimates

• SE, a numeric vector of bootstrapped standard errors

• t, a t-statistic for the effect

• p, a two-tailed p-value

The return value will also carry an attribute “alpha”, indicating the estimated proportion \alpha.

Author(s)

Thomas J. Leeper <[e-mail]>

References

Brian J. Gaines and James H. Kuklinski, (2011), "Experimental Estimation of Heterogeneous Treatment Effects Related to Self-Selection," American Journal of Political Science 55(3): 724-736.

See Also

ajps

Examples

# create fake data
set.seed(12345)
d <- 
data.frame(rand = c(rep(1, 200), rep(0, 100)),
           tr = c(rep(0, 100), rep(1, 100), rep(0, 37), rep(1, 63)),
           y = c(rnorm(100), rnorm(100) + 1, rnorm(37), rnorm(63) + 3))

# estimate effects
estimate(rand = d$rand, tr = d$tr, y = d$y)